HPC-Forran2Cpp/HPC_Fortran_CPP · Datasets at Hugging Face

cpp stringlengths 74 8.89k	fortran stringlengths 112 13.8k
#include <omp.h>\n#include <stdio.h>\n\nint main()\n{\n int numThreads=0 ; \n#pragma omp parallel\n {\n if ( omp_get_thread_num()==0 ) {\n numThreads = omp_get_num_threads();\n }\n }\n printf ("numThreads=%d\n", numThreads);\n return 0;\n}\n	program DRB051_getthreadnum_orig_no\n use omp_lib\n implicit none\n\n integer :: numThreads\n\n !$omp parallel\n if (omp_get_thread_num() == 0) then\n numThreads = omp_get_num_threads()\n end if\n !$omp end parallel\n\n print 100, numThreads\n 100 format ('numThreads =',i3)\nend program
#include <stdio.h>\n#include <assert.h>\n\nint sum0=0, sum1=0;\n#pragma omp threadprivate(sum0)\n\nvoid foo (int i)\n{\n sum0=sum0+i;\n}\n\nint main()\n{\n int len=1000;\n int i, sum=0;\n#pragma omp parallel copyin(sum0)\n {\n#pragma omp for\n for (i=0;i<len;i++)\n {\n foo (i);\n } \n#pragma omp critical\n {\n sum= sum+sum0;\n } \n } \n/* reference calculation */\n for (i=0;i<len;i++)\n {\n sum1=sum1+i;\n }\n printf("sum=%d; sum1=%d\n",sum,sum1);\n assert(sum==sum1);\n return 0;\n}\n\n	program DRB085_threadprivate_orig_no\n use omp_lib\n use DRB085\n implicit none\n\n integer :: len\n integer (kind=8) :: i, sum\n len = 1000\n sum = 0\n\n !$omp parallel copyin(sum0)\n !$omp do\n do i = 1, len\n call foo(i)\n end do\n !$omp end do\n !$omp critical\n sum = sum+sum0\n !$omp end critical\n !$omp end parallel\n\n do i = 1, len\n sum1=sum1+i\n end do\n\n print*,'sum = ',sum,'sum1 =',sum1\nend program
#include <assert.h>\n#include <stdio.h>\n#include <stdlib.h>\n\n#define N 180\nint indexSet[N] = {\n521, 523, 525, 533, 529, 531, // 521+12=533\n547, 549, 551, 553, 555, 557,\n573, 575, 577, 579, 581, 583,\n599, 601, 603, 605, 607, 609,\n625, 627, 629, 631, 633, 635,\n\n651, 653, 655, 657, 659, 661,\n859, 861, 863, 865, 867, 869,\n885, 887, 889, 891, 893, 895,\n911, 913, 915, 917, 919, 921, \n937, 939, 941, 943, 945, 947,\n\n963, 965, 967, 969, 971, 973,\n989, 991, 993, 995, 997, 999, \n1197, 1199, 1201, 1203, 1205, 1207,\n1223, 1225, 1227, 1229, 1231, 1233,\n1249, 1251, 1253, 1255, 1257, 1259,\n\n1275, 1277, 1279, 1281, 1283, 1285,\n1301, 1303, 1305, 1307, 1309, 1311,\n1327, 1329, 1331, 1333, 1335, 1337,\n1535, 1537, 1539, 1541, 1543, 1545,\n1561, 1563, 1565, 1567, 1569, 1571,\n\n1587, 1589, 1591, 1593, 1595, 1597,\n1613, 1615, 1617, 1619, 1621, 1623,\n1639, 1641, 1643, 1645, 1647, 1649,\n1665, 1667, 1669, 1671, 1673, 1675,\n1873, 1875, 1877, 1879, 1881, 1883,\n\n1899, 1901, 1903, 1905, 1907, 1909,\n1925, 1927, 1929, 1931, 1933, 1935,\n1951, 1953, 1955, 1957, 1959, 1961,\n1977, 1979, 1981, 1983, 1985, 1987,\n2003, 2005, 2007, 2009, 2011, 2013};\n\nint main (int argc, char* argv[])\n{\n double * base = (double) malloc(sizeof(double) (2013+12+1));\n if (base == 0)\n {\n printf ("Error in malloc(). Aborting ...\n");\n return 1; \n }\n\n double * xa1 = base;\n double * xa2 = xa1 + 12;\n int i;\n\n // initialize segments touched by indexSet\n for (i =521; i<= 2025; ++i)\n {\n base[i]=0.5*i;\n }\n\n#pragma omp parallel for // default static even scheduling may not trigger data race!\n for (i =0; i< N; ++i) \n {\n int idx = indexSet[i];\n xa1[idx]+= 1.0;\n xa2[idx]+= 3.0;\n }\n printf("x1[999]=%f xa2[1285]=%f\n", xa1[999], xa2[1285]);\n free (base);\n return 0;\n}\n\n	program DRB007_indirectaccess3_orig_yes\n use omp_lib\n use DRB007\n implicit none\n\n integer :: i, idx1, idx2\n integer, parameter :: dp = kind(1.0d0)\n real(dp), dimension(:), pointer :: xa1=>NULL(), xa2=>NULL()\n real(dp), dimension(2025), target :: base\n\n allocate (xa1(2025))\n allocate (xa2(2025))\n\n xa1 => base(1:2025)\n xa2 => base(1:2025)\n\n n=180\n\n indexSet = (/ 521, 523, 525, 533, 529, 531, 547, 549, &\n 551, 553, 555, 557, 573, 575, 577, 579, 581, 583, 599, &\n 601, 603, 605, 607, 609, 625, 627, 629, 631, 633, 635, &\n 651, 653, 655, 657, 659, 661, 859, 861, 863, 865, 867, &\n 869, 885, 887, 889, 891, 893, 895, 911, 913, 915, 917, &\n 919, 921, 937, 939, 941, 943, 945, 947, 963, 965, 967, &\n 969, 971, 973, 989, 991, 993, 995, 997, 999, 1197, 1199, &\n 1201, 1203, 1205, 1207, 1223, 1225, 1227, 1229, 1231, &\n 1233, 1249, 1251, 1253, 1255, 1257, 1259, 1275, 1277, &\n 1279, 1281, 1283, 1285, 1301, 1303, 1305, 1307, 1309, &\n 1311, 1327, 1329, 1331, 1333, 1335, 1337, 1535, 1537, &\n 1539, 1541, 1543, 1545, 1561, 1563, 1565, 1567, 1569, &\n 1571, 1587, 1589, 1591, 1593, 1595, 1597, 1613, 1615, &\n 1617, 1619, 1621, 1623, 1639, 1641, 1643, 1645, 1647, &\n 1649, 1665, 1667, 1669, 1671, 1673, 1675, 1873, 1875, &\n 1877, 1879, 1881, 1883, 1899, 1901, 1903, 1905, 1907, &\n 1909, 1925, 1927, 1929, 1931, 1933, 1935, 1951, 1953, &\n 1955, 1957, 1959, 1961, 1977, 1979, 1981, 1983, 1985, &\n 1987, 2003, 2005, 2007, 2009, 2011, 2013 /)\n\n do i = 521, 2025\n base(i) = 0.5i\n end do\n\n !$omp parallel do\n do i = 1, n\n idx1 = indexSet(i)\n idx2 = indexSet(i)+12\n base(idx1) = base(idx1)+1.0\n base(idx2) = base(idx2)+3.0\n end do\n !$omp end parallel do\n\n print,'xa1(999) =',base(999),' xa2(1285) =',base(1285)\n\n nullify(xa1,xa2)\nend program
#include <stdio.h>\n#define N 100\n#define M 100 \n#define K 100\ndouble a[N][M],b[M][K],c[N][K];\n \nint mmm() \n{ \n int i,j,k;\n#pragma omp parallel for private(j,k)\n for (i = 0; i < N; i++) \n for (k = 0; k < K; k++) \n for (j = 0; j < M; j++)\n c[i][j]= c[i][j]+a[i][k]*b[k][j];\n return 0; \n} \n\nint main()\n{\n mmm();\n return 0;\n} \n	program DRB060_matrixmultiply_orig_no\n use omp_lib\n implicit none\n\n integer :: N,M,K, len, i, j, l\n real, dimension(:,:), allocatable :: a, b, c\n\n len = 100\n N=len\n M=len\n K=len\n\n allocate (a(N,M))\n allocate (b(M,K))\n allocate (c(K,N))\n\n !$omp parallel do private(j, l)\n do i = 1, N\n do l = 1, K\n do j = 1, M\n c(i,j) = c(i,j)+a(i,l)*b(l,j)\n end do\n end do\n end do\n !$omp end parallel do\n\n deallocate(a,b,c)\nend program
#include <stdio.h> \nint main()\n{\n int i=0;\n#pragma omp parallel sections\n {\n#pragma omp section\n i = 1; \n#pragma omp section\n i = 2; \n }\n printf("i=%d\n",i);\n return 0;\n} \n	program DRB023_sections1_orig_yes\n use omp_lib\n implicit none\n\n integer :: i\n i = 0\n\n !$omp parallel sections\n !$omp section\n i=1\n !$omp section\n i=2\n !$omp end parallel sections\n\n print 100, i\n 100 format ("i=",i3)\n\nend program
#include <stdio.h>\n \nfloat x=0.0;\nint y=0;\n#pragma omp threadprivate(x,y)\n\nint main (int argc, char * argv[])\n{\n#pragma omp parallel\n {\n#pragma omp single copyprivate(x,y)\n {\n x=1.0;\n y=1;\n }\n }\n printf ("x=%f y=%d\n", x, y);\n return 0;\n}\n	program DRB102_copyprivate_orig_no\n use omp_lib\n use DRB102\n implicit none\n\n !$omp parallel\n !$omp single\n x=1.0\n y=1\n !$omp end single copyprivate(x,y)\n !$omp end parallel\n\n print 100, x, y\n 100 format ('x =',F3.1,2x,'y =',i3)\n\nend program
#include <stdio.h>\n#include <omp.h>\n#include <stdlib.h>\n#define N 100\n\nint main(){\n\n int var[N];\n\n for(int i=0; i<N; i++){\n var[i]=0;\n }\n\n #pragma omp target map(tofrom:var[0:N]) device(0)\n #pragma omp parallel for ordered\n for (int i=1; i<N; i++){\n #pragma omp ordered\n {\n var[i]=var[i-1]+1;\n }\n }\n\n for(int i=0; i<N; i++){\n if(var[i]!=i){\n printf("Data Race Present");\n return 0;\n }\n }\n\n return 0;\n}\n	program DRB155_missingordered_orig_gpu_no\n use omp_lib\n implicit none\n\n integer :: var(100)\n integer :: i\n\n do i = 1, 100\n var(i) = 1\n end do\n\n !$omp target map(tofrom:var) device(0)\n !$omp parallel do ordered\n do i = 2, 100\n !$omp ordered\n var(i) = var(i-1)+1\n !$omp end ordered\n end do\n !$omp end parallel do\n !$omp end target\n\n do i = 1, 100\n if (var(i)/=i) then\n print*,"Data Race Present"\n end if\n end do\n\nend program
#include <stdio.h>\n/\n loop missing the linear clause\n * Data race pairs (race on j allows wrong indexing of c): \n j@70:7:R vs. j@71:5:W\n j@71:5:W vs. j@71:5:W \n c[j]@70:5:W vs. c[j]@70:5:W\n/\nint main()\n{\n int len=100;\n double a[len], b[len], c[len];\n int i,j=0;\n\n for (i=0;i<len;i++)\n {\n a[i]=((double)i)/2.0; \n b[i]=((double)i)/3.0; \n c[i]=((double)i)/7.0; \n }\n\n#pragma omp parallel for \n for (i=0;i<len;i++)\n {\n c[j]+=a[i]b[i];\n j++;\n }\n\n printf ("c[50]=%f\n",c[50]);\n return 0;\n}\n	program DRB111_linearmissing_orig_yes\n use omp_lib\n implicit none\n\n integer len, i, j\n integer, parameter :: dp = kind(1.0d0)\n real(dp), dimension(:), allocatable :: a,b,c\n\n len = 100\n i = 0\n j = 0\n\n allocate (a(len))\n allocate (b(len))\n allocate (c(len))\n\n do i = 1, len\n a(i) = (real(i,dp))/2.0\n b(i) = (real(i,dp))/3.0\n c(i) = (real(i,dp))/7.0\n end do\n\n !$omp parallel do\n do i = 1, len\n c(j) = c(j)+a(i)b(i)\n j = j+1\n end do\n !$omp end parallel do\n\n print,'c(50) =',c(50)\n\n if(allocated(a))deallocate(a)\n if(allocated(b))deallocate(b)\n \nend program
#include <stdio.h>\n#define N 100\n\ndouble a[N][N],v[N],v_out[N];\nint mv()\n{ \n int i,j;\n#pragma omp parallel for private (i,j)\n for (i = 0; i < N; i++)\n { \n float sum = 0.0;\n for (j = 0; j < N; j++)\n { \n sum += a[i][j]*v[j];\n } \n v_out[i] = sum;\n } \n return 0; \n}\n\nint main()\n{\n mv();\n return 0;\n}\n\n	program DRB061_matrixvector1_orig_no\n use omp_lib\n implicit none\n call foo\ncontains\n subroutine foo()\n integer :: i, j, N\n real :: sum\n real, dimension(:,:), allocatable :: a\n real, dimension(:), allocatable :: v, v_out\n\n N = 100\n allocate (a(N,N))\n allocate (v(N))\n allocate (v_out(N))\n\n !$omp parallel do private (i,j,sum)\n do i = 1, N\n do j = 1, N\n sum = sum + a(i,j)*v(j)\n end do\n v_out(i) = sum\n end do\n !$omp end parallel do\n\n end subroutine foo\nend program
#include <stdio.h>\n#include <omp.h>\n#define N 100\n\nint main(){\n int var = 0;\n\n #pragma omp target map(tofrom:var) device(0)\n #pragma omp teams num_teams(1)\n #pragma omp distribute parallel for\n for (int i=0; i<N; i++){\n var++;\n }\n\n printf("%d\n ",var);\n return 0;\n}\n	program DRB153_missinglock2_orig_gpu_yes\n use omp_lib\n implicit none\n\n integer :: var, i\n var = 0\n\n !$omp target map(tofrom:var) device(0)\n !$omp teams num_teams(1)\n !$omp distribute parallel do\n do i = 1, 100\n var = var + 1\n end do\n !$omp end distribute parallel do\n !$omp end teams\n !$omp end target\n\n print*, var\nend program
#include <stdlib.h>\n#include <stdio.h>\nint main(int argc, char* argv[])\n{\n int i;\n\n int a[2000];\n\n for (i=0; i<2000; i++)\n a[i]=i; \n\n#pragma omp parallel for\n for (i=0;i<1000;i++)\n a[2*i+1]=a[i]+1;\n\n printf("a[1001]=%d\n", a[1001]); \n return 0;\n}\n\n	program DRB033_truedeplinear_orig_yes\n use omp_lib\n implicit none\n\n integer :: i, len\n integer, dimension(:), allocatable :: a\n\n len = 2000\n allocate (a(len))\n\n do i = 1, len\n a(i) = i\n end do\n\n !$omp parallel do\n do i = 1, 1000\n a(2*i) = a(i) + 1\n end do\n !$omp end parallel do\n\n print 100, a(1002)\n 100 format ('a(1002) =',i3)\n\n deallocate(a)\nend program
#include <stdio.h>\n#define N 20\n#define C 8\n\nint main(){\n int var[C];\n\n for(int i=0; i<C; i++){\n var[i] = 0;\n }\n\n #pragma omp target map(tofrom:var) device(0)\n #pragma omp teams num_teams(1) thread_limit(1048) \n #pragma omp distribute parallel for reduction(+:var)\n for (int i=0; i<N; i++){\n #pragma omp simd\n for(int i=0; i<C; i++){\n var[i]++;\n }\n }\n\n for(int i=0; i<C; i++){\n if(var[i]!=N) printf("%d\n ",var[i]);\n }\n\n return 0;\n}\n	program DRB162_nolocksimd_orig_gpu_no\n use omp_lib\n implicit none\n\n integer :: var(8)\n integer :: i,j\n\n do i = 1, 8\n var(i) = 0\n end do\n\n !$omp target map(tofrom:var) device(0)\n !$omp teams num_teams(1) thread_limit(1048)\n !$omp distribute parallel do reduction(+:var)\n do i = 1, 20\n !$omp simd\n do j = 1, 8\n var(j) = var(j)+1\n end do\n !$omp end simd\n end do\n !$omp end distribute parallel do\n !$omp end teams\n !$omp end target\n\n do i = 1, 8\n if (var(i) /= 20) then\n print*,var(i)\n end if\n end do\n\nend program
#include <omp.h>\n#include <stdio.h>\n\nint main()\n{\n int k;\n\n#pragma omp parallel\n {\n#pragma omp master\n {\n k = omp_get_num_threads();\n printf ("Number of Threads requested = %i\n",k);\n }\n }\n return 0;\n}\n	program DRB103_master_orig_no\n use omp_lib\n implicit none\n\n integer k\n\n !$omp parallel\n !$omp master\n k = omp_get_num_threads()\n print 100, k\n 100 format ('Number of threads requested =',3i8)\n !$omp end master\n !$omp end parallel\n\nend program
#include <stdio.h>\n#include <omp.h>\n\nvoid foo(){\n int x = 0, y = 2;\n\n #pragma omp task depend(inout: x) shared(x)\n x++; // 1st child task\n\n #pragma omp task depend(in: x) depend(inout: y) shared(x, y)\n y = y-x; //2nd child task\n\n #pragma omp taskwait depend(in: x) // 1st taskwait\n\n printf("x=%d\n",x);\n\n #pragma omp taskwait // 2nd taskwait\n\n printf("y=%d\n",y);\n}\n\nint main(){\n #pragma omp parallel\n #pragma omp single\n foo();\n\n return 0;\n}\n\n	program DRB167_taskdep5_orig_no_omp50\n use omp_lib\n implicit none\n\n !$omp parallel\n !$omp single\n call foo()\n !$omp end single\n !$omp end parallel\ncontains\n subroutine foo()\n implicit none\n integer :: x, y\n x = 0\n y = 2\n\n !$omp task depend(inout: x) shared(x)\n x = x+1 !!1st Child Task\n !$omp end task\n\n !$omp task shared(y)\n y = y-x !!2nd child task\n !$omp end task\n\n !$omp taskwait depend(in: x) !!1st taskwait\n\n print, "x=", x\n\n !$omp taskwait !!2nd taskwait\n\n print, "y=", y\n\n end subroutine\nend program
#include<stdio.h>\n#include<stdlib.h>\n\nint* counter; \n//#pragma omp threadprivate(counter)\n\nint main()\n{ \n counter = (int) malloc(sizeof(int));\n if (counter== NULL)\n {\n fprintf(stderr, "malloc() fails\n");\n exit(1);\n }\n counter = 0; \n #pragma omp parallel \n {\n (counter)++; \n }\n printf("%d \n", counter);\n free (counter);\n return 0; \n}\n\n	program DRB088_dynamic_storage_orig_yes\n use omp_lib\n implicit none\n integer, pointer :: counter\n\n allocate(counter)\n\n counter = 0\n\n !$omp parallel\n counter = counter+1\n !$omp end parallel\n\n print*,counter\n\n deallocate(counter)\n\nend program
#include <stdio.h>\n#define min(x, y) (((x) < (y)) ? (x) : (y))\n\n/\nuse of omp target + teams + distribute + parallel for\n/\nint main(int argc, char* argv[])\n{\n int i, i2;\n int len = 2560;\n double sum =0.0, sum2=0.0;\n double a[len], b[len];\n /Initialize with some values/\n for (i=0; i<len; i++)\n {\n a[i]= ((double)i)/2.0;\n b[i]= ((double)i)/3.0;\n }\n\n#pragma omp target map(to: a[0:len], b[0:len]) map(tofrom: sum)\n#pragma omp teams num_teams(10) thread_limit(256) reduction (+:sum) \n#pragma omp distribute\n for (i2=0; i2< len; i2+=256) \n#pragma omp parallel for reduction (+:sum)\n for (i=i2;i< min(i2+256, len); i++)\n sum += a[i]b[i];\n\n/ CPU reference computation / \n#pragma omp parallel for reduction (+:sum2)\n for (i=0;i< len; i++)\n sum2 += a[i]b[i];\n printf ("sum=%f sum2=%f\n", sum, sum2);\n return 0;\n}\n	program DRB097_target_teams_distribute_orig_no\n use omp_lib\n use ISO_C_Binding\n implicit none\n integer, parameter :: dp = kind(1.0d0)\n integer, parameter :: double_kind = c_double\n integer (kind=8) :: i, i2, len, l_limit, tmp\n real(dp) :: sum, sum2\n real(dp), dimension(:), allocatable :: a, b\n\n len = 2560\n sum = real(0.0,dp)\n sum2 = real(0.0,dp)\n\n allocate (a(len))\n allocate (b(len))\n\n do i = 1, len\n a(i) = real(i,dp)/real(2.0,dp)\n b(i) = real(i,dp)/real(3.0,dp)\n end do\n\n !$omp target map(to: a(0:len), b(0:len)) map(tofrom: sum)\n !$omp teams num_teams(10) thread_limit(256) reduction (+:sum)\n !$omp distribute\n do i2 = 1, len, 256\n !$omp parallel do reduction (+:sum)\n do i = i2+1, merge(i2+256,len,i2+256<len)\n sum = sum+a(i)b(i)\n end do\n !$omp end parallel do\n end do\n !$omp end distribute\n !$omp end teams\n !$omp end target\n\n !$omp parallel do reduction (+:sum2)\n do i = 1, len\n sum2 = sum2+a(i)b(i)\n end do\n !$omp end parallel do\n\n print*,'sum =',int(sum),'; sum2 =',int(sum2)\n\n deallocate(a,b)\nend program
#include<stdio.h>\n#include<assert.h>\n/* argument pass-by-value */\nvoid f1(int q)\n{\n q += 1;\n}\n\nint main()\n{\n int i=0;\n #pragma omp parallel \n {\n f1(i);\n }\n assert (i==0);\n printf ("i=%d\n",i);\n return 0;\n}\n\n	program DRB080_func_arg_orig_yes\n use omp_lib\n use global\n implicit none\n\n integer :: i\n i = 0\n\n !$omp parallel\n call f1(i)\n !$omp end parallel\n\n if (i /= 0) then\n print 100, i\n 100 format ('i =',i3)\n end if\nend program
#include <assert.h> \nint main()\n{\n int i=0;\n#pragma omp parallel\n#pragma omp single\n {\n#pragma omp task depend (out:i)\n i = 1; \n#pragma omp task depend (in:i)\n i = 2; \n }\n\n assert (i==2);\n return 0;\n} \n	program DRB072_taskdep1_orig_no\n use omp_lib\n implicit none\n\n integer :: i\n i = 0\n\n !$omp parallel\n !$omp single\n !$omp task depend (out:i)\n i = 1\n !$omp end task\n !$omp task depend (in:i)\n i = 2\n !$omp end task\n !$omp end single\n !$omp end parallel\n\n if (i/=2) then\n print*,'i is not equal to 2'\n end if\nend program
#include <stdio.h>\n#if (_OPENMP<201511)\n#error "An OpenMP 4.5 compiler is needed to compile this test."\n#endif\n#include <stdio.h>\nint a[100][100];\nint main()\n{\n int i, j;\n#pragma omp parallel for ordered(2)\n for (i = 0; i < 100; i++)\n for (j = 0; j < 100; j++)\n {\n a[i][j] = a[i][j] + 1;\n#pragma omp ordered depend(sink:i-1,j) depend (sink:i,j-1)\n printf ("test i=%d j=%d\n",i,j);\n#pragma omp ordered depend(source)\n }\n return 0;\n}\n\n	program DRB094_doall2_ordered_orig_no\n use omp_lib\n use DRB094\n implicit none\n\n integer :: len, i, j\n len = 100\n\n allocate (a(len,len))\n\n !$omp parallel do ordered(2)\n do i = 1, len\n do j = 1, len\n a(i,j) = a(i,j)+1\n !$omp ordered depend(sink:i-1,j) depend (sink:i,j-1)\n print*,'test i =',i,' j =',j\n !$omp ordered depend(source)\n end do\n end do\n !$omp end parallel do\n\n\nend program
#include <stdlib.h> \n#include <stdio.h>\nint main(int argc, char* argv[]) \n{\n int i;\n int len=100;\n\n int numNodes=len, numNodes2=0; \n int x[100]; \n\n // initialize x[]\n for (i=0; i< len; i++)\n {\n if (i%2==0)\n x[i]=5;\n else\n x[i]= -5;\n }\n\n#pragma omp parallel for\n for (i=numNodes-1 ; i>-1 ; --i) {\n if (x[i]<=0) {\n numNodes2-- ;\n }\n }\n printf ("numNodes2 = %d\n", numNodes2);\n return 0;\n} \n	program DRB011_minusminus_orig_yes\n use omp_lib\n implicit none\n\n integer :: i, len, numNodes, numNodes2\n integer :: x(100)\n len = 100\n numNodes=len\n numNodes2=0\n\n do i = 1, len\n if (MOD(i,2) == 0) then\n x(i) = 5\n else\n x(i) = -5\n end if\n end do\n\n !$omp parallel do\n do i = numNodes, 1, -1\n if (x(i) <= 0) then\n numNodes2 = numNodes2-1\n end if\n end do\n !$omp end parallel do\n\n print*,"numNodes2 =", numNodes2\nend program
#include <stdlib.h>\nint main (int argc, char* argv[])\n{\n int len=1000;\n int i; \n\n if (argc>1)\n len = atoi(argv[1]);\n int a[len];\n a[0] = 2;\n\n#pragma omp parallel for\n for (i=0;i<len;i++)\n a[i]=a[i]+a[0];\n\n return 0;\n}\n	program DRB040_truedepsingleelement_var_yes\n use omp_lib\n implicit none\n\n integer :: len, i, argCount, allocStatus, rdErr, ix\n character(len=80), dimension(:), allocatable :: args\n integer, dimension(:), allocatable :: a\n\n len = 1000\n\n argCount = command_argument_count()\n if (argCount == 0) then\n write (,'(a)') "No command line arguments provided."\n end if\n\n allocate(args(argCount), stat=allocStatus)\n if (allocStatus > 0) then\n write (,'(a)') "Allocation error, program terminated."\n stop\n end if\n\n do ix = 1, argCount\n call get_command_argument(ix,args(ix))\n end do\n\n if (argCount >= 1) then\n read (args(1), '(i10)', iostat=rdErr) len\n if (rdErr /= 0 ) then\n write (*,'(a)') "Error, invalid integer value."\n end if\n end if\n\n allocate (a(len))\n\n a(1) = 2\n\n !$omp parallel do\n do i = 1, len\n a(i) = a(i)+a(1)\n end do\n !$omp end parallel do\n\n print 100, a(0)\n 100 format ('a(0) =',i3)\n\n deallocate(args,a)\nend program
#include <stdio.h>\nvoid foo(int * a, int n, int g)\n{\n int i;\n#pragma omp parallel for firstprivate (g)\n for (i=0;i<n;i++)\n {\n a[i] = a[i]+g;\n }\n}\n\nint a[100];\nint main()\n{\n foo(a, 100, 7);\n return 0;\n} \n	program DRB048_firstprivate_orig_no\n use omp_lib\n use DRB048\n implicit none\n\n allocate (a(100))\n call foo(a, 100, 7)\n print*,a(50)\nend program
#include <stdio.h>\n#include <omp.h>\n#define N 100\n#define C 64\n\nint main(){\n\n int var[C];\n\n for(int i=0; i<C; i++){\n var[i]=0;\n }\n\n #pragma omp target map(tofrom:var[0:C]) device(0)\n #pragma omp teams distribute parallel for\n for (int i=0; i<N; i++){\n #pragma omp simd\n for(int i=0; i<C; i++){\n var[i]++;\n }\n }\n\n printf("%d\n",var[63]);\n\n return 0;\n}\n	program DRB163_simdmissinglock1_orig_gpu_no\n use omp_lib\n use DRB163\n implicit none\n\n do i = 1, 16\n var(i) = 0\n end do\n\n !$omp target map(tofrom:var) device(0)\n !$omp teams distribute parallel do\n do i = 1, 20\n !$omp simd\n do j = 1, 16\n var(j) = var(j)+1\n end do\n !$omp end simd\n end do\n !$omp end teams distribute parallel do\n !$omp end target\n\n print*,var(16)\n\nend program
#include <stdlib.h>\n#include <stdio.h>\ndouble b[1000][1000];\n\nint main(int argc, char* argv[]) \n{\n int i,j;\n int n=1000, m=1000;\n for (i=0;i<n;i++)\n#pragma omp parallel for\n for (j=1;j<m;j++)\n b[i][j]=b[i][j-1];\n\n printf("b[500][500]=%f\n", b[500][500]);\n return 0;\n}\n\n	program DRB037_truedepseconddimension_orig_yes\n use omp_lib\n implicit none\n\n integer i, j, n, m, len\n real, dimension(:,:), allocatable :: b\n\n len = 1000\n n = len\n m = len\n\n allocate (b(len,len))\n\n do i = 1, n\n !$omp parallel do\n do j = 2, m\n b(i,j) = b(i,j-1)\n end do\n !$omp end parallel do\n end do\n\n print 100, b(500,500)\n 100 format ('b(500,500) =', F20.6)\n\n deallocate(b)\nend program
#include <stdio.h>\nvoid foo()\n{\n int q=0; \n q += 1;\n}\n\nint main()\n{ \n #pragma omp parallel \n {\n foo();\n }\n return 0; \n}\n\n	program DRB083_declared_in_func_orig_no\n use omp_lib\n use DRB083\n implicit none\n\n !$omp parallel\n call foo()\n !$omp end parallel\nend program
#include <stdio.h>\nint main()\n{\n int i,j;\n int n=100, m=100;\n double b[n][m];\n\n for(i=0;i<n; i++) \n for(j=0;j<n; j++) \n b[i][j]=(double)(i*j);\n\n for (i=1;i<n;i++)\n#pragma omp parallel for\n for (j=1;j<m;j++)\n b[i][j]=b[i-1][j-1];\n return 0;\n}\n	program DRB054_inneronly2_orig_no\n use omp_lib\n implicit none\n\n integer i,j,n,m\n real, dimension(:,:), allocatable :: b\n\n n = 100\n m = 100\n\n allocate (b(n,m))\n\n do i = 1, n\n do j = 1, m\n b(i,j) = i*j\n end do\n end do\n\n do i = 2, n\n !$omp parallel do\n do j =2, m\n b(i,j)=b(i-1,j-1)\n end do\n !$omp end parallel do\n end do\n\n deallocate(b)\nend program
#include <stdlib.h>\nvoid setup(int N)\n{\n double * m_pdv_sum = (double* ) malloc (sizeof (double) * N );\n double * m_nvol = (double* ) malloc (sizeof (double) * N );\n\n#pragma omp parallel for schedule(static)\n for (int i=0; i < N; ++i ) \n { \n m_pdv_sum[ i ] = 0.0;\n m_nvol[ i ] = i*2.5;\n }\n\n free(m_pdv_sum);\n free(m_nvol);\n}\n\nint main()\n{\n int N =1000;\n setup(N);\n}\n \n	program DRB066_pointernoaliasing_orig_no\n use omp_lib\n use DRB066\n implicit none\n\n integer :: N\n N = 1000\n\n call setup(N)\n\nend program
#include <stdio.h>\nint main(int argc, char* argv[])\n{ \n int i;\n int len = 1000;\n\n int a[1000];\n\n for (i=0; i<len; i++)\n a[i]= i; \n\n#pragma omp parallel for\n for (i=0;i< len -1 ;i++)\n a[i]=a[i+1]+1;\n\n printf ("a[500]=%d\n", a[500] );\n return 0;\n} \n	program DRB001_antidep1_orig_yes\nuse omp_lib\n implicit none\n integer :: i, len\n integer :: a(1000)\n\n len = 1000\n\n do i = 1, len\n a(i) = i\n end do\n\n !$omp parallel do\n do i = 1, len-1\n a(i) = a(i+1) + 1\n end do\n !$omp end parallel do\n\n print 100, a(500)\n 100 format ('a(500)=',i3)\nend program
#include <stdio.h>\n#include <math.h>\n\n#define MSIZE 200\nint n=MSIZE, m=MSIZE;\ndouble alpha = 0.0543;\ndouble u[MSIZE][MSIZE], f[MSIZE][MSIZE], uold[MSIZE][MSIZE];\ndouble dx, dy;\n\nvoid\ninitialize ()\n{\n int i, j, xx, yy;\n\n dx = 2.0 / (n - 1);\n dy = 2.0 / (m - 1);\n\n /* Initialize initial condition and RHS /\n#pragma omp parallel for private(i,j,xx,yy)\n for (i = 0; i < n; i++)\n for (j = 0; j < m; j++)\n {\n xx = (int) (-1.0 + dx (i - 1)); /* -1 < x < 1 /\n yy = (int) (-1.0 + dy (j - 1)); /* -1 < y < 1 /\n u[i][j] = 0.0;\n f[i][j] = -1.0 alpha * (1.0 - xx * xx) * (1.0 - yy * yy)\n - 2.0 * (1.0 - xx * xx) - 2.0 * (1.0 - yy * yy);\n\n }\n}\n\nint main()\n{\n initialize();\n return 0;\n}\n	module DRB057\nuse omp_lib\nimplicit none\n\ninteger :: MSIZE\ninteger :: n,m,mits\ninteger, parameter :: dp = kind(1.0d0)\nreal(dp), dimension(:,:), pointer :: u,f,uold\nreal(dp) :: dx,dy,tol,relax,alpha\n\ncontains\nsubroutine initialize()\ninteger :: i,j,xx,yy\n\nMSIZE = 200\nmits = 1000\nrelax = 1.0\nalpha = 0.0543\nn = MSIZE\nm = MSIZE\nallocate(u(MSIZE,MSIZE))\nallocate(f(MSIZE,MSIZE))\nallocate(uold(MSIZE,MSIZE))\n\ndx = 2.0D0 / DBLE(n-1)\ndy = 2.0D0 / DBLE(m-1)\n\n!Initialize initial condition and RHS\n!$omp parallel do private(i,j,xx,yy)\ndo i = 1, n\ndo j = 1, m\nxx = int(-1.0 + dx * (i-1))\nyy = int(-1.0 + dy * (i-1))\nu(i,j) = 0.0\nf(i,j) = -1.0 * alpha * (1.0-xxxx) (1.0-yyyy) - 2.0 (1.0-xxxx) -2.0 (1.0-yy*yy)\nend do\nend do\n!$omp end parallel do\n\nend subroutine\nend module program DRB057_jacobiinitialize_orig_no\n use omp_lib\n use DRB057\n implicit none\n\n call initialize()\nend program
#include <stdio.h>\n#include <assert.h>\n#include <unistd.h>\n\nint main()\n{\n int result = 0;\n#pragma omp parallel\n {\n#pragma omp single\n {\n#pragma omp taskgroup\n {\n#pragma omp task\n {\n sleep(3);\n result = 1; \n }\n }\n#pragma omp task\n {\n result = 2; \n }\n }\n }\n printf ("result=%d\n", result);\n assert (result==2);\n return 0;\n}\n	program DRB107_taskgroup_orig_no\n use omp_lib\n implicit none\n\n integer result\n result = 0\n\n !$omp parallel\n !$omp single\n !$omp taskgroup\n !$omp task\n call sleep(3)\n result = 1\n !$omp end task\n !$omp end taskgroup\n !$omp task\n result = 2\n !$omp end task\n !$omp end single\n !$omp end parallel\n\n print 100, result\n 100 format ('result =',3i8)\n\nend program
#include <omp.h>\n#include <stdio.h>\n\nint main(){\n int section_count = 0;\n omp_set_dynamic(0);\n \n omp_set_num_threads(1);\n\n #pragma omp parallel\n #pragma omp sections firstprivate( section_count )\n {\n #pragma omp section\n {\n section_count++;\n printf("%d\n",section_count);\n }\n #pragma omp section\n {\n section_count++;\n printf("%d\n",section_count);\n }\n }\n return 0;\n}\n	program DRB126_firstprivatesections_orig_no\n use omp_lib\n implicit none\n\n integer :: section_count\n\n section_count = 0\n\n call omp_set_dynamic(.FALSE.)\n call omp_set_num_threads(1)\n\n !$omp parallel\n !$omp sections firstprivate( section_count )\n !$omp section\n section_count = section_count+1\n print 100, section_count\n 100 format ('section_count =',3i8)\n\n !$omp section\n section_count = section_count+1\n print 101, section_count\n 101 format ('section_count =',3i8)\n !$omp end sections\n !$omp end parallel\nend program
#include<stdio.h>\n#include<stdlib.h>\n\nint* counter; \n\nvoid foo()\n{\n (counter)++; \n}\n\nint main()\n{ \n counter = (int) malloc(sizeof(int));\n if (counter== NULL)\n {\n fprintf(stderr, "malloc() fails\n");\n exit(1);\n }\n counter = 0; \n #pragma omp parallel \n {\n foo();\n }\n printf("%d \n", counter);\n free (counter);\n return 0; \n}\n\n	program DRB088_dynamic_storage_orig_yes\n use omp_lib\n use DRB088\n implicit none\n\n allocate(counter)\n\n counter = 0\n\n !$omp parallel\n call foo()\n !$omp end parallel\n\n print*,counter\n\n deallocate(counter)\n\nend program
#include <omp.h>\n#include <stdio.h>\n\n\nint main(){\n int x = 2;\n\n #pragma omp task mergeable\n {\n x++;\n }\n #pragma omp taskwait\n\n printf("%d\n",x);\n return 0;\n}\n	program DRB129_mergeable_taskwait_orig_yes\n use omp_lib\n implicit none\n\n integer :: x\n x = 2\n\n !$omp task mergeable\n x = x+1\n !$omp end task\n\n print 100, x\n 100 format ('x =',3i8)\nend program
#include <stdio.h>\n#include <stdlib.h>\n\nint main(){\n\n int a[4];\n int psum[2];\n int sum;\n\n #pragma omp parallel num_threads(2)\n {\n #pragma omp for schedule(dynamic, 1)\n for (int i=0; i < 4; ++i){\n a[i] = i;\n int s;\n s = (- 3 - 3) / - 3;\n }\n\n #pragma omp single\n {\n #pragma omp task\n {\n #pragma omp task\n {\n psum[1] = a[2] + a[3];\n }\n psum[0] = a[0] + a[1];\n }\n\n #pragma omp taskwait\n sum = psum[1] + psum[0];\n }\n }\n\n printf("sum = %d\n", sum);\n return 0;\n }\n	program DRB117_taskwait_waitonlychild_orig_yes\n use omp_lib\n implicit none\n\n integer, dimension(:), allocatable :: a, psum\n integer :: sum, i\n\n allocate(a(4))\n allocate(psum(4))\n\n !$omp parallel num_threads(2)\n !$omp do schedule(dynamic, 1)\n do i = 1, 4\n a(i) = i\n end do\n !$omp end do\n\n !$omp single\n !$omp task\n !$omp task\n psum(2) = a(3)+a(4)\n !$omp end task\n psum(1) = a(1)+a(2)\n !$omp end task\n !$omp taskwait\n sum = psum(2)+psum(1)\n !$omp end single\n !$omp end parallel\n\n print*,'sum =',sum\n\n deallocate(a,psum)\nend program
#include<stdio.h>\n\nint main(int argc, char* argv[])\n{\n int i;\n int len=100;\n int a[len], b[len];\n\n for (i=0;i<len;i++)\n { a[i]=i; b[i]=i;} \n/* static storage for a local variable /\n#pragma omp parallel \n {\n static int tmp;\n#pragma omp for\n for (i=0;i<len;i++)\n {\n tmp = a[i]+i;\n a[i] = tmp;\n }\n }\n\n/ automatic storage for a local variable */\n#pragma omp parallel \n {\n int tmp;\n#pragma omp for\n for (i=0;i<len;i++)\n {\n tmp = b[i]+i;\n b[i] = tmp;\n }\n }\n\n printf("a[50]=%d b[50]=%d\n", a[50], b[50]);\n \n return 0;\n}\n	program DRB090_static_local_orig_yes\n use omp_lib\n implicit none\n\n integer :: i, len\n integer, dimension(:), allocatable :: a, b\n integer, save :: tmp\n integer :: tmp2\n\n len = 100\n allocate (a(len))\n allocate (b(len))\n\n do i = 1, len\n a(i) = i\n b(i) = i\n end do\n\n !$omp parallel\n !$omp do\n do i = 1, len\n tmp = a(i)+i\n a(i) = tmp\n end do\n !$omp end do\n !$omp end parallel\n\n !$omp parallel\n !$omp do\n do i = 1, len\n tmp2 = b(i)+i\n b(i) = tmp2\n end do\n !$omp end do\n !$omp end parallel\n\n print 100, a(50), b(50)\n 100 format (i3,3x,i3)\n\n deallocate(a,b)\n\nend program
#include <stdio.h>\n\nint main()\n{\n int count=0;\n\n#pragma omp parallel shared(count) \n {\n#pragma omp single\n count += 1;\n }\n\n printf ("count= %d\n", count);\n return 0;\n}\n	program DRB077_single_orig_no\n use omp_lib\n implicit none\n\n integer :: count\n count = 0\n\n !$omp parallel shared(count)\n !$omp single\n count = count + 1\n !$omp end single\n !$omp end parallel\n\n print 100, count\n 100 format ('count =',i3)\nend program
#include <omp.h>\n#include <stdio.h>\n#include <stdlib.h>\n\ntypedef struct {\n int a, b;\n omp_nest_lock_t lck;\n} pair;\n\nvoid incr_a(pair p){\n p->a += 1;\n}\n\nvoid incr_b(pair p){\n p->b += 1;\n}\n\n\nint main(int argc, char* argv[])\n{\n pair p[1];\n p->a = 0;\n p->b = 0;\n omp_init_nest_lock(&p->lck);\n\n #pragma omp parallel sections\n {\n #pragma omp section\n {\n omp_set_nest_lock(&p->lck);\n incr_b(p);\n incr_a(p);\n omp_unset_nest_lock(&p->lck);\n }\n #pragma omp section\n incr_b(p);\n }\n\n omp_destroy_nest_lock(&p->lck);\n\n printf("%d\n",p->b);\n return 0;\n}\n	program DRB118_nestlock_orig_no\n use omp_lib\n use DRB118\n implicit none\n\n integer :: a, b\n\n type(pair) :: p\n p%a = 0\n p%b = 0\n call omp_init_nest_lock(p%lck);\n\n !$omp parallel sections\n !$omp section\n call omp_set_nest_lock(p%lck)\n call incr_b(p, a)\n call incr_a(p, b)\n call omp_unset_nest_lock(p%lck)\n\n !$omp section\n call incr_b(p, b);\n\n !$omp end parallel sections\n\n call omp_destroy_nest_lock(p%lck)\n\n print*,p%b\n\nend program
#include <omp.h>\n#include <stdio.h>\n\nint main(int argc, char* argv[])\n{\n int var = 0, i, res;\n int sum1 = 0;\n int sum2 = 0;\n\n res = omp_get_max_threads();\n\n #pragma omp parallel reduction(+: var)\n {\n #pragma omp for schedule(static) reduction(+: sum1)\n for (i=0; i<5; i++)\n sum1+=i;\n #pragma omp for schedule(static) reduction(+: sum2)\n for (i=0; i<5; i++)\n sum2+=i;\n\n var = sum1 + sum2;\n }\n\n int error = (var != 20res);\n if (error) printf("%d %d\n",var,20res);\n return error;\n}\n	program DRB121_reduction_orig_no\n use omp_lib\n implicit none\n\n integer :: var, i, sum1, sum2\n\n var = 0\n sum1 = 0\n sum2 = 0\n\n !$omp parallel reduction(+: var)\n !$omp do schedule(static) reduction(+: sum1)\n do i = 1, 5\n sum1 = sum1+i\n end do\n !$omp end do\n\n !$omp do schedule(static) reduction(+: sum2)\n do i = 1, 5\n sum2 = sum2+i\n end do\n !$omp end do\n\n var = sum1 + sum2\n !$omp end parallel\n\n print 100, var\n 100 format ('var =',3i8)\nend program
#include <stdio.h>\n/\nuse of omp target + map + array sections derived from pointers\n/\nvoid foo (double* a, double* b, int N)\n{\n int i; \n#pragma omp target map(to:a[0:N]) map(from:b[0:N])\n#pragma omp parallel for\n for (i=0;i< N ;i++)\n b[i]=a[i](double)i;\n}\n\nint main(int argc, char argv[])\n{\n int i;\n int len = 1000;\n double a[len], b[len];\n for (i=0; i<len; i++)\n {\n a[i]= ((double)i)/2.0;\n b[i]=0.0;\n }\n\n foo(a, b, len);\n\n printf("b[50]=%f\n",b[50]);\n return 0;\n}\n	program DRB099_targetparallelfor2_orig_no\n use omp_lib\n use DRB099\n implicit none\n\n integer :: i, len\n integer, parameter :: dp = kind(1.0d0)\n real(dp), dimension(:), allocatable :: a,b\n real :: x\n\n len = 1000\n\n allocate(a(len))\n allocate(b(len))\n\n do i = 1, len\n a(i) = (real(i,dp))/2.0\n b(i) = 0.0\n end do\n\n x=foo(a,b,len)\n print*,'b(50) =',b(50)\n \n deallocate(a,b)\nend program
#include <omp.h>\n#include <stdio.h>\n#include <stdlib.h>\n\ntypedef struct {\n int a, b;\n omp_nest_lock_t lck;\n} pair;\n\nvoid incr_a(pair p){\n p->a += 1;\n}\nvoid incr_b(pair p){\n omp_set_nest_lock(&p->lck);\n p->b += 1;\n omp_unset_nest_lock(&p->lck);\n}\n\n\nint main(int argc, char* argv[])\n{\n pair p[1];\n p->a = 0;\n p->b = 0;\n omp_init_nest_lock(&p->lck);\n\n #pragma omp parallel sections\n {\n #pragma omp section\n {\n omp_set_nest_lock(&p->lck);\n incr_b(p);\n incr_a(p);\n omp_unset_nest_lock(&p->lck);\n }\n #pragma omp section\n incr_b(p);\n }\n\n omp_destroy_nest_lock(&p->lck);\n\n printf("%d\n",p->b);\n return 0;\n}\n	program DRB118_nestlock_orig_no\n use omp_lib\n use DRB118\n implicit none\n\n integer :: a, b\n\n type(pair) :: p\n p%a = 0\n p%b = 0\n call omp_init_nest_lock(p%lck);\n\n !$omp parallel sections\n !$omp section\n call omp_set_nest_lock(p%lck)\n call incr_b(p, a)\n call incr_a(p, b)\n call omp_unset_nest_lock(p%lck)\n\n !$omp section\n call incr_b(p, b);\n\n !$omp end parallel sections\n\n call omp_destroy_nest_lock(p%lck)\n\n print*,p%b\n\nend program
#include <stdlib.h>\nint main(int argc, char* argv[])\n{\n int i;\n int len=2000;\n\n if (argc>1)\n len = atoi(argv[1]);\n int a[len];\n\n for (i=0; i<len; i++)\n a[i]=i; \n\n#pragma omp parallel for\n for (i=0;i<len/2;i++)\n a[2*i+1]=a[i]+1;\n\n return 0;\n}\n\n	program DRB034_truedeplinear_var_yes\n use omp_lib\n implicit none\n\n integer :: i, len, uLen, argCount, allocStatus, rdErr, ix\n character(len=80), dimension(:), allocatable :: args\n integer, dimension(:), allocatable :: a\n\n len = 2000\n\n argCount = command_argument_count()\n if (argCount == 0) then\n write (,'(a)') "No command line arguments provided."\n end if\n\n allocate(args(argCount), stat=allocStatus)\n if (allocStatus > 0) then\n write (,'(a)') "Allocation error, program terminated."\n stop\n end if\n\n do ix = 1, argCount\n call get_command_argument(ix,args(ix))\n end do\n\n if (argCount >= 1) then\n read (args(1), '(i10)', iostat=rdErr) len\n if (rdErr /= 0 ) then\n write (,'(a)') "Error, invalid integer value."\n end if\n end if\n\n allocate (a(len))\n\n do i = 1, len\n a(i) = i\n end do\n\n uLen = len/2\n\n !$omp parallel do\n do i = 1, uLen\n a(2i) = a(i) + 1\n end do\n !$omp end parallel do\n\n deallocate(args,a)\nend program
#include <stdio.h>\n#include <assert.h>\n\nint sum0=0, sum1=0;\n#pragma omp threadprivate(sum0)\n\nint main()\n{\n int len=1000;\n int i, sum=0;\n#pragma omp parallel copyin(sum0)\n {\n#pragma omp for\n for (i=0;i<len;i++)\n {\n sum0=sum0+i;\n } \n#pragma omp critical\n {\n sum= sum+sum0;\n } \n } \n /* reference calculation */\n for (i=0;i<len;i++)\n {\n sum1=sum1+i;\n }\n printf("sum=%d; sum1=%d\n",sum,sum1);\n assert(sum==sum1);\n return 0;\n}\n\n	program DRB091_threadprivate2_orig_no\n use omp_lib\n use DRB091\n implicit none\n\n integer :: len, i, sum\n len = 1000\n sum = 0\n\n !$omp parallel copyin(sum0)\n !$omp do\n do i = 1, len\n sum0 = sum0+i\n end do\n !$omp end do\n !$omp critical\n sum = sum+sum0\n !$omp end critical\n !$omp end parallel\n\n do i = 1, len\n sum1 = sum1+i\n end do\n\n print*,'sum =',sum,'sum1 =',sum1\n\nend program
#include <stdio.h>\n/* This is a program based on a test contributed by Yizi Gu@Rice Univ.\n * Classic Fibonacci calculation using task but missing taskwait. \n * Data races pairs: i@61:5:W vs. i@65:14:R\n * j@63:5:W vs. j@65:16:R\n * /\nunsigned int input = 10;\nint fib(unsigned int n)\n{\n if (n<2)\n return n;\n else\n {\n int i, j;\n#pragma omp task shared(i)\n i=fib(n-1);\n#pragma omp task shared(j)\n j=fib(n-2);\n\n int res= i+j; \n/ We move the original taskwait to a location after i+j to \n * simulate the missing taskwait mistake.\n * Directly removing the taskwait may cause a child task to write to i or j\n * within the stack of a parent task which may already be gone, causing seg fault.\n * This change is suggested by Joachim Protze @RWTH-Aachen. \n * */\n#pragma omp taskwait\n return res;\n }\n}\nint main()\n{\n int result = 0;\n#pragma omp parallel\n {\n #pragma omp single\n {\n result = fib(input);\n }\n }\n printf ("Fib(%d)=%d (correct answer should be 55)\n", input, result);\n return 0;\n}\n	module DRB106\n implicit none\n integer (kind=4) input\n\ncontains\n recursive function fib(n) result(r)\n use omp_lib\n implicit none\n integer (kind=4) :: n, i, j, r\n\n if (n<2) then\n r = n\n else\n !$omp task shared(i)\n i = fib(n-1)\n !$omp end task\n !$omp task shared(j)\n j = fib(n-2)\n !$omp end task\n r = i+j\n end if\n !$omp taskwait\n end function\nend module\n\nprogram DRB106_taskwaitmissing_orig_yes\n use omp_lib\n use DRB106\n implicit none\n\n integer :: result\n input = 30\n\n !$omp parallel\n !$omp single\n result = fib(input)\n !$omp end single\n !$omp end parallel\n\n print*,'Fib for ',input,' =',result\n\nend program
#include <stdio.h>\n#define N 1000\ndouble a[N][N],v[N],v_out[N];\n\nvoid mv()\n{ \n int i,j;\n for (i = 0; i < N; i++)\n { \n float sum = 0.0;\n#pragma omp parallel for reduction(+:sum)\n for (j = 0; j < N; j++)\n { \n sum += a[i][j]*v[j];\n } \n v_out[i] = sum;\n } \n}\n\nint main()\n{\n mv();\n return 0;\n}\n	program DRB062_matrixvector2_orig_no\n use omp_lib\n implicit none\n\n call foo\ncontains\n subroutine foo()\n integer :: i, j, N\n real :: sum\n real, dimension(:,:), allocatable :: a\n real, dimension(:), allocatable :: v, v_out\n\n N = 1000\n allocate (a(N,N))\n allocate (v(N))\n allocate (v_out(N))\n\n do i = 1, N\n sum = 0.0\n !$omp parallel do reduction(+:sum)\n do j = 1, N\n sum = sum + a(i,j)v(j)\n print,sum\n end do\n !$omp end parallel do\n v_out(i) = sum\n end do\n\n end subroutine foo\nend program
#include <stdio.h>\n#include <stdlib.h>\n\nint main(int argc, char* argv[])\n{\n int len=100; \n\n if (argc>1)\n len = atoi(argv[1]);\n\n int a[len];\n int i,x=10;\n\n#pragma omp parallel for \n for (i=0;i<len;i++)\n {\n a[i] = x;\n x=i;\n }\n printf("x=%d, a[0]=%d\n",x,a[0]); \n return 0;\n} \n\n	program DRB017_outputdep_var_yes\n use omp_lib\n implicit none\n\n integer len, i, x, argCount, allocStatus, rdErr, ix\n character(len=80), dimension(:), allocatable :: args\n integer, dimension (:), allocatable :: a\n\n len = 100\n x = 10\n\n argCount = command_argument_count()\n if (argCount == 0) then\n write (,'(a)') "No command line arguments provided."\n end if\n\n allocate(args(argCount), stat=allocStatus)\n if (allocStatus > 0) then\n write (,'(a)') "Allocation error, program terminated."\n stop\n end if\n\n do ix = 1, argCount\n call get_command_argument(ix,args(ix))\n end do\n\n if (argCount >= 1) then\n read (args(1), '(i10)', iostat=rdErr) len\n if (rdErr /= 0 ) then\n write (*,'(a)') "Error, invalid integer value."\n end if\n end if\n\n allocate (a(len))\n !$omp parallel do\n do i = 1, len\n a(i) = x\n x = i\n end do\n !$omp end parallel do\n\n print 100, x, a(0)\n 100 format ("x=",i3,2x,"a(0)=",i3)\n\n deallocate(args,a)\nend program
#include <omp.h>\n#include <stdio.h>\nint main()\n{\n int numThreads=0 ; \n#pragma omp parallel\n {\n if ( omp_get_thread_num()==0 ) {\n numThreads = omp_get_num_threads();\n }\n else\n {\n printf("numThreads=%d\n", numThreads);\n }\n }\n return 0;\n}\n	program DRB075_getthreadnum_orig_yes\n use omp_lib\n implicit none\n\n integer :: numThreads\n numThreads = 0\n\n !$omp parallel\n if ( omp_get_thread_num()==0 ) then\n numThreads = omp_get_num_threads();\n else\n print*,'numThreads =',numThreads\n end if\n !$omp endparallel\nend program
void error_norm(double rms[]){\nint i, j, k, m, d;\ndouble xi, eta, zeta, u_exact[5], add;\nfor(m=0; m<5; m++){rms[m]=0.0;}\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)jdnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nexact_solution(xi, eta, zeta, u_exact);\nfor(m=0; m<5; m++){\nadd=u[k][j][i][m]-u_exact[m];\nrms[m]=rms[m]+addadd;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}	subroutine error_norm(rms)\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, m, d\ndouble precision xi, eta, zeta, u_exact(5), rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, u_exact)\n\ndo m = 1, 5\nadd = u(m,i,j,k)-u_exact(m)\nrms(m) = rms(m) + addadd\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nend do\nrms(m) = dsqrt(rms(m))\nend do\n\nreturn\nend\n\n\n\nsubroutine rhs_norm(rms)\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, d, m\ndouble precision rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\ndo m = 1, 5\nadd = rhs(m,i,j,k)\nrms(m) = rms(m) + addadd\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nend do\nrms(m) = dsqrt(rms(m))\nend do\n\nreturn\nend
void set_constants(){\nce[0][0]=2.0;\nce[1][0]=0.0;\nce[2][0]=0.0;\nce[3][0]=4.0;\nce[4][0]=5.0;\nce[5][0]=3.0;\nce[6][0]=0.5;\nce[7][0]=0.02;\nce[8][0]=0.01;\nce[9][0]=0.03;\nce[10][0]=0.5;\nce[11][0]=0.4;\nce[12][0]=0.3;\n\nce[0][1]=1.0;\nce[1][1]=0.0;\nce[2][1]=0.0;\nce[3][1]=0.0;\nce[4][1]=1.0;\nce[5][1]=2.0;\nce[6][1]=3.0;\nce[7][1]=0.01;\nce[8][1]=0.03;\nce[9][1]=0.02;\nce[10][1]=0.4;\nce[11][1]=0.3;\nce[12][1]=0.5;\n\nce[0][2]=2.0;\nce[1][2]=2.0;\nce[2][2]=0.0;\nce[3][2]=0.0;\nce[4][2]=0.0;\nce[5][2]=2.0;\nce[6][2]=3.0;\nce[7][2]=0.04;\nce[8][2]=0.03;\nce[9][2]=0.05;\nce[10][2]=0.3;\nce[11][2]=0.5;\nce[12][2]=0.4;\n\nce[0][3]=2.0;\nce[1][3]=2.0;\nce[2][3]=0.0;\nce[3][3]=0.0;\nce[4][3]=0.0;\nce[5][3]=2.0;\nce[6][3]=3.0;\nce[7][3]=0.03;\nce[8][3]=0.05;\nce[9][3]=0.04;\nce[10][3]=0.2;\nce[11][3]=0.1;\nce[12][3]=0.3;\n\nce[0][4]=5.0;\nce[1][4]=4.0;\nce[2][4]=3.0;\nce[3][4]=2.0;\nce[4][4]=0.1;\nce[5][4]=0.4;\nce[6][4]=0.3;\nce[7][4]=0.05;\nce[8][4]=0.04;\nce[9][4]=0.03;\nce[10][4]=0.1;\nce[11][4]=0.3;\nce[12][4]=0.2;\n\nc1=1.4;\nc2=0.4;\nc3=0.1;\nc4=1.0;\nc5=1.4;\ndnxm1=1.0/(double)(grid_points[0]-1);\ndnym1=1.0/(double)(grid_points[1]-1);\ndnzm1=1.0/(double)(grid_points[2]-1);\nc1c2=c1c2;\nc1c5=c1c5;\nc3c4=c3c4;\nc1345=c1c5c3c4;\nconz1=(1.0-c1c5);\ntx1=1.0/(dnxm1dnxm1);\ntx2=1.0/(2.0dnxm1);\ntx3=1.0/dnxm1;\nty1=1.0/(dnym1dnym1);\nty2=1.0/(2.0dnym1);\nty3=1.0/dnym1;\ntz1=1.0/(dnzm1dnzm1);\ntz2=1.0/(2.0dnzm1);\ntz3=1.0/dnzm1;\ndx1=0.75;\ndx2=0.75;\ndx3=0.75;\ndx4=0.75;\ndx5=0.75;\ndy1=0.75;\ndy2=0.75;\ndy3=0.75;\ndy4=0.75;\ndy5=0.75;\ndz1=1.0;\ndz2=1.0;\ndz3=1.0;\ndz4=1.0;\ndz5=1.0;\ndxmax=max(dx3, dx4);\ndymax=max(dy2, dy4);\ndzmax=max(dz2, dz3);\ndssp=0.25max(dx1, max(dy1, dz1));\nc4dssp=4.0dssp;\nc5dssp=5.0dssp;\ndttx1=dttx1;\ndttx2=dttx2;\ndtty1=dtty1;\ndtty2=dtty2;\ndttz1=dttz1;\ndttz2=dttz2;\nc2dttx1=2.0dttx1;\nc2dtty1=2.0dtty1;\nc2dttz1=2.0dttz1;\ndtdssp=dtdssp;\ncomz1=dtdssp;\ncomz4=4.0dtdssp;\ncomz5=5.0dtdssp;\ncomz6=6.0dtdssp;\nc3c4tx3=c3c4tx3;\nc3c4ty3=c3c4ty3;\nc3c4tz3=c3c4tz3;\ndx1tx1=dx1tx1;\ndx2tx1=dx2tx1;\ndx3tx1=dx3tx1;\ndx4tx1=dx4tx1;\ndx5tx1=dx5tx1;\ndy1ty1=dy1ty1;\ndy2ty1=dy2ty1;\ndy3ty1=dy3ty1;\ndy4ty1=dy4ty1;\ndy5ty1=dy5ty1;\ndz1tz1=dz1tz1;\ndz2tz1=dz2tz1;\ndz3tz1=dz3tz1;\ndz4tz1=dz4tz1;\ndz5tz1=dz5tz1;\nc2iv=2.5;\ncon43=4.0/3.0;\ncon16=1.0/6.0;\nxxcon1=c3c4tx3con43tx3;\nxxcon2=c3c4tx3tx3;\nxxcon3=c3c4tx3conz1tx3;\nxxcon4=c3c4tx3con16tx3;\nxxcon5=c3c4tx3c1c5tx3;\nyycon1=c3c4ty3con43ty3;\nyycon2=c3c4ty3ty3;\nyycon3=c3c4ty3conz1ty3;\nyycon4=c3c4ty3con16ty3;\nyycon5=c3c4ty3c1c5ty3;\nzzcon1=c3c4tz3con43tz3;\nzzcon2=c3c4tz3tz3;\nzzcon3=c3c4tz3conz1tz3;\nzzcon4=c3c4tz3con16tz3;\nzzcon5=c3c4tz3c1c5*tz3;\n}	subroutine set_constants\n\n\nuse bt_data\nimplicit none\n\nce(1,1) = 2.0d0\nce(1,2) = 0.0d0\nce(1,3) = 0.0d0\nce(1,4) = 4.0d0\nce(1,5) = 5.0d0\nce(1,6) = 3.0d0\nce(1,7) = 0.5d0\nce(1,8) = 0.02d0\nce(1,9) = 0.01d0\nce(1,10) = 0.03d0\nce(1,11) = 0.5d0\nce(1,12) = 0.4d0\nce(1,13) = 0.3d0\n\nce(2,1) = 1.0d0\nce(2,2) = 0.0d0\nce(2,3) = 0.0d0\nce(2,4) = 0.0d0\nce(2,5) = 1.0d0\nce(2,6) = 2.0d0\nce(2,7) = 3.0d0\nce(2,8) = 0.01d0\nce(2,9) = 0.03d0\nce(2,10) = 0.02d0\nce(2,11) = 0.4d0\nce(2,12) = 0.3d0\nce(2,13) = 0.5d0\n\nce(3,1) = 2.0d0\nce(3,2) = 2.0d0\nce(3,3) = 0.0d0\nce(3,4) = 0.0d0\nce(3,5) = 0.0d0\nce(3,6) = 2.0d0\nce(3,7) = 3.0d0\nce(3,8) = 0.04d0\nce(3,9) = 0.03d0\nce(3,10) = 0.05d0\nce(3,11) = 0.3d0\nce(3,12) = 0.5d0\nce(3,13) = 0.4d0\n\nce(4,1) = 2.0d0\nce(4,2) = 2.0d0\nce(4,3) = 0.0d0\nce(4,4) = 0.0d0\nce(4,5) = 0.0d0\nce(4,6) = 2.0d0\nce(4,7) = 3.0d0\nce(4,8) = 0.03d0\nce(4,9) = 0.05d0\nce(4,10) = 0.04d0\nce(4,11) = 0.2d0\nce(4,12) = 0.1d0\nce(4,13) = 0.3d0\n\nce(5,1) = 5.0d0\nce(5,2) = 4.0d0\nce(5,3) = 3.0d0\nce(5,4) = 2.0d0\nce(5,5) = 0.1d0\nce(5,6) = 0.4d0\nce(5,7) = 0.3d0\nce(5,8) = 0.05d0\nce(5,9) = 0.04d0\nce(5,10) = 0.03d0\nce(5,11) = 0.1d0\nce(5,12) = 0.3d0\nce(5,13) = 0.2d0\n\nc1 = 1.4d0\nc2 = 0.4d0\nc3 = 0.1d0\nc4 = 1.0d0\nc5 = 1.4d0\n\ndnxm1 = 1.0d0 / dble(grid_points(1)-1)\ndnym1 = 1.0d0 / dble(grid_points(2)-1)\ndnzm1 = 1.0d0 / dble(grid_points(3)-1)\n\nc1c2 = c1 * c2\nc1c5 = c1 * c5\nc3c4 = c3 * c4\nc1345 = c1c5 * c3c4\n\nconz1 = (1.0d0-c1c5)\n\ntx1 = 1.0d0 / (dnxm1 * dnxm1)\ntx2 = 1.0d0 / (2.0d0 * dnxm1)\ntx3 = 1.0d0 / dnxm1\n\nty1 = 1.0d0 / (dnym1 * dnym1)\nty2 = 1.0d0 / (2.0d0 * dnym1)\nty3 = 1.0d0 / dnym1\n\ntz1 = 1.0d0 / (dnzm1 * dnzm1)\ntz2 = 1.0d0 / (2.0d0 * dnzm1)\ntz3 = 1.0d0 / dnzm1\n\ndx1 = 0.75d0\ndx2 = 0.75d0\ndx3 = 0.75d0\ndx4 = 0.75d0\ndx5 = 0.75d0\n\ndy1 = 0.75d0\ndy2 = 0.75d0\ndy3 = 0.75d0\ndy4 = 0.75d0\ndy5 = 0.75d0\n\ndz1 = 1.0d0\ndz2 = 1.0d0\ndz3 = 1.0d0\ndz4 = 1.0d0\ndz5 = 1.0d0\n\ndxmax = dmax1(dx3, dx4)\ndymax = dmax1(dy2, dy4)\ndzmax = dmax1(dz2, dz3)\n\ndssp = 0.25d0 * dmax1(dx1, dmax1(dy1, dz1) )\n\nc4dssp = 4.0d0 * dssp\nc5dssp = 5.0d0 * dssp\n\ndttx1 = dttx1\ndttx2 = dttx2\ndtty1 = dtty1\ndtty2 = dtty2\ndttz1 = dttz1\ndttz2 = dttz2\n\nc2dttx1 = 2.0d0dttx1\nc2dtty1 = 2.0d0dtty1\nc2dttz1 = 2.0d0dttz1\n\ndtdssp = dtdssp\n\ncomz1 = dtdssp\ncomz4 = 4.0d0dtdssp\ncomz5 = 5.0d0dtdssp\ncomz6 = 6.0d0dtdssp\n\nc3c4tx3 = c3c4tx3\nc3c4ty3 = c3c4ty3\nc3c4tz3 = c3c4tz3\n\ndx1tx1 = dx1tx1\ndx2tx1 = dx2tx1\ndx3tx1 = dx3tx1\ndx4tx1 = dx4tx1\ndx5tx1 = dx5tx1\n\ndy1ty1 = dy1ty1\ndy2ty1 = dy2ty1\ndy3ty1 = dy3ty1\ndy4ty1 = dy4ty1\ndy5ty1 = dy5ty1\n\ndz1tz1 = dz1tz1\ndz2tz1 = dz2tz1\ndz3tz1 = dz3tz1\ndz4tz1 = dz4tz1\ndz5tz1 = dz5tz1\n\nc2iv = 2.5d0\ncon43 = 4.0d0/3.0d0\ncon16 = 1.0d0/6.0d0\n\nxxcon1 = c3c4tx3con43tx3\nxxcon2 = c3c4tx3tx3\nxxcon3 = c3c4tx3conz1tx3\nxxcon4 = c3c4tx3con16tx3\nxxcon5 = c3c4tx3c1c5tx3\n\nyycon1 = c3c4ty3con43ty3\nyycon2 = c3c4ty3ty3\nyycon3 = c3c4ty3conz1ty3\nyycon4 = c3c4ty3con16ty3\nyycon5 = c3c4ty3c1c5ty3\n\nzzcon1 = c3c4tz3con43tz3\nzzcon2 = c3c4tz3tz3\nzzcon3 = c3c4tz3conz1tz3\nzzcon4 = c3c4tz3con16tz3\nzzcon5 = c3c4tz3c1c5tz3\n\nreturn\nend
void rhs_norm(double rms[]){\nint i, j, k, d, m;\ndouble add;\nfor(m=0;m<5;m++){rms[m]=0.0;}\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nfor(m=0; m<5; m++){\nadd=rhs[k][j][i][m];\nrms[m]=rms[m]+add*add;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}	subroutine compute_rhs\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision aux, rho_inv, uijk, up1, um1, vijk, vp1, vm1, &\n& wijk, wp1, wm1\n\n\nif (timeron) call timer_start(t_rhs)\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\nrho_inv = 1.0d0/u(1,i,j,k)\nrho_i(i,j,k) = rho_inv\nus(i,j,k) = u(2,i,j,k) * rho_inv\nvs(i,j,k) = u(3,i,j,k) * rho_inv\nws(i,j,k) = u(4,i,j,k) * rho_inv\nsquare(i,j,k) = 0.5d0* ( &\n& u(2,i,j,k)u(2,i,j,k) + &\n& u(3,i,j,k)u(3,i,j,k) + &\n& u(4,i,j,k)u(4,i,j,k) ) rho_inv\nqs(i,j,k) = square(i,j,k) * rho_inv\naux = c1c2rho_inv (u(5,i,j,k) - square(i,j,k))\nspeed(i,j,k) = dsqrt(aux)\nend do\nend do\nend do\n\n\ndo k = 0, nz2+1\ndo j = 0, ny2+1\ndo i = 0, nx2+1\ndo m = 1, 5\nrhs(m,i,j,k) = forcing(m,i,j,k)\nend do\nend do\nend do\nend do\n\nif (timeron) call timer_start(t_rhsx)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\nuijk = us(i,j,k)\nup1 = us(i+1,j,k)\num1 = us(i-1,j,k)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dx1tx1 * &\n& (u(1,i+1,j,k) - 2.0d0u(1,i,j,k) + &\n& u(1,i-1,j,k)) - &\n& tx2 (u(2,i+1,j,k) - u(2,i-1,j,k))\n\nrhs(2,i,j,k) = rhs(2,i,j,k) + dx2tx1 * &\n& (u(2,i+1,j,k) - 2.0d0u(2,i,j,k) + &\n& u(2,i-1,j,k)) + &\n& xxcon2con43 * (up1 - 2.0d0uijk + um1) - &\n& tx2 (u(2,i+1,j,k)up1 - &\n& u(2,i-1,j,k)um1 + &\n& (u(5,i+1,j,k)- square(i+1,j,k)- &\n& u(5,i-1,j,k)+ square(i-1,j,k))* &\n& c2)\n\nrhs(3,i,j,k) = rhs(3,i,j,k) + dx3tx1 * &\n& (u(3,i+1,j,k) - 2.0d0u(3,i,j,k) + &\n& u(3,i-1,j,k)) + &\n& xxcon2 (vs(i+1,j,k) - 2.0d0vs(i,j,k) + &\n& vs(i-1,j,k)) - &\n& tx2 (u(3,i+1,j,k)up1 - &\n& u(3,i-1,j,k)um1)\n\nrhs(4,i,j,k) = rhs(4,i,j,k) + dx4tx1 * &\n& (u(4,i+1,j,k) - 2.0d0u(4,i,j,k) + &\n& u(4,i-1,j,k)) + &\n& xxcon2 (ws(i+1,j,k) - 2.0d0ws(i,j,k) + &\n& ws(i-1,j,k)) - &\n& tx2 (u(4,i+1,j,k)up1 - &\n& u(4,i-1,j,k)um1)\n\nrhs(5,i,j,k) = rhs(5,i,j,k) + dx5tx1 * &\n& (u(5,i+1,j,k) - 2.0d0u(5,i,j,k) + &\n& u(5,i-1,j,k)) + &\n& xxcon3 (qs(i+1,j,k) - 2.0d0qs(i,j,k) + &\n& qs(i-1,j,k)) + &\n& xxcon4 (up1up1 - 2.0d0uijkuijk + &\n& um1um1) + &\n& xxcon5 * (u(5,i+1,j,k)rho_i(i+1,j,k) - &\n& 2.0d0u(5,i,j,k)rho_i(i,j,k) + &\n& u(5,i-1,j,k)rho_i(i-1,j,k)) - &\n& tx2 * ( (c1u(5,i+1,j,k) - &\n& c2square(i+1,j,k))up1 - &\n& (c1u(5,i-1,j,k) - &\n& c2square(i-1,j,k))um1 )\nend do\n\ni = 1\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0u(m,i,j,k) - 4.0d0u(m,i+1,j,k) + &\n& u(m,i+2,j,k))\nend do\n\ni = 2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0u(m,i-1,j,k) + 6.0d0u(m,i,j,k) - &\n& 4.0d0u(m,i+1,j,k) + u(m,i+2,j,k))\nend do\n\ndo i = 3, nx2-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i-2,j,k) - 4.0d0u(m,i-1,j,k) + &\n& 6.0u(m,i,j,k) - 4.0d0u(m,i+1,j,k) + &\n& u(m,i+2,j,k) )\nend do\nend do\n\ni = nx2-1\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i-2,j,k) - 4.0d0u(m,i-1,j,k) + &\n& 6.0d0u(m,i,j,k) - 4.0d0u(m,i+1,j,k) )\nend do\n\ni = nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i-2,j,k) - 4.d0u(m,i-1,j,k) + &\n& 5.d0u(m,i,j,k) )\nend do\nend do\nend do\nif (timeron) call timer_stop(t_rhsx)\n\nif (timeron) call timer_start(t_rhsy)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\nvijk = vs(i,j,k)\nvp1 = vs(i,j+1,k)\nvm1 = vs(i,j-1,k)\nrhs(1,i,j,k) = rhs(1,i,j,k) + dy1ty1 * &\n& (u(1,i,j+1,k) - 2.0d0u(1,i,j,k) + &\n& u(1,i,j-1,k)) - &\n& ty2 (u(3,i,j+1,k) - u(3,i,j-1,k))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dy2ty1 * &\n& (u(2,i,j+1,k) - 2.0d0u(2,i,j,k) + &\n& u(2,i,j-1,k)) + &\n& yycon2 (us(i,j+1,k) - 2.0d0us(i,j,k) + &\n& us(i,j-1,k)) - &\n& ty2 (u(2,i,j+1,k)vp1 - &\n& u(2,i,j-1,k)vm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dy3ty1 * &\n& (u(3,i,j+1,k) - 2.0d0u(3,i,j,k) + &\n& u(3,i,j-1,k)) + &\n& yycon2con43 * (vp1 - 2.0d0vijk + vm1) - &\n& ty2 (u(3,i,j+1,k)vp1 - &\n& u(3,i,j-1,k)vm1 + &\n& (u(5,i,j+1,k) - square(i,j+1,k) - &\n& u(5,i,j-1,k) + square(i,j-1,k)) &\n& c2)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dy4ty1 &\n& (u(4,i,j+1,k) - 2.0d0u(4,i,j,k) + &\n& u(4,i,j-1,k)) + &\n& yycon2 (ws(i,j+1,k) - 2.0d0ws(i,j,k) + &\n& ws(i,j-1,k)) - &\n& ty2 (u(4,i,j+1,k)vp1 - &\n& u(4,i,j-1,k)vm1)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dy5ty1 * &\n& (u(5,i,j+1,k) - 2.0d0u(5,i,j,k) + &\n& u(5,i,j-1,k)) + &\n& yycon3 (qs(i,j+1,k) - 2.0d0qs(i,j,k) + &\n& qs(i,j-1,k)) + &\n& yycon4 (vp1vp1 - 2.0d0vijkvijk + &\n& vm1vm1) + &\n& yycon5 * (u(5,i,j+1,k)rho_i(i,j+1,k) - &\n& 2.0d0u(5,i,j,k)rho_i(i,j,k) + &\n& u(5,i,j-1,k)rho_i(i,j-1,k)) - &\n& ty2 * ((c1u(5,i,j+1,k) - &\n& c2square(i,j+1,k)) * vp1 - &\n& (c1u(5,i,j-1,k) - &\n& c2square(i,j-1,k)) * vm1)\nend do\n\n\n\nif (j .eq. 1) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0u(m,i,j,k) - 4.0d0u(m,i,j+1,k) + &\n& u(m,i,j+2,k))\nend do\nend do\n\nelse if (j .eq. 2) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0u(m,i,j-1,k) + 6.0d0u(m,i,j,k) - &\n& 4.0d0u(m,i,j+1,k) + u(m,i,j+2,k))\nend do\nend do\n\nelse if (j .eq. ny2-1) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j-2,k) - 4.0d0u(m,i,j-1,k) + &\n& 6.0d0u(m,i,j,k) - 4.0d0u(m,i,j+1,k) )\nend do\nend do\n\nelse if (j .eq. ny2) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j-2,k) - 4.d0u(m,i,j-1,k) + &\n& 5.d0u(m,i,j,k) )\nend do\nend do\n\nelse !do j = 3, ny2-2\ndo i = 1,nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.0d0u(m,i,j-1,k) + &\n& 6.0u(m,i,j,k) - 4.0d0u(m,i,j+1,k) + &\n& u(m,i,j+2,k) )\nend do\nend do\nendif\nend do\nend do\nif (timeron) call timer_stop(t_rhsy)\n\nif (timeron) call timer_start(t_rhsz)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nwijk = ws(i,j,k)\nwp1 = ws(i,j,k+1)\nwm1 = ws(i,j,k-1)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dz1tz1 &\n& (u(1,i,j,k+1) - 2.0d0u(1,i,j,k) + &\n& u(1,i,j,k-1)) - &\n& tz2 (u(4,i,j,k+1) - u(4,i,j,k-1))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dz2tz1 * &\n& (u(2,i,j,k+1) - 2.0d0u(2,i,j,k) + &\n& u(2,i,j,k-1)) + &\n& zzcon2 (us(i,j,k+1) - 2.0d0us(i,j,k) + &\n& us(i,j,k-1)) - &\n& tz2 (u(2,i,j,k+1)wp1 - &\n& u(2,i,j,k-1)wm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dz3tz1 * &\n& (u(3,i,j,k+1) - 2.0d0u(3,i,j,k) + &\n& u(3,i,j,k-1)) + &\n& zzcon2 (vs(i,j,k+1) - 2.0d0vs(i,j,k) + &\n& vs(i,j,k-1)) - &\n& tz2 (u(3,i,j,k+1)wp1 - &\n& u(3,i,j,k-1)wm1)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dz4tz1 * &\n& (u(4,i,j,k+1) - 2.0d0u(4,i,j,k) + &\n& u(4,i,j,k-1)) + &\n& zzcon2con43 * (wp1 - 2.0d0wijk + wm1) - &\n& tz2 (u(4,i,j,k+1)wp1 - &\n& u(4,i,j,k-1)wm1 + &\n& (u(5,i,j,k+1) - square(i,j,k+1) - &\n& u(5,i,j,k-1) + square(i,j,k-1)) &\n& c2)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dz5tz1 &\n& (u(5,i,j,k+1) - 2.0d0u(5,i,j,k) + &\n& u(5,i,j,k-1)) + &\n& zzcon3 (qs(i,j,k+1) - 2.0d0qs(i,j,k) + &\n& qs(i,j,k-1)) + &\n& zzcon4 (wp1wp1 - 2.0d0wijkwijk + &\n& wm1wm1) + &\n& zzcon5 * (u(5,i,j,k+1)rho_i(i,j,k+1) - &\n& 2.0d0u(5,i,j,k)rho_i(i,j,k) + &\n& u(5,i,j,k-1)rho_i(i,j,k-1)) - &\n& tz2 * ( (c1u(5,i,j,k+1) - &\n& c2square(i,j,k+1))wp1 - &\n& (c1u(5,i,j,k-1) - &\n& c2square(i,j,k-1))wm1)\nend do\n\n\nif (k .eq. 1) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0u(m,i,j,k) - 4.0d0u(m,i,j,k+1) + &\n& u(m,i,j,k+2))\nend do\nend do\n\nelse if (k .eq. 2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0u(m,i,j,k-1) + 6.0d0u(m,i,j,k) - &\n& 4.0d0u(m,i,j,k+1) + u(m,i,j,k+2))\nend do\nend do\n\nelse if (k .eq. grid_points(3)-3) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j,k-2) - 4.0d0u(m,i,j,k-1) + &\n& 6.0d0u(m,i,j,k) - 4.0d0u(m,i,j,k+1) )\nend do\nend do\n\nelse if (k .eq. grid_points(3)-2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j,k-2) - 4.d0u(m,i,j,k-1) + &\n& 5.d0u(m,i,j,k) )\nend do\nend do\n\nelse !do k = 3, grid_points(3)-4\ndo i = 1,grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.0d0u(m,i,j,k-1) + &\n& 6.0u(m,i,j,k) - 4.0d0u(m,i,j,k+1) + &\n& u(m,i,j,k+2) )\nend do\nend do\nendif\nend do\nend do\nif (timeron) call timer_stop(t_rhsz)\n\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) dt\nend do\nend do\nend do\nend do\nif (timeron) call timer_stop(t_rhs)\n\nreturn\nend
void set_constants(){\nce[0][0]=2.0;\nce[1][0]=0.0;\nce[2][0]=0.0;\nce[3][0]=4.0;\nce[4][0]=5.0;\nce[5][0]=3.0;\nce[6][0]=0.5;\nce[7][0]=0.02;\nce[8][0]=0.01;\nce[9][0]=0.03;\nce[10][0]=0.5;\nce[11][0]=0.4;\nce[12][0]=0.3;\n\nce[0][1]=1.0;\nce[1][1]=0.0;\nce[2][1]=0.0;\nce[3][1]=0.0;\nce[4][1]=1.0;\nce[5][1]=2.0;\nce[6][1]=3.0;\nce[7][1]=0.01;\nce[8][1]=0.03;\nce[9][1]=0.02;\nce[10][1]=0.4;\nce[11][1]=0.3;\nce[12][1]=0.5;\n\nce[0][2]=2.0;\nce[1][2]=2.0;\nce[2][2]=0.0;\nce[3][2]=0.0;\nce[4][2]=0.0;\nce[5][2]=2.0;\nce[6][2]=3.0;\nce[7][2]=0.04;\nce[8][2]=0.03;\nce[9][2]=0.05;\nce[10][2]=0.3;\nce[11][2]=0.5;\nce[12][2]=0.4;\n\nce[0][3]=2.0;\nce[1][3]=2.0;\nce[2][3]=0.0;\nce[3][3]=0.0;\nce[4][3]=0.0;\nce[5][3]=2.0;\nce[6][3]=3.0;\nce[7][3]=0.03;\nce[8][3]=0.05;\nce[9][3]=0.04;\nce[10][3]=0.2;\nce[11][3]=0.1;\nce[12][3]=0.3;\n\nce[0][4]=5.0;\nce[1][4]=4.0;\nce[2][4]=3.0;\nce[3][4]=2.0;\nce[4][4]=0.1;\nce[5][4]=0.4;\nce[6][4]=0.3;\nce[7][4]=0.05;\nce[8][4]=0.04;\nce[9][4]=0.03;\nce[10][4]=0.1;\nce[11][4]=0.3;\nce[12][4]=0.2;\n\nc1=1.4;\nc2=0.4;\nc3=0.1;\nc4=1.0;\nc5=1.4;\n\nbt=sqrt(0.5);\n\ndnxm1=1.0/(double)(grid_points[0]-1);\ndnym1=1.0/(double)(grid_points[1]-1);\ndnzm1=1.0/(double)(grid_points[2]-1);\n\nc1c2=c1c2;\nc1c5=c1c5;\nc3c4=c3c4;\nc1345=c1c5c3c4;\n\nconz1=(1.0-c1c5);\n\ntx1=1.0/(dnxm1dnxm1);\ntx2=1.0/(2.0dnxm1);\ntx3=1.0/dnxm1;\n\nty1=1.0/(dnym1dnym1);\nty2=1.0/(2.0dnym1);\nty3=1.0/dnym1;\n\ntz1=1.0/(dnzm1dnzm1);\ntz2=1.0/(2.0dnzm1);\ntz3=1.0/dnzm1;\n\ndx1=0.75;\ndx2=0.75;\ndx3=0.75;\ndx4=0.75;\ndx5=0.75;\n\ndy1=0.75;\ndy2=0.75;\ndy3=0.75;\ndy4=0.75;\ndy5=0.75;\n\ndz1=1.0;\ndz2=1.0;\ndz3=1.0;\ndz4=1.0;\ndz5=1.0;\n\ndxmax=max(dx3, dx4);\ndymax=max(dy2, dy4);\ndzmax=max(dz2, dz3);\n\ndssp=0.25max(dx1, max(dy1, dz1));\n\nc4dssp=4.0dssp;\nc5dssp=5.0dssp;\n\ndttx1=dttx1;\ndttx2=dttx2;\ndtty1=dtty1;\ndtty2=dtty2;\ndttz1=dttz1;\ndttz2=dttz2;\n\nc2dttx1=2.0dttx1;\nc2dtty1=2.0dtty1;\nc2dttz1=2.0dttz1;\n\ndtdssp=dtdssp;\n\ncomz1=dtdssp;\ncomz4=4.0dtdssp;\ncomz5=5.0dtdssp;\ncomz6=6.0dtdssp;\n\nc3c4tx3=c3c4tx3;\nc3c4ty3=c3c4ty3;\nc3c4tz3=c3c4tz3;\n\ndx1tx1=dx1tx1;\ndx2tx1=dx2tx1;\ndx3tx1=dx3tx1;\ndx4tx1=dx4tx1;\ndx5tx1=dx5tx1;\n\ndy1ty1=dy1ty1;\ndy2ty1=dy2ty1;\ndy3ty1=dy3ty1;\ndy4ty1=dy4ty1;\ndy5ty1=dy5ty1;\n\ndz1tz1=dz1tz1;\ndz2tz1=dz2tz1;\ndz3tz1=dz3tz1;\ndz4tz1=dz4tz1;\ndz5tz1=dz5tz1;\n\nc2iv=2.5;\ncon43=4.0/3.0;\ncon16=1.0/6.0;\n\nxxcon1=c3c4tx3con43tx3;\nxxcon2=c3c4tx3tx3;\nxxcon3=c3c4tx3conz1tx3;\nxxcon4=c3c4tx3con16tx3;\nxxcon5=c3c4tx3c1c5tx3;\n\nyycon1=c3c4ty3con43ty3;\nyycon2=c3c4ty3ty3;\nyycon3=c3c4ty3conz1ty3;\nyycon4=c3c4ty3con16ty3;\nyycon5=c3c4ty3c1c5ty3;\n\nzzcon1=c3c4tz3con43tz3;\nzzcon2=c3c4tz3tz3;\nzzcon3=c3c4tz3conz1tz3;\nzzcon4=c3c4tz3con16tz3;\nzzcon5=c3c4tz3c1c5*tz3;\n}	subroutine set_constants\n\n\nuse sp_data\nimplicit none\n\nce(1,1) = 2.0d0\nce(1,2) = 0.0d0\nce(1,3) = 0.0d0\nce(1,4) = 4.0d0\nce(1,5) = 5.0d0\nce(1,6) = 3.0d0\nce(1,7) = 0.5d0\nce(1,8) = 0.02d0\nce(1,9) = 0.01d0\nce(1,10) = 0.03d0\nce(1,11) = 0.5d0\nce(1,12) = 0.4d0\nce(1,13) = 0.3d0\n\nce(2,1) = 1.0d0\nce(2,2) = 0.0d0\nce(2,3) = 0.0d0\nce(2,4) = 0.0d0\nce(2,5) = 1.0d0\nce(2,6) = 2.0d0\nce(2,7) = 3.0d0\nce(2,8) = 0.01d0\nce(2,9) = 0.03d0\nce(2,10) = 0.02d0\nce(2,11) = 0.4d0\nce(2,12) = 0.3d0\nce(2,13) = 0.5d0\n\nce(3,1) = 2.0d0\nce(3,2) = 2.0d0\nce(3,3) = 0.0d0\nce(3,4) = 0.0d0\nce(3,5) = 0.0d0\nce(3,6) = 2.0d0\nce(3,7) = 3.0d0\nce(3,8) = 0.04d0\nce(3,9) = 0.03d0\nce(3,10) = 0.05d0\nce(3,11) = 0.3d0\nce(3,12) = 0.5d0\nce(3,13) = 0.4d0\n\nce(4,1) = 2.0d0\nce(4,2) = 2.0d0\nce(4,3) = 0.0d0\nce(4,4) = 0.0d0\nce(4,5) = 0.0d0\nce(4,6) = 2.0d0\nce(4,7) = 3.0d0\nce(4,8) = 0.03d0\nce(4,9) = 0.05d0\nce(4,10) = 0.04d0\nce(4,11) = 0.2d0\nce(4,12) = 0.1d0\nce(4,13) = 0.3d0\n\nce(5,1) = 5.0d0\nce(5,2) = 4.0d0\nce(5,3) = 3.0d0\nce(5,4) = 2.0d0\nce(5,5) = 0.1d0\nce(5,6) = 0.4d0\nce(5,7) = 0.3d0\nce(5,8) = 0.05d0\nce(5,9) = 0.04d0\nce(5,10) = 0.03d0\nce(5,11) = 0.1d0\nce(5,12) = 0.3d0\nce(5,13) = 0.2d0\n\nc1 = 1.4d0\nc2 = 0.4d0\nc3 = 0.1d0\nc4 = 1.0d0\nc5 = 1.4d0\n\nbt = dsqrt(0.5d0)\n\ndnxm1 = 1.0d0 / dble(grid_points(1)-1)\ndnym1 = 1.0d0 / dble(grid_points(2)-1)\ndnzm1 = 1.0d0 / dble(grid_points(3)-1)\n\nc1c2 = c1 * c2\nc1c5 = c1 * c5\nc3c4 = c3 * c4\nc1345 = c1c5 * c3c4\n\nconz1 = (1.0d0-c1c5)\n\ntx1 = 1.0d0 / (dnxm1 * dnxm1)\ntx2 = 1.0d0 / (2.0d0 * dnxm1)\ntx3 = 1.0d0 / dnxm1\n\nty1 = 1.0d0 / (dnym1 * dnym1)\nty2 = 1.0d0 / (2.0d0 * dnym1)\nty3 = 1.0d0 / dnym1\n\ntz1 = 1.0d0 / (dnzm1 * dnzm1)\ntz2 = 1.0d0 / (2.0d0 * dnzm1)\ntz3 = 1.0d0 / dnzm1\n\ndx1 = 0.75d0\ndx2 = 0.75d0\ndx3 = 0.75d0\ndx4 = 0.75d0\ndx5 = 0.75d0\n\ndy1 = 0.75d0\ndy2 = 0.75d0\ndy3 = 0.75d0\ndy4 = 0.75d0\ndy5 = 0.75d0\n\ndz1 = 1.0d0\ndz2 = 1.0d0\ndz3 = 1.0d0\ndz4 = 1.0d0\ndz5 = 1.0d0\n\ndxmax = dmax1(dx3, dx4)\ndymax = dmax1(dy2, dy4)\ndzmax = dmax1(dz2, dz3)\n\ndssp = 0.25d0 * dmax1(dx1, dmax1(dy1, dz1) )\n\nc4dssp = 4.0d0 * dssp\nc5dssp = 5.0d0 * dssp\n\ndttx1 = dttx1\ndttx2 = dttx2\ndtty1 = dtty1\ndtty2 = dtty2\ndttz1 = dttz1\ndttz2 = dttz2\n\nc2dttx1 = 2.0d0dttx1\nc2dtty1 = 2.0d0dtty1\nc2dttz1 = 2.0d0dttz1\n\ndtdssp = dtdssp\n\ncomz1 = dtdssp\ncomz4 = 4.0d0dtdssp\ncomz5 = 5.0d0dtdssp\ncomz6 = 6.0d0dtdssp\n\nc3c4tx3 = c3c4tx3\nc3c4ty3 = c3c4ty3\nc3c4tz3 = c3c4tz3\n\ndx1tx1 = dx1tx1\ndx2tx1 = dx2tx1\ndx3tx1 = dx3tx1\ndx4tx1 = dx4tx1\ndx5tx1 = dx5tx1\n\ndy1ty1 = dy1ty1\ndy2ty1 = dy2ty1\ndy3ty1 = dy3ty1\ndy4ty1 = dy4ty1\ndy5ty1 = dy5ty1\n\ndz1tz1 = dz1tz1\ndz2tz1 = dz2tz1\ndz3tz1 = dz3tz1\ndz4tz1 = dz4tz1\ndz5tz1 = dz5tz1\n\nc2iv = 2.5d0\ncon43 = 4.0d0/3.0d0\ncon16 = 1.0d0/6.0d0\n\nxxcon1 = c3c4tx3con43tx3\nxxcon2 = c3c4tx3tx3\nxxcon3 = c3c4tx3conz1tx3\nxxcon4 = c3c4tx3con16tx3\nxxcon5 = c3c4tx3c1c5tx3\n\nyycon1 = c3c4ty3con43ty3\nyycon2 = c3c4ty3ty3\nyycon3 = c3c4ty3conz1ty3\nyycon4 = c3c4ty3con16ty3\nyycon5 = c3c4ty3c1c5ty3\n\nzzcon1 = c3c4tz3con43tz3\nzzcon2 = c3c4tz3tz3\nzzcon3 = c3c4tz3conz1tz3\nzzcon4 = c3c4tz3con16tz3\nzzcon5 = c3c4tz3c1c5tz3\n\nreturn\nend
static void makea(int n,\nint nz,\ndouble a[],\nint colidx[],\nint rowstr[],\nint firstrow,\nint lastrow,\nint firstcol,\nint lastcol,\nint arow[],\nint acol[][NONZER+1],\ndouble aelt[][NONZER+1],\nint iv[]){\nint iouter, ivelt, nzv, nn1;\nint ivc[NONZER+1];\ndouble vc[NONZER+1];\n\n\nnn1 = 1;\ndo{\nnn1 = 2 * nn1;\n}while(nn1 < n);\n\n\nfor(iouter = 0; iouter < n; iouter++){\nnzv = NONZER;\nsprnvc(n, nzv, nn1, vc, ivc);\nvecset(n, vc, ivc, &nzv, iouter+1, 0.5);\narow[iouter] = nzv;\nfor(ivelt = 0; ivelt < nzv; ivelt++){\nacol[iouter][ivelt] = ivc[ivelt] - 1;\naelt[iouter][ivelt] = vc[ivelt];\n}\n}\n\n\nsparse(a,\ncolidx,\nrowstr,\nn,\nnz,\nNONZER,\narow,\nacol,\naelt,\nfirstrow,\nlastrow,\niv,\nRCOND,\nSHIFT);\n}	subroutine makea( n, nz, a, colidx, rowstr, &\n& firstrow, lastrow, firstcol, lastcol, &\n& arow, acol, aelt, v, iv )\n\nuse tinfo\nuse cg_data, only : nonzer, rcond, shift\n\nimplicit none\n\ninteger n\ninteger(kz) nz, rowstr(n+1)\ninteger firstrow, lastrow, firstcol, lastcol\ninteger colidx(nz)\ninteger iv(n+nz), arow(n), acol(nonzer+1,n)\ndouble precision aelt(nonzer+1,n), v(nz)\ndouble precision a(nz)\n\n\ninteger i, iouter, ivelt, nzv, nn1\ninteger ivc(nonzer+1)\ndouble precision vc(nonzer+1)\n\n\nexternal sparse, sprnvc, vecset\ninteger work\n\n\n\nnn1 = 1\n50 continue\nnn1 = 2 * nn1\nif (nn1 .lt. n) goto 50\n\nnum_threads = 1\nmyid = 0\nif (num_threads .gt. max_threads) then\nif (myid .eq. 0) write(,100) num_threads, max_threads\n100 format(' Warning: num_threads',i6, &\n& ' exceeded an internal limit',i6)\nnum_threads = max_threads\nendif\nwork = (n + num_threads - 1)/num_threads\nilow = work myid + 1\nihigh = ilow + work - 1\nif (ihigh .gt. n) ihigh = n\n\ndo iouter = 1, ihigh\nnzv = nonzer\ncall sprnvc( n, nzv, nn1, vc, ivc )\nif ( iouter .ge. ilow ) then\ncall vecset( n, vc, ivc, nzv, iouter, .5D0 )\narow(iouter) = nzv\ndo ivelt = 1, nzv\nacol(ivelt, iouter) = ivc(ivelt)\naelt(ivelt, iouter) = vc(ivelt)\nenddo\nendif\nenddo\n\ncall sparse( a, colidx, rowstr, n, nz, nonzer, arow, acol, &\n& aelt, firstrow, lastrow, &\n& v, iv(1), iv(nz+1), rcond, shift )\nreturn\n\nend
void initialize(){\nint i, j, k, m, ix, iy, iz;\ndouble xi, eta, zeta, Pface[2][3][5], Pxi, Peta, Pzeta, temp[5];\n\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<=grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nu[k][j][i][0]=1.0;\nu[k][j][i][1]=0.0;\nu[k][j][i][2]=0.0;\nu[k][j][i][3]=0.0;\nu[k][j][i][4]=1.0;\n}\n}\n}\n\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)jdnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nfor(ix=0; ix<2; ix++){\nPxi=(double)ix;\nexact_solution(Pxi, eta, zeta, &Pface[ix][0][0]);\n}\nfor(iy=0; iy<2; iy++){\nPeta=(double)iy;\nexact_solution(xi, Peta, zeta, &Pface[iy][1][0]);\n}\nfor(iz=0; iz<2; iz++){\nPzeta=(double)iz;\nexact_solution(xi, eta, Pzeta, &Pface[iz][2][0]);\n}\nfor(m=0; m<5; m++){\nPxi=xiPface[1][0][m]+(1.0-xi)Pface[0][0][m];\nPeta=etaPface[1][1][m]+(1.0-eta)Pface[0][1][m];\nPzeta=zetaPface[1][2][m]+(1.0-zeta)Pface[0][2][m];\nu[k][j][i][m]=Pxi+Peta+Pzeta-\nPxiPeta-PxiPzeta-PetaPzeta+\nPxiPetaPzeta;\n}\n}\n}\n}\n\nxi=0.0;\ni=0;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)jdnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nxi=1.0;\ni=grid_points[0]-1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)jdnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\neta=0.0;\nj=0;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\neta=1.0;\nj=grid_points[1]-1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nzeta=0.0;\nk=0;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)jdnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nzeta=1.0;\nk=grid_points[2]-1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)jdnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n}	subroutine initialize\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, m, ix, iy, iz\ndouble precision xi, eta, zeta, Pface(5,3,2), Pxi, Peta, &\n& Pzeta, temp(5)\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\nu(1,i,j,k) = 1.0\nu(2,i,j,k) = 0.0\nu(3,i,j,k) = 0.0\nu(4,i,j,k) = 0.0\nu(5,i,j,k) = 1.0\nend do\nend do\nend do\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ndo ix = 1, 2\nPxi = dble(ix-1)\ncall exact_solution(Pxi, eta, zeta, &\n& Pface(1,1,ix))\nend do\n\ndo iy = 1, 2\nPeta = dble(iy-1)\ncall exact_solution(xi, Peta, zeta, &\n& Pface(1,2,iy))\nend do\n\ndo iz = 1, 2\nPzeta = dble(iz-1)\ncall exact_solution(xi, eta, Pzeta, &\n& Pface(1,3,iz))\nend do\n\ndo m = 1, 5\nPxi = xi * Pface(m,1,2) + &\n& (1.0d0-xi) * Pface(m,1,1)\nPeta = eta * Pface(m,2,2) + &\n& (1.0d0-eta) * Pface(m,2,1)\nPzeta = zeta * Pface(m,3,2) + &\n& (1.0d0-zeta) * Pface(m,3,1)\n\nu(m,i,j,k) = Pxi + Peta + Pzeta - &\n& PxiPeta - PxiPzeta - PetaPzeta + &\n& PxiPetaPzeta\n\nend do\nend do\nend do\nend do\n\n\n\nxi = 0.0d0\ni = 0\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\nxi = 1.0d0\ni = grid_points(1)-1\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\neta = 0.0d0\nj = 0\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\n\neta = 1.0d0\nj = grid_points(2)-1\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\nzeta = 0.0d0\nk = 0\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) * dnym1\nxi = dble(i) dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\nzeta = 1.0d0\nk = grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) dnym1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\nreturn\nend
void read_input(){\n\nFILE* fp; int avoid_warning;\nif((fp=fopen("inputlu.data","r"))!=NULL){\nprintf("Reading from input file inputlu.data\n");\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%d%d",&ipr,&inorm);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%d",&itmax);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%lf",&dt);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%lf",&omega);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%lf%lf%lf%lf%lf",&tolrsd[0],\n&tolrsd[1],\n&tolrsd[2],\n&tolrsd[3],\n&tolrsd[4]);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%d%d%d",&nx0,&ny0,&nz0);\nfclose(fp);\n}else{\nipr=IPR_DEFAULT;\ninorm=INORM_DEFAULT;\nitmax=ITMAX_DEFAULT;\ndt=DT_DEFAULT;\nomega=OMEGA_DEFAULT;\ntolrsd[0]=TOLRSD1_DEF;\ntolrsd[1]=TOLRSD2_DEF;\ntolrsd[2]=TOLRSD3_DEF;\ntolrsd[3]=TOLRSD4_DEF;\ntolrsd[4]=TOLRSD5_DEF;\nnx0=ISIZ1;\nny0=ISIZ2;\nnz0=ISIZ3;\n}\n\nif((nx0<4)\|\|(ny0<4)\|\|(nz0<4)){\nprintf(" PROBLEM SIZE IS TOO SMALL -\n"\n" SET EACH OF NX, NY AND NZ AT LEAST EQUAL TO 5\n");\nexit(EXIT_FAILURE);\n}\nif((nx0>ISIZ1)\|\|(ny0>ISIZ2)\|\|(nz0>ISIZ3)){\nprintf(" PROBLEM SIZE IS TOO LARGE -\n"\n" NX, NY AND NZ SHOULD BE EQUAL TO\n"\n" ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY\n");\nexit(EXIT_FAILURE);\n}\nprintf("\n\nNAS Parallel Benchmarks 4.1 Parallel C++ version with OpenMP - LU Benchmark\n\n");\nprintf(" Size: %4dx%4dx%4d\n",nx0,ny0,nz0);\nprintf(" Iterations: %4d\n",itmax);\nprintf("\n");\n}	subroutine read_input\n\n\nuse lu_data\nimplicit none\n\ninteger fstatus\n\n\n\nwrite(, 1000)\n\nopen (unit=3,file='inputlu.data',status='old', &\n& access='sequential',form='formatted', iostat=fstatus)\nif (fstatus .eq. 0) then\n\nwrite(, ) 'Reading from input file inputlu.data'\n\nread (3,)\nread (3,)\nread (3,) ipr, inorm\nread (3,)\nread (3,)\nread (3,) itmax\nread (3,)\nread (3,)\nread (3,) dt\nread (3,)\nread (3,)\nread (3,) omega\nread (3,)\nread (3,)\nread (3,) tolrsd(1),tolrsd(2),tolrsd(3),tolrsd(4),tolrsd(5)\nread (3,)\nread (3,)\nread (3,) nx0, ny0, nz0\nclose(3)\nelse\nipr = ipr_default\ninorm = inorm_default\nitmax = itmax_default\ndt = dt_default\nomega = omega_default\ntolrsd(1) = tolrsd1_def\ntolrsd(2) = tolrsd2_def\ntolrsd(3) = tolrsd3_def\ntolrsd(4) = tolrsd4_def\ntolrsd(5) = tolrsd5_def\nnx0 = isiz1\nny0 = isiz2\nnz0 = isiz3\nendif\n\n\nif ( ( nx0 .lt. 4 ) .or. &\n& ( ny0 .lt. 4 ) .or. &\n& ( nz0 .lt. 4 ) ) then\n\nwrite (,2001)\n2001 format (5x,'PROBLEM SIZE IS TOO SMALL - ', &\n& /5x,'SET EACH OF NX, NY AND NZ AT LEAST EQUAL TO 5')\nstop\n\nend if\n\nif ( ( nx0 .gt. isiz1 ) .or. &\n& ( ny0 .gt. isiz2 ) .or. &\n& ( nz0 .gt. isiz3 ) ) then\n\nwrite (,2002)\n2002 format (5x,'PROBLEM SIZE IS TOO LARGE - ', &\n& /5x,'NX, NY AND NZ SHOULD BE EQUAL TO ', &\n& /5x,'ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY')\nstop\n\nend if\n\n\nwrite(, 1001) nx0, ny0, nz0\nwrite(, 1002) itmax\nwrite(, *)\n\n\n1000 format(//,' NAS Parallel Benchmarks (NPB3.4-OMP)', &\n& ' - LU Benchmark', /)\n1001 format(' Size: ', i4, 'x', i4, 'x', i4)\n1002 format(' Iterations: ', i5)\n1003 format(' Number of available threads: ', i5)\n\n\n\nreturn\nend
void ninvr(){\nint i, j, k;\ndouble r1, r2, r3, r4, r5, t1, t2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_NINVR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nt1=btr3;\nt2=0.5(r4+r5);\nrhs[k][j][i][0]=-r2;\nrhs[k][j][i][1]=r1;\nrhs[k][j][i][2]=bt*(r4-r5);\nrhs[k][j][i][3]=-t1+t2;\nrhs[k][j][i][4]=t1+t2;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_NINVR);}\n}	subroutine ninvr\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision r1, r2, r3, r4, r5, t1, t2\n\nif (timeron) call timer_start(t_ninvr)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nt1 = bt * r3\nt2 = 0.5d0 * ( r4 + r5 )\n\nrhs(1,i,j,k) = -r2\nrhs(2,i,j,k) = r1\nrhs(3,i,j,k) = bt * ( r4 - r5 )\nrhs(4,i,j,k) = -t1 + t2\nrhs(5,i,j,k) = t1 + t2\nenddo\nenddo\nenddo\nif (timeron) call timer_stop(t_ninvr)\n\nreturn\nend
void l2norm(int nx0,\nint ny0,\nint nz0,\nint ist,\nint iend,\nint jst,\nint jend,\ndouble v[][ISIZ2/22+1][ISIZ1/22+1][5],\ndouble sum[]){\n\nint i, j, k, m;\ndouble sum0=0.0, sum1=0.0, sum2=0.0, sum3=0.0, sum4=0.0;\n\n#pragma omp single\nfor (m = 0; m < 5; m++) {\nsum[m] = 0.0;\n}\n\n#pragma omp for nowait\nfor(k=1; k<nz0-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nsum0 = sum0 + v[i][j][k][0] * v[i][j][k][0];\nsum1 = sum1 + v[i][j][k][1] * v[i][j][k][1];\nsum2 = sum2 + v[i][j][k][2] * v[i][j][k][2];\nsum3 = sum3 + v[i][j][k][3] * v[i][j][k][3];\nsum4 = sum4 + v[i][j][k][4] * v[i][j][k][4];\n}\n}\n}\n\n#pragma omp critical\n{\nsum[0] += sum0;\nsum[1] += sum1;\nsum[2] += sum2;\nsum[3] += sum3;\nsum[4] += sum4;\n}\n#pragma omp barrier\n\n#pragma omp single\nfor(m=0; m<5; m++){\nsum[m]=sqrt(sum[m]/((nx0-2)(ny0-2)(nz0-2)));\n}\n}	subroutine l2norm ( ldx, ldy, ldz, &\n& nx0, ny0, nz0, &\n& ist, iend, &\n& jst, jend, &\n& v, sum )\n\n\nimplicit none\n\ninteger ldx, ldy, ldz\ninteger nx0, ny0, nz0\ninteger ist, iend\ninteger jst, jend\ndouble precision v(5,ldx/22+1,ldy/22+1,), sum(5)\n\ninteger i, j, k, m\n\n\ndo m = 1, 5\nsum(m) = 0.0d+00\nend do\n\ndo k = 2, nz0-1\ndo j = jst, jend\ndo i = ist, iend\ndo m = 1, 5\nsum(m) = sum(m) + v(m,i,j,k)v(m,i,j,k)\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\nsum(m) = sqrt ( sum(m) / ( dble(nx0-2)(ny0-2)(nz0-2) ) )\nend do\n\nreturn\nend
void verify(int no_time_steps, char* class_npb, boolean* verified){\ndouble xcrref[5], xceref[5], xcrdif[5], xcedif[5];\ndouble epsilon, xce[5], xcr[5], dtref=0.0;\nint m;\n\nepsilon=1.0e-08;\n\nerror_norm(xce);\ncompute_rhs();\nrhs_norm(xcr);\nfor(m=0; m<5; m++){\nxcr[m]=xcr[m]/dt;\n}\nclass_npb='U';\nverified=TRUE;\nfor(m=0; m<5; m++){\nxcrref[m]=1.0;\nxceref[m]=1.0;\n}\n\nif((grid_points[0]==12)&&\n(grid_points[1]==12)&&\n(grid_points[2]==12)&&\n(no_time_steps==60)){\nclass_npb='S';\ndtref=1.0e-2;\n\nxcrref[0]=1.7034283709541311e-01;\nxcrref[1]=1.2975252070034097e-02;\nxcrref[2]=3.2527926989486055e-02;\nxcrref[3]=2.6436421275166801e-02;\nxcrref[4]=1.9211784131744430e-01;\n\nxceref[0]=4.9976913345811579e-04;\nxceref[1]=4.5195666782961927e-05;\nxceref[2]=7.3973765172921357e-05;\nxceref[3]=7.3821238632439731e-05;\nxceref[4]=8.9269630987491446e-04;\n\n}else if((grid_points[0]==24)&&\n(grid_points[1]==24)&&\n(grid_points[2]==24)&&\n(no_time_steps==200)){\nclass_npb='W';\ndtref = 0.8e-3;\n\nxcrref[0]=0.1125590409344e+03;\nxcrref[1]=0.1180007595731e+02;\nxcrref[2]=0.2710329767846e+02;\nxcrref[3]=0.2469174937669e+02;\nxcrref[4]=0.2638427874317e+03;\n\nxceref[0]=0.4419655736008e+01;\nxceref[1]=0.4638531260002e+00;\nxceref[2]=0.1011551749967e+01;\nxceref[3]=0.9235878729944e+00;\nxceref[4]=0.1018045837718e+02;\n\n}else if((grid_points[0]==64)&&\n(grid_points[1]==64)&&\n(grid_points[2]==64)&&\n(no_time_steps==200)){\nclass_npb='A';\ndtref=0.8e-3;\n\nxcrref[0]=1.0806346714637264e+02;\nxcrref[1]=1.1319730901220813e+01;\nxcrref[2]=2.5974354511582465e+01;\nxcrref[3]=2.3665622544678910e+01;\nxcrref[4]=2.5278963211748344e+02;\n\nxceref[0]=4.2348416040525025e+00;\nxceref[1]=4.4390282496995698e-01;\nxceref[2]=9.6692480136345650e-01;\nxceref[3]=8.8302063039765474e-01;\nxceref[4]=9.7379901770829278e+00;\n\n}else if((grid_points[0]==102)&&\n(grid_points[1]==102)&&\n(grid_points[2]==102)&&\n(no_time_steps==200)){\nclass_npb='B';\ndtref=3.0e-4;\n\nxcrref[0]=1.4233597229287254e+03;\nxcrref[1]=9.9330522590150238e+01;\nxcrref[2]=3.5646025644535285e+02;\nxcrref[3]=3.2485447959084092e+02;\nxcrref[4]=3.2707541254659363e+03;\n\nxceref[0]=5.2969847140936856e+01;\nxceref[1]=4.4632896115670668e+00;\nxceref[2]=1.3122573342210174e+01;\nxceref[3]=1.2006925323559144e+01;\nxceref[4]=1.2459576151035986e+02;\n\n}else if((grid_points[0]==162)&&\n(grid_points[1]==162)&&\n(grid_points[2]==162)&&\n(no_time_steps==200)){\nclass_npb='C';\ndtref=1.0e-4;\n\nxcrref[0]=0.62398116551764615e+04;\nxcrref[1]=0.50793239190423964e+03;\nxcrref[2]=0.15423530093013596e+04;\nxcrref[3]=0.13302387929291190e+04;\nxcrref[4]=0.11604087428436455e+05;\n\nxceref[0]=0.16462008369091265e+03;\nxceref[1]=0.11497107903824313e+02;\nxceref[2]=0.41207446207461508e+02;\nxceref[3]=0.37087651059694167e+02;\nxceref[4]=0.36211053051841265e+03;\n\n}else if((grid_points[0]==408)&&\n(grid_points[1]==408)&&\n(grid_points[2]==408)&&\n(no_time_steps==250)){\nclass_npb='D';\ndtref=0.2e-4;\n\nxcrref[0]=0.2533188551738e+05;\nxcrref[1]=0.2346393716980e+04;\nxcrref[2]=0.6294554366904e+04;\nxcrref[3]=0.5352565376030e+04;\nxcrref[4]=0.3905864038618e+05;\n\nxceref[0]=0.3100009377557e+03;\nxceref[1]=0.2424086324913e+02;\nxceref[2]=0.7782212022645e+02;\nxceref[3]=0.6835623860116e+02;\nxceref[4]=0.6065737200368e+03;\n\n}else if((grid_points[0]==1020)&&\n(grid_points[1]==1020)&&\n(grid_points[2]==1020)&&\n(no_time_steps==250)){\nclass_npb='E';\ndtref=0.4e-5;\n\nxcrref[0]=0.9795372484517e+05;\nxcrref[1]=0.9739814511521e+04;\nxcrref[2]=0.2467606342965e+05;\nxcrref[3]=0.2092419572860e+05;\nxcrref[4]=0.1392138856939e+06;\n\nxceref[0]=0.4327562208414e+03;\nxceref[1]=0.3699051964887e+02;\nxceref[2]=0.1089845040954e+03;\nxceref[3]=0.9462517622043e+02;\nxceref[4]=0.7765512765309e+03;\n}else{\nverified=FALSE;\n}\n\nfor(m=0; m<5; m++){\nxcrdif[m]=fabs((xcr[m]-xcrref[m])/xcrref[m]);\nxcedif[m]=fabs((xce[m]-xceref[m])/xceref[m]);\n}\n\nif(class_npb!='U'){\nprintf(" Verification being performed for class_npb %c\n",class_npb);\nprintf(" accuracy setting for epsilon = %20.13E\n",epsilon);\nverified=(fabs(dt-dtref)<=epsilon);\nif(!(verified)){\nclass_npb='U';\nprintf(" DT does not match the reference value of %15.8E\n",dtref);\n}\n}else{\nprintf(" Unknown class_npb\n");\n}\nif(class_npb!='U'){\nprintf(" Comparison of RMS-norms of residual\n");\n}else{\nprintf(" RMS-norms of residual\n");\n}\nfor(m=0; m<5; m++){\nif(class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xcr[m]);\n}else if(xcrdif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}else{\nverified=FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}\n}\nif(class_npb!='U'){\nprintf(" Comparison of RMS-norms of solution error\n");\n}else{\nprintf(" RMS-norms of solution error\n");\n}\nfor(m=0; m<5; m++){\nif(class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xce[m]);\n}else if(xcedif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}else{\nverified=FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}\n}\nif(class_npb=='U'){\nprintf(" No reference values provided\n");\nprintf(" No verification performed\n");\n}else if(*verified){\nprintf(" Verification Successful\n");\n}else{\nprintf(" Verification failed\n");\n}\n}	subroutine verify(no_time_steps, class, verified)\n\n\n\nuse, intrinsic :: ieee_arithmetic, only : ieee_is_nan\n\nuse bt_data\n\nimplicit none\n\ndouble precision xcrref(5),xceref(5),xcrdif(5),xcedif(5), &\n& epsilon, xce(5), xcr(5), dtref\ninteger m, no_time_steps\ncharacter class\nlogical verified\n\nepsilon = 1.0d-08\n\n\ncall error_norm(xce)\ncall compute_rhs\n\ncall rhs_norm(xcr)\n\ndo m = 1, 5\nxcr(m) = xcr(m) / dt\nenddo\n\n\nclass = 'U'\nverified = .true.\n\ndo m = 1,5\nxcrref(m) = 1.0\nxceref(m) = 1.0\nend do\n\nif ( (grid_points(1) .eq. 12 ) .and. &\n& (grid_points(2) .eq. 12 ) .and. &\n& (grid_points(3) .eq. 12 ) .and. &\n& (no_time_steps .eq. 60 )) then\n\nclass = 'S'\ndtref = 1.0d-2\n\nxcrref(1) = 1.7034283709541311d-01\nxcrref(2) = 1.2975252070034097d-02\nxcrref(3) = 3.2527926989486055d-02\nxcrref(4) = 2.6436421275166801d-02\nxcrref(5) = 1.9211784131744430d-01\n\nxceref(1) = 4.9976913345811579d-04\nxceref(2) = 4.5195666782961927d-05\nxceref(3) = 7.3973765172921357d-05\nxceref(4) = 7.3821238632439731d-05\nxceref(5) = 8.9269630987491446d-04\n\nelseif ( (grid_points(1) .eq. 24) .and. &\n& (grid_points(2) .eq. 24) .and. &\n& (grid_points(3) .eq. 24) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'W'\ndtref = 0.8d-3\nxcrref(1) = 0.1125590409344d+03\nxcrref(2) = 0.1180007595731d+02\nxcrref(3) = 0.2710329767846d+02\nxcrref(4) = 0.2469174937669d+02\nxcrref(5) = 0.2638427874317d+03\n\nxceref(1) = 0.4419655736008d+01\nxceref(2) = 0.4638531260002d+00\nxceref(3) = 0.1011551749967d+01\nxceref(4) = 0.9235878729944d+00\nxceref(5) = 0.1018045837718d+02\n\n\nelseif ( (grid_points(1) .eq. 64) .and. &\n& (grid_points(2) .eq. 64) .and. &\n& (grid_points(3) .eq. 64) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'A'\ndtref = 0.8d-3\nxcrref(1) = 1.0806346714637264d+02\nxcrref(2) = 1.1319730901220813d+01\nxcrref(3) = 2.5974354511582465d+01\nxcrref(4) = 2.3665622544678910d+01\nxcrref(5) = 2.5278963211748344d+02\n\nxceref(1) = 4.2348416040525025d+00\nxceref(2) = 4.4390282496995698d-01\nxceref(3) = 9.6692480136345650d-01\nxceref(4) = 8.8302063039765474d-01\nxceref(5) = 9.7379901770829278d+00\n\nelseif ( (grid_points(1) .eq. 102) .and. &\n& (grid_points(2) .eq. 102) .and. &\n& (grid_points(3) .eq. 102) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'B'\ndtref = 3.0d-4\n\nxcrref(1) = 1.4233597229287254d+03\nxcrref(2) = 9.9330522590150238d+01\nxcrref(3) = 3.5646025644535285d+02\nxcrref(4) = 3.2485447959084092d+02\nxcrref(5) = 3.2707541254659363d+03\n\nxceref(1) = 5.2969847140936856d+01\nxceref(2) = 4.4632896115670668d+00\nxceref(3) = 1.3122573342210174d+01\nxceref(4) = 1.2006925323559144d+01\nxceref(5) = 1.2459576151035986d+02\n\nelseif ( (grid_points(1) .eq. 162) .and. &\n& (grid_points(2) .eq. 162) .and. &\n& (grid_points(3) .eq. 162) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'C'\ndtref = 1.0d-4\n\nxcrref(1) = 0.62398116551764615d+04\nxcrref(2) = 0.50793239190423964d+03\nxcrref(3) = 0.15423530093013596d+04\nxcrref(4) = 0.13302387929291190d+04\nxcrref(5) = 0.11604087428436455d+05\n\nxceref(1) = 0.16462008369091265d+03\nxceref(2) = 0.11497107903824313d+02\nxceref(3) = 0.41207446207461508d+02\nxceref(4) = 0.37087651059694167d+02\nxceref(5) = 0.36211053051841265d+03\n\nelseif ( (grid_points(1) .eq. 408) .and. &\n& (grid_points(2) .eq. 408) .and. &\n& (grid_points(3) .eq. 408) .and. &\n& (no_time_steps .eq. 250) ) then\n\nclass = 'D'\ndtref = 0.2d-4\n\nxcrref(1) = 0.2533188551738d+05\nxcrref(2) = 0.2346393716980d+04\nxcrref(3) = 0.6294554366904d+04\nxcrref(4) = 0.5352565376030d+04\nxcrref(5) = 0.3905864038618d+05\n\n\nxceref(1) = 0.3100009377557d+03\nxceref(2) = 0.2424086324913d+02\nxceref(3) = 0.7782212022645d+02\nxceref(4) = 0.6835623860116d+02\nxceref(5) = 0.6065737200368d+03\n\nelseif ( (grid_points(1) .eq. 1020) .and. &\n& (grid_points(2) .eq. 1020) .and. &\n& (grid_points(3) .eq. 1020) .and. &\n& (no_time_steps .eq. 250) ) then\n\nclass = 'E'\ndtref = 0.4d-5\n\nxcrref(1) = 0.9795372484517d+05\nxcrref(2) = 0.9739814511521d+04\nxcrref(3) = 0.2467606342965d+05\nxcrref(4) = 0.2092419572860d+05\nxcrref(5) = 0.1392138856939d+06\n\n\nxceref(1) = 0.4327562208414d+03\nxceref(2) = 0.3699051964887d+02\nxceref(3) = 0.1089845040954d+03\nxceref(4) = 0.9462517622043d+02\nxceref(5) = 0.7765512765309d+03\n\nelseif ( (grid_points(1) .eq. 2560) .and. &\n& (grid_points(2) .eq. 2560) .and. &\n& (grid_points(3) .eq. 2560) .and. &\n& (no_time_steps .eq. 250) ) then\n\nclass = 'F'\ndtref = 0.6d-6\n\nxcrref(1) = 0.4240735175585d+06\nxcrref(2) = 0.4348701133212d+05\nxcrref(3) = 0.1078114688845d+06\nxcrref(4) = 0.9142160938556d+05\nxcrref(5) = 0.5879842143431d+06\n\n\nxceref(1) = 0.5095577042351d+03\nxceref(2) = 0.4557065541652d+02\nxceref(3) = 0.1286632140581d+03\nxceref(4) = 0.1111419378722d+03\nxceref(5) = 0.8720011709356d+03\n\nelse\nverified = .false.\nendif\n\n\ndo m = 1, 5\n\nxcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))\nxcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))\n\nenddo\n\n\nif (class .ne. 'U') then\nwrite(, 1990) class\n1990 format(' Verification being performed for class ', a)\nwrite (,2000) epsilon\n2000 format(' accuracy setting for epsilon = ', E20.13)\nverified = (dabs(dt-dtref) .le. epsilon)\nif (.not.verified) then\nclass = 'U'\nwrite (,1000) dtref\n1000 format(' DT does not match the reference value of ', &\n& E15.8)\nendif\nelse\nwrite(, 1995)\n1995 format(' Unknown class')\nendif\n\n\nif (class .ne. 'U') then\nwrite (, 2001)\nelse\nwrite (, 2005)\nendif\n\n2001 format(' Comparison of RMS-norms of residual')\n2005 format(' RMS-norms of residual')\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(, 2015) m, xcr(m)\nelse if ((.not.ieee_is_nan(xcrdif(m))) .and. &\n& xcrdif(m) .le. epsilon) then\nwrite (,2011) m,xcr(m),xcrref(m),xcrdif(m)\nelse\nverified = .false.\nwrite (,2010) m,xcr(m),xcrref(m),xcrdif(m)\nendif\nenddo\n\nif (class .ne. 'U') then\nwrite (,2002)\nelse\nwrite (,2006)\nendif\n2002 format(' Comparison of RMS-norms of solution error')\n2006 format(' RMS-norms of solution error')\n\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(, 2015) m, xce(m)\nelse if ((.not.ieee_is_nan(xcedif(m))) .and. &\n& xcedif(m) .le. epsilon) then\nwrite (,2011) m,xce(m),xceref(m),xcedif(m)\nelse\nverified = .false.\nwrite (,2010) m,xce(m),xceref(m),xcedif(m)\nendif\nenddo\n\n2010 format(' FAILURE: ', i2, E20.13, E20.13, E20.13)\n2011 format(' ', i2, E20.13, E20.13, E20.13)\n2015 format(' ', i2, E20.13)\n\nif (class .eq. 'U') then\nwrite(, 2022)\nwrite(, 2023)\n2022 format(' No reference values provided')\n2023 format(' No verification performed')\nelse if (verified) then\nwrite(, 2020)\n2020 format(' Verification Successful')\nelse\nwrite(, 2021)\n2021 format(' Verification failed')\nendif\n\nreturn\n\n\nend
void x_solve(){\nint i, j, k, i1, i2, m;\ndouble ru1, fac1, fac2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_XSOLVE);}\n\n#pragma omp for\nfor(k=1; k<=nz2; k++){\ndouble cv[PROBLEM_SIZE], rhon[PROBLEM_SIZE];\ndouble lhs[IMAXP+1][IMAXP+1][5];\ndouble lhsp[IMAXP+1][IMAXP+1][5];\ndouble lhsm[IMAXP+1][IMAXP+1][5];\n\nfor(j=1; j<=ny2; j++){\nfor(m=0; m<5; m++){\nlhs[j][0][m]=0.0;\nlhsp[j][0][m]=0.0;\nlhsm[j][0][m]=0.0;\nlhs[j][nx2+1][m]=0.0;\nlhsp[j][nx2+1][m]=0.0;\nlhsm[j][nx2+1][m]=0.0;\n}\nlhs[j][0][2]=1.0;\nlhsp[j][0][2]=1.0;\nlhsm[j][0][2]=1.0;\nlhs[j][nx2+1][2]=1.0;\nlhsp[j][nx2+1][2]=1.0;\nlhsm[j][nx2+1][2]=1.0;\n}\n\n\nfor(j=1; j<=ny2; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nru1=c3c4rho_i[k][j][i];\ncv[i]=us[k][j][i];\nrhon[i]=max(max(dx2+con43ru1,dx5+c1c5ru1), max(dxmax+ru1,dx1));\n}\nfor(i=1; i<=nx2; i++){\nlhs[j][i][0]=0.0;\nlhs[j][i][1]=-dttx2cv[i-1]-dttx1rhon[i-1];\nlhs[j][i][2]=1.0+c2dttx1rhon[i];\nlhs[j][i][3]=dttx2cv[i+1]-dttx1rhon[i+1];\nlhs[j][i][4]=0.0;\n}\n}\n\nfor(j=1; j<=ny2; j++){\ni=1;\nlhs[j][i][2]=lhs[j][i][2]+comz5;\nlhs[j][i][3]=lhs[j][i][3]-comz4;\nlhs[j][i][4]=lhs[j][i][4]+comz1;\nlhs[j][i+1][1]=lhs[j][i+1][1]-comz4;\nlhs[j][i+1][2]=lhs[j][i+1][2]+comz6;\nlhs[j][i+1][3]=lhs[j][i+1][3]-comz4;\nlhs[j][i+1][4]=lhs[j][i+1][4]+comz1;\n}\nfor(j=1; j<=ny2; j++){\nfor(i=3; i<=grid_points[0]-4; i++){\nlhs[j][i][0]=lhs[j][i][0]+comz1;\nlhs[j][i][1]=lhs[j][i][1]-comz4;\nlhs[j][i][2]=lhs[j][i][2]+comz6;\nlhs[j][i][3]=lhs[j][i][3]-comz4;\nlhs[j][i][4]=lhs[j][i][4]+comz1;\n}\n}\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-3;\nlhs[j][i][0]=lhs[j][i][0]+comz1;\nlhs[j][i][1]=lhs[j][i][1]-comz4;\nlhs[j][i][2]=lhs[j][i][2]+comz6;\nlhs[j][i][3]=lhs[j][i][3]-comz4;\nlhs[j][i+1][0]=lhs[j][i+1][0]+comz1;\nlhs[j][i+1][1]=lhs[j][i+1][1]-comz4;\nlhs[j][i+1][2]=lhs[j][i+1][2]+comz5;\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nlhsp[j][i][0]=lhs[j][i][0];\nlhsp[j][i][1]=lhs[j][i][1]-dttx2speed[k][j][i-1];\nlhsp[j][i][2]=lhs[j][i][2];\nlhsp[j][i][3]=lhs[j][i][3]+dttx2speed[k][j][i+1];\nlhsp[j][i][4]=lhs[j][i][4];\nlhsm[j][i][0]=lhs[j][i][0];\nlhsm[j][i][1]=lhs[j][i][1]+dttx2speed[k][j][i-1];\nlhsm[j][i][2]=lhs[j][i][2];\nlhsm[j][i][3]=lhs[j][i][3]-dttx2speed[k][j][i+1];\nlhsm[j][i][4]=lhs[j][i][4];\n}\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=0; i<=grid_points[0]-3; i++){\ni1=i+1;\ni2=i+2;\nfac1=1.0/lhs[j][i][2];\nlhs[j][i][3]=fac1lhs[j][i][3];\nlhs[j][i][4]=fac1lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\n}\nlhs[j][i1][2]=lhs[j][i1][2]-lhs[j][i1][1]lhs[j][i][3];\nlhs[j][i1][3]=lhs[j][i1][3]-lhs[j][i1][1]lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhs[j][i1][1]rhs[k][j][i][m];\n}\nlhs[j][i2][1]=lhs[j][i2][1]-lhs[j][i2][0]lhs[j][i][3];\nlhs[j][i2][2]=lhs[j][i2][2]-lhs[j][i2][0]lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i2][m]=rhs[k][j][i2][m]-lhs[j][i2][0]rhs[k][j][i][m];\n}\n}\n}\n\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-2;\ni1=grid_points[0]-1;\nfac1=1.0/lhs[j][i][2];\nlhs[j][i][3]=fac1lhs[j][i][3];\nlhs[j][i][4]=fac1lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\n}\nlhs[j][i1][2]=lhs[j][i1][2]-lhs[j][i1][1]lhs[j][i][3];\nlhs[j][i1][3]=lhs[j][i1][3]-lhs[j][i1][1]lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhs[j][i1][1]rhs[k][j][i][m];\n}\n\nfac2 = 1.0/lhs[j][i1][2];\nfor(m=0; m<3; m++){\nrhs[k][j][i1][m]=fac2rhs[k][j][i1][m];\n}\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=0; i<=grid_points[0]-3; i++){\ni1=i+1;\ni2=i+2;\nm=3;\nfac1=1.0/lhsp[j][i][2];\nlhsp[j][i][3]=fac1lhsp[j][i][3];\nlhsp[j][i][4]=fac1lhsp[j][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsp[j][i1][2]=lhsp[j][i1][2]-lhsp[j][i1][1]lhsp[j][i][3];\nlhsp[j][i1][3]=lhsp[j][i1][3]-lhsp[j][i1][1]lhsp[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsp[j][i1][1]rhs[k][j][i][m];\nlhsp[j][i2][1]=lhsp[j][i2][1]-lhsp[j][i2][0]lhsp[j][i][3];\nlhsp[j][i2][2]=lhsp[j][i2][2]-lhsp[j][i2][0]lhsp[j][i][4];\nrhs[k][j][i2][m]=rhs[k][j][i2][m]-lhsp[j][i2][0]rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[j][i][2];\nlhsm[j][i][3]=fac1lhsm[j][i][3];\nlhsm[j][i][4]=fac1lhsm[j][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsm[j][i1][2]=lhsm[j][i1][2]-lhsm[j][i1][1]lhsm[j][i][3];\nlhsm[j][i1][3]=lhsm[j][i1][3]-lhsm[j][i1][1]lhsm[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsm[j][i1][1]rhs[k][j][i][m];\nlhsm[j][i2][1]=lhsm[j][i2][1]-lhsm[j][i2][0]lhsm[j][i][3];\nlhsm[j][i2][2]=lhsm[j][i2][2]-lhsm[j][i2][0]lhsm[j][i][4];\nrhs[k][j][i2][m]=rhs[k][j][i2][m]-lhsm[j][i2][0]rhs[k][j][i][m];\n}\n}\n\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-2;\ni1=grid_points[0]-1;\nm=3;\nfac1=1.0/lhsp[j][i][2];\nlhsp[j][i][3]=fac1lhsp[j][i][3];\nlhsp[j][i][4]=fac1lhsp[j][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsp[j][i1][2]=lhsp[j][i1][2]-lhsp[j][i1][1]lhsp[j][i][3];\nlhsp[j][i1][3]=lhsp[j][i1][3]-lhsp[j][i1][1]lhsp[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsp[j][i1][1]rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[j][i][2];\nlhsm[j][i][3]=fac1lhsm[j][i][3];\nlhsm[j][i][4]=fac1lhsm[j][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsm[j][i1][2]=lhsm[j][i1][2]-lhsm[j][i1][1]lhsm[j][i][3];\nlhsm[j][i1][3]=lhsm[j][i1][3]-lhsm[j][i1][1]lhsm[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsm[j][i1][1]rhs[k][j][i][m];\n\nrhs[k][j][i1][3]=rhs[k][j][i1][3]/lhsp[j][i1][2];\nrhs[k][j][i1][4]=rhs[k][j][i1][4]/lhsm[j][i1][2];\n}\n\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-2;\ni1=grid_points[0]-1;\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[j][i][3]rhs[k][j][i1][m];\n}\nrhs[k][j][i][3]=rhs[k][j][i][3]-lhsp[j][i][3]rhs[k][j][i1][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-lhsm[j][i][3]rhs[k][j][i1][4];\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=grid_points[0]-3; i>=0; i--){\ni1=i+1;\ni2=i+2;\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-\nlhs[j][i][3]rhs[k][j][i1][m]-\nlhs[j][i][4]rhs[k][j][i2][m];\n}\n\nrhs[k][j][i][3]=rhs[k][j][i][3]-\nlhsp[j][i][3]rhs[k][j][i1][3] -\nlhsp[j][i][4]rhs[k][j][i2][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-\nlhsm[j][i][3]rhs[k][j][i1][4]-\nlhsm[j][i][4]*rhs[k][j][i2][4];\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_XSOLVE);}\n\nninvr();\n}	subroutine x_solve\n\n\n\nuse sp_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, i1, i2, m\ndouble precision ru1, fac1, fac2\n\n\n\nif (timeron) call timer_start(t_xsolve)\ndo k = 1, nz2\ndo j = 1, ny2\n\ncall lhsinit(nx2+1, lhs, lhsp, lhsm)\n\n\ndo i = 0, grid_points(1)-1\nru1 = c3c4rho_i(i,j,k)\ncv(i) = us(i,j,k)\nrhov(i) = dmax1(dx2+con43ru1, &\n& dx5+c1c5ru1, &\n& dxmax+ru1, &\n& dx1)\nend do\n\ndo i = 1, nx2\nlhs(1,i) = 0.0d0\nlhs(2,i) = -dttx2 cv(i-1) - dttx1 * rhov(i-1)\nlhs(3,i) = 1.0d0 + c2dttx1 * rhov(i)\nlhs(4,i) = dttx2 * cv(i+1) - dttx1 * rhov(i+1)\nlhs(5,i) = 0.0d0\nend do\n\n\ni = 1\nlhs(3,i) = lhs(3,i) + comz5\nlhs(4,i) = lhs(4,i) - comz4\nlhs(5,i) = lhs(5,i) + comz1\n\nlhs(2,i+1) = lhs(2,i+1) - comz4\nlhs(3,i+1) = lhs(3,i+1) + comz6\nlhs(4,i+1) = lhs(4,i+1) - comz4\nlhs(5,i+1) = lhs(5,i+1) + comz1\n\ndo i=3, grid_points(1)-4\nlhs(1,i) = lhs(1,i) + comz1\nlhs(2,i) = lhs(2,i) - comz4\nlhs(3,i) = lhs(3,i) + comz6\nlhs(4,i) = lhs(4,i) - comz4\nlhs(5,i) = lhs(5,i) + comz1\nend do\n\ni = grid_points(1)-3\nlhs(1,i) = lhs(1,i) + comz1\nlhs(2,i) = lhs(2,i) - comz4\nlhs(3,i) = lhs(3,i) + comz6\nlhs(4,i) = lhs(4,i) - comz4\n\nlhs(1,i+1) = lhs(1,i+1) + comz1\nlhs(2,i+1) = lhs(2,i+1) - comz4\nlhs(3,i+1) = lhs(3,i+1) + comz5\n\ndo i = 1, nx2\nlhsp(1,i) = lhs(1,i)\nlhsp(2,i) = lhs(2,i) - &\n& dttx2 * speed(i-1,j,k)\nlhsp(3,i) = lhs(3,i)\nlhsp(4,i) = lhs(4,i) + &\n& dttx2 * speed(i+1,j,k)\nlhsp(5,i) = lhs(5,i)\nlhsm(1,i) = lhs(1,i)\nlhsm(2,i) = lhs(2,i) + &\n& dttx2 * speed(i-1,j,k)\nlhsm(3,i) = lhs(3,i)\nlhsm(4,i) = lhs(4,i) - &\n& dttx2 * speed(i+1,j,k)\nlhsm(5,i) = lhs(5,i)\nend do\n\n\n\ndo i = 0, grid_points(1)-3\ni1 = i + 1\ni2 = i + 2\nfac1 = 1.d0/lhs(3,i)\nlhs(4,i) = fac1lhs(4,i)\nlhs(5,i) = fac1lhs(5,i)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nend do\nlhs(3,i1) = lhs(3,i1) - &\n& lhs(2,i1)lhs(4,i)\nlhs(4,i1) = lhs(4,i1) - &\n& lhs(2,i1)lhs(5,i)\ndo m = 1, 3\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhs(2,i1)rhs(m,i,j,k)\nend do\nlhs(2,i2) = lhs(2,i2) - &\n& lhs(1,i2)lhs(4,i)\nlhs(3,i2) = lhs(3,i2) - &\n& lhs(1,i2)lhs(5,i)\ndo m = 1, 3\nrhs(m,i2,j,k) = rhs(m,i2,j,k) - &\n& lhs(1,i2)rhs(m,i,j,k)\nend do\nend do\n\n\ni = grid_points(1)-2\ni1 = grid_points(1)-1\nfac1 = 1.d0/lhs(3,i)\nlhs(4,i) = fac1lhs(4,i)\nlhs(5,i) = fac1lhs(5,i)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nend do\nlhs(3,i1) = lhs(3,i1) - &\n& lhs(2,i1)lhs(4,i)\nlhs(4,i1) = lhs(4,i1) - &\n& lhs(2,i1)lhs(5,i)\ndo m = 1, 3\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhs(2,i1)rhs(m,i,j,k)\nend do\nfac2 = 1.d0/lhs(3,i1)\ndo m = 1, 3\nrhs(m,i1,j,k) = fac2rhs(m,i1,j,k)\nend do\n\n\ndo i = 0, grid_points(1)-3\ni1 = i + 1\ni2 = i + 2\nm = 4\nfac1 = 1.d0/lhsp(3,i)\nlhsp(4,i) = fac1lhsp(4,i)\nlhsp(5,i) = fac1lhsp(5,i)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsp(3,i1) = lhsp(3,i1) - &\n& lhsp(2,i1)lhsp(4,i)\nlhsp(4,i1) = lhsp(4,i1) - &\n& lhsp(2,i1)lhsp(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsp(2,i1)rhs(m,i,j,k)\nlhsp(2,i2) = lhsp(2,i2) - &\n& lhsp(1,i2)lhsp(4,i)\nlhsp(3,i2) = lhsp(3,i2) - &\n& lhsp(1,i2)lhsp(5,i)\nrhs(m,i2,j,k) = rhs(m,i2,j,k) - &\n& lhsp(1,i2)rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,i)\nlhsm(4,i) = fac1lhsm(4,i)\nlhsm(5,i) = fac1lhsm(5,i)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsm(3,i1) = lhsm(3,i1) - &\n& lhsm(2,i1)lhsm(4,i)\nlhsm(4,i1) = lhsm(4,i1) - &\n& lhsm(2,i1)lhsm(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsm(2,i1)rhs(m,i,j,k)\nlhsm(2,i2) = lhsm(2,i2) - &\n& lhsm(1,i2)lhsm(4,i)\nlhsm(3,i2) = lhsm(3,i2) - &\n& lhsm(1,i2)lhsm(5,i)\nrhs(m,i2,j,k) = rhs(m,i2,j,k) - &\n& lhsm(1,i2)rhs(m,i,j,k)\nend do\n\ni = grid_points(1)-2\ni1 = grid_points(1)-1\nm = 4\nfac1 = 1.d0/lhsp(3,i)\nlhsp(4,i) = fac1lhsp(4,i)\nlhsp(5,i) = fac1lhsp(5,i)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsp(3,i1) = lhsp(3,i1) - &\n& lhsp(2,i1)lhsp(4,i)\nlhsp(4,i1) = lhsp(4,i1) - &\n& lhsp(2,i1)lhsp(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsp(2,i1)rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,i)\nlhsm(4,i) = fac1lhsm(4,i)\nlhsm(5,i) = fac1lhsm(5,i)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsm(3,i1) = lhsm(3,i1) - &\n& lhsm(2,i1)lhsm(4,i)\nlhsm(4,i1) = lhsm(4,i1) - &\n& lhsm(2,i1)lhsm(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsm(2,i1)rhs(m,i,j,k)\nrhs(4,i1,j,k) = rhs(4,i1,j,k)/lhsp(3,i1)\nrhs(5,i1,j,k) = rhs(5,i1,j,k)/lhsm(3,i1)\n\n\n\n\ni = grid_points(1)-2\ni1 = grid_points(1)-1\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,i)rhs(m,i1,j,k)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,i)rhs(4,i1,j,k)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,i)rhs(5,i1,j,k)\n\ndo i = grid_points(1)-3, 0, -1\ni1 = i + 1\ni2 = i + 2\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,i)rhs(m,i1,j,k) - &\n& lhs(5,i)rhs(m,i2,j,k)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,i)rhs(4,i1,j,k) - &\n& lhsp(5,i)rhs(4,i2,j,k)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,i)rhs(5,i1,j,k) - &\n& lhsm(5,i)*rhs(5,i2,j,k)\nend do\nend do\n\nend do\nif (timeron) call timer_stop(t_xsolve)\n\ncall ninvr\n\nreturn\nend
static void evolve(void* pointer_u0,\nvoid* pointer_u1,\nvoid* pointer_twiddle,\nint d1,\nint d2,\nint d3){\ndcomplex (u0)[NY][NX] = (dcomplex()[NY][NX])pointer_u0;\ndcomplex (u1)[NY][NX] = (dcomplex()[NY][NX])pointer_u1;\ndouble (twiddle)[NY][NX] = (double()[NY][NX])pointer_twiddle;\n\nint i, j, k;\n#pragma omp for\nfor(k=0; k<d3; k++){\nfor(j=0; j<d2; j++){\nfor(i=0; i<d1; i++){\nu0[k][j][i] = dcomplex_mul2(u0[k][j][i], twiddle[k][j][i]);\nu1[k][j][i] = u0[k][j][i];\n}\n}\n}\n}	subroutine evolve(u0, u1, twiddle, d1, d2, d3)\n\n\n\nuse ft_data\nimplicit none\n\ninteger d1, d2, d3\ndouble complex u0(d1+1,d2,d3)\ndouble complex u1(d1+1,d2,d3)\ndouble precision twiddle(d1+1,d2,d3)\ninteger i, j, k\n\ndo k = 1, d3\ndo j = 1, d2\ndo i = 1, d1\nu0(i,j,k) = u0(i,j,k) * twiddle(i,j,k)\nu1(i,j,k) = u0(i,j,k)\nend do\nend do\nend do\n\nreturn\nend
void domain(){\n\nnx=nx0;\nny=ny0;\nnz=nz0;\n\nif((nx<4)\|\|(ny<4)\|\|(nz<4)){\nprintf(" SUBDOMAIN SIZE IS TOO SMALL -\n"\n" ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS\n"\n" SO THAT NX, NY AND NZ ARE GREATER THAN OR EQUAL\n"\n" TO 4 THEY ARE CURRENTLY%3d%3d%3d\n",nx,ny,nz);\nexit(EXIT_FAILURE);\n}\nif((nx>ISIZ1)\|\|(ny>ISIZ2)\|\|(nz>ISIZ3)){\nprintf(" SUBDOMAIN SIZE IS TOO LARGE -\n"\n" ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS\n"\n" SO THAT NX, NY AND NZ ARE LESS THAN OR EQUAL TO\n"\n" ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY. THEY ARE\n"\n" CURRENTLYi%4d%4d%4d\n", nx, ny, nz);\nexit(EXIT_FAILURE);\n}\n\nist=1;\niend=nx-1;\njst=1;\njend=ny-1;\nii1=1;\nii2=nx0-1;\nji1=1;\nji2=ny0-2;\nki1=2;\nki2=nz0-1;\n}	subroutine domain\n\n\nuse lu_data\nimplicit none\n\n\n\nnx = nx0\nny = ny0\nnz = nz0\n\nif ( ( nx .lt. 4 ) .or. &\n& ( ny .lt. 4 ) .or. &\n& ( nz .lt. 4 ) ) then\nwrite (,2001) nx, ny, nz\n2001 format (5x,'SUBDOMAIN SIZE IS TOO SMALL - ', &\n& /5x,'ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS', &\n& /5x,'SO THAT NX, NY AND NZ ARE GREATER THAN OR EQUAL', &\n& /5x,'TO 4 THEY ARE CURRENTLY', 3I3)\nstop\nend if\n\nif ( ( nx .gt. isiz1 ) .or. &\n& ( ny .gt. isiz2 ) .or. &\n& ( nz .gt. isiz3 ) ) then\nwrite (,2002) nx, ny, nz\n2002 format (5x,'SUBDOMAIN SIZE IS TOO LARGE - ', &\n& /5x,'ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS', &\n& /5x,'SO THAT NX, NY AND NZ ARE LESS THAN OR EQUAL TO ', &\n& /5x,'ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY. THEY ARE', &\n& /5x,'CURRENTLY', 3I4)\nstop\nend if\n\nist = 2\niend = nx - 1\n\njst = 2\njend = ny - 1\n\nii1 = 2\nii2 = nx0 - 1\nji1 = 2\nji2 = ny0 - 2\nki1 = 3\nki2 = nz0 - 1\n\nreturn\nend
void tzetar(){\nint i, j, k;\ndouble t1, t2, t3, ac, xvel, yvel, zvel, r1, r2, r3, r4, r5, btuz, ac2u, uzik1;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_TZETAR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nxvel=us[k][j][i];\nyvel=vs[k][j][i];\nzvel=ws[k][j][i];\nac=speed[k][j][i];\nac2u=acac;\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nuzik1=u[k][j][i][0];\nbtuz=btuzik1;\nt1=btuz/ac(r4+r5);\nt2=r3+t1;\nt3=btuz(r4-r5);\nrhs[k][j][i][0]=t2;\nrhs[k][j][i][1]=-uzik1r2+xvelt2;\nrhs[k][j][i][2]=uzik1r1+yvelt2;\nrhs[k][j][i][3]=zvelt2+t3;\nrhs[k][j][i][4]=uzik1(-xvelr2+yvelr1) +\nqs[k][j][i]t2+c2ivac2ut1+zvelt3;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_TZETAR);}\n}	subroutine tzetar\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision t1, t2, t3, ac, xvel, yvel, zvel, r1, r2, r3, &\n& r4, r5, btuz, ac2u, uzik1\n\n\nif (timeron) call timer_start(t_tzetar)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nxvel = us(i,j,k)\nyvel = vs(i,j,k)\nzvel = ws(i,j,k)\nac = speed(i,j,k)\n\nac2u = acac\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nuzik1 = u(1,i,j,k)\nbtuz = bt uzik1\n\nt1 = btuz/ac * (r4 + r5)\nt2 = r3 + t1\nt3 = btuz * (r4 - r5)\n\nrhs(1,i,j,k) = t2\nrhs(2,i,j,k) = -uzik1r2 + xvelt2\nrhs(3,i,j,k) = uzik1r1 + yvelt2\nrhs(4,i,j,k) = zvelt2 + t3\nrhs(5,i,j,k) = uzik1(-xvelr2 + yvelr1) + &\n& qs(i,j,k)t2 + c2ivac2ut1 + zvelt3\n\nend do\nend do\nend do\nif (timeron) call timer_stop(t_tzetar)\n\nreturn\nend
static void rep_nrm(void* pointer_u, int n1, int n2, int n3, char* title, int kk){\ndouble rnm2, rnmu;\nnorm2u3(pointer_u,n1,n2,n3,&rnm2,&rnmu,nx[kk],ny[kk],nz[kk]);\n#pragma omp master\nprintf(" Level%2d in %8s: norms =%21.14e%21.14e\n", kk, title, rnm2, rnmu);\n}	subroutine rep_nrm(u,n1,n2,n3,title,kk)\n\n\n\nuse mg_data\nimplicit none\n\ninteger n1, n2, n3, kk\ndouble precision u(n1,n2,n3)\ncharacter8 title\n\ndouble precision rnm2, rnmu\n\n\ncall norm2u3(u,n1,n2,n3,rnm2,rnmu,nx(kk),ny(kk),nz(kk))\nwrite(,7)kk,title,rnm2,rnmu\n7 format(' Level',i2,' in ',a8,': norms =',D21.14,D21.14)\n\nreturn\nend
void exact_rhs(){\ndouble dtemp[5], xi, eta, zeta, dtpp;\nint m, i, j, k, ip1, im1, jp1, jm1, km1, kp1;\n\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<=grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=0.0;\n}\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)(k)dnzm1;\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)(j)dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)dnxm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][i]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][i]=dtppdtemp[m];\n}\ncuf[i]=buf[1][i]buf[1][i];\nbuf[0][i]=cuf[i]+buf[2][i]buf[2][i]+buf[3][i]buf[3][i];\nq[i]=0.5(buf[1][i]ue[1][i]+buf[2][i]ue[2][i]+\nbuf[3][i]ue[3][i]);\n}\nfor(i=1; i<=grid_points[0]-2; i++){\nim1=i-1;\nip1=i+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntx2(ue[1][ip1]-ue[1][im1])+\ndx1tx1(ue[0][ip1]-2.0ue[0][i]+ue[0][im1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tx2(\n(ue[1][ip1]buf[1][ip1]+c2(ue[4][ip1]-q[ip1]))-\n(ue[1][im1]buf[1][im1]+c2(ue[4][im1]-q[im1])))+\nxxcon1(buf[1][ip1]-2.0buf[1][i]+buf[1][im1])+\ndx2tx1(ue[1][ip1]-2.0ue[1][i]+ue[1][im1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tx2(\nue[2][ip1]buf[1][ip1]-ue[2][im1]buf[1][im1])+\nxxcon2(buf[2][ip1]-2.0buf[2][i]+buf[2][im1])+\ndx3tx1(ue[2][ip1]-2.0ue[2][i] +ue[2][im1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tx2(\nue[3][ip1]buf[1][ip1]-ue[3][im1]buf[1][im1])+\nxxcon2(buf[3][ip1]-2.0buf[3][i]+buf[3][im1])+\ndx4tx1(ue[3][ip1]-2.0ue[3][i]+ue[3][im1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tx2(\nbuf[1][ip1](c1ue[4][ip1]-c2q[ip1])-\nbuf[1][im1](c1ue[4][im1]-c2q[im1]))+\n0.5xxcon3(buf[0][ip1]-2.0buf[0][i]+\nbuf[0][im1])+\nxxcon4(cuf[ip1]-2.0cuf[i]+cuf[im1])+\nxxcon5(buf[4][ip1]-2.0buf[4][i]+buf[4][im1])+\ndx5tx1(ue[4][ip1]-2.0ue[4][i]+ue[4][im1]);\n}\n\nfor(m=0; m<5; m++){\ni=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(5.0ue[m][i]-4.0ue[m][i+1]+ue[m][i+2]);\ni=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(-4.0ue[m][i-1]+6.0ue[m][i]-\n4.0ue[m][i+1]+ue[m][i+2]);\n}\nfor(i=3; i<=grid_points[0]-4; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][i-2]-4.0ue[m][i-1]+\n6.0ue[m][i]-4.0ue[m][i+1]+ue[m][i+2]);\n}\n}\nfor(m=0; m<5; m++){\ni=grid_points[0]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][i-2]-4.0ue[m][i-1]+\n6.0ue[m][i]-4.0ue[m][i+1]);\ni=grid_points[0]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][i-2]-4.0ue[m][i-1]+5.0ue[m][i]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)(k)dnzm1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)(i)dnxm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][j]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][j]=dtppdtemp[m];\n}\ncuf[j]=buf[2][j]buf[2][j];\nbuf[0][j]=cuf[j]+buf[1][j]buf[1][j]+buf[3][j]buf[3][j];\nq[j]=0.5(buf[1][j]ue[1][j]+buf[2][j]ue[2][j]+\nbuf[3][j]ue[3][j]);\n}\nfor(j=1; j<=grid_points[1]-2; j++){\njm1=j-1;\njp1=j+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\nty2(ue[2][jp1]-ue[2][jm1])+\ndy1ty1(ue[0][jp1]-2.0ue[0][j]+ue[0][jm1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-ty2(\nue[1][jp1]buf[2][jp1]-ue[1][jm1]buf[2][jm1])+\nyycon2(buf[1][jp1]-2.0buf[1][j]+buf[1][jm1])+\ndy2ty1(ue[1][jp1]-2.0ue[1][j]+ue[1][jm1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-ty2(\n(ue[2][jp1]buf[2][jp1]+c2(ue[4][jp1]-q[jp1]))-\n(ue[2][jm1]buf[2][jm1]+c2(ue[4][jm1]-q[jm1])))+\nyycon1(buf[2][jp1]-2.0buf[2][j]+buf[2][jm1])+\ndy3ty1(ue[2][jp1]-2.0ue[2][j]+ue[2][jm1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-ty2(\nue[3][jp1]buf[2][jp1]-ue[3][jm1]buf[2][jm1])+\nyycon2(buf[3][jp1]-2.0buf[3][j]+buf[3][jm1])+\ndy4ty1(ue[3][jp1]-2.0ue[3][j]+ue[3][jm1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-ty2(\nbuf[2][jp1](c1ue[4][jp1]-c2q[jp1])-\nbuf[2][jm1](c1ue[4][jm1]-c2q[jm1]))+\n0.5yycon3(buf[0][jp1]-2.0buf[0][j]+\nbuf[0][jm1])+\nyycon4(cuf[jp1]-2.0cuf[j]+cuf[jm1])+\nyycon5(buf[4][jp1]-2.0buf[4][j]+buf[4][jm1])+\ndy5ty1(ue[4][jp1]-2.0ue[4][j]+ue[4][jm1]);\n}\n\nfor(m=0; m<5; m++){\nj=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(5.0ue[m][j]-4.0ue[m][j+1] +ue[m][j+2]);\nj=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(-4.0ue[m][j-1]+6.0ue[m][j]-\n4.0ue[m][j+1]+ue[m][j+2]);\n}\nfor(j=3; j<=grid_points[1]-4; j++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][j-2]-4.0ue[m][j-1]+\n6.0ue[m][j]-4.0ue[m][j+1]+ue[m][j+2]);\n}\n}\nfor(m=0; m<5; m++){\nj=grid_points[1]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][j-2]-4.0ue[m][j-1]+\n6.0ue[m][j]-4.0ue[m][j+1]);\nj=grid_points[1]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][j-2]-4.0ue[m][j-1]+5.0ue[m][j]);\n}\n}\n}\n\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)(j)dnym1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)(i)dnxm1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)dnzm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][k]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][k]=dtppdtemp[m];\n}\ncuf[k]=buf[3][k]buf[3][k];\nbuf[0][k]=cuf[k]+buf[1][k]buf[1][k]+buf[2][k]buf[2][k];\nq[k]=0.5(buf[1][k]ue[1][k]+buf[2][k]ue[2][k]+\nbuf[3][k]ue[3][k]);\n}\nfor(k=1; k<=grid_points[2]-2; k++){\nkm1=k-1;\nkp1=k+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntz2(ue[3][kp1]-ue[3][km1])+\ndz1tz1(ue[0][kp1]-2.0ue[0][k]+ue[0][km1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tz2(\nue[1][kp1]buf[3][kp1]-ue[1][km1]buf[3][km1])+\nzzcon2(buf[1][kp1]-2.0buf[1][k]+buf[1][km1])+\ndz2tz1(ue[1][kp1]-2.0ue[1][k]+ue[1][km1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tz2(\nue[2][kp1]buf[3][kp1]-ue[2][km1]buf[3][km1])+\nzzcon2(buf[2][kp1]-2.0buf[2][k]+buf[2][km1])+\ndz3tz1(ue[2][kp1]-2.0ue[2][k]+ue[2][km1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tz2(\n(ue[3][kp1]buf[3][kp1]+c2(ue[4][kp1]-q[kp1]))-\n(ue[3][km1]buf[3][km1]+c2(ue[4][km1]-q[km1])))+\nzzcon1(buf[3][kp1]-2.0buf[3][k]+buf[3][km1])+\ndz4tz1(ue[3][kp1]-2.0ue[3][k]+ue[3][km1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tz2(\nbuf[3][kp1](c1ue[4][kp1]-c2q[kp1])-\nbuf[3][km1](c1ue[4][km1]-c2q[km1]))+\n0.5zzcon3(buf[0][kp1]-2.0buf[0][k]\n+buf[0][km1])+\nzzcon4(cuf[kp1]-2.0cuf[k]+cuf[km1])+\nzzcon5(buf[4][kp1]-2.0buf[4][k]+buf[4][km1])+\ndz5tz1(ue[4][kp1]-2.0ue[4][k]+ue[4][km1]);\n}\n\nfor(m=0; m<5; m++){\nk=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(5.0ue[m][k]-4.0ue[m][k+1]+ue[m][k+2]);\nk=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(-4.0ue[m][k-1]+6.0ue[m][k]-\n4.0ue[m][k+1]+ue[m][k+2]);\n}\nfor(k=3; k<=grid_points[2]-4; k++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][k-2]-4.0ue[m][k-1]+\n6.0ue[m][k]-4.0ue[m][k+1]+ue[m][k+2]);\n}\n}\nfor(m=0; m<5; m++){\nk=grid_points[2]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][k-2]-4.0ue[m][k-1]+\n6.0ue[m][k]-4.0ue[m][k+1]);\nk=grid_points[2]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][k-2]-4.0ue[m][k-1]+5.0ue[m][k]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=-1.0forcing[k][j][i][m];\n}\n}\n}\n}\n}	subroutine exact_rhs\n\n\n\nuse bt_data\nimplicit none\n\ndouble precision dtemp(5), xi, eta, zeta, dtpp\ninteger m, i, j, k, ip1, im1, jp1, jm1, km1, kp1\n\ndo k= 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nforcing(m,i,j,k) = 0.0d0\nenddo\nenddo\nenddo\nenddo\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\n\ndo i=0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(i,m) = dtemp(m)\nenddo\n\ndtpp = 1.0d0 / dtemp(1)\n\ndo m = 2, 5\nbuf(i,m) = dtpp * dtemp(m)\nenddo\n\ncuf(i) = buf(i,2) * buf(i,2)\nbuf(i,1) = cuf(i) + buf(i,3) * buf(i,3) + &\n& buf(i,4) * buf(i,4)\nq(i) = 0.5d0(buf(i,2)ue(i,2) + buf(i,3)ue(i,3) + &\n& buf(i,4)ue(i,4))\n\nenddo\n\ndo i = 1, grid_points(1)-2\nim1 = i-1\nip1 = i+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tx2( ue(ip1,2)-ue(im1,2) )+ &\n& dx1tx1(ue(ip1,1)-2.0d0ue(i,1)+ue(im1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tx2 ( &\n& (ue(ip1,2)buf(ip1,2)+c2(ue(ip1,5)-q(ip1)))- &\n& (ue(im1,2)buf(im1,2)+c2(ue(im1,5)-q(im1))))+ &\n& xxcon1(buf(ip1,2)-2.0d0buf(i,2)+buf(im1,2))+ &\n& dx2tx1( ue(ip1,2)-2.0d0 ue(i,2)+ue(im1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tx2 * ( &\n& ue(ip1,3)buf(ip1,2)-ue(im1,3)buf(im1,2))+ &\n& xxcon2(buf(ip1,3)-2.0d0buf(i,3)+buf(im1,3))+ &\n& dx3tx1( ue(ip1,3)-2.0d0ue(i,3) +ue(im1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tx2( &\n& ue(ip1,4)buf(ip1,2)-ue(im1,4)buf(im1,2))+ &\n& xxcon2(buf(ip1,4)-2.0d0buf(i,4)+buf(im1,4))+ &\n& dx4tx1( ue(ip1,4)-2.0d0* ue(i,4)+ ue(im1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tx2( &\n& buf(ip1,2)(c1ue(ip1,5)-c2q(ip1))- &\n& buf(im1,2)(c1ue(im1,5)-c2q(im1)))+ &\n& 0.5d0xxcon3(buf(ip1,1)-2.0d0buf(i,1)+ &\n& buf(im1,1))+ &\n& xxcon4(cuf(ip1)-2.0d0cuf(i)+cuf(im1))+ &\n& xxcon5(buf(ip1,5)-2.0d0buf(i,5)+buf(im1,5))+ &\n& dx5tx1( ue(ip1,5)-2.0d0 ue(i,5)+ ue(im1,5))\nenddo\n\n\ndo m = 1, 5\ni = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0ue(i,m) - 4.0d0ue(i+1,m) +ue(i+2,m))\ni = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0ue(i-1,m) + 6.0d0ue(i,m) - &\n& 4.0d0ue(i+1,m) + ue(i+2,m))\nenddo\n\ndo i = 3, grid_points(1)-4\ndo m = 1, 5\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(i-2,m) - 4.0d0ue(i-1,m) + &\n& 6.0d0ue(i,m) - 4.0d0ue(i+1,m) + ue(i+2,m))\nenddo\nenddo\n\ndo m = 1, 5\ni = grid_points(1)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(i-2,m) - 4.0d0ue(i-1,m) + &\n& 6.0d0ue(i,m) - 4.0d0ue(i+1,m))\ni = grid_points(1)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(i-2,m) - 4.0d0ue(i-1,m) + 5.0d0ue(i,m))\nenddo\n\nenddo\nenddo\n\ndo k = 1, grid_points(3)-2\ndo i=1, grid_points(1)-2\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\n\ndo j=0, grid_points(2)-1\neta = dble(j) * dnym1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(j,m) = dtemp(m)\nenddo\n\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(j,m) = dtpp * dtemp(m)\nenddo\n\ncuf(j) = buf(j,3) * buf(j,3)\nbuf(j,1) = cuf(j) + buf(j,2) * buf(j,2) + &\n& buf(j,4) * buf(j,4)\nq(j) = 0.5d0(buf(j,2)ue(j,2) + buf(j,3)ue(j,3) + &\n& buf(j,4)ue(j,4))\nenddo\n\ndo j = 1, grid_points(2)-2\njm1 = j-1\njp1 = j+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& ty2( ue(jp1,3)-ue(jm1,3) )+ &\n& dy1ty1(ue(jp1,1)-2.0d0ue(j,1)+ue(jm1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - ty2( &\n& ue(jp1,2)buf(jp1,3)-ue(jm1,2)buf(jm1,3))+ &\n& yycon2(buf(jp1,2)-2.0d0buf(j,2)+buf(jm1,2))+ &\n& dy2ty1( ue(jp1,2)-2.0 ue(j,2)+ ue(jm1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - ty2( &\n& (ue(jp1,3)buf(jp1,3)+c2(ue(jp1,5)-q(jp1)))- &\n& (ue(jm1,3)buf(jm1,3)+c2(ue(jm1,5)-q(jm1))))+ &\n& yycon1(buf(jp1,3)-2.0d0buf(j,3)+buf(jm1,3))+ &\n& dy3ty1( ue(jp1,3)-2.0d0ue(j,3) +ue(jm1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - ty2( &\n& ue(jp1,4)buf(jp1,3)-ue(jm1,4)buf(jm1,3))+ &\n& yycon2(buf(jp1,4)-2.0d0buf(j,4)+buf(jm1,4))+ &\n& dy4ty1( ue(jp1,4)-2.0d0ue(j,4)+ ue(jm1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - ty2( &\n& buf(jp1,3)(c1ue(jp1,5)-c2q(jp1))- &\n& buf(jm1,3)(c1ue(jm1,5)-c2q(jm1)))+ &\n& 0.5d0yycon3(buf(jp1,1)-2.0d0buf(j,1)+ &\n& buf(jm1,1))+ &\n& yycon4(cuf(jp1)-2.0d0cuf(j)+cuf(jm1))+ &\n& yycon5(buf(jp1,5)-2.0d0buf(j,5)+buf(jm1,5))+ &\n& dy5ty1(ue(jp1,5)-2.0d0ue(j,5)+ue(jm1,5))\nenddo\n\ndo m = 1, 5\nj = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0ue(j,m) - 4.0d0ue(j+1,m) +ue(j+2,m))\nj = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0ue(j-1,m) + 6.0d0ue(j,m) - &\n& 4.0d0ue(j+1,m) + ue(j+2,m))\nenddo\n\ndo j = 3, grid_points(2)-4\ndo m = 1, 5\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(j-2,m) - 4.0d0ue(j-1,m) + &\n& 6.0d0ue(j,m) - 4.0d0ue(j+1,m) + ue(j+2,m))\nenddo\nenddo\n\ndo m = 1, 5\nj = grid_points(2)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(j-2,m) - 4.0d0ue(j-1,m) + &\n& 6.0d0ue(j,m) - 4.0d0ue(j+1,m))\nj = grid_points(2)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(j-2,m) - 4.0d0ue(j-1,m) + 5.0d0ue(j,m))\n\nenddo\n\nenddo\nenddo\n\ndo j=1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\neta = dble(j) * dnym1\nxi = dble(i) * dnxm1\n\ndo k=0, grid_points(3)-1\nzeta = dble(k) * dnzm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(k,m) = dtemp(m)\nenddo\n\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(k,m) = dtpp * dtemp(m)\nenddo\n\ncuf(k) = buf(k,4) * buf(k,4)\nbuf(k,1) = cuf(k) + buf(k,2) * buf(k,2) + &\n& buf(k,3) * buf(k,3)\nq(k) = 0.5d0(buf(k,2)ue(k,2) + buf(k,3)ue(k,3) + &\n& buf(k,4)ue(k,4))\nenddo\n\ndo k=1, grid_points(3)-2\nkm1 = k-1\nkp1 = k+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tz2( ue(kp1,4)-ue(km1,4) )+ &\n& dz1tz1(ue(kp1,1)-2.0d0ue(k,1)+ue(km1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tz2 ( &\n& ue(kp1,2)buf(kp1,4)-ue(km1,2)buf(km1,4))+ &\n& zzcon2(buf(kp1,2)-2.0d0buf(k,2)+buf(km1,2))+ &\n& dz2tz1( ue(kp1,2)-2.0d0 ue(k,2)+ ue(km1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tz2 * ( &\n& ue(kp1,3)buf(kp1,4)-ue(km1,3)buf(km1,4))+ &\n& zzcon2(buf(kp1,3)-2.0d0buf(k,3)+buf(km1,3))+ &\n& dz3tz1(ue(kp1,3)-2.0d0ue(k,3)+ue(km1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tz2 * ( &\n& (ue(kp1,4)buf(kp1,4)+c2(ue(kp1,5)-q(kp1)))- &\n& (ue(km1,4)buf(km1,4)+c2(ue(km1,5)-q(km1))))+ &\n& zzcon1(buf(kp1,4)-2.0d0buf(k,4)+buf(km1,4))+ &\n& dz4tz1( ue(kp1,4)-2.0d0ue(k,4) +ue(km1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tz2 * ( &\n& buf(kp1,4)(c1ue(kp1,5)-c2q(kp1))- &\n& buf(km1,4)(c1ue(km1,5)-c2q(km1)))+ &\n& 0.5d0zzcon3(buf(kp1,1)-2.0d0buf(k,1) &\n& +buf(km1,1))+ &\n& zzcon4(cuf(kp1)-2.0d0cuf(k)+cuf(km1))+ &\n& zzcon5(buf(kp1,5)-2.0d0buf(k,5)+buf(km1,5))+ &\n& dz5tz1( ue(kp1,5)-2.0d0ue(k,5)+ ue(km1,5))\nenddo\n\ndo m = 1, 5\nk = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (5.0d0ue(k,m) - 4.0d0ue(k+1,m) +ue(k+2,m))\nk = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0ue(k-1,m) + 6.0d0ue(k,m) - &\n& 4.0d0ue(k+1,m) + ue(k+2,m))\nenddo\n\ndo k = 3, grid_points(3)-4\ndo m = 1, 5\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(k-2,m) - 4.0d0ue(k-1,m) + &\n& 6.0d0ue(k,m) - 4.0d0ue(k+1,m) + ue(k+2,m))\nenddo\nenddo\n\ndo m = 1, 5\nk = grid_points(3)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(k-2,m) - 4.0d0ue(k-1,m) + &\n& 6.0d0ue(k,m) - 4.0d0ue(k+1,m))\nk = grid_points(3)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(k-2,m) - 4.0d0ue(k-1,m) + 5.0d0ue(k,m))\nenddo\n\nenddo\nenddo\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nforcing(m,i,j,k) = -1.d0 * forcing(m,i,j,k)\nenddo\nenddo\nenddo\nenddo\n\nreturn\nend
void pinvr(){\nint i, j, k;\ndouble r1, r2, r3, r4, r5, t1, t2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_PINVR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nt1=btr1;\nt2=0.5(r4+r5);\nrhs[k][j][i][0]=bt*(r4-r5);\nrhs[k][j][i][1]=-r3;\nrhs[k][j][i][2]=r2;\nrhs[k][j][i][3]=-t1+t2;\nrhs[k][j][i][4]=t1+t2;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_PINVR);}\n}	subroutine pinvr\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision r1, r2, r3, r4, r5, t1, t2\n\nif (timeron) call timer_start(t_pinvr)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nt1 = bt * r1\nt2 = 0.5d0 * ( r4 + r5 )\n\nrhs(1,i,j,k) = bt * ( r4 - r5 )\nrhs(2,i,j,k) = -r3\nrhs(3,i,j,k) = r2\nrhs(4,i,j,k) = -t1 + t2\nrhs(5,i,j,k) = t1 + t2\nend do\nend do\nend do\nif (timeron) call timer_stop(t_pinvr)\n\nreturn\nend
static void cffts1(int is,\nint d1,\nint d2,\nint d3,\nvoid* pointer_x,\nvoid* pointer_xout,\ndcomplex y1[][FFTBLOCKPAD],\ndcomplex y2[][FFTBLOCKPAD]){\ndcomplex (x)[NY][NX] = (dcomplex()[NY][NX])pointer_x;\ndcomplex (xout)[NY][NX] = (dcomplex()[NY][NX])pointer_xout;\n\nint logd1;\nint i, j, k, jj;\n\nlogd1 = ilog2(d1);\n\n\nif(timers_enabled){\n#pragma omp master\ntimer_start(T_FFTX);\n}\n\n#pragma omp for\nfor(k=0; k<d3; k++){\nfor(jj=0; jj<=d2-FFTBLOCK; jj+=FFTBLOCK){\nfor(j=0; j<FFTBLOCK; j++){\nfor(i=0; i<d1; i++){\ny1[i][j] = x[k][j+jj][i];\n}\n}\ncfftz(is, logd1, d1, y1, y2);\nfor(j=0; j<FFTBLOCK; j++){\nfor(i=0; i<d1; i++){\nxout[k][j+jj][i] = y1[i][j];\n}\n}\n}\n}\n\nif(timers_enabled){\n#pragma omp master\ntimer_stop(T_FFTX);\n}\n}	subroutine cffts1(is, d1, d2, d3, x, xout, y1, y2)\n\n\nuse ft_data\nimplicit none\n\ninteger is, d1, d2, d3, logd1\ndouble complex x(d1+1,d2,d3)\ndouble complex xout(d1+1,d2,d3)\ndouble complex y1(fftblockpad, d1), y2(fftblockpad, d1)\ninteger i, j, k, jj, jn\n\nlogd1 = ilog2(d1)\n\nif (timers_enabled) call timer_start(T_fftx)\ndo k = 1, d3\ndo jn = 0, d2/fftblock - 1\njj = jn*fftblock\ndo j = 1, fftblock\ndo i = 1, d1\ny1(j,i) = x(i,j+jj,k)\nenddo\nenddo\n\ncall cfftz (is, logd1, d1, y1, y2)\n\n\ndo j = 1, fftblock\ndo i = 1, d1\nxout(i,j+jj,k) = y1(j,i)\nenddo\nenddo\nenddo\nenddo\nif (timers_enabled) call timer_stop(T_fftx)\n\nreturn\nend
void error(){\n\nint i, j, k, m;\ndouble tmp;\ndouble u000ijk[5];\nfor(m=0;m<5;m++){errnm[m]=0.0;}\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nexact(i, j, k, u000ijk);\nfor(m=0; m<5; m++){\ntmp=(u000ijk[m]-u[k][j][i][m]);\nerrnm[m]=errnm[m]+tmptmp;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nerrnm[m]=sqrt(errnm[m]/((nx0-2)(ny0-2)*(nz0-2)));\n}\n}	subroutine error\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision tmp\ndouble precision u000ijk(5)\n\n\ndo m = 1, 5\nerrnm(m) = 0.0d+00\nend do\n\ndo k = 2, nz-1\ndo j = jst, jend\ndo i = ist, iend\ncall exact( i, j, k, u000ijk )\ndo m = 1, 5\ntmp = ( u000ijk(m) - u(m,i,j,k) )\nerrnm(m) = errnm(m) + tmp * tmp\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\nerrnm(m) = sqrt ( errnm(m) / ( dble(nx0-2)(ny0-2)(nz0-2) ) )\nend do\n\n\n1002 format (1x/1x,'RMS-norm of error in soln. to ', &\n& 'first pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'second pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'third pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'fourth pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'fifth pde = ',1pe12.5)\n\nreturn\nend
static void cffts3(int is,\nint d1,\nint d2,\nint d3,\nvoid* pointer_x,\nvoid* pointer_xout,\ndcomplex y1[][FFTBLOCKPAD],\ndcomplex y2[][FFTBLOCKPAD]){\ndcomplex (x)[NY][NX] = (dcomplex()[NY][NX])pointer_x;\ndcomplex (xout)[NY][NX] = (dcomplex()[NY][NX])pointer_xout;\n\nint logd3;\nint i, j, k, ii;\n\nlogd3 = ilog2(d3);\n\nif(timers_enabled){\n#pragma omp master\ntimer_start(T_FFTZ);\n}\n\n#pragma omp for\nfor(j=0; j<d2; j++){\nfor(ii=0; ii<=d1-FFTBLOCK; ii+=FFTBLOCK){\nfor(k=0; k<d3; k++){\nfor(i=0; i<FFTBLOCK; i++){\ny1[k][i] = x[k][j][i+ii];\n}\n}\ncfftz(is, logd3, d3, y1, y2);\nfor(k=0; k<d3; k++){\nfor(i=0; i<FFTBLOCK; i++){\nxout[k][j][i+ii] = y1[k][i];\n}\n}\n}\n}\n\nif(timers_enabled){\n#pragma omp master\ntimer_stop(T_FFTZ);\n}\n}	subroutine cffts3(is, d1, d2, d3, x, xout, y1, y2)\n\n\nuse ft_data\nimplicit none\n\ninteger is, d1, d2, d3, logd3\ndouble complex x(d1+1,d2,d3)\ndouble complex xout(d1+1,d2,d3)\ndouble complex y1(fftblockpad, d3), y2(fftblockpad, d3)\ninteger i, j, k, ii, in\n\nlogd3 = ilog2(d3)\n\nif (timers_enabled) call timer_start(T_fftz)\ndo j = 1, d2\ndo in = 0, d1/fftblock - 1\nii = in*fftblock\ndo k = 1, d3\ndo i = 1, fftblock\ny1(i,k) = x(i+ii,j,k)\nenddo\nenddo\n\ncall cfftz (is, logd3, d3, y1, y2)\n\ndo k = 1, d3\ndo i = 1, fftblock\nxout(i+ii,j,k) = y1(i,k)\nenddo\nenddo\nenddo\nenddo\nif (timers_enabled) call timer_stop(T_fftz)\n\nreturn\nend
void setcoeff(){\n\ndxi=1.0/(nx0-1);\ndeta=1.0/(ny0-1);\ndzeta=1.0/(nz0-1);\ntx1=1.0/(dxidxi);\ntx2=1.0/(2.0dxi);\ntx3=1.0/dxi;\nty1=1.0/(detadeta);\nty2=1.0/(2.0deta);\nty3=1.0/deta;\ntz1=1.0/(dzetadzeta);\ntz2=1.0/(2.0dzeta);\ntz3=1.0/dzeta;\n\ndx1=0.75;\ndx2=dx1;\ndx3=dx1;\ndx4=dx1;\ndx5=dx1;\ndy1=0.75;\ndy2=dy1;\ndy3=dy1;\ndy4=dy1;\ndy5=dy1;\ndz1=1.00;\ndz2=dz1;\ndz3=dz1;\ndz4=dz1;\ndz5=dz1;\n\ndssp=(max(max(dx1,dy1),dz1))/4.0;\n\nce[0][0]=2.0;\nce[1][0]=0.0;\nce[2][0]=0.0;\nce[3][0]=4.0;\nce[4][0]=5.0;\nce[5][0]=3.0;\nce[6][0]=5.0e-01;\nce[7][0]=2.0e-02;\nce[8][0]=1.0e-02;\nce[9][0]=3.0e-02;\nce[10][0]=5.0e-01;\nce[11][0]=4.0e-01;\nce[12][0]=3.0e-01;\n\nce[0][1]=1.0;\nce[1][1]=0.0;\nce[2][1]=0.0;\nce[3][1]=0.0;\nce[4][1]=1.0;\nce[5][1]=2.0;\nce[6][1]=3.0;\nce[7][1]=1.0e-02;\nce[8][1]=3.0e-02;\nce[9][1]=2.0e-02;\nce[10][1]=4.0e-01;\nce[11][1]=3.0e-01;\nce[12][1]=5.0e-01;\n\nce[0][2]=2.0;\nce[1][2]=2.0;\nce[2][2]=0.0;\nce[3][2]=0.0;\nce[4][2]=0.0;\nce[5][2]=2.0;\nce[6][2]=3.0;\nce[7][2]=4.0e-02;\nce[8][2]=3.0e-02;\nce[9][2]=5.0e-02;\nce[10][2]=3.0e-01;\nce[11][2]=5.0e-01;\nce[12][2]=4.0e-01;\n\nce[0][3]=2.0;\nce[1][3]=2.0;\nce[2][3]=0.0;\nce[3][3]=0.0;\nce[4][3]=0.0;\nce[5][3]=2.0;\nce[6][3]=3.0;\nce[7][3]=3.0e-02;\nce[8][3]=5.0e-02;\nce[9][3]=4.0e-02;\nce[10][3]=2.0e-01;\nce[11][3]=1.0e-01;\nce[12][3]=3.0e-01;\n\nce[0][4]=5.0;\nce[1][4]=4.0;\nce[2][4]=3.0;\nce[3][4]=2.0;\nce[4][4]=1.0e-01;\nce[5][4]=4.0e-01;\nce[6][4]=3.0e-01;\nce[7][4]=5.0e-02;\nce[8][4]=4.0e-02;\nce[9][4]=3.0e-02;\nce[10][4]=1.0e-01;\nce[11][4]=3.0e-01;\nce[12][4]=2.0e-01;\n}	subroutine setcoeff\n\n\nuse lu_data\nimplicit none\n\n\n\ndxi = 1.0d+00 / ( nx0 - 1 )\ndeta = 1.0d+00 / ( ny0 - 1 )\ndzeta = 1.0d+00 / ( nz0 - 1 )\n\ntx1 = 1.0d+00 / ( dxi * dxi )\ntx2 = 1.0d+00 / ( 2.0d+00 * dxi )\ntx3 = 1.0d+00 / dxi\n\nty1 = 1.0d+00 / ( deta * deta )\nty2 = 1.0d+00 / ( 2.0d+00 * deta )\nty3 = 1.0d+00 / deta\n\ntz1 = 1.0d+00 / ( dzeta * dzeta )\ntz2 = 1.0d+00 / ( 2.0d+00 * dzeta )\ntz3 = 1.0d+00 / dzeta\n\ndx1 = 0.75d+00\ndx2 = dx1\ndx3 = dx1\ndx4 = dx1\ndx5 = dx1\n\ndy1 = 0.75d+00\ndy2 = dy1\ndy3 = dy1\ndy4 = dy1\ndy5 = dy1\n\ndz1 = 1.00d+00\ndz2 = dz1\ndz3 = dz1\ndz4 = dz1\ndz5 = dz1\n\ndssp = ( max (dx1, dy1, dz1 ) ) / 4.0d+00\n\nce(1,1) = 2.0d+00\nce(1,2) = 0.0d+00\nce(1,3) = 0.0d+00\nce(1,4) = 4.0d+00\nce(1,5) = 5.0d+00\nce(1,6) = 3.0d+00\nce(1,7) = 5.0d-01\nce(1,8) = 2.0d-02\nce(1,9) = 1.0d-02\nce(1,10) = 3.0d-02\nce(1,11) = 5.0d-01\nce(1,12) = 4.0d-01\nce(1,13) = 3.0d-01\n\nce(2,1) = 1.0d+00\nce(2,2) = 0.0d+00\nce(2,3) = 0.0d+00\nce(2,4) = 0.0d+00\nce(2,5) = 1.0d+00\nce(2,6) = 2.0d+00\nce(2,7) = 3.0d+00\nce(2,8) = 1.0d-02\nce(2,9) = 3.0d-02\nce(2,10) = 2.0d-02\nce(2,11) = 4.0d-01\nce(2,12) = 3.0d-01\nce(2,13) = 5.0d-01\n\nce(3,1) = 2.0d+00\nce(3,2) = 2.0d+00\nce(3,3) = 0.0d+00\nce(3,4) = 0.0d+00\nce(3,5) = 0.0d+00\nce(3,6) = 2.0d+00\nce(3,7) = 3.0d+00\nce(3,8) = 4.0d-02\nce(3,9) = 3.0d-02\nce(3,10) = 5.0d-02\nce(3,11) = 3.0d-01\nce(3,12) = 5.0d-01\nce(3,13) = 4.0d-01\n\nce(4,1) = 2.0d+00\nce(4,2) = 2.0d+00\nce(4,3) = 0.0d+00\nce(4,4) = 0.0d+00\nce(4,5) = 0.0d+00\nce(4,6) = 2.0d+00\nce(4,7) = 3.0d+00\nce(4,8) = 3.0d-02\nce(4,9) = 5.0d-02\nce(4,10) = 4.0d-02\nce(4,11) = 2.0d-01\nce(4,12) = 1.0d-01\nce(4,13) = 3.0d-01\n\nce(5,1) = 5.0d+00\nce(5,2) = 4.0d+00\nce(5,3) = 3.0d+00\nce(5,4) = 2.0d+00\nce(5,5) = 1.0d-01\nce(5,6) = 4.0d-01\nce(5,7) = 3.0d-01\nce(5,8) = 5.0d-02\nce(5,9) = 4.0d-02\nce(5,10) = 3.0d-02\nce(5,11) = 1.0d-01\nce(5,12) = 3.0d-01\nce(5,13) = 2.0d-01\n\nreturn\nend
void y_solve(){\nint i, j, k, m, n, jsize;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_YSOLVE);}\n\njsize=grid_points[1]-1;\n\n#pragma omp for\nfor(k=1; k<=grid_points[2]-2; k++){\ndouble fjac[PROBLEM_SIZE+1][5][5];\ndouble njac[PROBLEM_SIZE+1][5][5];\ndouble lhs[PROBLEM_SIZE+1][3][5][5];\ndouble tmp1, tmp2, tmp3;\n\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(j=0; j<=jsize; j++){\ntmp1=rho_i[k][j][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nfjac[j][0][0]=0.0;\nfjac[j][1][0]=0.0;\nfjac[j][2][0]=1.0;\nfjac[j][3][0]=0.0;\nfjac[j][4][0]=0.0;\nfjac[j][0][1]=-(u[k][j][i][1]u[k][j][i][2])tmp2;\nfjac[j][1][1]=u[k][j][i][2]tmp1;\nfjac[j][2][1]=u[k][j][i][1]tmp1;\nfjac[j][3][1]=0.0;\nfjac[j][4][1]=0.0;\nfjac[j][0][2]=-(u[k][j][i][2]u[k][j][i][2]tmp2)+c2qs[k][j][i];\nfjac[j][1][2]=-c2u[k][j][i][1]tmp1;\nfjac[j][2][2]=(2.0-c2)u[k][j][i][2]tmp1;\nfjac[j][3][2]=-c2u[k][j][i][3]tmp1;\nfjac[j][4][2]=c2;\nfjac[j][0][3]=-(u[k][j][i][2]u[k][j][i][3])tmp2;\nfjac[j][1][3]=0.0;\nfjac[j][2][3]=u[k][j][i][3]tmp1;\nfjac[j][3][3]=u[k][j][i][2]tmp1;\nfjac[j][4][3]=0.0;\nfjac[j][0][4]=(c22.0square[k][j][i]-c1u[k][j][i][4])u[k][j][i][2]tmp2;\nfjac[j][1][4]=-c2u[k][j][i][1]u[k][j][i][2]tmp2;\nfjac[j][2][4]=c1u[k][j][i][4]tmp1-c2(qs[k][j][i]+u[k][j][i][2]u[k][j][i][2]tmp2);\nfjac[j][3][4]=-c2(u[k][j][i][2]u[k][j][i][3])tmp2;\nfjac[j][4][4]=c1u[k][j][i][2]tmp1;\nnjac[j][0][0]=0.0;\nnjac[j][1][0]=0.0;\nnjac[j][2][0]=0.0;\nnjac[j][3][0]=0.0;\nnjac[j][4][0]=0.0;\nnjac[j][0][1]=-c3c4tmp2u[k][j][i][1];\nnjac[j][1][1]=c3c4tmp1;\nnjac[j][2][1]=0.0;\nnjac[j][3][1]=0.0;\nnjac[j][4][1]=0.0;\nnjac[j][0][2]=-con43c3c4tmp2u[k][j][i][2];\nnjac[j][1][2]=0.0;\nnjac[j][2][2]=con43c3c4tmp1;\nnjac[j][3][2]=0.0;\nnjac[j][4][2]=0.0;\nnjac[j][0][3]=-c3c4tmp2u[k][j][i][3];\nnjac[j][1][3]=0.0;\nnjac[j][2][3]=0.0;\nnjac[j][3][3]=c3c4tmp1;\nnjac[j][4][3]=0.0;\nnjac[j][0][4]=-(c3c4-c1345)tmp3(u[k][j][i][1]u[k][j][i][1])\n-(con43c3c4-c1345)tmp3(u[k][j][i][2]u[k][j][i][2])\n-(c3c4-c1345)tmp3(u[k][j][i][3]u[k][j][i][3])\n-c1345tmp2u[k][j][i][4];\nnjac[j][1][4]=(c3c4-c1345)tmp2u[k][j][i][1];\nnjac[j][2][4]=(con43c3c4-c1345)tmp2u[k][j][i][2];\nnjac[j][3][4]=(c3c4-c1345)tmp2u[k][j][i][3];\nnjac[j][4][4]=(c1345)tmp1;\n}\n\nlhsinit(lhs, jsize);\nfor(j=1; j<=jsize-1; j++){\ntmp1=dtty1;\ntmp2=dtty2;\nlhs[j][AA][0][0]=-tmp2fjac[j-1][0][0]\n-tmp1njac[j-1][0][0]\n-tmp1dy1;\nlhs[j][AA][1][0]=-tmp2fjac[j-1][1][0]\n-tmp1njac[j-1][1][0];\nlhs[j][AA][2][0]=-tmp2fjac[j-1][2][0]\n-tmp1njac[j-1][2][0];\nlhs[j][AA][3][0]=-tmp2fjac[j-1][3][0]\n-tmp1njac[j-1][3][0];\nlhs[j][AA][4][0]=-tmp2fjac[j-1][4][0]\n-tmp1njac[j-1][4][0];\nlhs[j][AA][0][1]=-tmp2fjac[j-1][0][1]\n-tmp1njac[j-1][0][1];\nlhs[j][AA][1][1]=-tmp2fjac[j-1][1][1]\n-tmp1njac[j-1][1][1]\n-tmp1dy2;\nlhs[j][AA][2][1]=-tmp2fjac[j-1][2][1]\n-tmp1njac[j-1][2][1];\nlhs[j][AA][3][1]=-tmp2fjac[j-1][3][1]\n-tmp1njac[j-1][3][1];\nlhs[j][AA][4][1]=-tmp2fjac[j-1][4][1]\n-tmp1njac[j-1][4][1];\nlhs[j][AA][0][2]=-tmp2fjac[j-1][0][2]\n-tmp1njac[j-1][0][2];\nlhs[j][AA][1][2]=-tmp2fjac[j-1][1][2]\n-tmp1njac[j-1][1][2];\nlhs[j][AA][2][2]=-tmp2fjac[j-1][2][2]\n-tmp1njac[j-1][2][2]\n-tmp1dy3;\nlhs[j][AA][3][2]=-tmp2fjac[j-1][3][2]\n-tmp1njac[j-1][3][2];\nlhs[j][AA][4][2]=-tmp2fjac[j-1][4][2]\n-tmp1njac[j-1][4][2];\nlhs[j][AA][0][3]=-tmp2fjac[j-1][0][3]\n-tmp1njac[j-1][0][3];\nlhs[j][AA][1][3]=-tmp2fjac[j-1][1][3]\n-tmp1njac[j-1][1][3];\nlhs[j][AA][2][3]=-tmp2fjac[j-1][2][3]\n-tmp1njac[j-1][2][3];\nlhs[j][AA][3][3]=-tmp2fjac[j-1][3][3]\n-tmp1njac[j-1][3][3]\n-tmp1dy4;\nlhs[j][AA][4][3]=-tmp2fjac[j-1][4][3]\n-tmp1njac[j-1][4][3];\nlhs[j][AA][0][4]=-tmp2fjac[j-1][0][4]\n-tmp1njac[j-1][0][4];\nlhs[j][AA][1][4]=-tmp2fjac[j-1][1][4]\n-tmp1njac[j-1][1][4];\nlhs[j][AA][2][4]=-tmp2fjac[j-1][2][4]\n-tmp1njac[j-1][2][4];\nlhs[j][AA][3][4]=-tmp2fjac[j-1][3][4]\n-tmp1njac[j-1][3][4];\nlhs[j][AA][4][4]=-tmp2fjac[j-1][4][4]\n-tmp1njac[j-1][4][4]\n-tmp1dy5;\nlhs[j][BB][0][0]=1.0\n+tmp12.0njac[j][0][0]\n+tmp12.0dy1;\nlhs[j][BB][1][0]=tmp12.0njac[j][1][0];\nlhs[j][BB][2][0]=tmp12.0njac[j][2][0];\nlhs[j][BB][3][0]=tmp12.0njac[j][3][0];\nlhs[j][BB][4][0]=tmp12.0njac[j][4][0];\nlhs[j][BB][0][1]=tmp12.0njac[j][0][1];\nlhs[j][BB][1][1]=1.0\n+tmp12.0njac[j][1][1]\n+tmp12.0dy2;\nlhs[j][BB][2][1]=tmp12.0njac[j][2][1];\nlhs[j][BB][3][1]=tmp12.0njac[j][3][1];\nlhs[j][BB][4][1]=tmp12.0njac[j][4][1];\nlhs[j][BB][0][2]=tmp12.0njac[j][0][2];\nlhs[j][BB][1][2]=tmp12.0njac[j][1][2];\nlhs[j][BB][2][2]=1.0\n+tmp12.0njac[j][2][2]\n+tmp12.0dy3;\nlhs[j][BB][3][2]=tmp12.0njac[j][3][2];\nlhs[j][BB][4][2]=tmp12.0njac[j][4][2];\nlhs[j][BB][0][3]=tmp12.0njac[j][0][3];\nlhs[j][BB][1][3]=tmp12.0njac[j][1][3];\nlhs[j][BB][2][3]=tmp12.0njac[j][2][3];\nlhs[j][BB][3][3]=1.0\n+tmp12.0njac[j][3][3]\n+tmp12.0dy4;\nlhs[j][BB][4][3]=tmp12.0njac[j][4][3];\nlhs[j][BB][0][4]=tmp12.0njac[j][0][4];\nlhs[j][BB][1][4]=tmp12.0njac[j][1][4];\nlhs[j][BB][2][4]=tmp12.0njac[j][2][4];\nlhs[j][BB][3][4]=tmp12.0njac[j][3][4];\nlhs[j][BB][4][4]=1.0\n+tmp12.0njac[j][4][4]\n+tmp12.0dy5;\nlhs[j][CC][0][0]=tmp2fjac[j+1][0][0]\n-tmp1njac[j+1][0][0]\n-tmp1dy1;\nlhs[j][CC][1][0]=tmp2fjac[j+1][1][0]\n-tmp1njac[j+1][1][0];\nlhs[j][CC][2][0]=tmp2fjac[j+1][2][0]\n-tmp1njac[j+1][2][0];\nlhs[j][CC][3][0]=tmp2fjac[j+1][3][0]\n-tmp1njac[j+1][3][0];\nlhs[j][CC][4][0]=tmp2fjac[j+1][4][0]\n-tmp1njac[j+1][4][0];\nlhs[j][CC][0][1]=tmp2fjac[j+1][0][1]\n-tmp1njac[j+1][0][1];\nlhs[j][CC][1][1]=tmp2fjac[j+1][1][1]\n-tmp1njac[j+1][1][1]\n-tmp1dy2;\nlhs[j][CC][2][1]=tmp2fjac[j+1][2][1]\n-tmp1njac[j+1][2][1];\nlhs[j][CC][3][1]=tmp2fjac[j+1][3][1]\n-tmp1njac[j+1][3][1];\nlhs[j][CC][4][1]=tmp2fjac[j+1][4][1]\n-tmp1njac[j+1][4][1];\nlhs[j][CC][0][2]=tmp2fjac[j+1][0][2]\n-tmp1njac[j+1][0][2];\nlhs[j][CC][1][2]=tmp2fjac[j+1][1][2]\n-tmp1njac[j+1][1][2];\nlhs[j][CC][2][2]=tmp2fjac[j+1][2][2]\n-tmp1njac[j+1][2][2]\n-tmp1dy3;\nlhs[j][CC][3][2]=tmp2fjac[j+1][3][2]\n-tmp1njac[j+1][3][2];\nlhs[j][CC][4][2]=tmp2fjac[j+1][4][2]\n-tmp1njac[j+1][4][2];\nlhs[j][CC][0][3]=tmp2fjac[j+1][0][3]\n-tmp1njac[j+1][0][3];\nlhs[j][CC][1][3]=tmp2fjac[j+1][1][3]\n-tmp1njac[j+1][1][3];\nlhs[j][CC][2][3]=tmp2fjac[j+1][2][3]\n-tmp1njac[j+1][2][3];\nlhs[j][CC][3][3]=tmp2fjac[j+1][3][3]\n-tmp1njac[j+1][3][3]\n-tmp1dy4;\nlhs[j][CC][4][3]=tmp2fjac[j+1][4][3]\n-tmp1njac[j+1][4][3];\nlhs[j][CC][0][4]=tmp2fjac[j+1][0][4]\n-tmp1njac[j+1][0][4];\nlhs[j][CC][1][4]=tmp2fjac[j+1][1][4]\n-tmp1njac[j+1][1][4];\nlhs[j][CC][2][4]=tmp2fjac[j+1][2][4]\n-tmp1njac[j+1][2][4];\nlhs[j][CC][3][4]=tmp2fjac[j+1][3][4]\n-tmp1njac[j+1][3][4];\nlhs[j][CC][4][4]=tmp2fjac[j+1][4][4]\n-tmp1njac[j+1][4][4]\n-tmp1dy5;\n}\n\nbinvcrhs(lhs[0][BB], lhs[0][CC], rhs[k][0][i]);\n\nfor(j=1; j<=jsize-1; j++){\n\nmatvec_sub(lhs[j][AA], rhs[k][j-1][i], rhs[k][j][i]);\n\nmatmul_sub(lhs[j][AA], lhs[j-1][CC], lhs[j][BB]);\n\nbinvcrhs(lhs[j][BB], lhs[j][CC], rhs[k][j][i]);\n}\n\nmatvec_sub(lhs[jsize][AA], rhs[k][jsize-1][i], rhs[k][jsize][i]);\n\nmatmul_sub(lhs[jsize][AA], lhs[jsize-1][CC], lhs[jsize][BB]);\n\nbinvrhs(lhs[jsize][BB], rhs[k][jsize][i]);\n\nfor(j=jsize-1; j>=0; j--){\nfor(m=0; m<BLOCK_SIZE; m++){\nfor(n=0; n<BLOCK_SIZE; n++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[j][CC][n][m]*rhs[k][j+1][i][n];\n}\n}\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_YSOLVE);}\n}	subroutine y_solve\n\n\n\nuse bt_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, m, n, jsize\ndouble precision tmp1, tmp2, tmp3\n\n\nif (timeron) call timer_start(t_ysolve)\n\n\n\njsize = grid_points(2)-1\n\ndo k = 1, grid_points(3)-2\ndo i = 1, grid_points(1)-2\ndo j = 0, jsize\n\ntmp1 = rho_i(i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nfjac(1,1,j) = 0.0d+00\nfjac(1,2,j) = 0.0d+00\nfjac(1,3,j) = 1.0d+00\nfjac(1,4,j) = 0.0d+00\nfjac(1,5,j) = 0.0d+00\n\nfjac(2,1,j) = - ( u(2,i,j,k)u(3,i,j,k) ) &\n& tmp2\nfjac(2,2,j) = u(3,i,j,k) * tmp1\nfjac(2,3,j) = u(2,i,j,k) * tmp1\nfjac(2,4,j) = 0.0d+00\nfjac(2,5,j) = 0.0d+00\n\nfjac(3,1,j) = - ( u(3,i,j,k)u(3,i,j,k)tmp2) &\n& + c2 * qs(i,j,k)\nfjac(3,2,j) = - c2 * u(2,i,j,k) * tmp1\nfjac(3,3,j) = ( 2.0d+00 - c2 ) &\n& * u(3,i,j,k) * tmp1\nfjac(3,4,j) = - c2 * u(4,i,j,k) * tmp1\nfjac(3,5,j) = c2\n\nfjac(4,1,j) = - ( u(3,i,j,k)u(4,i,j,k) ) &\n& tmp2\nfjac(4,2,j) = 0.0d+00\nfjac(4,3,j) = u(4,i,j,k) * tmp1\nfjac(4,4,j) = u(3,i,j,k) * tmp1\nfjac(4,5,j) = 0.0d+00\n\nfjac(5,1,j) = ( c2 * 2.0d0 * square(i,j,k) &\n& - c1 * u(5,i,j,k) ) &\n& * u(3,i,j,k) * tmp2\nfjac(5,2,j) = - c2 * u(2,i,j,k)u(3,i,j,k) &\n& tmp2\nfjac(5,3,j) = c1 * u(5,i,j,k) * tmp1 &\n& - c2 &\n& * ( qs(i,j,k) &\n& + u(3,i,j,k)u(3,i,j,k) tmp2 )\nfjac(5,4,j) = - c2 * ( u(3,i,j,k)u(4,i,j,k) ) &\n& tmp2\nfjac(5,5,j) = c1 * u(3,i,j,k) * tmp1\n\nnjac(1,1,j) = 0.0d+00\nnjac(1,2,j) = 0.0d+00\nnjac(1,3,j) = 0.0d+00\nnjac(1,4,j) = 0.0d+00\nnjac(1,5,j) = 0.0d+00\n\nnjac(2,1,j) = - c3c4 * tmp2 * u(2,i,j,k)\nnjac(2,2,j) = c3c4 * tmp1\nnjac(2,3,j) = 0.0d+00\nnjac(2,4,j) = 0.0d+00\nnjac(2,5,j) = 0.0d+00\n\nnjac(3,1,j) = - con43 * c3c4 * tmp2 * u(3,i,j,k)\nnjac(3,2,j) = 0.0d+00\nnjac(3,3,j) = con43 * c3c4 * tmp1\nnjac(3,4,j) = 0.0d+00\nnjac(3,5,j) = 0.0d+00\n\nnjac(4,1,j) = - c3c4 * tmp2 * u(4,i,j,k)\nnjac(4,2,j) = 0.0d+00\nnjac(4,3,j) = 0.0d+00\nnjac(4,4,j) = c3c4 * tmp1\nnjac(4,5,j) = 0.0d+00\n\nnjac(5,1,j) = - ( c3c4 &\n& - c1345 ) * tmp3 * (u(2,i,j,k)*2) &\n& - ( con43 c3c4 &\n& - c1345 ) * tmp3 * (u(3,i,j,k)*2) &\n& - ( c3c4 - c1345 ) tmp3 * (u(4,i,j,k)*2) &\n& - c1345 tmp2 * u(5,i,j,k)\n\nnjac(5,2,j) = ( c3c4 - c1345 ) * tmp2 * u(2,i,j,k)\nnjac(5,3,j) = ( con43 * c3c4 &\n& - c1345 ) * tmp2 * u(3,i,j,k)\nnjac(5,4,j) = ( c3c4 - c1345 ) * tmp2 * u(4,i,j,k)\nnjac(5,5,j) = ( c1345 ) * tmp1\n\nenddo\n\ncall lhsinit(lhs, jsize)\ndo j = 1, jsize-1\n\ntmp1 = dt * ty1\ntmp2 = dt * ty2\n\nlhs(1,1,aa,j) = - tmp2 * fjac(1,1,j-1) &\n& - tmp1 * njac(1,1,j-1) &\n& - tmp1 * dy1\nlhs(1,2,aa,j) = - tmp2 * fjac(1,2,j-1) &\n& - tmp1 * njac(1,2,j-1)\nlhs(1,3,aa,j) = - tmp2 * fjac(1,3,j-1) &\n& - tmp1 * njac(1,3,j-1)\nlhs(1,4,aa,j) = - tmp2 * fjac(1,4,j-1) &\n& - tmp1 * njac(1,4,j-1)\nlhs(1,5,aa,j) = - tmp2 * fjac(1,5,j-1) &\n& - tmp1 * njac(1,5,j-1)\n\nlhs(2,1,aa,j) = - tmp2 * fjac(2,1,j-1) &\n& - tmp1 * njac(2,1,j-1)\nlhs(2,2,aa,j) = - tmp2 * fjac(2,2,j-1) &\n& - tmp1 * njac(2,2,j-1) &\n& - tmp1 * dy2\nlhs(2,3,aa,j) = - tmp2 * fjac(2,3,j-1) &\n& - tmp1 * njac(2,3,j-1)\nlhs(2,4,aa,j) = - tmp2 * fjac(2,4,j-1) &\n& - tmp1 * njac(2,4,j-1)\nlhs(2,5,aa,j) = - tmp2 * fjac(2,5,j-1) &\n& - tmp1 * njac(2,5,j-1)\n\nlhs(3,1,aa,j) = - tmp2 * fjac(3,1,j-1) &\n& - tmp1 * njac(3,1,j-1)\nlhs(3,2,aa,j) = - tmp2 * fjac(3,2,j-1) &\n& - tmp1 * njac(3,2,j-1)\nlhs(3,3,aa,j) = - tmp2 * fjac(3,3,j-1) &\n& - tmp1 * njac(3,3,j-1) &\n& - tmp1 * dy3\nlhs(3,4,aa,j) = - tmp2 * fjac(3,4,j-1) &\n& - tmp1 * njac(3,4,j-1)\nlhs(3,5,aa,j) = - tmp2 * fjac(3,5,j-1) &\n& - tmp1 * njac(3,5,j-1)\n\nlhs(4,1,aa,j) = - tmp2 * fjac(4,1,j-1) &\n& - tmp1 * njac(4,1,j-1)\nlhs(4,2,aa,j) = - tmp2 * fjac(4,2,j-1) &\n& - tmp1 * njac(4,2,j-1)\nlhs(4,3,aa,j) = - tmp2 * fjac(4,3,j-1) &\n& - tmp1 * njac(4,3,j-1)\nlhs(4,4,aa,j) = - tmp2 * fjac(4,4,j-1) &\n& - tmp1 * njac(4,4,j-1) &\n& - tmp1 * dy4\nlhs(4,5,aa,j) = - tmp2 * fjac(4,5,j-1) &\n& - tmp1 * njac(4,5,j-1)\n\nlhs(5,1,aa,j) = - tmp2 * fjac(5,1,j-1) &\n& - tmp1 * njac(5,1,j-1)\nlhs(5,2,aa,j) = - tmp2 * fjac(5,2,j-1) &\n& - tmp1 * njac(5,2,j-1)\nlhs(5,3,aa,j) = - tmp2 * fjac(5,3,j-1) &\n& - tmp1 * njac(5,3,j-1)\nlhs(5,4,aa,j) = - tmp2 * fjac(5,4,j-1) &\n& - tmp1 * njac(5,4,j-1)\nlhs(5,5,aa,j) = - tmp2 * fjac(5,5,j-1) &\n& - tmp1 * njac(5,5,j-1) &\n& - tmp1 * dy5\n\nlhs(1,1,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(1,1,j) &\n& + tmp1 * 2.0d+00 * dy1\nlhs(1,2,bb,j) = tmp1 * 2.0d+00 * njac(1,2,j)\nlhs(1,3,bb,j) = tmp1 * 2.0d+00 * njac(1,3,j)\nlhs(1,4,bb,j) = tmp1 * 2.0d+00 * njac(1,4,j)\nlhs(1,5,bb,j) = tmp1 * 2.0d+00 * njac(1,5,j)\n\nlhs(2,1,bb,j) = tmp1 * 2.0d+00 * njac(2,1,j)\nlhs(2,2,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(2,2,j) &\n& + tmp1 * 2.0d+00 * dy2\nlhs(2,3,bb,j) = tmp1 * 2.0d+00 * njac(2,3,j)\nlhs(2,4,bb,j) = tmp1 * 2.0d+00 * njac(2,4,j)\nlhs(2,5,bb,j) = tmp1 * 2.0d+00 * njac(2,5,j)\n\nlhs(3,1,bb,j) = tmp1 * 2.0d+00 * njac(3,1,j)\nlhs(3,2,bb,j) = tmp1 * 2.0d+00 * njac(3,2,j)\nlhs(3,3,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(3,3,j) &\n& + tmp1 * 2.0d+00 * dy3\nlhs(3,4,bb,j) = tmp1 * 2.0d+00 * njac(3,4,j)\nlhs(3,5,bb,j) = tmp1 * 2.0d+00 * njac(3,5,j)\n\nlhs(4,1,bb,j) = tmp1 * 2.0d+00 * njac(4,1,j)\nlhs(4,2,bb,j) = tmp1 * 2.0d+00 * njac(4,2,j)\nlhs(4,3,bb,j) = tmp1 * 2.0d+00 * njac(4,3,j)\nlhs(4,4,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(4,4,j) &\n& + tmp1 * 2.0d+00 * dy4\nlhs(4,5,bb,j) = tmp1 * 2.0d+00 * njac(4,5,j)\n\nlhs(5,1,bb,j) = tmp1 * 2.0d+00 * njac(5,1,j)\nlhs(5,2,bb,j) = tmp1 * 2.0d+00 * njac(5,2,j)\nlhs(5,3,bb,j) = tmp1 * 2.0d+00 * njac(5,3,j)\nlhs(5,4,bb,j) = tmp1 * 2.0d+00 * njac(5,4,j)\nlhs(5,5,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(5,5,j) &\n& + tmp1 * 2.0d+00 * dy5\n\nlhs(1,1,cc,j) = tmp2 * fjac(1,1,j+1) &\n& - tmp1 * njac(1,1,j+1) &\n& - tmp1 * dy1\nlhs(1,2,cc,j) = tmp2 * fjac(1,2,j+1) &\n& - tmp1 * njac(1,2,j+1)\nlhs(1,3,cc,j) = tmp2 * fjac(1,3,j+1) &\n& - tmp1 * njac(1,3,j+1)\nlhs(1,4,cc,j) = tmp2 * fjac(1,4,j+1) &\n& - tmp1 * njac(1,4,j+1)\nlhs(1,5,cc,j) = tmp2 * fjac(1,5,j+1) &\n& - tmp1 * njac(1,5,j+1)\n\nlhs(2,1,cc,j) = tmp2 * fjac(2,1,j+1) &\n& - tmp1 * njac(2,1,j+1)\nlhs(2,2,cc,j) = tmp2 * fjac(2,2,j+1) &\n& - tmp1 * njac(2,2,j+1) &\n& - tmp1 * dy2\nlhs(2,3,cc,j) = tmp2 * fjac(2,3,j+1) &\n& - tmp1 * njac(2,3,j+1)\nlhs(2,4,cc,j) = tmp2 * fjac(2,4,j+1) &\n& - tmp1 * njac(2,4,j+1)\nlhs(2,5,cc,j) = tmp2 * fjac(2,5,j+1) &\n& - tmp1 * njac(2,5,j+1)\n\nlhs(3,1,cc,j) = tmp2 * fjac(3,1,j+1) &\n& - tmp1 * njac(3,1,j+1)\nlhs(3,2,cc,j) = tmp2 * fjac(3,2,j+1) &\n& - tmp1 * njac(3,2,j+1)\nlhs(3,3,cc,j) = tmp2 * fjac(3,3,j+1) &\n& - tmp1 * njac(3,3,j+1) &\n& - tmp1 * dy3\nlhs(3,4,cc,j) = tmp2 * fjac(3,4,j+1) &\n& - tmp1 * njac(3,4,j+1)\nlhs(3,5,cc,j) = tmp2 * fjac(3,5,j+1) &\n& - tmp1 * njac(3,5,j+1)\n\nlhs(4,1,cc,j) = tmp2 * fjac(4,1,j+1) &\n& - tmp1 * njac(4,1,j+1)\nlhs(4,2,cc,j) = tmp2 * fjac(4,2,j+1) &\n& - tmp1 * njac(4,2,j+1)\nlhs(4,3,cc,j) = tmp2 * fjac(4,3,j+1) &\n& - tmp1 * njac(4,3,j+1)\nlhs(4,4,cc,j) = tmp2 * fjac(4,4,j+1) &\n& - tmp1 * njac(4,4,j+1) &\n& - tmp1 * dy4\nlhs(4,5,cc,j) = tmp2 * fjac(4,5,j+1) &\n& - tmp1 * njac(4,5,j+1)\n\nlhs(5,1,cc,j) = tmp2 * fjac(5,1,j+1) &\n& - tmp1 * njac(5,1,j+1)\nlhs(5,2,cc,j) = tmp2 * fjac(5,2,j+1) &\n& - tmp1 * njac(5,2,j+1)\nlhs(5,3,cc,j) = tmp2 * fjac(5,3,j+1) &\n& - tmp1 * njac(5,3,j+1)\nlhs(5,4,cc,j) = tmp2 * fjac(5,4,j+1) &\n& - tmp1 * njac(5,4,j+1)\nlhs(5,5,cc,j) = tmp2 * fjac(5,5,j+1) &\n& - tmp1 * njac(5,5,j+1) &\n& - tmp1 * dy5\n\nenddo\n\n\n\nif (timeron) call timer_start(t_solsub)\ncall binvcrhs( lhs(1,1,bb,0), &\n& lhs(1,1,cc,0), &\n& rhs(1,i,0,k) )\n\ndo j=1,jsize-1\n\ncall matvec_sub(lhs(1,1,aa,j), &\n& rhs(1,i,j-1,k),rhs(1,i,j,k))\n\ncall matmul_sub(lhs(1,1,aa,j), &\n& lhs(1,1,cc,j-1), &\n& lhs(1,1,bb,j))\n\ncall binvcrhs( lhs(1,1,bb,j), &\n& lhs(1,1,cc,j), &\n& rhs(1,i,j,k) )\n\nenddo\n\n\ncall matvec_sub(lhs(1,1,aa,jsize), &\n& rhs(1,i,jsize-1,k),rhs(1,i,jsize,k))\n\ncall matmul_sub(lhs(1,1,aa,jsize), &\n& lhs(1,1,cc,jsize-1), &\n& lhs(1,1,bb,jsize))\n\ncall binvrhs( lhs(1,1,bb,jsize), &\n& rhs(1,i,jsize,k) )\nif (timeron) call timer_stop(t_solsub)\n\n\n\ndo j=jsize-1,0,-1\ndo m=1,BLOCK_SIZE\ndo n=1,BLOCK_SIZE\nrhs(m,i,j,k) = rhs(m,i,j,k) &\n& - lhs(m,n,cc,j)*rhs(n,i,j+1,k)\nenddo\nenddo\nenddo\n\nenddo\nenddo\nif (timeron) call timer_stop(t_ysolve)\n\nreturn\nend
void initialize(){\nint i, j, k, m, ix, iy, iz;\ndouble xi, eta, zeta, Pface[2][3][5], Pxi, Peta, Pzeta, temp[5];\n\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<=grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nfor(m=0; m<5; m++){\nu[k][j][i][m]=1.0;\n}\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)* dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)dnxm1;\nfor(ix=0; ix<2; ix++){\nexact_solution((double)ix, eta, zeta, &Pface[ix][0][0]);\n}\nfor(iy=0; iy<2; iy++){\nexact_solution(xi, (double)iy , zeta, &Pface[iy][1][0]);\n}\nfor(iz=0; iz<2; iz++){\nexact_solution(xi, eta, (double)iz, &Pface[iz][2][0]);\n}\nfor(m=0; m<5; m++){\nPxi=xiPface[1][0][m]+(1.0-xi)Pface[0][0][m];\nPeta=etaPface[1][1][m]+(1.0-eta)Pface[0][1][m];\nPzeta=zetaPface[1][2][m]+(1.0-zeta)Pface[0][2][m];\nu[k][j][i][m]=Pxi+Peta+Pzeta-\nPxiPeta-PxiPzeta-PetaPzeta+\nPxiPetaPzeta;\n}\n}\n}\n}\n\ni=0;\nxi=0.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\ni=grid_points[0]-1;\nxi=1.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nj=0;\neta=0.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)dnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nj=grid_points[1]-1;\neta=1.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)dnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nk=0;\nzeta=0.0;\n#pragma omp for\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nk=grid_points[2]-1;\nzeta=1.0;\n#pragma omp for\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n}	subroutine initialize\n\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m, ix, iy, iz\ndouble precision xi, eta, zeta, Pface(5,3,2), Pxi, Peta, &\n& Pzeta, temp(5)\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nu(m,i,j,k) = 1.0\nend do\nend do\nend do\nend do\n\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ndo ix = 1, 2\ncall exact_solution(dble(ix-1), eta, zeta, &\n& Pface(1,1,ix))\nenddo\n\ndo iy = 1, 2\ncall exact_solution(xi, dble(iy-1) , zeta, &\n& Pface(1,2,iy))\nenddo\n\ndo iz = 1, 2\ncall exact_solution(xi, eta, dble(iz-1), &\n& Pface(1,3,iz))\nenddo\n\ndo m = 1, 5\nPxi = xi * Pface(m,1,2) + &\n& (1.0d0-xi) * Pface(m,1,1)\nPeta = eta * Pface(m,2,2) + &\n& (1.0d0-eta) * Pface(m,2,1)\nPzeta = zeta * Pface(m,3,2) + &\n& (1.0d0-zeta) * Pface(m,3,1)\n\nu(m,i,j,k) = Pxi + Peta + Pzeta - &\n& PxiPeta - PxiPzeta - PetaPzeta + &\n& PxiPetaPzeta\n\nenddo\nenddo\nenddo\nenddo\n\n\ni = 0\nxi = 0.0d0\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\n\ni = grid_points(1)-1\nxi = 1.0d0\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nj = 0\neta = 0.0d0\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\n\nj = grid_points(2)-1\neta = 1.0d0\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nk = 0\nzeta = 0.0d0\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) * dnym1\nxi = dble(i) dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nk = grid_points(3)-1\nzeta = 1.0d0\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) dnym1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nreturn\nend
static void conj_grad(int colidx[],\nint rowstr[],\ndouble x[],\ndouble z[],\ndouble a[],\ndouble p[],\ndouble q[],\ndouble r[],\ndouble* rnorm){\nint j, k;\nint cgit, cgitmax;\ndouble alpha, beta, suml;\nstatic double d, sum, rho, rho0;\n\ncgitmax = 25;\n#pragma omp single nowait\n{\n\nrho = 0.0;\nsum = 0.0;\n}\n\n#pragma omp for\nfor(j = 0; j < naa+1; j++){\nq[j] = 0.0;\nz[j] = 0.0;\nr[j] = x[j];\np[j] = r[j];\n}\n\n\n#pragma omp for reduction(+:rho)\nfor(j = 0; j < lastcol - firstcol + 1; j++){\nrho += r[j]r[j];\n}\n\n\nfor(cgit = 1; cgit <= cgitmax; cgit++){\n\n\n#pragma omp single nowait\n{\nd = 0.0;\n\nrho0 = rho;\nrho = 0.0;\n}\n\n#pragma omp for nowait\nfor(j = 0; j < lastrow - firstrow + 1; j++){\nsuml = 0.0;\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\nsuml += a[k]p[colidx[k]];\n}\nq[j] = suml;\n}\n\n\n\n#pragma omp for reduction(+:d)\nfor (j = 0; j < lastcol - firstcol + 1; j++) {\nd += p[j]q[j];\n}\n\n\nalpha = rho0 / d;\n\n\n\n#pragma omp for reduction(+:rho)\nfor(j = 0; j < lastcol - firstcol + 1; j++){\nz[j] += alphap[j];\nr[j] -= alphaq[j];\n\n\nrho += r[j]r[j];\n}\n\n\nbeta = rho / rho0;\n\n\n#pragma omp for\nfor(j = 0; j < lastcol - firstcol + 1; j++){\np[j] = r[j] + betap[j];\n}\n} \n\n\n#pragma omp for nowait\nfor(j = 0; j < lastrow - firstrow + 1; j++){\nsuml = 0.0;\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\nsuml += a[k]z[colidx[k]];\n}\nr[j] = suml;\n}\n\n\n#pragma omp for reduction(+:sum)\nfor(j = 0; j < lastcol-firstcol+1; j++){\nsuml = x[j] - r[j];\nsum += sumlsuml;\n}\n#pragma omp single\nrnorm = sqrt(sum);\n}	subroutine conj_grad ( rnorm )\n\n\nuse cg_data\nimplicit none\n\ninteger j\ninteger cgit, cgitmax\ninteger(kz) k\n\ndouble precision d, sum, rho, rho0, alpha, beta, rnorm, suml\n\ndata cgitmax / 25 /\n\n\nrho = 0.0d0\nsum = 0.0d0\n\n\ndo j=1,naa+1\nq(j) = 0.0d0\nz(j) = 0.0d0\nr(j) = x(j)\np(j) = r(j)\nenddo\n\n\ndo j=1, lastcol-firstcol+1\nrho = rho + r(j)r(j)\nenddo\n\ndo cgit = 1, cgitmax\n\nrho0 = rho\nd = 0.d0\nrho = 0.d0\n\ndo j=1,lastrow-firstrow+1\nsuml = 0.d0\ndo k=rowstr(j),rowstr(j+1)-1\nsuml = suml + a(k)p(colidx(k))\nenddo\nq(j) = suml\nenddo\n\n\n\n\ndo j=1, lastcol-firstcol+1\nd = d + p(j)q(j)\nenddo\n\n\nalpha = rho0 / d\n\ndo j=1, lastcol-firstcol+1\nz(j) = z(j) + alphap(j)\nr(j) = r(j) - alphaq(j)\n\nrho = rho + r(j)r(j)\nenddo\n\nbeta = rho / rho0\n\ndo j=1, lastcol-firstcol+1\np(j) = r(j) + betap(j)\nenddo\n\n\nenddo ! end of do cgit=1,cgitmax\n\n\ndo j=1,lastrow-firstrow+1\nsuml = 0.d0\ndo k=rowstr(j),rowstr(j+1)-1\nsuml = suml + a(k)z(colidx(k))\nenddo\nr(j) = suml\nenddo\n\n\ndo j=1, lastcol-firstcol+1\nsuml = x(j) - r(j)\nsum = sum + suml*suml\nenddo\n\nrnorm = sqrt( sum )\n\n\n\nreturn\nend
static void sparse(double a[],\nint colidx[],\nint rowstr[],\nint n,\nint nz,\nint nozer,\nint arow[],\nint acol[][NONZER+1],\ndouble aelt[][NONZER+1],\nint firstrow,\nint lastrow,\nint nzloc[],\ndouble rcond,\ndouble shift){\nint nrows;\n\n\nint i, j, j1, j2, nza, k, kk, nzrow, jcol;\ndouble size, scale, ratio, va;\nboolean goto_40;\n\n\nnrows = lastrow - firstrow + 1;\n\n\nfor(j = 0; j < nrows+1; j++){\nrowstr[j] = 0;\n}\nfor(i = 0; i < n; i++){\nfor(nza = 0; nza < arow[i]; nza++){\nj = acol[i][nza] + 1;\nrowstr[j] = rowstr[j] + arow[i];\n}\n}\nrowstr[0] = 0;\nfor(j = 1; j < nrows+1; j++){\nrowstr[j] = rowstr[j] + rowstr[j-1];\n}\nnza = rowstr[nrows] - 1;\n\n\nif(nza > nz){\nprintf("Space for matrix elements exceeded in sparse\n");\nprintf("nza, nzmax = %d, %d\n", nza, nz);\nexit(EXIT_FAILURE);\n}\n\n\nfor(j = 0; j < nrows; j++){\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\na[k] = 0.0;\ncolidx[k] = -1;\n}\nnzloc[j] = 0;\n}\n\n\nsize = 1.0;\nratio = pow(rcond, (1.0 / (double)(n)));\nfor(i = 0; i < n; i++){\nfor(nza = 0; nza < arow[i]; nza++){\nj = acol[i][nza];\n\nscale = size * aelt[i][nza];\nfor(nzrow = 0; nzrow < arow[i]; nzrow++){\njcol = acol[i][nzrow];\nva = aelt[i][nzrow] * scale;\n\n\nif(jcol == j && j == i){\nva = va + rcond - shift;\n}\n\ngoto_40 = FALSE;\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\nif(colidx[k] > jcol){\n\nfor(kk = rowstr[j+1]-2; kk >= k; kk--){\nif(colidx[kk] > -1){\na[kk+1] = a[kk];\ncolidx[kk+1] = colidx[kk];\n}\n}\ncolidx[k] = jcol;\na[k] = 0.0;\ngoto_40 = TRUE;\nbreak;\n}else if(colidx[k] == -1){\ncolidx[k] = jcol;\ngoto_40 = TRUE;\nbreak;\n}else if(colidx[k] == jcol){\n\nnzloc[j] = nzloc[j] + 1;\ngoto_40 = TRUE;\nbreak;\n}\n}\nif(goto_40 == FALSE){\nprintf("internal error in sparse: i=%d\n", i);\nexit(EXIT_FAILURE);\n}\na[k] = a[k] + va;\n}\n}\nsize = size * ratio;\n}\n\n\nfor(j = 1; j < nrows; j++){\nnzloc[j] = nzloc[j] + nzloc[j-1];\n}\n\nfor(j = 0; j < nrows; j++){\nif(j > 0){\nj1 = rowstr[j] - nzloc[j-1];\n}else{\nj1 = 0;\n}\nj2 = rowstr[j+1] - nzloc[j];\nnza = rowstr[j];\nfor(k = j1; k < j2; k++){\na[k] = a[nza];\ncolidx[k] = colidx[nza];\nnza = nza + 1;\n}\n}\nfor(j = 1; j < nrows+1; j++){\nrowstr[j] = rowstr[j] - nzloc[j-1];\n}\nnza = rowstr[nrows] - 1;\n}	subroutine sparse( a, colidx, rowstr, n, nz, nonzer, arow, acol, &\n& aelt, firstrow, lastrow, &\n& v, iv, nzloc, rcond, shift )\n\nuse tinfo\n\nimplicit none\n\ninteger colidx(), iv()\ninteger firstrow, lastrow\ninteger n, nonzer, arow(), acol(nonzer+1,)\ninteger(kz) nz, rowstr()\ndouble precision a(), aelt(nonzer+1,), v(), rcond, shift\n\ninteger nzloc(n), nrows\n\n\ninteger i, j, jcol\ninteger(kz) j1, j2, nza, k, kk, nzrow\ndouble precision xi, size, scale, ratio, va\n\nnrows = lastrow - firstrow + 1\nj1 = ilow + 1\nj2 = ihigh + 1\n\ndo j = j1, j2\nrowstr(j) = 0\nenddo\n\ndo i = 1, n\ndo nza = 1, arow(i)\nj = acol(nza, i)\nif (j.ge.ilow .and. j.le.ihigh) then\nj = j + 1\nrowstr(j) = rowstr(j) + arow(i)\nendif\nend do\nend do\n\nif (myid .eq. 0) then\nrowstr(1) = 1\nj1 = 1\nendif\ndo j = j1+1, j2\nrowstr(j) = rowstr(j) + rowstr(j-1)\nenddo\nif (myid .lt. num_threads) last_n(myid) = rowstr(j2)\n\nnzrow = 0\nif (myid .lt. num_threads) then\ndo i = 0, myid-1\nnzrow = nzrow + last_n(i)\nend do\nendif\nif (nzrow .gt. 0) then\ndo j = j1, j2\nrowstr(j) = rowstr(j) + nzrow\nenddo\nendif\nnza = rowstr(nrows+1) - 1\n\n\nif (nza .gt. nz) then\nwrite(,) 'Space for matrix elements exceeded in sparse'\nwrite(,) 'nza, nzmax = ',nza, nz\nstop\nendif\n\n\ndo j = ilow, ihigh\ndo k = rowstr(j), rowstr(j+1)-1\nv(k) = 0.d0\niv(k) = 0\nenddo\nnzloc(j) = 0\nenddo\n\n\nsize = 1.0D0\nratio = rcond ** (1.0D0 / dfloat(n))\n\ndo i = 1, n\ndo nza = 1, arow(i)\nj = acol(nza, i)\n\nif (j .lt. ilow .or. j .gt. ihigh) goto 60\n\nscale = size * aelt(nza, i)\ndo nzrow = 1, arow(i)\njcol = acol(nzrow, i)\nva = aelt(nzrow, i) * scale\n\nif (jcol .eq. j .and. j .eq. i) then\nva = va + rcond - shift\nendif\n\ndo k = rowstr(j), rowstr(j+1)-1\nif (iv(k) .gt. jcol) then\ndo kk = rowstr(j+1)-2, k, -1\nif (iv(kk) .gt. 0) then\nv(kk+1) = v(kk)\niv(kk+1) = iv(kk)\nendif\nenddo\niv(k) = jcol\nv(k) = 0.d0\ngoto 40\nelse if (iv(k) .eq. 0) then\niv(k) = jcol\ngoto 40\nelse if (iv(k) .eq. jcol) then\nnzloc(j) = nzloc(j) + 1\ngoto 40\nendif\nenddo\nprint ,'internal error in sparse: i=',i\nstop\n40 continue\nv(k) = v(k) + va\nenddo\n60 continue\nenddo\nsize = size ratio\nenddo\n\n\ndo j = ilow+1, ihigh\nnzloc(j) = nzloc(j) + nzloc(j-1)\nenddo\nif (myid .lt. num_threads) last_n(myid) = nzloc(ihigh)\n\nnzrow = 0\nif (myid .lt. num_threads) then\ndo i = 0, myid-1\nnzrow = nzrow + last_n(i)\nend do\nendif\nif (nzrow .gt. 0) then\ndo j = ilow, ihigh\nnzloc(j) = nzloc(j) + nzrow\nenddo\nendif\n\ndo j = 1, nrows\nif (j .gt. 1) then\nj1 = rowstr(j) - nzloc(j-1)\nelse\nj1 = 1\nendif\nj2 = rowstr(j+1) - nzloc(j) - 1\nnza = rowstr(j)\ndo k = j1, j2\na(k) = v(nza)\ncolidx(k) = iv(nza)\nnza = nza + 1\nenddo\nenddo\ndo j = 2, nrows+1\nrowstr(j) = rowstr(j) - nzloc(j-1)\nenddo\nnza = rowstr(nrows+1) - 1\n\n\nreturn\n11000 format ( //,'final nonzero count in sparse ', &\n& /,'number of nonzeros = ', i16 )\nend
void rhs_norm(double rms[5]){\nint i, j, k, d, m;\ndouble add;\nfor(m=0; m<5; m++){\nrms[m]=0.0;\n}\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++) {\nadd=rhs[k][j][i][m];\nrms[m]=rms[m]+add*add;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}	subroutine compute_rhs\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision rho_inv, uijk, up1, um1, vijk, vp1, vm1, &\n& wijk, wp1, wm1\n\n\nif (timeron) call timer_start(t_rhs)\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\nrho_inv = 1.0d0/u(1,i,j,k)\nrho_i(i,j,k) = rho_inv\nus(i,j,k) = u(2,i,j,k) * rho_inv\nvs(i,j,k) = u(3,i,j,k) * rho_inv\nws(i,j,k) = u(4,i,j,k) * rho_inv\nsquare(i,j,k) = 0.5d0* ( &\n& u(2,i,j,k)u(2,i,j,k) + &\n& u(3,i,j,k)u(3,i,j,k) + &\n& u(4,i,j,k)u(4,i,j,k) ) rho_inv\nqs(i,j,k) = square(i,j,k) * rho_inv\nenddo\nenddo\nenddo\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nrhs(m,i,j,k) = forcing(m,i,j,k)\nenddo\nenddo\nenddo\nenddo\n\n\nif (timeron) call timer_start(t_rhsx)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nuijk = us(i,j,k)\nup1 = us(i+1,j,k)\num1 = us(i-1,j,k)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dx1tx1 * &\n& (u(1,i+1,j,k) - 2.0d0u(1,i,j,k) + &\n& u(1,i-1,j,k)) - &\n& tx2 (u(2,i+1,j,k) - u(2,i-1,j,k))\n\nrhs(2,i,j,k) = rhs(2,i,j,k) + dx2tx1 * &\n& (u(2,i+1,j,k) - 2.0d0u(2,i,j,k) + &\n& u(2,i-1,j,k)) + &\n& xxcon2con43 * (up1 - 2.0d0uijk + um1) - &\n& tx2 (u(2,i+1,j,k)up1 - &\n& u(2,i-1,j,k)um1 + &\n& (u(5,i+1,j,k)- square(i+1,j,k)- &\n& u(5,i-1,j,k)+ square(i-1,j,k))* &\n& c2)\n\nrhs(3,i,j,k) = rhs(3,i,j,k) + dx3tx1 * &\n& (u(3,i+1,j,k) - 2.0d0u(3,i,j,k) + &\n& u(3,i-1,j,k)) + &\n& xxcon2 (vs(i+1,j,k) - 2.0d0vs(i,j,k) + &\n& vs(i-1,j,k)) - &\n& tx2 (u(3,i+1,j,k)up1 - &\n& u(3,i-1,j,k)um1)\n\nrhs(4,i,j,k) = rhs(4,i,j,k) + dx4tx1 * &\n& (u(4,i+1,j,k) - 2.0d0u(4,i,j,k) + &\n& u(4,i-1,j,k)) + &\n& xxcon2 (ws(i+1,j,k) - 2.0d0ws(i,j,k) + &\n& ws(i-1,j,k)) - &\n& tx2 (u(4,i+1,j,k)up1 - &\n& u(4,i-1,j,k)um1)\n\nrhs(5,i,j,k) = rhs(5,i,j,k) + dx5tx1 * &\n& (u(5,i+1,j,k) - 2.0d0u(5,i,j,k) + &\n& u(5,i-1,j,k)) + &\n& xxcon3 (qs(i+1,j,k) - 2.0d0qs(i,j,k) + &\n& qs(i-1,j,k)) + &\n& xxcon4 (up1up1 - 2.0d0uijkuijk + &\n& um1um1) + &\n& xxcon5 * (u(5,i+1,j,k)rho_i(i+1,j,k) - &\n& 2.0d0u(5,i,j,k)rho_i(i,j,k) + &\n& u(5,i-1,j,k)rho_i(i-1,j,k)) - &\n& tx2 * ( (c1u(5,i+1,j,k) - &\n& c2square(i+1,j,k))up1 - &\n& (c1u(5,i-1,j,k) - &\n& c2square(i-1,j,k))um1 )\nenddo\n\ni = 1\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0u(m,i,j,k) - 4.0d0u(m,i+1,j,k) + &\n& u(m,i+2,j,k))\nenddo\n\ni = 2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0u(m,i-1,j,k) + 6.0d0u(m,i,j,k) - &\n& 4.0d0u(m,i+1,j,k) + u(m,i+2,j,k))\nenddo\n\ndo i = 3,grid_points(1)-4\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i-2,j,k) - 4.0d0u(m,i-1,j,k) + &\n& 6.0u(m,i,j,k) - 4.0d0u(m,i+1,j,k) + &\n& u(m,i+2,j,k) )\nenddo\nenddo\n\ni = grid_points(1)-3\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i-2,j,k) - 4.0d0u(m,i-1,j,k) + &\n& 6.0d0u(m,i,j,k) - 4.0d0u(m,i+1,j,k) )\nenddo\n\ni = grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i-2,j,k) - 4.d0u(m,i-1,j,k) + &\n& 5.d0u(m,i,j,k) )\nenddo\nenddo\nenddo\nif (timeron) call timer_stop(t_rhsx)\n\nif (timeron) call timer_start(t_rhsy)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nvijk = vs(i,j,k)\nvp1 = vs(i,j+1,k)\nvm1 = vs(i,j-1,k)\nrhs(1,i,j,k) = rhs(1,i,j,k) + dy1ty1 * &\n& (u(1,i,j+1,k) - 2.0d0u(1,i,j,k) + &\n& u(1,i,j-1,k)) - &\n& ty2 (u(3,i,j+1,k) - u(3,i,j-1,k))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dy2ty1 * &\n& (u(2,i,j+1,k) - 2.0d0u(2,i,j,k) + &\n& u(2,i,j-1,k)) + &\n& yycon2 (us(i,j+1,k) - 2.0d0us(i,j,k) + &\n& us(i,j-1,k)) - &\n& ty2 (u(2,i,j+1,k)vp1 - &\n& u(2,i,j-1,k)vm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dy3ty1 * &\n& (u(3,i,j+1,k) - 2.0d0u(3,i,j,k) + &\n& u(3,i,j-1,k)) + &\n& yycon2con43 * (vp1 - 2.0d0vijk + vm1) - &\n& ty2 (u(3,i,j+1,k)vp1 - &\n& u(3,i,j-1,k)vm1 + &\n& (u(5,i,j+1,k) - square(i,j+1,k) - &\n& u(5,i,j-1,k) + square(i,j-1,k)) &\n& c2)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dy4ty1 &\n& (u(4,i,j+1,k) - 2.0d0u(4,i,j,k) + &\n& u(4,i,j-1,k)) + &\n& yycon2 (ws(i,j+1,k) - 2.0d0ws(i,j,k) + &\n& ws(i,j-1,k)) - &\n& ty2 (u(4,i,j+1,k)vp1 - &\n& u(4,i,j-1,k)vm1)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dy5ty1 * &\n& (u(5,i,j+1,k) - 2.0d0u(5,i,j,k) + &\n& u(5,i,j-1,k)) + &\n& yycon3 (qs(i,j+1,k) - 2.0d0qs(i,j,k) + &\n& qs(i,j-1,k)) + &\n& yycon4 (vp1vp1 - 2.0d0vijkvijk + &\n& vm1vm1) + &\n& yycon5 * (u(5,i,j+1,k)rho_i(i,j+1,k) - &\n& 2.0d0u(5,i,j,k)rho_i(i,j,k) + &\n& u(5,i,j-1,k)rho_i(i,j-1,k)) - &\n& ty2 * ((c1u(5,i,j+1,k) - &\n& c2square(i,j+1,k)) * vp1 - &\n& (c1u(5,i,j-1,k) - &\n& c2square(i,j-1,k)) * vm1)\nenddo\n\nif (j .eq. 1) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0u(m,i,j,k) - 4.0d0u(m,i,j+1,k) + &\n& u(m,i,j+2,k))\nenddo\nenddo\n\nelse if (j .eq. 2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0u(m,i,j-1,k) + 6.0d0u(m,i,j,k) - &\n& 4.0d0u(m,i,j+1,k) + u(m,i,j+2,k))\nenddo\nenddo\n\nelse if (j .eq. grid_points(2)-3) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j-2,k) - 4.0d0u(m,i,j-1,k) + &\n& 6.0d0u(m,i,j,k) - 4.0d0u(m,i,j+1,k) )\nenddo\nenddo\n\nelse if (j .eq. grid_points(2)-2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j-2,k) - 4.d0u(m,i,j-1,k) + &\n& 5.d0u(m,i,j,k) )\nenddo\nenddo\n\nelse\ndo i = 1,grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.0d0u(m,i,j-1,k) + &\n& 6.0u(m,i,j,k) - 4.0d0u(m,i,j+1,k) + &\n& u(m,i,j+2,k) )\nenddo\nenddo\nendif\nenddo\nenddo\nif (timeron) call timer_stop(t_rhsy)\n\nif (timeron) call timer_start(t_rhsz)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nwijk = ws(i,j,k)\nwp1 = ws(i,j,k+1)\nwm1 = ws(i,j,k-1)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dz1tz1 &\n& (u(1,i,j,k+1) - 2.0d0u(1,i,j,k) + &\n& u(1,i,j,k-1)) - &\n& tz2 (u(4,i,j,k+1) - u(4,i,j,k-1))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dz2tz1 * &\n& (u(2,i,j,k+1) - 2.0d0u(2,i,j,k) + &\n& u(2,i,j,k-1)) + &\n& zzcon2 (us(i,j,k+1) - 2.0d0us(i,j,k) + &\n& us(i,j,k-1)) - &\n& tz2 (u(2,i,j,k+1)wp1 - &\n& u(2,i,j,k-1)wm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dz3tz1 * &\n& (u(3,i,j,k+1) - 2.0d0u(3,i,j,k) + &\n& u(3,i,j,k-1)) + &\n& zzcon2 (vs(i,j,k+1) - 2.0d0vs(i,j,k) + &\n& vs(i,j,k-1)) - &\n& tz2 (u(3,i,j,k+1)wp1 - &\n& u(3,i,j,k-1)wm1)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dz4tz1 * &\n& (u(4,i,j,k+1) - 2.0d0u(4,i,j,k) + &\n& u(4,i,j,k-1)) + &\n& zzcon2con43 * (wp1 - 2.0d0wijk + wm1) - &\n& tz2 (u(4,i,j,k+1)wp1 - &\n& u(4,i,j,k-1)wm1 + &\n& (u(5,i,j,k+1) - square(i,j,k+1) - &\n& u(5,i,j,k-1) + square(i,j,k-1)) &\n& c2)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dz5tz1 &\n& (u(5,i,j,k+1) - 2.0d0u(5,i,j,k) + &\n& u(5,i,j,k-1)) + &\n& zzcon3 (qs(i,j,k+1) - 2.0d0qs(i,j,k) + &\n& qs(i,j,k-1)) + &\n& zzcon4 (wp1wp1 - 2.0d0wijkwijk + &\n& wm1wm1) + &\n& zzcon5 * (u(5,i,j,k+1)rho_i(i,j,k+1) - &\n& 2.0d0u(5,i,j,k)rho_i(i,j,k) + &\n& u(5,i,j,k-1)rho_i(i,j,k-1)) - &\n& tz2 * ( (c1u(5,i,j,k+1) - &\n& c2square(i,j,k+1))wp1 - &\n& (c1u(5,i,j,k-1) - &\n& c2square(i,j,k-1))wm1)\nenddo\n\nif (k.eq.1) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0u(m,i,j,k) - 4.0d0u(m,i,j,k+1) + &\n& u(m,i,j,k+2))\nenddo\nenddo\n\nelse if (k.eq.2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0u(m,i,j,k-1) + 6.0d0u(m,i,j,k) - &\n& 4.0d0u(m,i,j,k+1) + u(m,i,j,k+2))\nenddo\nenddo\n\nelse if (k.eq.grid_points(3)-3) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j,k-2) - 4.0d0u(m,i,j,k-1) + &\n& 6.0d0u(m,i,j,k) - 4.0d0u(m,i,j,k+1) )\nenddo\nenddo\n\nelse if (k.eq.grid_points(3)-2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp &\n& ( u(m,i,j,k-2) - 4.d0u(m,i,j,k-1) + &\n& 5.d0u(m,i,j,k) )\nenddo\nenddo\n\nelse\ndo i = 1,grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.0d0u(m,i,j,k-1) + &\n& 6.0u(m,i,j,k) - 4.0d0u(m,i,j,k+1) + &\n& u(m,i,j,k+2) )\nenddo\nenddo\nendif\nenddo\nenddo\nif (timeron) call timer_stop(t_rhsz)\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nrhs(1,i,j,k) = rhs(1,i,j,k) dt\nrhs(2,i,j,k) = rhs(2,i,j,k) * dt\nrhs(3,i,j,k) = rhs(3,i,j,k) * dt\nrhs(4,i,j,k) = rhs(4,i,j,k) * dt\nrhs(5,i,j,k) = rhs(5,i,j,k) * dt\nenddo\nenddo\nenddo\n\n\nif (timeron) call timer_stop(t_rhs)\n\nreturn\nend
void exact_solution(double xi, double eta, double zeta, double dtemp[5]){\nint m;\nfor(m=0; m<5; m++){\ndtemp[m]=ce[0][m]+\nxi(ce[1][m]+\nxi(ce[4][m]+\nxi(ce[7][m]+\nxice[10][m])))+\neta(ce[2][m]+\neta(ce[5][m]+\neta(ce[8][m]+\netace[11][m])))+\nzeta(ce[3][m]+\nzeta(ce[6][m]+\nzeta(ce[9][m]+\nzetace[12][m])));\n}\n}	subroutine exact_solution(xi,eta,zeta,dtemp)\n\n\n\nuse bt_data\nimplicit none\n\ndouble precision xi, eta, zeta, dtemp(5)\ninteger m\n\ndo m = 1, 5\ndtemp(m) = ce(m,1) + &\n& xi(ce(m,2) + xi(ce(m,5) + xi(ce(m,8) + xice(m,11)))) + &\n& eta(ce(m,3) + eta(ce(m,6) + eta(ce(m,9) + etace(m,12))))+ &\n& zeta(ce(m,4) + zeta(ce(m,7) + zeta(ce(m,10) + &\n& zetace(m,13))))\nenddo\n\nreturn\nend
void jacu(int k){\n\nint i, j;\ndouble r43;\ndouble c1345;\ndouble c34;\ndouble tmp1, tmp2, tmp3;\nr43=(4.0/3.0);\nc1345=C1C3C4C5;\nc34=C3C4;\n\n#pragma omp for nowait schedule(static)\nfor (j=jend-1; j>=jst; j--) {\nfor (i=iend-1; i>=ist; i--) {\n\ntmp1=rho_i[k][j][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nd[j][i][0][0]=1.0+dt2.0(tx1dx1+ty1dy1+tz1dz1);\nd[j][i][1][0]=0.0;\nd[j][i][2][0]=0.0;\nd[j][i][3][0]=0.0;\nd[j][i][4][0]=0.0;\nd[j][i][0][1]=dt2.0\n(-tx1r43-ty1-tz1)\n(c34tmp2u[k][j][i][1]);\nd[j][i][1][1]=1.0\n+dt2.0c34tmp1\n(tx1r43+ty1+tz1)\n+dt2.0(tx1dx2+ty1dy2+tz1dz2);\nd[j][i][2][1]=0.0;\nd[j][i][3][1]=0.0;\nd[j][i][4][1]=0.0;\nd[j][i][0][2]=dt2.0\n(-tx1-ty1r43-tz1)\n(c34tmp2u[k][j][i][2]);\nd[j][i][1][2]=0.0;\nd[j][i][2][2]=1.0\n+dt2.0c34tmp1\n(tx1+ty1r43+tz1)\n+dt2.0(tx1dx3+ty1dy3+tz1dz3);\nd[j][i][3][2]=0.0;\nd[j][i][4][2]=0.0;\nd[j][i][0][3]=dt2.0\n(-tx1-ty1-tz1r43)\n(c34tmp2u[k][j][i][3]);\nd[j][i][1][3]=0.0;\nd[j][i][2][3]=0.0;\nd[j][i][3][3]=1.0\n+dt2.0c34tmp1\n(tx1+ty1+tz1r43)\n+dt2.0(tx1dx4+ty1dy4+tz1dz4);\nd[j][i][4][3]=0.0;\nd[j][i][0][4]=-dt2.0\n(((tx1(r43c34-c1345)\n+ty1(c34-c1345)\n+tz1(c34-c1345))(u[k][j][i][1]u[k][j][i][1])\n+(tx1(c34-c1345)\n+ty1(r43c34-c1345)\n+tz1(c34-c1345))(u[k][j][i][2]u[k][j][i][2])\n+(tx1(c34-c1345)\n+ty1(c34-c1345)\n+tz1(r43c34-c1345))(u[k][j][i][3]u[k][j][i][3])\n)tmp3\n+(tx1+ty1+tz1)c1345tmp2u[k][j][i][4]);\nd[j][i][1][4]=dt2.0\n(tx1(r43c34-c1345)\n+ty1(c34-c1345)\n+tz1(c34-c1345))tmp2u[k][j][i][1];\nd[j][i][2][4]=dt2.0\n(tx1(c34-c1345)\n+ty1(r43c34-c1345)\n+tz1(c34-c1345))tmp2u[k][j][i][2];\nd[j][i][3][4]=dt2.0\n(tx1(c34-c1345)\n+ty1(c34-c1345)\n+tz1(r43c34-c1345))tmp2u[k][j][i][3];\nd[j][i][4][4]=1.0\n+dt2.0(tx1+ty1+tz1)c1345tmp1\n+dt2.0(tx1dx5+ty1dy5+tz1dz5);\n\ntmp1=rho_i[k][j][i+1];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\na[j][i][0][0]=-dttx1dx1;\na[j][i][1][0]=dttx2;\na[j][i][2][0]=0.0;\na[j][i][3][0]=0.0;\na[j][i][4][0]=0.0;\na[j][i][0][1]=dttx2\n(-(u[k][j][i+1][1]tmp1)(u[k][j][i+1][1]tmp1)\n+C2qs[k][j][i+1]tmp1)\n-dttx1(-r43c34tmp2u[k][j][i+1][1]);\na[j][i][1][1]=dttx2\n((2.0-C2)(u[k][j][i+1][1]tmp1))\n-dttx1(r43c34tmp1)\n-dttx1dx2;\na[j][i][2][1]=dttx2\n(-C2(u[k][j][i+1][2]tmp1));\na[j][i][3][1]=dttx2\n(-C2(u[k][j][i+1][3]tmp1));\na[j][i][4][1]=dttx2C2;\na[j][i][0][2]=dttx2\n(-(u[k][j][i+1][1]u[k][j][i+1][2])tmp2)\n-dttx1(-c34tmp2u[k][j][i+1][2]);\na[j][i][1][2]=dttx2(u[k][j][i+1][2]tmp1);\na[j][i][2][2]=dttx2(u[k][j][i+1][1]tmp1)\n-dttx1(c34tmp1)\n-dttx1dx3;\na[j][i][3][2]=0.0;\na[j][i][4][2]=0.0;\na[j][i][0][3]=dttx2\n(-(u[k][j][i+1][1]u[k][j][i+1][3])tmp2)\n-dttx1(-c34tmp2u[k][j][i+1][3]);\na[j][i][1][3]=dttx2(u[k][j][i+1][3]tmp1);\na[j][i][2][3]=0.0;\na[j][i][3][3]=dttx2(u[k][j][i+1][1]tmp1)\n-dttx1(c34tmp1)\n-dttx1dx4;\na[j][i][4][3]=0.0;\na[j][i][0][4]=dttx2\n((C22.0qs[k][j][i+1]\n-C1u[k][j][i+1][4])\n(u[k][j][i+1][1]tmp2))\n-dttx1\n(-(r43c34-c1345)tmp3(u[k][j][i+1][1]u[k][j][i+1][1])\n-(c34-c1345)tmp3(u[k][j][i+1][2]u[k][j][i+1][2])\n-(c34-c1345)tmp3( u[k][j][i+1][3]u[k][j][i+1][3])\n-c1345tmp2u[k][j][i+1][4]);\na[j][i][1][4]=dttx2\n(C1(u[k][j][i+1][4]tmp1)\n-C2\n(u[k][j][i+1][1]u[k][j][i+1][1]tmp2\n+qs[k][j][i+1]tmp1))\n-dttx1\n(r43c34-c1345)tmp2u[k][j][i+1][1];\na[j][i][2][4]=dttx2\n(-C2(u[k][j][i+1][2]u[k][j][i+1][1])tmp2)\n-dttx1\n(c34-c1345)tmp2u[k][j][i+1][2];\na[j][i][3][4]=dttx2\n(-C2(u[k][j][i+1][3]u[k][j][i+1][1])tmp2)\n-dttx1\n(c34-c1345)tmp2u[k][j][i+1][3];\na[j][i][4][4]=dttx2\n(C1(u[k][j][i+1][1]tmp1))\n-dttx1c1345tmp1\n-dttx1dx5;\n\ntmp1=rho_i[k][j+1][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nb[j][i][0][0]=-dtty1dy1;\nb[j][i][1][0]=0.0;\nb[j][i][2][0]=dtty2;\nb[j][i][3][0]=0.0;\nb[j][i][4][0]=0.0;\nb[j][i][0][1]=dtty2\n(-(u[k][j+1][i][1]u[k][j+1][i][2])tmp2)\n-dtty1(-c34tmp2u[k][j+1][i][1]);\nb[j][i][1][1]=dtty2(u[k][j+1][i][2]tmp1)\n-dtty1(c34tmp1)\n-dtty1dy2;\nb[j][i][2][1]=dtty2(u[k][j+1][i][1]tmp1);\nb[j][i][3][1]=0.0;\nb[j][i][4][1]=0.0;\nb[j][i][0][2]=dtty2\n(-(u[k][j+1][i][2]tmp1)(u[k][j+1][i][2]tmp1)\n+C2(qs[k][j+1][i]tmp1))\n-dtty1(-r43c34tmp2u[k][j+1][i][2]);\nb[j][i][1][2]=dtty2\n(-C2(u[k][j+1][i][1]tmp1));\nb[j][i][2][2]=dtty2((2.0-C2)\n(u[k][j+1][i][2]tmp1))\n-dtty1(r43c34tmp1)\n-dtty1dy3;\nb[j][i][3][2]=dtty2\n(-C2(u[k][j+1][i][3]tmp1));\nb[j][i][4][2]=dtty2C2;\nb[j][i][0][3]=dtty2\n(-(u[k][j+1][i][2]u[k][j+1][i][3])tmp2)\n-dtty1(-c34tmp2u[k][j+1][i][3]);\nb[j][i][1][3]=0.0;\nb[j][i][2][3]=dtty2(u[k][j+1][i][3]tmp1);\nb[j][i][3][3]=dtty2(u[k][j+1][i][2]tmp1)\n-dtty1(c34tmp1)\n-dtty1dy4;\nb[j][i][4][3]=0.0;\nb[j][i][0][4]=dtty2\n((C22.0qs[k][j+1][i]\n-C1u[k][j+1][i][4])\n(u[k][j+1][i][2]tmp2))\n-dtty1\n(-(c34-c1345)tmp3(u[k][j+1][i][1]u[k][j+1][i][1])\n-(r43c34-c1345)tmp3(u[k][j+1][i][2]u[k][j+1][i][2])\n-(c34-c1345)tmp3(u[k][j+1][i][3]u[k][j+1][i][3])\n-c1345tmp2u[k][j+1][i][4]);\nb[j][i][1][4]=dtty2\n(-C2(u[k][j+1][i][1]u[k][j+1][i][2])tmp2)\n-dtty1\n(c34-c1345)tmp2u[k][j+1][i][1];\nb[j][i][2][4]=dtty2\n(C1(u[k][j+1][i][4]tmp1)\n-C2\n(qs[k][j+1][i]tmp1\n+u[k][j+1][i][2]u[k][j+1][i][2]tmp2))\n-dtty1\n(r43c34-c1345)tmp2u[k][j+1][i][2];\nb[j][i][3][4]=dtty2\n(-C2(u[k][j+1][i][2]u[k][j+1][i][3])tmp2)\n-dtty1(c34-c1345)tmp2u[k][j+1][i][3];\nb[j][i][4][4]=dtty2\n(C1(u[k][j+1][i][2]tmp1))\n-dtty1c1345tmp1\n-dtty1dy5;\n\ntmp1=rho_i[k+1][j][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nc[j][i][0][0]=-dttz1dz1;\nc[j][i][1][0]=0.0;\nc[j][i][2][0]=0.0;\nc[j][i][3][0]=dttz2;\nc[j][i][4][0]=0.0;\nc[j][i][0][1]=dttz2\n(-(u[k+1][j][i][1]u[k+1][j][i][3])tmp2)\n-dttz1(-c34tmp2u[k+1][j][i][1]);\nc[j][i][1][1]=dttz2(u[k+1][j][i][3]tmp1)\n-dttz1c34tmp1\n-dttz1dz2;\nc[j][i][2][1]=0.0;\nc[j][i][3][1]=dttz2(u[k+1][j][i][1]tmp1);\nc[j][i][4][1]=0.0;\nc[j][i][0][2]=dttz2\n(-(u[k+1][j][i][2]u[k+1][j][i][3])tmp2)\n-dttz1(-c34tmp2u[k+1][j][i][2]);\nc[j][i][1][2]=0.0;\nc[j][i][2][2]=dttz2(u[k+1][j][i][3]tmp1)\n-dttz1(c34tmp1)\n-dttz1dz3;\nc[j][i][3][2]=dttz2(u[k+1][j][i][2]tmp1);\nc[j][i][4][2]=0.0;\nc[j][i][0][3]=dttz2\n(-(u[k+1][j][i][3]tmp1)(u[k+1][j][i][3]tmp1)\n+C2(qs[k+1][j][i]tmp1))\n-dttz1(-r43c34tmp2u[k+1][j][i][3]);\nc[j][i][1][3]=dttz2\n(-C2(u[k+1][j][i][1]tmp1));\nc[j][i][2][3]=dttz2\n(-C2(u[k+1][j][i][2]tmp1));\nc[j][i][3][3]=dttz2(2.0-C2)\n(u[k+1][j][i][3]tmp1)\n-dttz1(r43c34tmp1)\n-dttz1dz4;\nc[j][i][4][3]=dttz2C2;\nc[j][i][0][4]=dttz2\n((C22.0qs[k+1][j][i]\n-C1u[k+1][j][i][4])\n(u[k+1][j][i][3]tmp2))\n-dttz1\n(-(c34-c1345)tmp3(u[k+1][j][i][1]u[k+1][j][i][1])\n-(c34-c1345)tmp3(u[k+1][j][i][2]u[k+1][j][i][2])\n-(r43c34-c1345)tmp3(u[k+1][j][i][3]u[k+1][j][i][3])\n-c1345tmp2u[k+1][j][i][4]);\nc[j][i][1][4]=dttz2\n(-C2(u[k+1][j][i][1]u[k+1][j][i][3])tmp2)\n-dttz1(c34-c1345)tmp2u[k+1][j][i][1];\nc[j][i][2][4]=dttz2\n(-C2(u[k+1][j][i][2]u[k+1][j][i][3])tmp2)\n-dttz1(c34-c1345)tmp2u[k+1][j][i][2];\nc[j][i][3][4]=dttz2\n(C1(u[k+1][j][i][4]tmp1)\n-C2\n(qs[k+1][j][i]tmp1\n+u[k+1][j][i][3]u[k+1][j][i][3]tmp2))\n-dttz1(r43c34-c1345)tmp2u[k+1][j][i][3];\nc[j][i][4][4]=dttz2\n(C1(u[k+1][j][i][3]tmp1))\n-dttz1c1345tmp1\n-dttz1dz5;\n}\n}\n}	subroutine jacu(j, k)\n\n\n\nuse lu_data\nimplicit none\n\ninteger j, k\n\ninteger i\ndouble precision r43\ndouble precision c1345\ndouble precision c34\ndouble precision tmp1, tmp2, tmp3\n\n\n\nr43 = ( 4.0d+00 / 3.0d+00 )\nc1345 = c1 * c3 * c4 * c5\nc34 = c3 * c4\n\ndo i = iend, ist, -1\n\ntmp1 = rho_i(i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nd(1,1,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 * dx1 &\n& + ty1 * dy1 &\n& + tz1 * dz1 )\nd(1,2,i) = 0.0d+00\nd(1,3,i) = 0.0d+00\nd(1,4,i) = 0.0d+00\nd(1,5,i) = 0.0d+00\n\nd(2,1,i) = dt * 2.0d+00 &\n& * ( - tx1 * r43 - ty1 - tz1 ) &\n& * ( c34 * tmp2 * u(2,i,j,k) )\nd(2,2,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 * r43 + ty1 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx2 &\n& + ty1 * dy2 &\n& + tz1 * dz2 )\nd(2,3,i) = 0.0d+00\nd(2,4,i) = 0.0d+00\nd(2,5,i) = 0.0d+00\n\nd(3,1,i) = dt * 2.0d+00 &\n& * ( - tx1 - ty1 * r43 - tz1 ) &\n& * ( c34 * tmp2 * u(3,i,j,k) )\nd(3,2,i) = 0.0d+00\nd(3,3,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 * r43 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx3 &\n& + ty1 * dy3 &\n& + tz1 * dz3 )\nd(3,4,i) = 0.0d+00\nd(3,5,i) = 0.0d+00\n\nd(4,1,i) = dt * 2.0d+00 &\n& * ( - tx1 - ty1 - tz1 * r43 ) &\n& * ( c34 * tmp2 * u(4,i,j,k) )\nd(4,2,i) = 0.0d+00\nd(4,3,i) = 0.0d+00\nd(4,4,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 + tz1 * r43 ) &\n& + dt * 2.0d+00 * ( tx1 * dx4 &\n& + ty1 * dy4 &\n& + tz1 * dz4 )\nd(4,5,i) = 0.0d+00\n\nd(5,1,i) = -dt * 2.0d+00 &\n& * ( ( ( tx1 * ( r43c34 - c1345 ) &\n& + ty1 ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * ( u(2,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43c34 - c1345 ) &\n& + tz1 ( c34 - c1345 ) ) * ( u(3,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43c34 - c1345 ) ) ( u(4,i,j,k) ** 2 ) &\n& ) * tmp3 &\n& + ( tx1 + ty1 + tz1 ) * c1345 * tmp2 * u(5,i,j,k) )\n\nd(5,2,i) = dt * 2.0d+00 &\n& * ( tx1 * ( r43c34 - c1345 ) &\n& + ty1 ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * tmp2 * u(2,i,j,k)\nd(5,3,i) = dt * 2.0d+00 &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43c34 -c1345 ) &\n& + tz1 ( c34 - c1345 ) ) * tmp2 * u(3,i,j,k)\nd(5,4,i) = dt * 2.0d+00 &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43c34 - c1345 ) ) tmp2 * u(4,i,j,k)\nd(5,5,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 + ty1 + tz1 ) * c1345 * tmp1 &\n& + dt * 2.0d+00 * ( tx1 * dx5 &\n& + ty1 * dy5 &\n& + tz1 * dz5 )\n\ntmp1 = rho_i(i+1,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\na(1,1,i) = - dt * tx1 * dx1\na(1,2,i) = dt * tx2\na(1,3,i) = 0.0d+00\na(1,4,i) = 0.0d+00\na(1,5,i) = 0.0d+00\n\na(2,1,i) = dt * tx2 &\n& * ( - ( u(2,i+1,j,k) * tmp1 ) ** 2 &\n& + c2 * qs(i+1,j,k) * tmp1 ) &\n& - dt * tx1 * ( - r43 * c34 * tmp2 * u(2,i+1,j,k) )\na(2,2,i) = dt * tx2 &\n& * ( ( 2.0d+00 - c2 ) * ( u(2,i+1,j,k) * tmp1 ) ) &\n& - dt * tx1 * ( r43 * c34 * tmp1 ) &\n& - dt * tx1 * dx2\na(2,3,i) = dt * tx2 &\n& * ( - c2 * ( u(3,i+1,j,k) * tmp1 ) )\na(2,4,i) = dt * tx2 &\n& * ( - c2 * ( u(4,i+1,j,k) * tmp1 ) )\na(2,5,i) = dt * tx2 * c2\n\na(3,1,i) = dt * tx2 &\n& * ( - ( u(2,i+1,j,k) * u(3,i+1,j,k) ) * tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(3,i+1,j,k) )\na(3,2,i) = dt * tx2 * ( u(3,i+1,j,k) * tmp1 )\na(3,3,i) = dt * tx2 * ( u(2,i+1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx3\na(3,4,i) = 0.0d+00\na(3,5,i) = 0.0d+00\n\na(4,1,i) = dt * tx2 &\n& * ( - ( u(2,i+1,j,k)u(4,i+1,j,k) ) tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(4,i+1,j,k) )\na(4,2,i) = dt * tx2 * ( u(4,i+1,j,k) * tmp1 )\na(4,3,i) = 0.0d+00\na(4,4,i) = dt * tx2 * ( u(2,i+1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx4\na(4,5,i) = 0.0d+00\n\na(5,1,i) = dt * tx2 &\n& * ( ( c2 * 2.0d0 * qs(i+1,j,k) &\n& - c1 * u(5,i+1,j,k) ) &\n& * ( u(2,i+1,j,k) * tmp2 ) ) &\n& - dt * tx1 &\n& * ( - ( r43c34 - c1345 ) tmp3 * ( u(2,i+1,j,k)*2 ) &\n& - ( c34 - c1345 ) tmp3 * ( u(3,i+1,j,k)*2 ) &\n& - ( c34 - c1345 ) tmp3 * ( u(4,i+1,j,k)*2 ) &\n& - c1345 tmp2 * u(5,i+1,j,k) )\na(5,2,i) = dt * tx2 &\n& * ( c1 * ( u(5,i+1,j,k) * tmp1 ) &\n& - c2 &\n& * ( u(2,i+1,j,k)u(2,i+1,j,k) tmp2 &\n& + qs(i+1,j,k) * tmp1 ) ) &\n& - dt * tx1 &\n& * ( r43c34 - c1345 ) tmp2 * u(2,i+1,j,k)\na(5,3,i) = dt * tx2 &\n& * ( - c2 * ( u(3,i+1,j,k)u(2,i+1,j,k) ) tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(3,i+1,j,k)\na(5,4,i) = dt * tx2 &\n& * ( - c2 * ( u(4,i+1,j,k)u(2,i+1,j,k) ) tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(4,i+1,j,k)\na(5,5,i) = dt * tx2 &\n& * ( c1 * ( u(2,i+1,j,k) * tmp1 ) ) &\n& - dt * tx1 * c1345 * tmp1 &\n& - dt * tx1 * dx5\n\ntmp1 = rho_i(i,j+1,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nb(1,1,i) = - dt * ty1 * dy1\nb(1,2,i) = 0.0d+00\nb(1,3,i) = dt * ty2\nb(1,4,i) = 0.0d+00\nb(1,5,i) = 0.0d+00\n\nb(2,1,i) = dt * ty2 &\n& * ( - ( u(2,i,j+1,k)u(3,i,j+1,k) ) tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(2,i,j+1,k) )\nb(2,2,i) = dt * ty2 * ( u(3,i,j+1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy2\nb(2,3,i) = dt * ty2 * ( u(2,i,j+1,k) * tmp1 )\nb(2,4,i) = 0.0d+00\nb(2,5,i) = 0.0d+00\n\nb(3,1,i) = dt * ty2 &\n& * ( - ( u(3,i,j+1,k) * tmp1 ) ** 2 &\n& + c2 * ( qs(i,j+1,k) * tmp1 ) ) &\n& - dt * ty1 * ( - r43 * c34 * tmp2 * u(3,i,j+1,k) )\nb(3,2,i) = dt * ty2 &\n& * ( - c2 * ( u(2,i,j+1,k) * tmp1 ) )\nb(3,3,i) = dt * ty2 * ( ( 2.0d+00 - c2 ) &\n& * ( u(3,i,j+1,k) * tmp1 ) ) &\n& - dt * ty1 * ( r43 * c34 * tmp1 ) &\n& - dt * ty1 * dy3\nb(3,4,i) = dt * ty2 &\n& * ( - c2 * ( u(4,i,j+1,k) * tmp1 ) )\nb(3,5,i) = dt * ty2 * c2\n\nb(4,1,i) = dt * ty2 &\n& * ( - ( u(3,i,j+1,k)u(4,i,j+1,k) ) tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(4,i,j+1,k) )\nb(4,2,i) = 0.0d+00\nb(4,3,i) = dt * ty2 * ( u(4,i,j+1,k) * tmp1 )\nb(4,4,i) = dt * ty2 * ( u(3,i,j+1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy4\nb(4,5,i) = 0.0d+00\n\nb(5,1,i) = dt * ty2 &\n& * ( ( c2 * 2.0d0 * qs(i,j+1,k) &\n& - c1 * u(5,i,j+1,k) ) &\n& * ( u(3,i,j+1,k) * tmp2 ) ) &\n& - dt * ty1 &\n& * ( - ( c34 - c1345 )tmp3(u(2,i,j+1,k)*2) &\n& - ( r43c34 - c1345 )tmp3(u(3,i,j+1,k)*2) &\n& - ( c34 - c1345 )tmp3(u(4,i,j+1,k)2) &\n& - c1345tmp2u(5,i,j+1,k) )\nb(5,2,i) = dt ty2 &\n& * ( - c2 * ( u(2,i,j+1,k)u(3,i,j+1,k) ) tmp2 ) &\n& - dt * ty1 &\n& * ( c34 - c1345 ) * tmp2 * u(2,i,j+1,k)\nb(5,3,i) = dt * ty2 &\n& * ( c1 * ( u(5,i,j+1,k) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j+1,k) * tmp1 &\n& + u(3,i,j+1,k)u(3,i,j+1,k) tmp2 ) ) &\n& - dt * ty1 &\n& * ( r43c34 - c1345 ) tmp2 * u(3,i,j+1,k)\nb(5,4,i) = dt * ty2 &\n& * ( - c2 * ( u(3,i,j+1,k)u(4,i,j+1,k) ) tmp2 ) &\n& - dt * ty1 * ( c34 - c1345 ) * tmp2 * u(4,i,j+1,k)\nb(5,5,i) = dt * ty2 &\n& * ( c1 * ( u(3,i,j+1,k) * tmp1 ) ) &\n& - dt * ty1 * c1345 * tmp1 &\n& - dt * ty1 * dy5\n\ntmp1 = rho_i(i,j,k+1)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nc(1,1,i) = - dt * tz1 * dz1\nc(1,2,i) = 0.0d+00\nc(1,3,i) = 0.0d+00\nc(1,4,i) = dt * tz2\nc(1,5,i) = 0.0d+00\n\nc(2,1,i) = dt * tz2 &\n& * ( - ( u(2,i,j,k+1)u(4,i,j,k+1) ) tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(2,i,j,k+1) )\nc(2,2,i) = dt * tz2 * ( u(4,i,j,k+1) * tmp1 ) &\n& - dt * tz1 * c34 * tmp1 &\n& - dt * tz1 * dz2\nc(2,3,i) = 0.0d+00\nc(2,4,i) = dt * tz2 * ( u(2,i,j,k+1) * tmp1 )\nc(2,5,i) = 0.0d+00\n\nc(3,1,i) = dt * tz2 &\n& * ( - ( u(3,i,j,k+1)u(4,i,j,k+1) ) tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(3,i,j,k+1) )\nc(3,2,i) = 0.0d+00\nc(3,3,i) = dt * tz2 * ( u(4,i,j,k+1) * tmp1 ) &\n& - dt * tz1 * ( c34 * tmp1 ) &\n& - dt * tz1 * dz3\nc(3,4,i) = dt * tz2 * ( u(3,i,j,k+1) * tmp1 )\nc(3,5,i) = 0.0d+00\n\nc(4,1,i) = dt * tz2 &\n& * ( - ( u(4,i,j,k+1) * tmp1 ) ** 2 &\n& + c2 * ( qs(i,j,k+1) * tmp1 ) ) &\n& - dt * tz1 * ( - r43 * c34 * tmp2 * u(4,i,j,k+1) )\nc(4,2,i) = dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k+1) * tmp1 ) )\nc(4,3,i) = dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k+1) * tmp1 ) )\nc(4,4,i) = dt * tz2 * ( 2.0d+00 - c2 ) &\n& * ( u(4,i,j,k+1) * tmp1 ) &\n& - dt * tz1 * ( r43 * c34 * tmp1 ) &\n& - dt * tz1 * dz4\nc(4,5,i) = dt * tz2 * c2\n\nc(5,1,i) = dt * tz2 &\n& * ( ( c2 * 2.0d0 * qs(i,j,k+1) &\n& - c1 * u(5,i,j,k+1) ) &\n& * ( u(4,i,j,k+1) * tmp2 ) ) &\n& - dt * tz1 &\n& * ( - ( c34 - c1345 ) * tmp3 * (u(2,i,j,k+1)*2) &\n& - ( c34 - c1345 ) tmp3 * (u(3,i,j,k+1)*2) &\n& - ( r43c34 - c1345 )* tmp3 * (u(4,i,j,k+1)*2) &\n& - c1345 tmp2 * u(5,i,j,k+1) )\nc(5,2,i) = dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k+1)u(4,i,j,k+1) ) tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(2,i,j,k+1)\nc(5,3,i) = dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k+1)u(4,i,j,k+1) ) tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(3,i,j,k+1)\nc(5,4,i) = dt * tz2 &\n& * ( c1 * ( u(5,i,j,k+1) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j,k+1) * tmp1 &\n& + u(4,i,j,k+1)u(4,i,j,k+1) tmp2 ) ) &\n& - dt * tz1 * ( r43c34 - c1345 ) tmp2 * u(4,i,j,k+1)\nc(5,5,i) = dt * tz2 &\n& * ( c1 * ( u(4,i,j,k+1) * tmp1 ) ) &\n& - dt * tz1 * c1345 * tmp1 &\n& - dt * tz1 * dz5\n\nend do\n\n\nreturn\nend
void exact(int i, int j, int k, double u000ijk[]){\n\nint m;\ndouble xi, eta, zeta;\nxi=((double)i)/(nx0-1);\neta=((double)j)/(ny0-1);\nzeta=((double)k)/(nz-1);\nfor(m=0; m<5; m++){\nu000ijk[m]=ce[0][m]+\n(ce[1][m]+\n(ce[4][m]+\n(ce[7][m]+\nce[10][m]xi)xi)xi)xi+\n(ce[2][m]+\n(ce[5][m]+\n(ce[8][m]+\nce[11][m]eta)eta)eta)eta+\n(ce[3][m]+\n(ce[6][m]+\n(ce[9][m]+\nce[12][m]zeta)zeta)zeta)zeta;\n}\n}	subroutine exact( i, j, k, u000ijk )\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k\ndouble precision u000ijk()\n\ninteger m\ndouble precision xi, eta, zeta\n\nxi = ( dble ( i - 1 ) ) / ( nx0 - 1 )\neta = ( dble ( j - 1 ) ) / ( ny0 - 1 )\nzeta = ( dble ( k - 1 ) ) / ( nz - 1 )\n\n\ndo m = 1, 5\nu000ijk(m) = ce(m,1) &\n& + (ce(m,2) &\n& + (ce(m,5) &\n& + (ce(m,8) &\n& + ce(m,11) xi) * xi) * xi) * xi &\n& + (ce(m,3) &\n& + (ce(m,6) &\n& + (ce(m,9) &\n& + ce(m,12) * eta) * eta) * eta) * eta &\n& + (ce(m,4) &\n& + (ce(m,7) &\n& + (ce(m,10) &\n& + ce(m,13) * zeta) * zeta) * zeta) * zeta\nend do\n\nreturn\nend
void z_solve(){\nint i, j, k, m, n, ksize;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_ZSOLVE);}\n\nksize = grid_points[2]-1;\n\n#pragma omp for\nfor(j=1; j<=grid_points[1]-2; j++){\ndouble fjac[PROBLEM_SIZE+1][5][5];\ndouble njac[PROBLEM_SIZE+1][5][5];\ndouble lhs[PROBLEM_SIZE+1][3][5][5];\ndouble tmp1, tmp2, tmp3;\n\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(k=0; k<=ksize; k++){\ntmp1=1.0/u[k][j][i][0];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nfjac[k][0][0]=0.0;\nfjac[k][1][0]=0.0;\nfjac[k][2][0]=0.0;\nfjac[k][3][0]=1.0;\nfjac[k][4][0]=0.0;\nfjac[k][0][1]=-(u[k][j][i][1]u[k][j][i][3])tmp2;\nfjac[k][1][1]=u[k][j][i][3]tmp1;\nfjac[k][2][1]=0.0;\nfjac[k][3][1]=u[k][j][i][1]tmp1;\nfjac[k][4][1]=0.0;\nfjac[k][0][2]=-(u[k][j][i][2]u[k][j][i][3])tmp2;\nfjac[k][1][2]=0.0;\nfjac[k][2][2]=u[k][j][i][3]tmp1;\nfjac[k][3][2]=u[k][j][i][2]tmp1;\nfjac[k][4][2]=0.0;\nfjac[k][0][3]=-(u[k][j][i][3]u[k][j][i][3]tmp2)+c2qs[k][j][i];\nfjac[k][1][3]=-c2u[k][j][i][1]tmp1;\nfjac[k][2][3]=-c2u[k][j][i][2]tmp1;\nfjac[k][3][3]=(2.0-c2)u[k][j][i][3]tmp1;\nfjac[k][4][3]=c2;\nfjac[k][0][4]=(c22.0square[k][j][i]-c1u[k][j][i][4])u[k][j][i][3]tmp2;\nfjac[k][1][4]=-c2(u[k][j][i][1]u[k][j][i][3])tmp2;\nfjac[k][2][4]=-c2(u[k][j][i][2]u[k][j][i][3])tmp2;\nfjac[k][3][4]=c1(u[k][j][i][4]tmp1)-c2(qs[k][j][i]+u[k][j][i][3]u[k][j][i][3]tmp2);\nfjac[k][4][4]=c1u[k][j][i][3]tmp1;\nnjac[k][0][0]=0.0;\nnjac[k][1][0]=0.0;\nnjac[k][2][0]=0.0;\nnjac[k][3][0]=0.0;\nnjac[k][4][0]=0.0;\nnjac[k][0][1]=-c3c4tmp2u[k][j][i][1];\nnjac[k][1][1]=c3c4tmp1;\nnjac[k][2][1]=0.0;\nnjac[k][3][1]=0.0;\nnjac[k][4][1]=0.0;\nnjac[k][0][2]=-c3c4tmp2u[k][j][i][2];\nnjac[k][1][2]=0.0;\nnjac[k][2][2]=c3c4tmp1;\nnjac[k][3][2]=0.0;\nnjac[k][4][2]=0.0;\nnjac[k][0][3]=-con43c3c4tmp2u[k][j][i][3];\nnjac[k][1][3]=0.0;\nnjac[k][2][3]=0.0;\nnjac[k][3][3]=con43c3c4tmp1;\nnjac[k][4][3]=0.0;\nnjac[k][0][4]=-(c3c4-c1345)tmp3(u[k][j][i][1]u[k][j][i][1])\n-(c3c4-c1345)tmp3(u[k][j][i][2]u[k][j][i][2])\n-(con43c3c4-c1345)tmp3(u[k][j][i][3]u[k][j][i][3])\n-c1345tmp2u[k][j][i][4];\nnjac[k][1][4]=(c3c4-c1345)tmp2u[k][j][i][1];\nnjac[k][2][4]=(c3c4-c1345)tmp2u[k][j][i][2];\nnjac[k][3][4]=(con43c3c4-c1345)tmp2u[k][j][i][3];\nnjac[k][4][4]=(c1345)tmp1;\n}\n\nlhsinit(lhs, ksize);\nfor(k=1; k<=ksize-1; k++){\ntmp1=dttz1;\ntmp2=dttz2;\nlhs[k][AA][0][0]=-tmp2fjac[k-1][0][0]\n-tmp1njac[k-1][0][0]\n-tmp1dz1;\nlhs[k][AA][1][0]=-tmp2fjac[k-1][1][0]\n-tmp1njac[k-1][1][0];\nlhs[k][AA][2][0]=-tmp2fjac[k-1][2][0]\n-tmp1njac[k-1][2][0];\nlhs[k][AA][3][0]=-tmp2fjac[k-1][3][0]\n-tmp1njac[k-1][3][0];\nlhs[k][AA][4][0]=-tmp2fjac[k-1][4][0]\n-tmp1njac[k-1][4][0];\nlhs[k][AA][0][1]=-tmp2fjac[k-1][0][1]\n-tmp1njac[k-1][0][1];\nlhs[k][AA][1][1]=-tmp2fjac[k-1][1][1]\n-tmp1njac[k-1][1][1]\n-tmp1dz2;\nlhs[k][AA][2][1]=-tmp2fjac[k-1][2][1]\n-tmp1njac[k-1][2][1];\nlhs[k][AA][3][1]=-tmp2fjac[k-1][3][1]\n-tmp1njac[k-1][3][1];\nlhs[k][AA][4][1]=-tmp2fjac[k-1][4][1]\n-tmp1njac[k-1][4][1];\nlhs[k][AA][0][2]=-tmp2fjac[k-1][0][2]\n-tmp1njac[k-1][0][2];\nlhs[k][AA][1][2]=-tmp2fjac[k-1][1][2]\n-tmp1njac[k-1][1][2];\nlhs[k][AA][2][2]=-tmp2fjac[k-1][2][2]\n-tmp1njac[k-1][2][2]\n-tmp1dz3;\nlhs[k][AA][3][2]=-tmp2fjac[k-1][3][2]\n-tmp1njac[k-1][3][2];\nlhs[k][AA][4][2]=-tmp2fjac[k-1][4][2]\n-tmp1njac[k-1][4][2];\nlhs[k][AA][0][3]=-tmp2fjac[k-1][0][3]\n-tmp1njac[k-1][0][3];\nlhs[k][AA][1][3]=-tmp2fjac[k-1][1][3]\n-tmp1njac[k-1][1][3];\nlhs[k][AA][2][3]=-tmp2fjac[k-1][2][3]\n-tmp1njac[k-1][2][3];\nlhs[k][AA][3][3]=-tmp2fjac[k-1][3][3]\n-tmp1njac[k-1][3][3]\n-tmp1dz4;\nlhs[k][AA][4][3]=-tmp2fjac[k-1][4][3]\n-tmp1njac[k-1][4][3];\nlhs[k][AA][0][4]=-tmp2fjac[k-1][0][4]\n-tmp1njac[k-1][0][4];\nlhs[k][AA][1][4]=-tmp2fjac[k-1][1][4]\n-tmp1njac[k-1][1][4];\nlhs[k][AA][2][4]=-tmp2fjac[k-1][2][4]\n-tmp1njac[k-1][2][4];\nlhs[k][AA][3][4]=-tmp2fjac[k-1][3][4]\n-tmp1njac[k-1][3][4];\nlhs[k][AA][4][4]=-tmp2fjac[k-1][4][4]\n-tmp1njac[k-1][4][4]\n-tmp1dz5;\nlhs[k][BB][0][0]=1.0\n+tmp12.0njac[k][0][0]\n+tmp12.0dz1;\nlhs[k][BB][1][0]=tmp12.0njac[k][1][0];\nlhs[k][BB][2][0]=tmp12.0njac[k][2][0];\nlhs[k][BB][3][0]=tmp12.0njac[k][3][0];\nlhs[k][BB][4][0]=tmp12.0njac[k][4][0];\nlhs[k][BB][0][1]=tmp12.0njac[k][0][1];\nlhs[k][BB][1][1]=1.0\n+tmp12.0njac[k][1][1]\n+tmp12.0dz2;\nlhs[k][BB][2][1]=tmp12.0njac[k][2][1];\nlhs[k][BB][3][1]=tmp12.0njac[k][3][1];\nlhs[k][BB][4][1]=tmp12.0njac[k][4][1];\nlhs[k][BB][0][2]=tmp12.0njac[k][0][2];\nlhs[k][BB][1][2]=tmp12.0njac[k][1][2];\nlhs[k][BB][2][2]=1.0\n+tmp12.0njac[k][2][2]\n+tmp12.0dz3;\nlhs[k][BB][3][2]=tmp12.0njac[k][3][2];\nlhs[k][BB][4][2]=tmp12.0njac[k][4][2];\nlhs[k][BB][0][3]=tmp12.0njac[k][0][3];\nlhs[k][BB][1][3]=tmp12.0njac[k][1][3];\nlhs[k][BB][2][3]=tmp12.0njac[k][2][3];\nlhs[k][BB][3][3]=1.0\n+tmp12.0njac[k][3][3]\n+tmp12.0dz4;\nlhs[k][BB][4][3]=tmp12.0njac[k][4][3];\nlhs[k][BB][0][4]=tmp12.0njac[k][0][4];\nlhs[k][BB][1][4]=tmp12.0njac[k][1][4];\nlhs[k][BB][2][4]=tmp12.0njac[k][2][4];\nlhs[k][BB][3][4]=tmp12.0njac[k][3][4];\nlhs[k][BB][4][4]=1.0\n+tmp12.0njac[k][4][4]\n+tmp12.0dz5;\nlhs[k][CC][0][0]=tmp2fjac[k+1][0][0]\n-tmp1njac[k+1][0][0]\n-tmp1dz1;\nlhs[k][CC][1][0]=tmp2fjac[k+1][1][0]\n-tmp1njac[k+1][1][0];\nlhs[k][CC][2][0]=tmp2fjac[k+1][2][0]\n-tmp1njac[k+1][2][0];\nlhs[k][CC][3][0]=tmp2fjac[k+1][3][0]\n-tmp1njac[k+1][3][0];\nlhs[k][CC][4][0]=tmp2fjac[k+1][4][0]\n-tmp1njac[k+1][4][0];\nlhs[k][CC][0][1]=tmp2fjac[k+1][0][1]\n-tmp1njac[k+1][0][1];\nlhs[k][CC][1][1]=tmp2fjac[k+1][1][1]\n-tmp1njac[k+1][1][1]\n-tmp1dz2;\nlhs[k][CC][2][1]=tmp2fjac[k+1][2][1]\n-tmp1njac[k+1][2][1];\nlhs[k][CC][3][1]=tmp2fjac[k+1][3][1]\n-tmp1njac[k+1][3][1];\nlhs[k][CC][4][1]=tmp2fjac[k+1][4][1]\n-tmp1njac[k+1][4][1];\nlhs[k][CC][0][2]=tmp2fjac[k+1][0][2]\n-tmp1njac[k+1][0][2];\nlhs[k][CC][1][2]= tmp2fjac[k+1][1][2]\n-tmp1njac[k+1][1][2];\nlhs[k][CC][2][2]=tmp2fjac[k+1][2][2]\n-tmp1njac[k+1][2][2]\n-tmp1dz3;\nlhs[k][CC][3][2]=tmp2fjac[k+1][3][2]\n-tmp1njac[k+1][3][2];\nlhs[k][CC][4][2]=tmp2fjac[k+1][4][2]\n-tmp1njac[k+1][4][2];\nlhs[k][CC][0][3]=tmp2fjac[k+1][0][3]\n-tmp1njac[k+1][0][3];\nlhs[k][CC][1][3]=tmp2fjac[k+1][1][3]\n-tmp1njac[k+1][1][3];\nlhs[k][CC][2][3]=tmp2fjac[k+1][2][3]\n-tmp1njac[k+1][2][3];\nlhs[k][CC][3][3]=tmp2fjac[k+1][3][3]\n-tmp1njac[k+1][3][3]\n-tmp1dz4;\nlhs[k][CC][4][3]=tmp2fjac[k+1][4][3]\n-tmp1njac[k+1][4][3];\nlhs[k][CC][0][4]=tmp2fjac[k+1][0][4]\n-tmp1njac[k+1][0][4];\nlhs[k][CC][1][4]=tmp2fjac[k+1][1][4]\n-tmp1njac[k+1][1][4];\nlhs[k][CC][2][4]=tmp2fjac[k+1][2][4]\n-tmp1njac[k+1][2][4];\nlhs[k][CC][3][4]=tmp2fjac[k+1][3][4]\n-tmp1njac[k+1][3][4];\nlhs[k][CC][4][4]=tmp2fjac[k+1][4][4]\n-tmp1njac[k+1][4][4]\n-tmp1dz5;\n}\n\nbinvcrhs(lhs[0][BB], lhs[0][CC], rhs[0][j][i]);\n\nfor(k=1; k<=ksize-1; k++){\n\nmatvec_sub(lhs[k][AA], rhs[k-1][j][i], rhs[k][j][i]);\n\nmatmul_sub(lhs[k][AA], lhs[k-1][CC], lhs[k][BB]);\n\nbinvcrhs(lhs[k][BB], lhs[k][CC], rhs[k][j][i]);\n}\n\nmatvec_sub(lhs[ksize][AA], rhs[ksize-1][j][i], rhs[ksize][j][i]);\n\nmatmul_sub(lhs[ksize][AA], lhs[ksize-1][CC], lhs[ksize][BB]);\n\nbinvrhs(lhs[ksize][BB], rhs[ksize][j][i]);\n\nfor(k=ksize-1; k>=0; k--){\nfor(m=0; m<BLOCK_SIZE; m++){\nfor(n=0; n<BLOCK_SIZE; n++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[k][CC][n][m]rhs[k+1][j][i][n];\n}\n}\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_ZSOLVE);}\n}	subroutine z_solve\n\n\n\nuse bt_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, m, n, ksize\ndouble precision tmp1, tmp2, tmp3\n\n\nif (timeron) call timer_start(t_zsolve)\n\n\n\nksize = grid_points(3)-1\n\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo k = 0, ksize\n\ntmp1 = 1.0d+00 / u(1,i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nfjac(1,1,k) = 0.0d+00\nfjac(1,2,k) = 0.0d+00\nfjac(1,3,k) = 0.0d+00\nfjac(1,4,k) = 1.0d+00\nfjac(1,5,k) = 0.0d+00\n\nfjac(2,1,k) = - ( u(2,i,j,k)u(4,i,j,k) ) &\n& tmp2\nfjac(2,2,k) = u(4,i,j,k) * tmp1\nfjac(2,3,k) = 0.0d+00\nfjac(2,4,k) = u(2,i,j,k) * tmp1\nfjac(2,5,k) = 0.0d+00\n\nfjac(3,1,k) = - ( u(3,i,j,k)u(4,i,j,k) ) &\n& tmp2\nfjac(3,2,k) = 0.0d+00\nfjac(3,3,k) = u(4,i,j,k) * tmp1\nfjac(3,4,k) = u(3,i,j,k) * tmp1\nfjac(3,5,k) = 0.0d+00\n\nfjac(4,1,k) = - (u(4,i,j,k)u(4,i,j,k) tmp2 ) &\n& + c2 * qs(i,j,k)\nfjac(4,2,k) = - c2 * u(2,i,j,k) * tmp1\nfjac(4,3,k) = - c2 * u(3,i,j,k) * tmp1\nfjac(4,4,k) = ( 2.0d+00 - c2 ) &\n& * u(4,i,j,k) * tmp1\nfjac(4,5,k) = c2\n\nfjac(5,1,k) = ( c2 * 2.0d0 * square(i,j,k) &\n& - c1 * u(5,i,j,k) ) &\n& * u(4,i,j,k) * tmp2\nfjac(5,2,k) = - c2 * ( u(2,i,j,k)u(4,i,j,k) ) &\n& tmp2\nfjac(5,3,k) = - c2 * ( u(3,i,j,k)u(4,i,j,k) ) &\n& tmp2\nfjac(5,4,k) = c1 * ( u(5,i,j,k) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j,k) &\n& + u(4,i,j,k)u(4,i,j,k) tmp2 )\nfjac(5,5,k) = c1 * u(4,i,j,k) * tmp1\n\nnjac(1,1,k) = 0.0d+00\nnjac(1,2,k) = 0.0d+00\nnjac(1,3,k) = 0.0d+00\nnjac(1,4,k) = 0.0d+00\nnjac(1,5,k) = 0.0d+00\n\nnjac(2,1,k) = - c3c4 * tmp2 * u(2,i,j,k)\nnjac(2,2,k) = c3c4 * tmp1\nnjac(2,3,k) = 0.0d+00\nnjac(2,4,k) = 0.0d+00\nnjac(2,5,k) = 0.0d+00\n\nnjac(3,1,k) = - c3c4 * tmp2 * u(3,i,j,k)\nnjac(3,2,k) = 0.0d+00\nnjac(3,3,k) = c3c4 * tmp1\nnjac(3,4,k) = 0.0d+00\nnjac(3,5,k) = 0.0d+00\n\nnjac(4,1,k) = - con43 * c3c4 * tmp2 * u(4,i,j,k)\nnjac(4,2,k) = 0.0d+00\nnjac(4,3,k) = 0.0d+00\nnjac(4,4,k) = con43 * c3 * c4 * tmp1\nnjac(4,5,k) = 0.0d+00\n\nnjac(5,1,k) = - ( c3c4 &\n& - c1345 ) * tmp3 * (u(2,i,j,k)*2) &\n& - ( c3c4 - c1345 ) tmp3 * (u(3,i,j,k)*2) &\n& - ( con43 c3c4 &\n& - c1345 ) * tmp3 * (u(4,i,j,k)*2) &\n& - c1345 tmp2 * u(5,i,j,k)\n\nnjac(5,2,k) = ( c3c4 - c1345 ) * tmp2 * u(2,i,j,k)\nnjac(5,3,k) = ( c3c4 - c1345 ) * tmp2 * u(3,i,j,k)\nnjac(5,4,k) = ( con43 * c3c4 &\n& - c1345 ) * tmp2 * u(4,i,j,k)\nnjac(5,5,k) = ( c1345 )* tmp1\n\nenddo\n\ncall lhsinit(lhs, ksize)\ndo k = 1, ksize-1\n\ntmp1 = dt * tz1\ntmp2 = dt * tz2\n\nlhs(1,1,aa,k) = - tmp2 * fjac(1,1,k-1) &\n& - tmp1 * njac(1,1,k-1) &\n& - tmp1 * dz1\nlhs(1,2,aa,k) = - tmp2 * fjac(1,2,k-1) &\n& - tmp1 * njac(1,2,k-1)\nlhs(1,3,aa,k) = - tmp2 * fjac(1,3,k-1) &\n& - tmp1 * njac(1,3,k-1)\nlhs(1,4,aa,k) = - tmp2 * fjac(1,4,k-1) &\n& - tmp1 * njac(1,4,k-1)\nlhs(1,5,aa,k) = - tmp2 * fjac(1,5,k-1) &\n& - tmp1 * njac(1,5,k-1)\n\nlhs(2,1,aa,k) = - tmp2 * fjac(2,1,k-1) &\n& - tmp1 * njac(2,1,k-1)\nlhs(2,2,aa,k) = - tmp2 * fjac(2,2,k-1) &\n& - tmp1 * njac(2,2,k-1) &\n& - tmp1 * dz2\nlhs(2,3,aa,k) = - tmp2 * fjac(2,3,k-1) &\n& - tmp1 * njac(2,3,k-1)\nlhs(2,4,aa,k) = - tmp2 * fjac(2,4,k-1) &\n& - tmp1 * njac(2,4,k-1)\nlhs(2,5,aa,k) = - tmp2 * fjac(2,5,k-1) &\n& - tmp1 * njac(2,5,k-1)\n\nlhs(3,1,aa,k) = - tmp2 * fjac(3,1,k-1) &\n& - tmp1 * njac(3,1,k-1)\nlhs(3,2,aa,k) = - tmp2 * fjac(3,2,k-1) &\n& - tmp1 * njac(3,2,k-1)\nlhs(3,3,aa,k) = - tmp2 * fjac(3,3,k-1) &\n& - tmp1 * njac(3,3,k-1) &\n& - tmp1 * dz3\nlhs(3,4,aa,k) = - tmp2 * fjac(3,4,k-1) &\n& - tmp1 * njac(3,4,k-1)\nlhs(3,5,aa,k) = - tmp2 * fjac(3,5,k-1) &\n& - tmp1 * njac(3,5,k-1)\n\nlhs(4,1,aa,k) = - tmp2 * fjac(4,1,k-1) &\n& - tmp1 * njac(4,1,k-1)\nlhs(4,2,aa,k) = - tmp2 * fjac(4,2,k-1) &\n& - tmp1 * njac(4,2,k-1)\nlhs(4,3,aa,k) = - tmp2 * fjac(4,3,k-1) &\n& - tmp1 * njac(4,3,k-1)\nlhs(4,4,aa,k) = - tmp2 * fjac(4,4,k-1) &\n& - tmp1 * njac(4,4,k-1) &\n& - tmp1 * dz4\nlhs(4,5,aa,k) = - tmp2 * fjac(4,5,k-1) &\n& - tmp1 * njac(4,5,k-1)\n\nlhs(5,1,aa,k) = - tmp2 * fjac(5,1,k-1) &\n& - tmp1 * njac(5,1,k-1)\nlhs(5,2,aa,k) = - tmp2 * fjac(5,2,k-1) &\n& - tmp1 * njac(5,2,k-1)\nlhs(5,3,aa,k) = - tmp2 * fjac(5,3,k-1) &\n& - tmp1 * njac(5,3,k-1)\nlhs(5,4,aa,k) = - tmp2 * fjac(5,4,k-1) &\n& - tmp1 * njac(5,4,k-1)\nlhs(5,5,aa,k) = - tmp2 * fjac(5,5,k-1) &\n& - tmp1 * njac(5,5,k-1) &\n& - tmp1 * dz5\n\nlhs(1,1,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(1,1,k) &\n& + tmp1 * 2.0d+00 * dz1\nlhs(1,2,bb,k) = tmp1 * 2.0d+00 * njac(1,2,k)\nlhs(1,3,bb,k) = tmp1 * 2.0d+00 * njac(1,3,k)\nlhs(1,4,bb,k) = tmp1 * 2.0d+00 * njac(1,4,k)\nlhs(1,5,bb,k) = tmp1 * 2.0d+00 * njac(1,5,k)\n\nlhs(2,1,bb,k) = tmp1 * 2.0d+00 * njac(2,1,k)\nlhs(2,2,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(2,2,k) &\n& + tmp1 * 2.0d+00 * dz2\nlhs(2,3,bb,k) = tmp1 * 2.0d+00 * njac(2,3,k)\nlhs(2,4,bb,k) = tmp1 * 2.0d+00 * njac(2,4,k)\nlhs(2,5,bb,k) = tmp1 * 2.0d+00 * njac(2,5,k)\n\nlhs(3,1,bb,k) = tmp1 * 2.0d+00 * njac(3,1,k)\nlhs(3,2,bb,k) = tmp1 * 2.0d+00 * njac(3,2,k)\nlhs(3,3,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(3,3,k) &\n& + tmp1 * 2.0d+00 * dz3\nlhs(3,4,bb,k) = tmp1 * 2.0d+00 * njac(3,4,k)\nlhs(3,5,bb,k) = tmp1 * 2.0d+00 * njac(3,5,k)\n\nlhs(4,1,bb,k) = tmp1 * 2.0d+00 * njac(4,1,k)\nlhs(4,2,bb,k) = tmp1 * 2.0d+00 * njac(4,2,k)\nlhs(4,3,bb,k) = tmp1 * 2.0d+00 * njac(4,3,k)\nlhs(4,4,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(4,4,k) &\n& + tmp1 * 2.0d+00 * dz4\nlhs(4,5,bb,k) = tmp1 * 2.0d+00 * njac(4,5,k)\n\nlhs(5,1,bb,k) = tmp1 * 2.0d+00 * njac(5,1,k)\nlhs(5,2,bb,k) = tmp1 * 2.0d+00 * njac(5,2,k)\nlhs(5,3,bb,k) = tmp1 * 2.0d+00 * njac(5,3,k)\nlhs(5,4,bb,k) = tmp1 * 2.0d+00 * njac(5,4,k)\nlhs(5,5,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(5,5,k) &\n& + tmp1 * 2.0d+00 * dz5\n\nlhs(1,1,cc,k) = tmp2 * fjac(1,1,k+1) &\n& - tmp1 * njac(1,1,k+1) &\n& - tmp1 * dz1\nlhs(1,2,cc,k) = tmp2 * fjac(1,2,k+1) &\n& - tmp1 * njac(1,2,k+1)\nlhs(1,3,cc,k) = tmp2 * fjac(1,3,k+1) &\n& - tmp1 * njac(1,3,k+1)\nlhs(1,4,cc,k) = tmp2 * fjac(1,4,k+1) &\n& - tmp1 * njac(1,4,k+1)\nlhs(1,5,cc,k) = tmp2 * fjac(1,5,k+1) &\n& - tmp1 * njac(1,5,k+1)\n\nlhs(2,1,cc,k) = tmp2 * fjac(2,1,k+1) &\n& - tmp1 * njac(2,1,k+1)\nlhs(2,2,cc,k) = tmp2 * fjac(2,2,k+1) &\n& - tmp1 * njac(2,2,k+1) &\n& - tmp1 * dz2\nlhs(2,3,cc,k) = tmp2 * fjac(2,3,k+1) &\n& - tmp1 * njac(2,3,k+1)\nlhs(2,4,cc,k) = tmp2 * fjac(2,4,k+1) &\n& - tmp1 * njac(2,4,k+1)\nlhs(2,5,cc,k) = tmp2 * fjac(2,5,k+1) &\n& - tmp1 * njac(2,5,k+1)\n\nlhs(3,1,cc,k) = tmp2 * fjac(3,1,k+1) &\n& - tmp1 * njac(3,1,k+1)\nlhs(3,2,cc,k) = tmp2 * fjac(3,2,k+1) &\n& - tmp1 * njac(3,2,k+1)\nlhs(3,3,cc,k) = tmp2 * fjac(3,3,k+1) &\n& - tmp1 * njac(3,3,k+1) &\n& - tmp1 * dz3\nlhs(3,4,cc,k) = tmp2 * fjac(3,4,k+1) &\n& - tmp1 * njac(3,4,k+1)\nlhs(3,5,cc,k) = tmp2 * fjac(3,5,k+1) &\n& - tmp1 * njac(3,5,k+1)\n\nlhs(4,1,cc,k) = tmp2 * fjac(4,1,k+1) &\n& - tmp1 * njac(4,1,k+1)\nlhs(4,2,cc,k) = tmp2 * fjac(4,2,k+1) &\n& - tmp1 * njac(4,2,k+1)\nlhs(4,3,cc,k) = tmp2 * fjac(4,3,k+1) &\n& - tmp1 * njac(4,3,k+1)\nlhs(4,4,cc,k) = tmp2 * fjac(4,4,k+1) &\n& - tmp1 * njac(4,4,k+1) &\n& - tmp1 * dz4\nlhs(4,5,cc,k) = tmp2 * fjac(4,5,k+1) &\n& - tmp1 * njac(4,5,k+1)\n\nlhs(5,1,cc,k) = tmp2 * fjac(5,1,k+1) &\n& - tmp1 * njac(5,1,k+1)\nlhs(5,2,cc,k) = tmp2 * fjac(5,2,k+1) &\n& - tmp1 * njac(5,2,k+1)\nlhs(5,3,cc,k) = tmp2 * fjac(5,3,k+1) &\n& - tmp1 * njac(5,3,k+1)\nlhs(5,4,cc,k) = tmp2 * fjac(5,4,k+1) &\n& - tmp1 * njac(5,4,k+1)\nlhs(5,5,cc,k) = tmp2 * fjac(5,5,k+1) &\n& - tmp1 * njac(5,5,k+1) &\n& - tmp1 * dz5\n\nenddo\n\n\n\n\nif (timeron) call timer_start(t_solsub)\ncall binvcrhs( lhs(1,1,bb,0), &\n& lhs(1,1,cc,0), &\n& rhs(1,i,j,0) )\n\n\ndo k=1,ksize-1\n\ncall matvec_sub(lhs(1,1,aa,k), &\n& rhs(1,i,j,k-1),rhs(1,i,j,k))\n\ncall matmul_sub(lhs(1,1,aa,k), &\n& lhs(1,1,cc,k-1), &\n& lhs(1,1,bb,k))\n\ncall binvcrhs( lhs(1,1,bb,k), &\n& lhs(1,1,cc,k), &\n& rhs(1,i,j,k) )\n\nenddo\n\n\ncall matvec_sub(lhs(1,1,aa,ksize), &\n& rhs(1,i,j,ksize-1),rhs(1,i,j,ksize))\n\ncall matmul_sub(lhs(1,1,aa,ksize), &\n& lhs(1,1,cc,ksize-1), &\n& lhs(1,1,bb,ksize))\n\ncall binvrhs( lhs(1,1,bb,ksize), &\n& rhs(1,i,j,ksize) )\nif (timeron) call timer_stop(t_solsub)\n\n\n\n\ndo k=ksize-1,0,-1\ndo m=1,BLOCK_SIZE\ndo n=1,BLOCK_SIZE\nrhs(m,i,j,k) = rhs(m,i,j,k) &\n& - lhs(m,n,cc,k)*rhs(n,i,j,k+1)\nenddo\nenddo\nenddo\n\nenddo\nenddo\nif (timeron) call timer_stop(t_zsolve)\n\nreturn\nend
static void cfftz(int is,\nint m,\nint n,\ndcomplex x[][FFTBLOCKPAD],\ndcomplex y[][FFTBLOCKPAD]){\nint i,j,l,mx;\n\n\nmx = (int)(u[0].real);\nif((is != 1 && is != -1) \|\| m < 1 \|\| m > mx){\nprintf("CFFTZ: Either U has not been initialized, or else\n"\n"one of the input parameters is invalid%5d%5d%5d\n", is, m, mx);\nexit(EXIT_FAILURE);\n}\n\n\nfor(l=1; l<=m; l+=2){\nfftz2(is, l, m, n, FFTBLOCK, FFTBLOCKPAD, u, x, y);\nif(l==m){\n\nfor(j=0; j<n; j++){\nfor(i=0; i<FFTBLOCK; i++){\nx[j][i] = y[j][i];\n}\n}\nbreak;\n}\nfftz2(is, l + 1, m, n, FFTBLOCK, FFTBLOCKPAD, u, y, x);\n}\n}	subroutine cfftz (is, m, n, x, y)\n\n\n\nuse ft_data\nimplicit none\n\ninteger is,m,n,i,j,l,mx\ndouble complex x, y\n\ndimension x(fftblockpad,n), y(fftblockpad,n)\n\nmx = u(1)\nif ((is .ne. 1 .and. is .ne. -1) .or. m .lt. 1 .or. m .gt. mx) &\n& then\nwrite (*, 1) is, m, mx\n1 format ('CFFTZ: Either U has not been initialized, or else'/ &\n& 'one of the input parameters is invalid', 3I5)\nstop\nendif\n\ndo l = 1, m, 2\ncall fftz2 (is, l, m, n, fftblock, fftblockpad, u, x, y)\nif (l .eq. m) goto 160\ncall fftz2 (is, l + 1, m, n, fftblock, fftblockpad, u, y, x)\nenddo\n\ngoto 180\n\n160 do j = 1, n\ndo i = 1, fftblock\nx(i,j) = y(i,j)\nenddo\nenddo\n\n180 continue\n\nreturn\nend
void verify(double xcr[],\ndouble xce[],\ndouble xci,\nchar* class_npb,\nboolean* verified){\ndouble xcrref[5], xceref[5], xciref;\ndouble xcrdif[5], xcedif[5], xcidif;\ndouble epsilon, dtref=0.0;\nint m;\n\nepsilon=1.0e-08;\nclass_npb='U';\nverified=TRUE;\nfor(m=0; m<5; m++){\nxcrref[m]=1.0;\nxceref[m]=1.0;\n}\nxciref=1.0;\nif((nx0==12)&&(ny0==12)&&(nz0==12)&&(itmax==50)){\nclass_npb='S';\ndtref=5.0e-1;\n\nxcrref[0]=1.6196343210976702e-02;\nxcrref[1]=2.1976745164821318e-03;\nxcrref[2]=1.5179927653399185e-03;\nxcrref[3]=1.5029584435994323e-03;\nxcrref[4]=3.4264073155896461e-02;\n\nxceref[0]=6.4223319957960924e-04;\nxceref[1]=8.4144342047347926e-05;\nxceref[2]=5.8588269616485186e-05;\nxceref[3]=5.8474222595157350e-05;\nxceref[4]=1.3103347914111294e-03;\n\nxciref=7.8418928865937083e+00;\n}else if((nx0==33)&&(ny0==33)&&(nz0==33)&&(itmax==300)){\nclass_npb='W'; \ndtref=1.5e-3;\n\nxcrref[0]=0.1236511638192e+02;\nxcrref[1]=0.1317228477799e+01;\nxcrref[2]=0.2550120713095e+01;\nxcrref[3]=0.2326187750252e+01;\nxcrref[4]=0.2826799444189e+02;\n\nxceref[0]=0.4867877144216e+00;\nxceref[1]=0.5064652880982e-01;\nxceref[2]=0.9281818101960e-01;\nxceref[3]=0.8570126542733e-01;\nxceref[4]=0.1084277417792e+01;\n\nxciref=0.1161399311023e+02;\n}else if((nx0==64)&&(ny0==64)&&(nz0==64)&&(itmax==250)){\nclass_npb='A';\ndtref=2.0e+0;\n\nxcrref[0]=7.7902107606689367e+02;\nxcrref[1]=6.3402765259692870e+01;\nxcrref[2]=1.9499249727292479e+02;\nxcrref[3]=1.7845301160418537e+02;\nxcrref[4]=1.8384760349464247e+03;\n\nxceref[0]=2.9964085685471943e+01;\nxceref[1]=2.8194576365003349e+00;\nxceref[2]=7.3473412698774742e+00;\nxceref[3]=6.7139225687777051e+00;\nxceref[4]=7.0715315688392578e+01;\n\nxciref=2.6030925604886277e+01;\n}else if((nx0==102)&&(ny0==102)&&(nz0==102)&&(itmax==250)){\nclass_npb='B';\ndtref=2.0e+0;\n\nxcrref[0]=3.5532672969982736e+03;\nxcrref[1]=2.6214750795310692e+02;\nxcrref[2]=8.8333721850952190e+02;\nxcrref[3]=7.7812774739425265e+02;\nxcrref[4]=7.3087969592545314e+03;\n\nxceref[0]=1.1401176380212709e+02;\nxceref[1]=8.1098963655421574e+00;\nxceref[2]=2.8480597317698308e+01;\nxceref[3]=2.5905394567832939e+01;\nxceref[4]=2.6054907504857413e+02;\n\nxciref=4.7887162703308227e+01;\n}else if((nx0==162)&&(ny0==162)&&(nz0==162)&&(itmax==250)){\nclass_npb='C';\ndtref=2.0e+0;\n\nxcrref[0]=1.03766980323537846e+04;\nxcrref[1]=8.92212458801008552e+02;\nxcrref[2]=2.56238814582660871e+03;\nxcrref[3]=2.19194343857831427e+03;\nxcrref[4]=1.78078057261061185e+04;\n\nxceref[0]=2.15986399716949279e+02;\nxceref[1]=1.55789559239863600e+01;\nxceref[2]=5.41318863077207766e+01;\nxceref[3]=4.82262643154045421e+01;\nxceref[4]=4.55902910043250358e+02;\n\nxciref=6.66404553572181300e+01;\n\nxciref=6.66404553572181300e+01;\n}else if((nx0==408)&&(ny0==408)&&(nz0==408)&&(itmax== 300)){\nclass_npb='D';\ndtref=1.0e+0;\n\nxcrref[0]=0.4868417937025e+05;\nxcrref[1]=0.4696371050071e+04;\nxcrref[2]=0.1218114549776e+05;\nxcrref[3]=0.1033801493461e+05;\nxcrref[4]=0.7142398413817e+05;\n\nxceref[0]=0.3752393004482e+03;\nxceref[1]=0.3084128893659e+02;\nxceref[2]=0.9434276905469e+02;\nxceref[3]=0.8230686681928e+02;\nxceref[4]=0.7002620636210e+03;\n\nxciref=0.8334101392503e+02;\n}else if((nx0==1020)&&(ny0==1020)&&(nz0==1020)&&(itmax==300)){\nclass_npb='E';\ndtref=0.5e+0;\n\nxcrref[0]=0.2099641687874e+06;\nxcrref[1]=0.2130403143165e+05;\nxcrref[2]=0.5319228789371e+05;\nxcrref[3]=0.4509761639833e+05;\nxcrref[4]=0.2932360006590e+06;\n\nxceref[0]=0.4800572578333e+03;\nxceref[1]=0.4221993400184e+02;\nxceref[2]=0.1210851906824e+03;\nxceref[3]=0.1047888986770e+03;\nxceref[4]=0.8363028257389e+03;\n\nxciref=0.9512163272273e+02;\n}else{\nverified=FALSE;\n}\n\nfor(m=0; m<5; m++){\nxcrdif[m]=fabs((xcr[m]-xcrref[m])/xcrref[m]);\nxcedif[m]=fabs((xce[m]-xceref[m])/xceref[m]);\n}\nxcidif=fabs((xci-xciref)/xciref);\n\nif(class_npb!='U'){\nprintf("\nVerification being performed for class_npb %c\n",class_npb);\nprintf(" Accuracy setting for epsilon = %20.13E\n",epsilon);\nverified=(fabs(dt-dtref)<=epsilon);\nif(!(verified)){\nclass_npb='U';\nprintf(" DT does not match the reference value of %15.8E\n",dtref);\n}\n}else{\nprintf(" Unknown class_npb\n");\n}\nif(class_npb!='U'){\nprintf(" Comparison of RMS-norms of residual\n");\n}else{\nprintf(" RMS-norms of residual\n");\n}\nfor(m=0; m<5; m++){\nif(class_npb=='U'){\nprintf(" %2d %20.13E\n",m+1,xcr[m]);\n}else if(xcrdif[m]<=epsilon){\nprintf(" %2d %20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}else{\nverified=FALSE;\nprintf(" FAILURE: %2d %20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}\n}\nif(class_npb!='U'){\nprintf(" Comparison of RMS-norms of solution error\n");\n}else{\nprintf(" RMS-norms of solution error\n");\n}\nfor(m=0; m<5; m++){\nif(class_npb=='U'){\nprintf(" %2d %20.13E\n",m+1,xce[m]);\n}else if(xcedif[m]<=epsilon){\nprintf(" %2d %20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}else{\nverified=FALSE;\nprintf(" FAILURE: %2d %20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}\n}\nif(class_npb!='U'){\nprintf(" Comparison of surface integral\n");\n}else{\nprintf(" Surface integral\n");\n}\nif(class_npb=='U'){\nprintf(" %20.13E\n",xci);\n}else if(xcidif<=epsilon){\nprintf(" %20.13E%20.13E%20.13E\n",xci,xciref,xcidif);\n}else{\nverified=FALSE;\nprintf(" FAILURE: %20.13E%20.13E%20.13E\n",xci,xciref,xcidif);\n}\nif(class_npb=='U'){\nprintf(" No reference values provided\n");\nprintf("No verification performed\n");\n}else if(verified){\nprintf(" Verification Successful\n");\n}else{\nprintf(" Verification failed\n");\n}\n}	subroutine verify(xcr, xce, xci, class, verified)\n\n\n\nuse, intrinsic :: ieee_arithmetic, only : ieee_is_nan\n\nuse lu_data\n\nimplicit none\n\ndouble precision xcr(5), xce(5), xci\ndouble precision xcrref(5),xceref(5),xciref, &\n& xcrdif(5),xcedif(5),xcidif, &\n& epsilon, dtref\ninteger m\ncharacter class\nlogical verified\n\nepsilon = 1.0d-08\n\nclass = 'U'\nverified = .true.\n\ndo m = 1,5\nxcrref(m) = 1.0\nxceref(m) = 1.0\nend do\nxciref = 1.0\n\nif ( (nx0 .eq. 12 ) .and. &\n& (ny0 .eq. 12 ) .and. &\n& (nz0 .eq. 12 ) .and. &\n& (itmax .eq. 50 )) then\n\nclass = 'S'\ndtref = 5.0d-1\nxcrref(1) = 1.6196343210976702d-02\nxcrref(2) = 2.1976745164821318d-03\nxcrref(3) = 1.5179927653399185d-03\nxcrref(4) = 1.5029584435994323d-03\nxcrref(5) = 3.4264073155896461d-02\n\nxceref(1) = 6.4223319957960924d-04\nxceref(2) = 8.4144342047347926d-05\nxceref(3) = 5.8588269616485186d-05\nxceref(4) = 5.8474222595157350d-05\nxceref(5) = 1.3103347914111294d-03\n\nxciref = 7.8418928865937083d+00\n\n\nelseif ( (nx0 .eq. 33) .and. &\n& (ny0 .eq. 33) .and. &\n& (nz0 .eq. 33) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'W' !SPEC95fp size\ndtref = 1.5d-3\nxcrref(1) = 0.1236511638192d+02\nxcrref(2) = 0.1317228477799d+01\nxcrref(3) = 0.2550120713095d+01\nxcrref(4) = 0.2326187750252d+01\nxcrref(5) = 0.2826799444189d+02\n\n\nxceref(1) = 0.4867877144216d+00\nxceref(2) = 0.5064652880982d-01\nxceref(3) = 0.9281818101960d-01\nxceref(4) = 0.8570126542733d-01\nxceref(5) = 0.1084277417792d+01\n\n\nxciref = 0.1161399311023d+02\n\nelseif ( (nx0 .eq. 64) .and. &\n& (ny0 .eq. 64) .and. &\n& (nz0 .eq. 64) .and. &\n& (itmax .eq. 250) ) then\n\nclass = 'A'\ndtref = 2.0d+0\nxcrref(1) = 7.7902107606689367d+02\nxcrref(2) = 6.3402765259692870d+01\nxcrref(3) = 1.9499249727292479d+02\nxcrref(4) = 1.7845301160418537d+02\nxcrref(5) = 1.8384760349464247d+03\n\nxceref(1) = 2.9964085685471943d+01\nxceref(2) = 2.8194576365003349d+00\nxceref(3) = 7.3473412698774742d+00\nxceref(4) = 6.7139225687777051d+00\nxceref(5) = 7.0715315688392578d+01\n\nxciref = 2.6030925604886277d+01\n\n\nelseif ( (nx0 .eq. 102) .and. &\n& (ny0 .eq. 102) .and. &\n& (nz0 .eq. 102) .and. &\n& (itmax .eq. 250) ) then\n\nclass = 'B'\ndtref = 2.0d+0\n\nxcrref(1) = 3.5532672969982736d+03\nxcrref(2) = 2.6214750795310692d+02\nxcrref(3) = 8.8333721850952190d+02\nxcrref(4) = 7.7812774739425265d+02\nxcrref(5) = 7.3087969592545314d+03\n\nxceref(1) = 1.1401176380212709d+02\nxceref(2) = 8.1098963655421574d+00\nxceref(3) = 2.8480597317698308d+01\nxceref(4) = 2.5905394567832939d+01\nxceref(5) = 2.6054907504857413d+02\n\nxciref = 4.7887162703308227d+01\n\nelseif ( (nx0 .eq. 162) .and. &\n& (ny0 .eq. 162) .and. &\n& (nz0 .eq. 162) .and. &\n& (itmax .eq. 250) ) then\n\nclass = 'C'\ndtref = 2.0d+0\n\nxcrref(1) = 1.03766980323537846d+04\nxcrref(2) = 8.92212458801008552d+02\nxcrref(3) = 2.56238814582660871d+03\nxcrref(4) = 2.19194343857831427d+03\nxcrref(5) = 1.78078057261061185d+04\n\nxceref(1) = 2.15986399716949279d+02\nxceref(2) = 1.55789559239863600d+01\nxceref(3) = 5.41318863077207766d+01\nxceref(4) = 4.82262643154045421d+01\nxceref(5) = 4.55902910043250358d+02\n\nxciref = 6.66404553572181300d+01\n\nxciref = 6.66404553572181300d+01\n\nelseif ( (nx0 .eq. 408) .and. &\n& (ny0 .eq. 408) .and. &\n& (nz0 .eq. 408) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'D'\ndtref = 1.0d+0\n\nxcrref(1) = 0.4868417937025d+05\nxcrref(2) = 0.4696371050071d+04\nxcrref(3) = 0.1218114549776d+05\nxcrref(4) = 0.1033801493461d+05\nxcrref(5) = 0.7142398413817d+05\n\nxceref(1) = 0.3752393004482d+03\nxceref(2) = 0.3084128893659d+02\nxceref(3) = 0.9434276905469d+02\nxceref(4) = 0.8230686681928d+02\nxceref(5) = 0.7002620636210d+03\n\nxciref = 0.8334101392503d+02\n\nelseif ( (nx0 .eq. 1020) .and. &\n& (ny0 .eq. 1020) .and. &\n& (nz0 .eq. 1020) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'E'\ndtref = 0.5d+0\n\nxcrref(1) = 0.2099641687874d+06\nxcrref(2) = 0.2130403143165d+05\nxcrref(3) = 0.5319228789371d+05\nxcrref(4) = 0.4509761639833d+05\nxcrref(5) = 0.2932360006590d+06\n\nxceref(1) = 0.4800572578333d+03\nxceref(2) = 0.4221993400184d+02\nxceref(3) = 0.1210851906824d+03\nxceref(4) = 0.1047888986770d+03\nxceref(5) = 0.8363028257389d+03\n\nxciref = 0.9512163272273d+02\n\nelseif ( (nx0 .eq. 2560) .and. &\n& (ny0 .eq. 2560) .and. &\n& (nz0 .eq. 2560) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'F'\ndtref = 0.2d+0\n\nxcrref(1) = 0.8505125358152d+06\nxcrref(2) = 0.8774655318044d+05\nxcrref(3) = 0.2167258198851d+06\nxcrref(4) = 0.1838245257371d+06\nxcrref(5) = 0.1175556512415d+07\n\nxceref(1) = 0.5293914132486d+03\nxceref(2) = 0.4784861621068d+02\nxceref(3) = 0.1337701281659d+03\nxceref(4) = 0.1154215049655d+03\nxceref(5) = 0.8956266851467d+03\n\nxciref = 0.1002509436546d+03\n\nelse\nverified = .FALSE.\nendif\n\n\ndo m = 1, 5\n\nxcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))\nxcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))\n\nenddo\nxcidif = dabs((xci - xciref)/xciref)\n\n\n\nif (class .ne. 'U') then\nwrite(, 1990) class\n1990 format(/, ' Verification being performed for class ', a)\nwrite (,2000) epsilon\n2000 format(' Accuracy setting for epsilon = ', E20.13)\nverified = (dabs(dt-dtref) .le. epsilon)\nif (.not.verified) then\nclass = 'U'\nwrite (,1000) dtref\n1000 format(' DT does not match the reference value of ', &\n& E15.8)\nendif\nelse\nwrite(, 1995)\n1995 format(' Unknown class')\nendif\n\n\nif (class .ne. 'U') then\nwrite (, 2001)\nelse\nwrite (, 2005)\nendif\n\n2001 format(' Comparison of RMS-norms of residual')\n2005 format(' RMS-norms of residual')\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(, 2015) m, xcr(m)\nelse if ((.not.ieee_is_nan(xcrdif(m))) .and. &\n& xcrdif(m) .le. epsilon) then\nwrite (,2011) m,xcr(m),xcrref(m),xcrdif(m)\nelse\nverified = .false.\nwrite (,2010) m,xcr(m),xcrref(m),xcrdif(m)\nendif\nenddo\n\nif (class .ne. 'U') then\nwrite (,2002)\nelse\nwrite (,2006)\nendif\n2002 format(' Comparison of RMS-norms of solution error')\n2006 format(' RMS-norms of solution error')\n\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(, 2015) m, xce(m)\nelse if ((.not.ieee_is_nan(xcedif(m))) .and. &\n& xcedif(m) .le. epsilon) then\nwrite (,2011) m,xce(m),xceref(m),xcedif(m)\nelse\nverified = .false.\nwrite (,2010) m,xce(m),xceref(m),xcedif(m)\nendif\nenddo\n\n2010 format(' FAILURE: ', i2, 2x, E20.13, E20.13, E20.13)\n2011 format(' ', i2, 2x, E20.13, E20.13, E20.13)\n2015 format(' ', i2, 2x, E20.13)\n\nif (class .ne. 'U') then\nwrite (,2025)\nelse\nwrite (,2026)\nendif\n2025 format(' Comparison of surface integral')\n2026 format(' Surface integral')\n\n\nif (class .eq. 'U') then\nwrite(, 2030) xci\nelse if ((.not.ieee_is_nan(xcidif)) .and. &\n& xcidif .le. epsilon) then\nwrite(, 2032) xci, xciref, xcidif\nelse\nverified = .false.\nwrite(, 2031) xci, xciref, xcidif\nendif\n\n2030 format(' ', 4x, E20.13)\n2031 format(' FAILURE: ', 4x, E20.13, E20.13, E20.13)\n2032 format(' ', 4x, E20.13, E20.13, E20.13)\n\n\n\nif (class .eq. 'U') then\nwrite(, 2022)\nwrite(, 2023)\n2022 format(' No reference values provided')\n2023 format(' No verification performed')\nelse if (verified) then\nwrite(, 2020)\n2020 format(' Verification Successful')\nelse\nwrite(*, 2021)\n2021 format(' Verification failed')\nendif\n\nreturn\n\n\nend
static void ipow46(double a,\nint exponent,\ndouble* result){\ndouble q, r;\nint n, n2;\n\n\nresult = 1;\nif(exponent==0){return;}\nq = a;\nr = 1;\nn = exponent;\n\nwhile(n > 1){\nn2 = n/2;\nif(n22==n){\nrandlc(&q, q);\nn = n2;\n}else{\nrandlc(&r, q);\nn = n-1;\n}\n}\nrandlc(&r, q);\nresult = r;\n}\n\nstatic void print_timers(){\nint i;\ndouble t, t_m;\nchar tstrings[T_MAX+1];\ntstrings[1] = (char)" total ";\ntstrings[2] = (char)" setup ";\ntstrings[3] = (char)" fft ";\ntstrings[4] = (char)" evolve ";\ntstrings[5] = (char)" checksum ";\ntstrings[6] = (char)" fftx ";\ntstrings[7] = (char)" ffty ";\ntstrings[8] = (char)" fftz ";\n\nt_m = timer_read(T_TOTAL);\nif(t_m <= 0.0){t_m = 1.00;}\nfor(i = 1; i <= T_MAX; i++){\nt = timer_read(i);\nprintf(" timer %2d(%16s) :%9.4f (%6.2f%%)\n",\ni, tstrings[i], t, t100.0/t_m);\n}\n}\n\nstatic void setup(){\nFILE fp;\ndebug = FALSE;\n\nif((fp = fopen("timer.flag", "r")) != NULL){\ntimers_enabled = TRUE;\nfclose(fp);\n}else{\ntimers_enabled = FALSE;\n}\n\nniter = NITER_DEFAULT;\n\nprintf("\n\nNAS Parallel Benchmarks 4.1 Parallel C++ version with OpenMP - FT Benchmark\n\n");\nprintf(" Size : %4dx%4dx%4d\n", NX, NY, NZ);\nprintf(" Iterations :%7d\n", niter);\nprintf("\n");\n\ndims[0] = NX;\ndims[1] = NY;\ndims[2] = NZ;\n\n\n\n\n\n\n}	subroutine ipow46(a, exponent, result)\n\n\n\nimplicit none\ndouble precision a, result, dummy, q, r\ninteger exponent, n, n2\nexternal randlc\ndouble precision randlc\nresult = 1\nif (exponent .eq. 0) return\nq = a\nr = 1\nn = exponent\n\n\ndo while (n .gt. 1)\nn2 = n/2\nif (n2 * 2 .eq. n) then\ndummy = randlc(q, q)\nn = n2\nelse\ndummy = randlc(r, q)\nn = n-1\nendif\nend do\ndummy = randlc(r, q)\nresult = r\nreturn\nend
void jacld(int k){\n\nint i, j;\ndouble r43;\ndouble c1345;\ndouble c34;\ndouble tmp1, tmp2, tmp3;\nr43=(4.0/3.0);\nc1345=C1C3C4C5;\nc34=C3C4;\n\n#pragma omp for nowait schedule(static)\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\n\ntmp1=rho_i[k][j][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nd[j][i][0][0]=1.0+dt2.0(tx1dx1+ty1dy1+tz1dz1);\nd[j][i][1][0]=0.0;\nd[j][i][2][0]=0.0;\nd[j][i][3][0]=0.0;\nd[j][i][4][0]=0.0;\nd[j][i][0][1]=-dt2.0\n(tx1r43+ty1+tz1)c34tmp2u[k][j][i][1];\nd[j][i][1][1]=1.0\n+dt2.0c34tmp1(tx1r43+ty1+tz1)\n+dt2.0(tx1dx2+ty1dy2+tz1dz2);\nd[j][i][2][1]=0.0;\nd[j][i][3][1]=0.0;\nd[j][i][4][1]=0.0;\nd[j][i][0][2]=-dt2.0\n(tx1+ty1r43+tz1)c34tmp2u[k][j][i][2];\nd[j][i][1][2]=0.0;\nd[j][i][2][2]=1.0\n+dt2.0c34tmp1(tx1+ty1r43+tz1)\n+dt2.0(tx1dx3+ty1dy3+tz1dz3);\nd[j][i][3][2]=0.0;\nd[j][i][4][2]=0.0;\nd[j][i][0][3]=-dt2.0\n(tx1+ty1+tz1r43)c34tmp2u[k][j][i][3];\nd[j][i][1][3]=0.0;\nd[j][i][2][3]=0.0;\nd[j][i][3][3]=1.0\n+dt2.0c34tmp1(tx1+ty1+tz1r43)\n+dt2.0(tx1dx4+ty1dy4+tz1dz4);\nd[j][i][4][3]=0.0;\nd[j][i][0][4]=-dt2.0\n(((tx1(r43c34-c1345)\n+ty1(c34-c1345)\n+tz1(c34-c1345))(u[k][j][i][1]u[k][j][i][1])\n+(tx1(c34-c1345)\n+ty1(r43c34-c1345)\n+tz1(c34-c1345))(u[k][j][i][2]u[k][j][i][2])\n+(tx1(c34-c1345)\n+ty1(c34-c1345)\n+tz1(r43c34-c1345))(u[k][j][i][3]u[k][j][i][3])\n)tmp3\n+(tx1+ty1+tz1)c1345tmp2u[k][j][i][4]);\nd[j][i][1][4]=dt2.0tmp2u[k][j][i][1]\n(tx1(r43c34-c1345)\n+ty1(c34-c1345)\n+tz1(c34-c1345));\nd[j][i][2][4]=dt2.0tmp2u[k][j][i][2]\n(tx1(c34-c1345)\n+ty1(r43c34-c1345)\n+tz1(c34-c1345));\nd[j][i][3][4]=dt2.0tmp2u[k][j][i][3]\n(tx1(c34-c1345)\n+ty1(c34-c1345)\n+tz1(r43c34-c1345));\nd[j][i][4][4]=1.0\n+dt2.0(tx1+ty1+tz1)c1345tmp1\n+dt2.0(tx1dx5+ty1dy5+tz1dz5);\n\ntmp1=rho_i[k-1][j][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\na[j][i][0][0]=-dttz1dz1;\na[j][i][1][0]=0.0;\na[j][i][2][0]=0.0;\na[j][i][3][0]=-dttz2;\na[j][i][4][0]=0.0;\na[j][i][0][1]=-dttz2\n(-(u[k-1][j][i][1]u[k-1][j][i][3])tmp2)\n-dttz1(-c34tmp2u[k-1][j][i][1]);\na[j][i][1][1]=-dttz2(u[k-1][j][i][3]tmp1)\n-dttz1c34tmp1\n-dttz1dz2;\na[j][i][2][1]=0.0;\na[j][i][3][1]=-dttz2(u[k-1][j][i][1]tmp1);\na[j][i][4][1]=0.0;\na[j][i][0][2]=-dttz2\n(-(u[k-1][j][i][2]u[k-1][j][i][3])tmp2)\n-dttz1(-c34tmp2u[k-1][j][i][2]);\na[j][i][1][2]=0.0;\na[j][i][2][2]=-dttz2(u[k-1][j][i][3]tmp1)\n-dttz1(c34tmp1)\n-dttz1dz3;\na[j][i][3][2]=-dttz2(u[k-1][j][i][2]tmp1);\na[j][i][4][2]=0.0;\na[j][i][0][3]=-dttz2\n(-(u[k-1][j][i][3]tmp1)(u[k-1][j][i][3]tmp1)\n+C2qs[k-1][j][i]tmp1)\n-dttz1(-r43c34tmp2u[k-1][j][i][3]);\na[j][i][1][3]=-dttz2\n(-C2(u[k-1][j][i][1]tmp1));\na[j][i][2][3]=-dttz2\n(-C2(u[k-1][j][i][2]tmp1));\na[j][i][3][3]=-dttz2(2.0-C2)\n(u[k-1][j][i][3]tmp1)\n-dttz1(r43c34tmp1)\n-dttz1dz4;\na[j][i][4][3]=-dttz2C2;\na[j][i][0][4]=-dttz2\n((C22.0qs[k-1][j][i]-C1u[k-1][j][i][4])\nu[k-1][j][i][3]tmp2)\n-dttz1\n(-(c34-c1345)tmp3(u[k-1][j][i][1]u[k-1][j][i][1])\n-(c34-c1345)tmp3(u[k-1][j][i][2]u[k-1][j][i][2])\n-(r43c34-c1345)tmp3(u[k-1][j][i][3]u[k-1][j][i][3])\n-c1345tmp2u[k-1][j][i][4]);\na[j][i][1][4]=-dttz2\n(-C2(u[k-1][j][i][1]u[k-1][j][i][3])tmp2)\n-dttz1(c34-c1345)tmp2u[k-1][j][i][1];\na[j][i][2][4]=-dttz2\n(-C2(u[k-1][j][i][2]u[k-1][j][i][3])tmp2)\n-dttz1(c34-c1345)tmp2u[k-1][j][i][2];\na[j][i][3][4]=-dttz2\n(C1(u[k-1][j][i][4]tmp1)\n-C2(qs[k-1][j][i]tmp1\n+u[k-1][j][i][3]u[k-1][j][i][3]tmp2))\n-dttz1(r43c34-c1345)tmp2u[k-1][j][i][3];\na[j][i][4][4]=-dttz2\n(C1(u[k-1][j][i][3]tmp1))\n-dttz1c1345tmp1\n-dttz1dz5;\n\ntmp1=rho_i[k][j-1][i];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nb[j][i][0][0]=-dtty1dy1;\nb[j][i][1][0]=0.0;\nb[j][i][2][0]=-dtty2;\nb[j][i][3][0]=0.0;\nb[j][i][4][0]=0.0;\nb[j][i][0][1]=-dtty2\n(-(u[k][j-1][i][1]u[k][j-1][i][2])tmp2)\n-dtty1(-c34tmp2u[k][j-1][i][1]);\nb[j][i][1][1]=-dtty2(u[k][j-1][i][2]tmp1)\n-dtty1(c34tmp1)\n-dtty1dy2;\nb[j][i][2][1]=-dtty2(u[k][j-1][i][1]tmp1);\nb[j][i][3][1]=0.0;\nb[j][i][4][1]=0.0;\nb[j][i][0][2]=-dtty2\n(-(u[k][j-1][i][2]tmp1)(u[k][j-1][i][2]tmp1)\n+C2(qs[k][j-1][i]tmp1))\n-dtty1(-r43c34tmp2u[k][j-1][i][2]);\nb[j][i][1][2]=-dtty2\n(-C2(u[k][j-1][i][1]tmp1));\nb[j][i][2][2]=-dtty2((2.0-C2)(u[k][j-1][i][2]tmp1))\n-dtty1(r43c34tmp1)\n-dtty1dy3;\nb[j][i][3][2]=-dtty2(-C2(u[k][j-1][i][3]tmp1));\nb[j][i][4][2]=-dtty2C2;\nb[j][i][0][3]=-dtty2\n(-(u[k][j-1][i][2]u[k][j-1][i][3])tmp2)\n-dtty1(-c34tmp2u[k][j-1][i][3]);\nb[j][i][1][3]=0.0;\nb[j][i][2][3]=-dtty2(u[k][j-1][i][3]tmp1);\nb[j][i][3][3]=-dtty2(u[k][j-1][i][2]tmp1)\n-dtty1(c34tmp1)\n-dtty1dy4;\nb[j][i][4][3]=0.0;\nb[j][i][0][4]=-dtty2\n((C22.0qs[k][j-1][i]-C1u[k][j-1][i][4])\n(u[k][j-1][i][2]tmp2))\n-dtty1\n(-(c34-c1345)tmp3(u[k][j-1][i][1]u[k][j-1][i][1])\n-(r43c34-c1345)tmp3(u[k][j-1][i][2]u[k][j-1][i][2])\n-(c34-c1345)tmp3(u[k][j-1][i][3]u[k][j-1][i][3])\n-c1345tmp2u[k][j-1][i][4]);\nb[j][i][1][4]=-dtty2\n(-C2(u[k][j-1][i][1]u[k][j-1][i][2])tmp2)\n-dtty1(c34-c1345)tmp2u[k][j-1][i][1];\nb[j][i][2][4]=-dtty2\n(C1(u[k][j-1][i][4]tmp1)\n-C2(qs[k][j-1][i]tmp1\n+u[k][j-1][i][2]u[k][j-1][i][2]tmp2))\n-dtty1(r43c34-c1345)tmp2u[k][j-1][i][2];\nb[j][i][3][4]=-dtty2\n(-C2(u[k][j-1][i][2]u[k][j-1][i][3])tmp2)\n-dtty1(c34-c1345)tmp2u[k][j-1][i][3];\nb[j][i][4][4]=-dtty2\n(C1(u[k][j-1][i][2]tmp1))\n-dtty1c1345tmp1\n-dtty1dy5;\n\ntmp1=rho_i[k][j][i-1];\ntmp2=tmp1tmp1;\ntmp3=tmp1tmp2;\nc[j][i][0][0]=-dttx1dx1;\nc[j][i][1][0]=-dttx2;\nc[j][i][2][0]=0.0;\nc[j][i][3][0]=0.0;\nc[j][i][4][0]=0.0;\nc[j][i][0][1]=-dttx2\n(-(u[k][j][i-1][1]tmp1)(u[k][j][i-1][1]tmp1)\n+C2qs[k][j][i-1]tmp1)\n-dttx1(-r43c34tmp2u[k][j][i-1][1]);\nc[j][i][1][1]=-dttx2\n((2.0-C2)(u[k][j][i-1][1]tmp1))\n-dttx1(r43c34tmp1)\n-dttx1dx2;\nc[j][i][2][1]=-dttx2\n(-C2(u[k][j][i-1][2]tmp1));\nc[j][i][3][1]=-dttx2\n(-C2(u[k][j][i-1][3]tmp1));\nc[j][i][4][1]=-dttx2C2;\nc[j][i][0][2]=-dttx2\n(-(u[k][j][i-1][1]u[k][j][i-1][2])tmp2)\n-dttx1(-c34tmp2u[k][j][i-1][2]);\nc[j][i][1][2]=-dttx2(u[k][j][i-1][2]tmp1);\nc[j][i][2][2]=-dttx2(u[k][j][i-1][1]tmp1)\n-dttx1(c34tmp1)\n-dttx1dx3;\nc[j][i][3][2]=0.0;\nc[j][i][4][2]=0.0;\nc[j][i][0][3]=-dttx2\n(-(u[k][j][i-1][1]u[k][j][i-1][3])tmp2)\n-dttx1(-c34tmp2u[k][j][i-1][3]);\nc[j][i][1][3]=-dttx2(u[k][j][i-1][3]tmp1);\nc[j][i][2][3]=0.0;\nc[j][i][3][3]=-dttx2(u[k][j][i-1][1]tmp1)\n-dttx1(c34tmp1)-dttx1dx4;\nc[j][i][4][3]=0.0;\nc[j][i][0][4]=-dttx2\n((C22.0qs[k][j][i-1]-C1u[k][j][i-1][4])\nu[k][j][i-1][1]tmp2)\n-dttx1\n(-(r43c34-c1345)tmp3(u[k][j][i-1][1]u[k][j][i-1][1])\n-(c34-c1345)tmp3(u[k][j][i-1][2]u[k][j][i-1][2])\n-(c34-c1345)tmp3(u[k][j][i-1][3]u[k][j][i-1][3])\n-c1345tmp2u[k][j][i-1][4]);\nc[j][i][1][4]=-dttx2\n(C1(u[k][j][i-1][4]tmp1)\n-C2(u[k][j][i-1][1]u[k][j][i-1][1]tmp2\n+qs[k][j][i-1]tmp1))\n-dttx1(r43c34-c1345)tmp2u[k][j][i-1][1];\nc[j][i][2][4]=-dttx2\n(-C2(u[k][j][i-1][2]u[k][j][i-1][1])tmp2)\n-dttx1(c34-c1345)tmp2u[k][j][i-1][2];\nc[j][i][3][4]=-dttx2\n(-C2(u[k][j][i-1][3]u[k][j][i-1][1])tmp2)\n-dttx1(c34-c1345)tmp2u[k][j][i-1][3];\nc[j][i][4][4]=-dttx2\n(C1(u[k][j][i-1][1]tmp1))\n-dttx1c1345tmp1\n-dttx1dx5;\n}\n}\n}	subroutine jacld(j, k)\n\n\n\n\nuse lu_data\nimplicit none\n\ninteger j, k\n\ninteger i\ndouble precision r43\ndouble precision c1345\ndouble precision c34\ndouble precision tmp1, tmp2, tmp3\n\n\n\nr43 = ( 4.0d+00 / 3.0d+00 )\nc1345 = c1 * c3 * c4 * c5\nc34 = c3 * c4\n\ndo i = ist, iend\n\ntmp1 = rho_i(i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nd(1,1,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 * dx1 &\n& + ty1 * dy1 &\n& + tz1 * dz1 )\nd(1,2,i) = 0.0d+00\nd(1,3,i) = 0.0d+00\nd(1,4,i) = 0.0d+00\nd(1,5,i) = 0.0d+00\n\nd(2,1,i) = -dt * 2.0d+00 &\n& * ( tx1 * r43 + ty1 + tz1 ) &\n& * c34 * tmp2 * u(2,i,j,k)\nd(2,2,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 * r43 + ty1 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx2 &\n& + ty1 * dy2 &\n& + tz1 * dz2 )\nd(2,3,i) = 0.0d+00\nd(2,4,i) = 0.0d+00\nd(2,5,i) = 0.0d+00\n\nd(3,1,i) = -dt * 2.0d+00 &\n& * ( tx1 + ty1 * r43 + tz1 ) &\n& * c34 * tmp2 * u(3,i,j,k)\nd(3,2,i) = 0.0d+00\nd(3,3,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 * r43 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx3 &\n& + ty1 * dy3 &\n& + tz1 * dz3 )\nd(3,4,i) = 0.0d+00\nd(3,5,i) = 0.0d+00\n\nd(4,1,i) = -dt * 2.0d+00 &\n& * ( tx1 + ty1 + tz1 * r43 ) &\n& * c34 * tmp2 * u(4,i,j,k)\nd(4,2,i) = 0.0d+00\nd(4,3,i) = 0.0d+00\nd(4,4,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 + tz1 * r43 ) &\n& + dt * 2.0d+00 * ( tx1 * dx4 &\n& + ty1 * dy4 &\n& + tz1 * dz4 )\nd(4,5,i) = 0.0d+00\n\nd(5,1,i) = -dt * 2.0d+00 &\n& * ( ( ( tx1 * ( r43c34 - c1345 ) &\n& + ty1 ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * ( u(2,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43c34 - c1345 ) &\n& + tz1 ( c34 - c1345 ) ) * ( u(3,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43c34 - c1345 ) ) ( u(4,i,j,k) ** 2 ) &\n& ) * tmp3 &\n& + ( tx1 + ty1 + tz1 ) * c1345 * tmp2 * u(5,i,j,k) )\n\nd(5,2,i) = dt * 2.0d+00 * tmp2 * u(2,i,j,k) &\n& * ( tx1 * ( r43c34 - c1345 ) &\n& + ty1 ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) )\nd(5,3,i) = dt * 2.0d+00 * tmp2 * u(3,i,j,k) &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43c34 -c1345 ) &\n& + tz1 ( c34 - c1345 ) )\nd(5,4,i) = dt * 2.0d+00 * tmp2 * u(4,i,j,k) &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43c34 - c1345 ) )\nd(5,5,i) = 1.0d+00 &\n& + dt 2.0d+00 * ( tx1 + ty1 + tz1 ) * c1345 * tmp1 &\n& + dt * 2.0d+00 * ( tx1 * dx5 &\n& + ty1 * dy5 &\n& + tz1 * dz5 )\n\ntmp1 = rho_i(i,j,k-1)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\na(1,1,i) = - dt * tz1 * dz1\na(1,2,i) = 0.0d+00\na(1,3,i) = 0.0d+00\na(1,4,i) = - dt * tz2\na(1,5,i) = 0.0d+00\n\na(2,1,i) = - dt * tz2 &\n& * ( - ( u(2,i,j,k-1)u(4,i,j,k-1) ) tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(2,i,j,k-1) )\na(2,2,i) = - dt * tz2 * ( u(4,i,j,k-1) * tmp1 ) &\n& - dt * tz1 * c34 * tmp1 &\n& - dt * tz1 * dz2\na(2,3,i) = 0.0d+00\na(2,4,i) = - dt * tz2 * ( u(2,i,j,k-1) * tmp1 )\na(2,5,i) = 0.0d+00\n\na(3,1,i) = - dt * tz2 &\n& * ( - ( u(3,i,j,k-1)u(4,i,j,k-1) ) tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(3,i,j,k-1) )\na(3,2,i) = 0.0d+00\na(3,3,i) = - dt * tz2 * ( u(4,i,j,k-1) * tmp1 ) &\n& - dt * tz1 * ( c34 * tmp1 ) &\n& - dt * tz1 * dz3\na(3,4,i) = - dt * tz2 * ( u(3,i,j,k-1) * tmp1 )\na(3,5,i) = 0.0d+00\n\na(4,1,i) = - dt * tz2 &\n& * ( - ( u(4,i,j,k-1) * tmp1 ) ** 2 &\n& + c2 * qs(i,j,k-1) * tmp1 ) &\n& - dt * tz1 * ( - r43 * c34 * tmp2 * u(4,i,j,k-1) )\na(4,2,i) = - dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k-1) * tmp1 ) )\na(4,3,i) = - dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k-1) * tmp1 ) )\na(4,4,i) = - dt * tz2 * ( 2.0d+00 - c2 ) &\n& * ( u(4,i,j,k-1) * tmp1 ) &\n& - dt * tz1 * ( r43 * c34 * tmp1 ) &\n& - dt * tz1 * dz4\na(4,5,i) = - dt * tz2 * c2\n\na(5,1,i) = - dt * tz2 &\n& * ( ( c2 * 2.0d0 * qs(i,j,k-1) &\n& - c1 * u(5,i,j,k-1) ) &\n& * u(4,i,j,k-1) * tmp2 ) &\n& - dt * tz1 &\n& * ( - ( c34 - c1345 ) * tmp3 * (u(2,i,j,k-1)*2) &\n& - ( c34 - c1345 ) tmp3 * (u(3,i,j,k-1)*2) &\n& - ( r43c34 - c1345 )* tmp3 * (u(4,i,j,k-1)*2) &\n& - c1345 tmp2 * u(5,i,j,k-1) )\na(5,2,i) = - dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k-1)u(4,i,j,k-1) ) tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(2,i,j,k-1)\na(5,3,i) = - dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k-1)u(4,i,j,k-1) ) tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(3,i,j,k-1)\na(5,4,i) = - dt * tz2 &\n& * ( c1 * ( u(5,i,j,k-1) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j,k-1) * tmp1 &\n& + u(4,i,j,k-1)u(4,i,j,k-1) tmp2 ) ) &\n& - dt * tz1 * ( r43c34 - c1345 ) tmp2 * u(4,i,j,k-1)\na(5,5,i) = - dt * tz2 &\n& * ( c1 * ( u(4,i,j,k-1) * tmp1 ) ) &\n& - dt * tz1 * c1345 * tmp1 &\n& - dt * tz1 * dz5\n\ntmp1 = rho_i(i,j-1,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nb(1,1,i) = - dt * ty1 * dy1\nb(1,2,i) = 0.0d+00\nb(1,3,i) = - dt * ty2\nb(1,4,i) = 0.0d+00\nb(1,5,i) = 0.0d+00\n\nb(2,1,i) = - dt * ty2 &\n& * ( - ( u(2,i,j-1,k)u(3,i,j-1,k) ) tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(2,i,j-1,k) )\nb(2,2,i) = - dt * ty2 * ( u(3,i,j-1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy2\nb(2,3,i) = - dt * ty2 * ( u(2,i,j-1,k) * tmp1 )\nb(2,4,i) = 0.0d+00\nb(2,5,i) = 0.0d+00\n\nb(3,1,i) = - dt * ty2 &\n& * ( - ( u(3,i,j-1,k) * tmp1 ) ** 2 &\n& + c2 * ( qs(i,j-1,k) * tmp1 ) ) &\n& - dt * ty1 * ( - r43 * c34 * tmp2 * u(3,i,j-1,k) )\nb(3,2,i) = - dt * ty2 &\n& * ( - c2 * ( u(2,i,j-1,k) * tmp1 ) )\nb(3,3,i) = - dt * ty2 * ( ( 2.0d+00 - c2 ) &\n& * ( u(3,i,j-1,k) * tmp1 ) ) &\n& - dt * ty1 * ( r43 * c34 * tmp1 ) &\n& - dt * ty1 * dy3\nb(3,4,i) = - dt * ty2 &\n& * ( - c2 * ( u(4,i,j-1,k) * tmp1 ) )\nb(3,5,i) = - dt * ty2 * c2\n\nb(4,1,i) = - dt * ty2 &\n& * ( - ( u(3,i,j-1,k)u(4,i,j-1,k) ) tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(4,i,j-1,k) )\nb(4,2,i) = 0.0d+00\nb(4,3,i) = - dt * ty2 * ( u(4,i,j-1,k) * tmp1 )\nb(4,4,i) = - dt * ty2 * ( u(3,i,j-1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy4\nb(4,5,i) = 0.0d+00\n\nb(5,1,i) = - dt * ty2 &\n& * ( ( c2 * 2.0d0 * qs(i,j-1,k) &\n& - c1 * u(5,i,j-1,k) ) &\n& * ( u(3,i,j-1,k) * tmp2 ) ) &\n& - dt * ty1 &\n& * ( - ( c34 - c1345 )tmp3(u(2,i,j-1,k)*2) &\n& - ( r43c34 - c1345 )tmp3(u(3,i,j-1,k)*2) &\n& - ( c34 - c1345 )tmp3(u(4,i,j-1,k)2) &\n& - c1345tmp2u(5,i,j-1,k) )\nb(5,2,i) = - dt ty2 &\n& * ( - c2 * ( u(2,i,j-1,k)u(3,i,j-1,k) ) tmp2 ) &\n& - dt * ty1 &\n& * ( c34 - c1345 ) * tmp2 * u(2,i,j-1,k)\nb(5,3,i) = - dt * ty2 &\n& * ( c1 * ( u(5,i,j-1,k) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j-1,k) * tmp1 &\n& + u(3,i,j-1,k)u(3,i,j-1,k) tmp2 ) ) &\n& - dt * ty1 &\n& * ( r43c34 - c1345 ) tmp2 * u(3,i,j-1,k)\nb(5,4,i) = - dt * ty2 &\n& * ( - c2 * ( u(3,i,j-1,k)u(4,i,j-1,k) ) tmp2 ) &\n& - dt * ty1 * ( c34 - c1345 ) * tmp2 * u(4,i,j-1,k)\nb(5,5,i) = - dt * ty2 &\n& * ( c1 * ( u(3,i,j-1,k) * tmp1 ) ) &\n& - dt * ty1 * c1345 * tmp1 &\n& - dt * ty1 * dy5\n\ntmp1 = rho_i(i-1,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nc(1,1,i) = - dt * tx1 * dx1\nc(1,2,i) = - dt * tx2\nc(1,3,i) = 0.0d+00\nc(1,4,i) = 0.0d+00\nc(1,5,i) = 0.0d+00\n\nc(2,1,i) = - dt * tx2 &\n& * ( - ( u(2,i-1,j,k) * tmp1 ) ** 2 &\n& + c2 * qs(i-1,j,k) * tmp1 ) &\n& - dt * tx1 * ( - r43 * c34 * tmp2 * u(2,i-1,j,k) )\nc(2,2,i) = - dt * tx2 &\n& * ( ( 2.0d+00 - c2 ) * ( u(2,i-1,j,k) * tmp1 ) ) &\n& - dt * tx1 * ( r43 * c34 * tmp1 ) &\n& - dt * tx1 * dx2\nc(2,3,i) = - dt * tx2 &\n& * ( - c2 * ( u(3,i-1,j,k) * tmp1 ) )\nc(2,4,i) = - dt * tx2 &\n& * ( - c2 * ( u(4,i-1,j,k) * tmp1 ) )\nc(2,5,i) = - dt * tx2 * c2\n\nc(3,1,i) = - dt * tx2 &\n& * ( - ( u(2,i-1,j,k) * u(3,i-1,j,k) ) * tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(3,i-1,j,k) )\nc(3,2,i) = - dt * tx2 * ( u(3,i-1,j,k) * tmp1 )\nc(3,3,i) = - dt * tx2 * ( u(2,i-1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx3\nc(3,4,i) = 0.0d+00\nc(3,5,i) = 0.0d+00\n\nc(4,1,i) = - dt * tx2 &\n& * ( - ( u(2,i-1,j,k)u(4,i-1,j,k) ) tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(4,i-1,j,k) )\nc(4,2,i) = - dt * tx2 * ( u(4,i-1,j,k) * tmp1 )\nc(4,3,i) = 0.0d+00\nc(4,4,i) = - dt * tx2 * ( u(2,i-1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx4\nc(4,5,i) = 0.0d+00\n\nc(5,1,i) = - dt * tx2 &\n& * ( ( c2 * 2.0d0 * qs(i-1,j,k) &\n& - c1 * u(5,i-1,j,k) ) &\n& * u(2,i-1,j,k) * tmp2 ) &\n& - dt * tx1 &\n& * ( - ( r43c34 - c1345 ) tmp3 * ( u(2,i-1,j,k)*2 ) &\n& - ( c34 - c1345 ) tmp3 * ( u(3,i-1,j,k)*2 ) &\n& - ( c34 - c1345 ) tmp3 * ( u(4,i-1,j,k)*2 ) &\n& - c1345 tmp2 * u(5,i-1,j,k) )\nc(5,2,i) = - dt * tx2 &\n& * ( c1 * ( u(5,i-1,j,k) * tmp1 ) &\n& - c2 &\n& * ( u(2,i-1,j,k)u(2,i-1,j,k) tmp2 &\n& + qs(i-1,j,k) * tmp1 ) ) &\n& - dt * tx1 &\n& * ( r43c34 - c1345 ) tmp2 * u(2,i-1,j,k)\nc(5,3,i) = - dt * tx2 &\n& * ( - c2 * ( u(3,i-1,j,k)u(2,i-1,j,k) ) tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(3,i-1,j,k)\nc(5,4,i) = - dt * tx2 &\n& * ( - c2 * ( u(4,i-1,j,k)u(2,i-1,j,k) ) tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(4,i-1,j,k)\nc(5,5,i) = - dt * tx2 &\n& * ( c1 * ( u(2,i-1,j,k) * tmp1 ) ) &\n& - dt * tx1 * c1345 * tmp1 &\n& - dt * tx1 * dx5\n\nend do\n\n\nreturn\nend
void adi(){\ncompute_rhs();\ntxinvr();\nx_solve();\ny_solve();\nz_solve();\nadd();\n}	subroutine adi\n\n\ncall compute_rhs\n\ncall txinvr\n\ncall x_solve\n\ncall y_solve\n\ncall z_solve\n\ncall add\n\nreturn\nend
static void sprnvc(int n, int nz, int nn1, double v[], int iv[]){\nint nzv, ii, i;\ndouble vecelt, vecloc;\n\nnzv = 0;\n\nwhile(nzv < nz){\nvecelt = randlc(&tran, amult);\n\n\nvecloc = randlc(&tran, amult);\ni = icnvrt(vecloc, nn1) + 1;\nif(i>n){continue;}\n\n\nboolean was_gen = FALSE;\nfor(ii = 0; ii < nzv; ii++){\nif(iv[ii] == i){\nwas_gen = TRUE;\nbreak;\n}\n}\nif(was_gen){continue;}\nv[nzv] = vecelt;\niv[nzv] = i;\nnzv = nzv + 1;\n}\n}	subroutine sprnvc( n, nz, nn1, v, iv )\n\nuse cg_data, only : amult, tran\n\nimplicit none\n\ndouble precision v()\ninteger n, nz, nn1, iv()\n\n\n\ninteger nzv, ii, i, icnvrt\n\nexternal randlc, icnvrt\ndouble precision randlc, vecelt, vecloc\n\n\nnzv = 0\n\n100 continue\nif (nzv .ge. nz) goto 110\n\nvecelt = randlc( tran, amult )\n\nvecloc = randlc(tran, amult)\ni = icnvrt(vecloc, nn1) + 1\nif (i .gt. n) goto 100\n\ndo ii = 1, nzv\nif (iv(ii) .eq. i) goto 100\nenddo\nnzv = nzv + 1\nv(nzv) = vecelt\niv(nzv) = i\ngoto 100\n110 continue\n\nreturn\nend
void ssor(int niter){\n\nint i, j, k, m, n;\nint istep;\ndouble tmp, tv[ISIZ2(ISIZ1/22+1)5];\ndouble delunm[5];\n\ntmp=1.0/(omega(2.0-omega));\n\n\n#pragma omp parallel for private(i,j,n,m)\nfor(j=0; j<ISIZ2; j++){\nfor(i=0; i<ISIZ1; i++){\nfor(n=0; n<5; n++){\nfor(m=0; m<5; m++){\na[j][i][n][m]=0.0;\nb[j][i][n][m]=0.0;\nc[j][i][n][m]=0.0;\nd[j][i][n][m]=0.0;\n}\n}\n}\n}\nfor(i=1;i<=T_LAST;i++){timer_clear(i);}\n\n\n#pragma omp parallel\n{\n\nrhs();\n\n\nl2norm( nx0,\nny0,\nnz0,\nist,\niend,\njst,\njend,\nrsd,\nrsdnm);\n} \n\n\nfor(i=1;i<=T_LAST;i++){timer_clear(i);}\ntimer_start(1);\n\n#pragma omp parallel private(istep,i,j,k,m)\n{\n\nfor(istep=1; istep<=niter; istep++){\nif((istep%20)==0\|\|istep==itmax\|\|istep==1){\n#pragma omp master\nif(niter>1){printf(" Time step %4d\n",istep);}\n}\n\nif(timeron){\n#pragma omp master\ntimer_start(T_RHS);\n}\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nrsd[k][j][i][m]=dtrsd[k][j][i][m];\n}\n}\n}\n}\nif(timeron){\n#pragma omp master\ntimer_stop(T_RHS);\n}\n\nfor(k=1; k<nz-1; k++){\n\nif(timeron){\n#pragma omp master\ntimer_start(T_JACLD);\n}\njacld(k);\nif(timeron){\n#pragma omp master\ntimer_stop(T_JACLD);\n}\n\n\nif(timeron){\n#pragma omp master\ntimer_start(T_BLTS);\n}\n\nblts( nx,\nny,\nnz,\nk,\nomega,\nrsd,\na,\nb,\nc,\nd,\nist,\niend,\njst,\njend,\nnx0,\nny0);\n\nif(timeron){\n#pragma omp master\ntimer_stop(T_BLTS);\n}\n}\n\n#pragma omp barrier\n\nfor(k=nz-2; k>0; k--){\n\nif(timeron){\n#pragma omp master\ntimer_start(T_JACU);\n}\njacu(k);\nif(timeron){\n#pragma omp master\ntimer_stop(T_JACU);\n}\n\nif(timeron){\n#pragma omp master\ntimer_start(T_BUTS);\n}\n\nbuts( nx,\nny,\nnz,\nk,\nomega,\nrsd,\ntv,\nd,\na,\nb,\nc,\nist,\niend,\njst,\njend,\nnx0,\nny0);\n\nif(timeron){\n#pragma omp master\ntimer_stop(T_BUTS);\n}\n}\n\n#pragma omp barrier\n\n\nif(timeron){\n#pragma omp master\ntimer_start(T_ADD);\n}\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nu[k][j][i][m]=u[k][j][i][m]+tmprsd[k][j][i][m];\n}\n}\n}\n}\nif(timeron){\n#pragma omp master\ntimer_stop(T_ADD);\n}\n\n\nif((istep%inorm)==0){\nif(timeron){\n#pragma omp master\ntimer_start(T_L2NORM);\n}\nl2norm( nx0,\nny0,\nnz0,\nist,\niend,\njst,\njend,\nrsd,\ndelunm);\nif(timeron){\n#pragma omp master\ntimer_stop(T_L2NORM);\n}\n}\n\nrhs();\n\n\nif(((istep%inorm)==0)\|\|( istep == itmax)){\nif(timeron){\n#pragma omp master\ntimer_start(T_L2NORM);\n}\nl2norm( nx0,\nny0,\nnz0,\nist,\niend,\njst,\njend,\nrsd,\nrsdnm);\nif(timeron){\n#pragma omp master\ntimer_stop(T_L2NORM);\n}\n}\n\nif((rsdnm[0]<tolrsd[0])&&\n(rsdnm[1]<tolrsd[1])&&\n(rsdnm[2]<tolrsd[2])&&\n(rsdnm[3]<tolrsd[3])&&\n(rsdnm[4]<tolrsd[4])){\n#pragma omp master\nprintf("\nconvergence was achieved after %4d pseudo-time steps\n",istep);\nbreak;\n}\n}\n} \n\ntimer_stop(1);\nmaxtime=timer_read(1);\n}	subroutine ssor(niter)\n\n\n\nuse lu_data\nimplicit none\n\ninteger niter\n\ninteger i, j, k, m, n\ninteger istep\ndouble precision tmp, tmp2\ndouble precision delunm(5)\n\nexternal timer_read\ndouble precision timer_read\n\n\ntmp = 1.0d+00 / ( omega * ( 2.0d+00 - omega ) )\n\ndo i = 1, t_last\ncall timer_clear(i)\nend do\n\ncall rhs\n\ncall l2norm( isiz1, isiz2, isiz3, nx0, ny0, nz0, &\n& ist, iend, jst, jend, &\n& rsd, rsdnm )\n\n\ndo i = 1, t_last\ncall timer_clear(i)\nend do\ncall timer_start(1)\n\ndo istep = 1, niter\n\nif (mod ( istep, 20) .eq. 0 .or. &\n& istep .eq. itmax .or. &\n& istep .eq. 1) then\nif (niter .gt. 1) write( , 200) istep\n200 format(' Time step ', i4)\nendif\n\nif (timeron) call timer_start(t_rhs)\ntmp2 = dt\ndo k = 2, nz - 1\ndo j = jst, jend\ndo i = ist, iend\ndo m = 1, 5\nrsd(m,i,j,k) = tmp2 rsd(m,i,j,k)\nend do\nend do\nend do\nend do\nif (timeron) call timer_stop(t_rhs)\n\nif (timeron) call timer_start(t_blts)\ndo k = 2, nz -1\ndo j = jst, jend\n\ncall jacld(j, k)\n\ncall blts( isiz1, isiz2, isiz3, &\n& nx, ny, nz, &\n& omega, &\n& rsd, &\n& a, b, c, d, &\n& ist, iend, j, k )\n\nend do\nend do\nif (timeron) call timer_stop(t_blts)\n\nif (timeron) call timer_start(t_buts)\ndo k = nz - 1, 2, -1\ndo j = jend, jst, -1\n\ncall jacu(j, k)\n\ncall buts( isiz1, isiz2, isiz3, &\n& nx, ny, nz, &\n& omega, &\n& rsd, &\n& d, a, b, c, &\n& ist, iend, j, k )\n\nend do\nend do\nif (timeron) call timer_stop(t_buts)\n\n\nif (timeron) call timer_start(t_add)\ntmp2 = tmp\ndo k = 2, nz-1\ndo j = jst, jend\ndo i = ist, iend\ndo m = 1, 5\nu( m, i, j, k ) = u( m, i, j, k ) &\n& + tmp2 * rsd( m, i, j, k )\nend do\nend do\nend do\nend do\nif (timeron) call timer_stop(t_add)\n\nif ( mod ( istep, inorm ) .eq. 0 ) then\nif (timeron) call timer_start(t_l2norm)\ncall l2norm( isiz1, isiz2, isiz3, nx0, ny0, nz0, &\n& ist, iend, jst, jend, &\n& rsd, delunm )\nif (timeron) call timer_stop(t_l2norm)\nend if\n\ncall rhs\n\nif ( ( mod ( istep, inorm ) .eq. 0 ) .or. &\n& ( istep .eq. itmax ) ) then\nif (timeron) call timer_start(t_l2norm)\ncall l2norm( isiz1, isiz2, isiz3, nx0, ny0, nz0, &\n& ist, iend, jst, jend, &\n& rsd, rsdnm )\nif (timeron) call timer_stop(t_l2norm)\nend if\n\nif ( ( rsdnm(1) .lt. tolrsd(1) ) .and. &\n& ( rsdnm(2) .lt. tolrsd(2) ) .and. &\n& ( rsdnm(3) .lt. tolrsd(3) ) .and. &\n& ( rsdnm(4) .lt. tolrsd(4) ) .and. &\n& ( rsdnm(5) .lt. tolrsd(5) ) ) then\nwrite (*,1004) istep\ngo to 900\nend if\n\nend do\n900 continue\n\ncall timer_stop(1)\nmaxtime= timer_read(1)\n\n\n\nreturn\n\n1001 format (1x/5x,'pseudo-time SSOR iteration no.=',i4/)\n1004 format (1x/1x,'convergence was achieved after ',i4, &\n& ' pseudo-time steps' )\n1006 format (1x/1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for first pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for second pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for third pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for fourth pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for fifth pde = ',1pe12.5)\n1007 format (1x/1x,'RMS-norm of steady-state residual for ', &\n& 'first pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'second pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'third pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'fourth pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'fifth pde = ',1pe12.5)\n\nend
static void comm3(void* pointer_u, int n1, int n2, int n3, int kk){\n#ifdef __clang__\nusing custom_cast = double ()[n2][n1];\ncustom_cast u = reinterpret_cast<custom_cast>(pointer_u);\n#else\ndouble (u)[n2][n1] = (double (*)[n2][n1])pointer_u;\n#endif\n\nint i1, i2, i3;\nif(timeron){\n#pragma omp master\ntimer_start(T_COMM3);\n}\n#pragma omp for\nfor(i3 = 1; i3 < n3-1; i3++){\n\nfor(i2 = 1; i2 < n2-1; i2++){\nu[i3][i2][0] = u[i3][i2][n1-2];\nu[i3][i2][n1-1] = u[i3][i2][1];\n}\n\nfor(i1 = 0; i1 < n1; i1++){\nu[i3][0][i1] = u[i3][n2-2][i1];\nu[i3][n2-1][i1] = u[i3][1][i1];\n}\n}\n\n#pragma omp for\nfor(i2 = 0; i2 < n2; i2++){\nfor(i1 = 0; i1 < n1; i1++){\nu[0][i2][i1] = u[n3-2][i2][i1];\nu[n3-1][i2][i1] = u[1][i2][i1];\n}\n}\n\nif(timeron){\n#pragma omp master\ntimer_stop(T_COMM3);\n}\n}	subroutine comm3(u,n1,n2,n3,kk)\n\n\n\nuse mg_data\nimplicit none\n\ninteger n1, n2, n3, kk\ndouble precision u(n1,n2,n3)\ninteger i1, i2, i3\n\nif (timeron) call timer_start(T_comm3)\ndo i3=2,n3-1\ndo i2=2,n2-1\nu( 1,i2,i3) = u(n1-1,i2,i3)\nu(n1,i2,i3) = u( 2,i2,i3)\nenddo\n\ndo i1=1,n1\nu(i1, 1,i3) = u(i1,n2-1,i3)\nu(i1,n2,i3) = u(i1, 2,i3)\nenddo\nenddo\n\ndo i2=1,n2\ndo i1=1,n1\nu(i1,i2, 1) = u(i1,i2,n3-1)\nu(i1,i2,n3) = u(i1,i2, 2)\nenddo\nenddo\nif (timeron) call timer_stop(T_comm3)\n\nreturn\nend
void exact_solution(double xi, double eta, double zeta, double dtemp[]){\nint m;\nfor(m=0; m<5; m++){\ndtemp[m]=ce[0][m]+xi\n(ce[1][m]+xi\n(ce[4][m]+xi\n(ce[7][m]+xi\nce[10][m])))+eta\n(ce[2][m]+eta\n(ce[5][m]+eta\n(ce[8][m]+eta\nce[11][m])))+zeta\n(ce[3][m]+zeta\n(ce[6][m]+zeta\n(ce[9][m]+zeta\nce[12][m])));\n}\n}	subroutine exact_solution(xi,eta,zeta,dtemp)\n\n\n\nuse sp_data\nimplicit none\n\ndouble precision xi, eta, zeta\ndouble precision dtemp(5)\ninteger m\n\ndo m = 1, 5\ndtemp(m) = ce(m,1) + &\n& xi(ce(m,2) + xi(ce(m,5) + xi(ce(m,8) + xice(m,11)))) + &\n& eta(ce(m,3) + eta(ce(m,6) + eta(ce(m,9) + etace(m,12))))+ &\n& zeta(ce(m,4) + zeta(ce(m,7) + zeta(ce(m,10) + &\n& zetace(m,13))))\nend do\n\nreturn\nend
static void compute_initial_conditions(void* pointer_u0,\nint d1,\nint d2,\nint d3){\ndcomplex (u0)[NY][NX] = (dcomplex()[NY][NX])pointer_u0;\n\nint k, j;\ndouble x0, start, an, starts[NZ];\nstart = SEED;\n\n\nipow46(A, 0, &an);\nrandlc(&start, an);\nipow46(A, 2NXNY, &an);\n\nstarts[0] = start;\nfor(int k=1; k<dims[2]; k++){\nrandlc(&start, an);\nstarts[k] = start;\n}\n\n\n#pragma omp parallel for private(k,j,x0)\nfor(k=0; k<dims[2]; k++){\nx0 = starts[k];\nfor(j=0; j<dims[1]; j++){\nvranlc(2NX, &x0, A, (double)&u0[k][j][0]);\n}\n}\n}	subroutine compute_initial_conditions(u0, d1, d2, d3)\n\n\n\nuse ft_data\nimplicit none\n\ninteger d1, d2, d3\ndouble complex u0(d1+1, d2, d3)\ninteger k, j\ndouble precision x0, start, an, dummy, starts(nz)\n\n\nstart = seed\ncall ipow46(a, 0, an)\ndummy = randlc(start, an)\ncall ipow46(a, 2nxny, an)\n\nstarts(1) = start\ndo k = 2, dims(3)\ndummy = randlc(start, an)\nstarts(k) = start\nend do\n\ndo k = 1, dims(3)\nx0 = starts(k)\ndo j = 1, dims(2)\ncall vranlc(2*nx, x0, a, u0(1, j, k))\nend do\nend do\n\nreturn\nend
void setiv(){\n\nint i, j, k, m;\ndouble xi, eta, zeta;\ndouble pxi, peta, pzeta;\ndouble ue_1jk[5], ue_nx0jk[5], ue_i1k[5];\ndouble ue_iny0k[5], ue_ij1[5], ue_ijnz[5];\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nzeta=((double)k)/(nz-1);\nfor(j=1; j<ny-1; j++){\neta=((double)j)/(ny0-1);\nfor(i=1; i<nx-1; i++){\nxi=((double)i)/(nx0-1);\nexact(0, j, k, ue_1jk);\nexact(nx0-1, j, k, ue_nx0jk);\nexact(i, 0, k, ue_i1k);\nexact(i, ny0-1, k, ue_iny0k);\nexact(i, j, 0, ue_ij1);\nexact(i, j, nz-1, ue_ijnz);\nfor(m=0; m<5; m++){\npxi=(1.0-xi)ue_1jk[m]\n+xiue_nx0jk[m];\npeta=(1.0-eta)ue_i1k[m]\n+etaue_iny0k[m];\npzeta=(1.0-zeta)ue_ij1[m]\n+zetaue_ijnz[m];\nu[k][j][i][m]=pxi+peta+pzeta\n-pxipeta-petapzeta-pzetapxi\n+pxipeta*pzeta;\n}\n}\n}\n}\n}	subroutine setiv\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision xi, eta, zeta\ndouble precision pxi, peta, pzeta\ndouble precision ue_1jk(5),ue_nx0jk(5),ue_i1k(5), &\n& ue_iny0k(5),ue_ij1(5),ue_ijnz(5)\n\n\ndo k = 2, nz - 1\ndo j = 2, ny - 1\nzeta = ( dble (k-1) ) / (nz-1)\neta = ( dble (j-1) ) / (ny0-1)\ndo i = 2, nx - 1\nxi = ( dble (i-1) ) / (nx0-1)\ncall exact (1,j,k,ue_1jk)\ncall exact (nx0,j,k,ue_nx0jk)\ncall exact (i,1,k,ue_i1k)\ncall exact (i,ny0,k,ue_iny0k)\ncall exact (i,j,1,ue_ij1)\ncall exact (i,j,nz,ue_ijnz)\ndo m = 1, 5\npxi = ( 1.0d+00 - xi ) * ue_1jk(m) &\n& + xi * ue_nx0jk(m)\npeta = ( 1.0d+00 - eta ) * ue_i1k(m) &\n& + eta * ue_iny0k(m)\npzeta = ( 1.0d+00 - zeta ) * ue_ij1(m) &\n& + zeta * ue_ijnz(m)\n\nu( m, i, j, k ) = pxi + peta + pzeta &\n& - pxi * peta - peta * pzeta - pzeta * pxi &\n& + pxi * peta * pzeta\n\nend do\nend do\nend do\nend do\n\nreturn\nend
void verify(int no_time_steps, char* class_npb, boolean* verified){\ndouble xcrref[5], xceref[5], xcrdif[5], xcedif[5], epsilon, xce[5], xcr[5], dtref;\nint m;\n\nepsilon=1.0e-08;\n\nerror_norm(xce);\ncompute_rhs();\nrhs_norm(xcr);\nfor(m=0;m<5;m++){xcr[m]=xcr[m]/dt;}\nclass_npb='U';\nverified=TRUE;\nfor(m=0;m<5;m++){xcrref[m]=1.0;xceref[m]=1.0;}\n\nif((grid_points[0]==12)&&(grid_points[1]==12)&&(grid_points[2]==12)&&(no_time_steps==100)){\nclass_npb='S';\ndtref=1.5e-2;\n\nxcrref[0]=2.7470315451339479e-02;\nxcrref[1]=1.0360746705285417e-02;\nxcrref[2]=1.6235745065095532e-02;\nxcrref[3]=1.5840557224455615e-02;\nxcrref[4]=3.4849040609362460e-02;\n\nxceref[0]=2.7289258557377227e-05;\nxceref[1]=1.0364446640837285e-05;\nxceref[2]=1.6154798287166471e-05;\nxceref[3]=1.5750704994480102e-05;\nxceref[4]=3.4177666183390531e-05;\n\n}else if((grid_points[0]==36)&&(grid_points[1]==36)&&(grid_points[2]==36)&&(no_time_steps==400)){\nclass_npb='W';\ndtref=1.5e-3;\n\nxcrref[0]=0.1893253733584e-02;\nxcrref[1]=0.1717075447775e-03;\nxcrref[2]=0.2778153350936e-03;\nxcrref[3]=0.2887475409984e-03;\nxcrref[4]=0.3143611161242e-02;\n\nxceref[0]=0.7542088599534e-04;\nxceref[1]=0.6512852253086e-05;\nxceref[2]=0.1049092285688e-04;\nxceref[3]=0.1128838671535e-04;\nxceref[4]=0.1212845639773e-03;\n\n}else if((grid_points[0]==64)&&(grid_points[1]==64)&&(grid_points[2]==64)&&(no_time_steps==400)){\nclass_npb='A';\ndtref=1.5e-3;\n\nxcrref[0]=2.4799822399300195;\nxcrref[1]=1.1276337964368832;\nxcrref[2]=1.5028977888770491;\nxcrref[3]=1.4217816211695179;\nxcrref[4]=2.1292113035138280;\n\nxceref[0]=1.0900140297820550e-04;\nxceref[1]=3.7343951769282091e-05;\nxceref[2]=5.0092785406541633e-05;\nxceref[3]=4.7671093939528255e-05;\nxceref[4]=1.3621613399213001e-04;\n\n}else if((grid_points[0]==102)&&(grid_points[1]==102)&&(grid_points[2]==102)&&(no_time_steps==400)){\nclass_npb='B';\ndtref=1.0e-3;\n\nxcrref[0]=0.6903293579998e+02;\nxcrref[1]=0.3095134488084e+02;\nxcrref[2]=0.4103336647017e+02;\nxcrref[3]=0.3864769009604e+02;\nxcrref[4]=0.5643482272596e+02;\n\nxceref[0]=0.9810006190188e-02;\nxceref[1]=0.1022827905670e-02;\nxceref[2]=0.1720597911692e-02;\nxceref[3]=0.1694479428231e-02;\nxceref[4]=0.1847456263981e-01;\n\n}else if((grid_points[0]==162)&&(grid_points[1]==162)&&(grid_points[2]==162)&&(no_time_steps==400)){\nclass_npb='C';\ndtref=0.67e-3;\n\nxcrref[0]=0.5881691581829e+03;\nxcrref[1]=0.2454417603569e+03;\nxcrref[2]=0.3293829191851e+03;\nxcrref[3]=0.3081924971891e+03;\nxcrref[4]=0.4597223799176e+03;\n\nxceref[0]=0.2598120500183e+00;\nxceref[1]=0.2590888922315e-01;\nxceref[2]=0.5132886416320e-01;\nxceref[3]=0.4806073419454e-01;\nxceref[4]=0.5483377491301e+00;\n\n}else if((grid_points[0]==408)&&(grid_points[1]==408)&&(grid_points[2]==408)&&(no_time_steps==500)){\nclass_npb='D';\ndtref=0.30e-3;\n\nxcrref[0]=0.1044696216887e+05;\nxcrref[1]=0.3204427762578e+04;\nxcrref[2]=0.4648680733032e+04;\nxcrref[3]=0.4238923283697e+04;\nxcrref[4]=0.7588412036136e+04;\n\nxceref[0]=0.5089471423669e+01;\nxceref[1]=0.5323514855894e+00;\nxceref[2]=0.1187051008971e+01;\nxceref[3]=0.1083734951938e+01;\nxceref[4]=0.1164108338568e+02;\n\n}else if((grid_points[0]==1020)&&(grid_points[1]==1020)&&(grid_points[2]==1020)&&(no_time_steps==500)){\nclass_npb='E';\ndtref=0.10e-3;\n\nxcrref[0]=0.6255387422609e+05;\nxcrref[1]=0.1495317020012e+05;\nxcrref[2]=0.2347595750586e+05;\nxcrref[3]=0.2091099783534e+05;\nxcrref[4]=0.4770412841218e+05;\n\nxceref[0]=0.6742735164909e+02;\nxceref[1]=0.5390656036938e+01;\nxceref[2]=0.1680647196477e+02;\nxceref[3]=0.1536963126457e+02;\nxceref[4]=0.1575330146156e+03;\n}else{\nverified=FALSE;\n}\n\nfor(m=0; m<5; m++){\nxcrdif[m]=fabs((xcr[m]-xcrref[m])/xcrref[m]);\nxcedif[m]=fabs((xce[m]-xceref[m])/xceref[m]);\n}\n\nif(class_npb!='U'){\nprintf(" Verification being performed for class %c\n",class_npb);\nprintf(" accuracy setting for epsilon = %20.13E\n",epsilon);\nverified=(fabs(dt-dtref)<=epsilon);\nif(!(verified)){\nclass_npb='U';\nprintf(" DT does not match the reference value of %15.8E\n",dtref);\n}\n}else{\nprintf(" Unknown class\n");\n}\nif(class_npb!='U'){\nprintf(" Comparison of RMS-norms of residual\n");\n}else{\nprintf(" RMS-norms of residual\n");\n}\nfor(m=0;m<5;m++){\nif(class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xcr[m]);\n}else if(xcrdif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}else {\nverified=FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}\n}\nif(class_npb!='U'){\nprintf(" Comparison of RMS-norms of solution error\n");\n}else{\nprintf(" RMS-norms of solution error\n");\n}\nfor(m=0;m<5;m++){\nif(class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xce[m]);\n}else if(xcedif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}else{\nverified = FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}\n}\nif(class_npb=='U'){\nprintf(" No reference values provided\n");\nprintf(" No verification performed\n");\n}else if(*verified){\nprintf(" Verification Successful\n");\n}else{\nprintf(" Verification failed\n");\n}\n}	subroutine verify(no_time_steps, class, verified)\n\n\n\nuse, intrinsic :: ieee_arithmetic, only : ieee_is_nan\n\nuse sp_data\n\nimplicit none\n\ndouble precision xcrref(5),xceref(5),xcrdif(5),xcedif(5), &\n& epsilon, xce(5), xcr(5), dtref\ninteger m, no_time_steps\ncharacter class\nlogical verified\n\nepsilon = 1.0d-08\n\n\ncall error_norm(xce)\ncall compute_rhs\n\ncall rhs_norm(xcr)\n\ndo m = 1, 5\nxcr(m) = xcr(m) / dt\nenddo\n\nclass = 'U'\nverified = .true.\n\ndo m = 1,5\nxcrref(m) = 1.0\nxceref(m) = 1.0\nend do\n\nif ( (grid_points(1) .eq. 12 ) .and. &\n& (grid_points(2) .eq. 12 ) .and. &\n& (grid_points(3) .eq. 12 ) .and. &\n& (no_time_steps .eq. 100 )) then\n\nclass = 'S'\ndtref = 1.5d-2\n\nxcrref(1) = 2.7470315451339479d-02\nxcrref(2) = 1.0360746705285417d-02\nxcrref(3) = 1.6235745065095532d-02\nxcrref(4) = 1.5840557224455615d-02\nxcrref(5) = 3.4849040609362460d-02\n\nxceref(1) = 2.7289258557377227d-05\nxceref(2) = 1.0364446640837285d-05\nxceref(3) = 1.6154798287166471d-05\nxceref(4) = 1.5750704994480102d-05\nxceref(5) = 3.4177666183390531d-05\n\n\nelseif ( (grid_points(1) .eq. 36) .and. &\n& (grid_points(2) .eq. 36) .and. &\n& (grid_points(3) .eq. 36) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'W'\ndtref = 1.5d-3\n\nxcrref(1) = 0.1893253733584d-02\nxcrref(2) = 0.1717075447775d-03\nxcrref(3) = 0.2778153350936d-03\nxcrref(4) = 0.2887475409984d-03\nxcrref(5) = 0.3143611161242d-02\n\nxceref(1) = 0.7542088599534d-04\nxceref(2) = 0.6512852253086d-05\nxceref(3) = 0.1049092285688d-04\nxceref(4) = 0.1128838671535d-04\nxceref(5) = 0.1212845639773d-03\n\nelseif ( (grid_points(1) .eq. 64) .and. &\n& (grid_points(2) .eq. 64) .and. &\n& (grid_points(3) .eq. 64) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'A'\ndtref = 1.5d-3\n\nxcrref(1) = 2.4799822399300195d0\nxcrref(2) = 1.1276337964368832d0\nxcrref(3) = 1.5028977888770491d0\nxcrref(4) = 1.4217816211695179d0\nxcrref(5) = 2.1292113035138280d0\n\nxceref(1) = 1.0900140297820550d-04\nxceref(2) = 3.7343951769282091d-05\nxceref(3) = 5.0092785406541633d-05\nxceref(4) = 4.7671093939528255d-05\nxceref(5) = 1.3621613399213001d-04\n\nelseif ( (grid_points(1) .eq. 102) .and. &\n& (grid_points(2) .eq. 102) .and. &\n& (grid_points(3) .eq. 102) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'B'\ndtref = 1.0d-3\n\nxcrref(1) = 0.6903293579998d+02\nxcrref(2) = 0.3095134488084d+02\nxcrref(3) = 0.4103336647017d+02\nxcrref(4) = 0.3864769009604d+02\nxcrref(5) = 0.5643482272596d+02\n\nxceref(1) = 0.9810006190188d-02\nxceref(2) = 0.1022827905670d-02\nxceref(3) = 0.1720597911692d-02\nxceref(4) = 0.1694479428231d-02\nxceref(5) = 0.1847456263981d-01\n\nelseif ( (grid_points(1) .eq. 162) .and. &\n& (grid_points(2) .eq. 162) .and. &\n& (grid_points(3) .eq. 162) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'C'\ndtref = 0.67d-3\n\nxcrref(1) = 0.5881691581829d+03\nxcrref(2) = 0.2454417603569d+03\nxcrref(3) = 0.3293829191851d+03\nxcrref(4) = 0.3081924971891d+03\nxcrref(5) = 0.4597223799176d+03\n\nxceref(1) = 0.2598120500183d+00\nxceref(2) = 0.2590888922315d-01\nxceref(3) = 0.5132886416320d-01\nxceref(4) = 0.4806073419454d-01\nxceref(5) = 0.5483377491301d+00\n\nelseif ( (grid_points(1) .eq. 408) .and. &\n& (grid_points(2) .eq. 408) .and. &\n& (grid_points(3) .eq. 408) .and. &\n& (no_time_steps .eq. 500) ) then\n\nclass = 'D'\ndtref = 0.30d-3\n\nxcrref(1) = 0.1044696216887d+05\nxcrref(2) = 0.3204427762578d+04\nxcrref(3) = 0.4648680733032d+04\nxcrref(4) = 0.4238923283697d+04\nxcrref(5) = 0.7588412036136d+04\n\nxceref(1) = 0.5089471423669d+01\nxceref(2) = 0.5323514855894d+00\nxceref(3) = 0.1187051008971d+01\nxceref(4) = 0.1083734951938d+01\nxceref(5) = 0.1164108338568d+02\n\nelseif ( (grid_points(1) .eq. 1020) .and. &\n& (grid_points(2) .eq. 1020) .and. &\n& (grid_points(3) .eq. 1020) .and. &\n& (no_time_steps .eq. 500) ) then\n\nclass = 'E'\ndtref = 0.10d-3\n\nxcrref(1) = 0.6255387422609d+05\nxcrref(2) = 0.1495317020012d+05\nxcrref(3) = 0.2347595750586d+05\nxcrref(4) = 0.2091099783534d+05\nxcrref(5) = 0.4770412841218d+05\n\nxceref(1) = 0.6742735164909d+02\nxceref(2) = 0.5390656036938d+01\nxceref(3) = 0.1680647196477d+02\nxceref(4) = 0.1536963126457d+02\nxceref(5) = 0.1575330146156d+03\n\nelseif ( (grid_points(1) .eq. 2560) .and. &\n& (grid_points(2) .eq. 2560) .and. &\n& (grid_points(3) .eq. 2560) .and. &\n& (no_time_steps .eq. 500) ) then\n\nclass = 'F'\ndtref = 0.15d-4\n\nxcrref(1) = 0.9281628449462d+05\nxcrref(2) = 0.2230152287675d+05\nxcrref(3) = 0.3493102358632d+05\nxcrref(4) = 0.3114096186689d+05\nxcrref(5) = 0.7424426448298d+05\n\nxceref(1) = 0.2683717702444d+03\nxceref(2) = 0.2030647554028d+02\nxceref(3) = 0.6734864248234d+02\nxceref(4) = 0.5947451301640d+02\nxceref(5) = 0.5417636652565d+03\n\n\nelse\nverified = .false.\nendif\n\n\ndo m = 1, 5\n\nxcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))\nxcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))\n\nenddo\n\n\nif (class .ne. 'U') then\nwrite(, 1990) class\n1990 format(' Verification being performed for class ', a)\nwrite (,2000) epsilon\n2000 format(' accuracy setting for epsilon = ', E20.13)\nverified = (dabs(dt-dtref) .le. epsilon)\nif (.not.verified) then\nclass = 'U'\nwrite (,1000) dtref\n1000 format(' DT does not match the reference value of ', &\n& E15.8)\nendif\nelse\nwrite(, 1995)\n1995 format(' Unknown class')\nendif\n\n\nif (class .ne. 'U') then\nwrite (, 2001)\nelse\nwrite (, 2005)\nendif\n\n2001 format(' Comparison of RMS-norms of residual')\n2005 format(' RMS-norms of residual')\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(, 2015) m, xcr(m)\nelse if ((.not.ieee_is_nan(xcrdif(m))) .and. &\n& xcrdif(m) .le. epsilon) then\nwrite (,2011) m,xcr(m),xcrref(m),xcrdif(m)\nelse\nverified = .false.\nwrite (,2010) m,xcr(m),xcrref(m),xcrdif(m)\nendif\nenddo\n\nif (class .ne. 'U') then\nwrite (,2002)\nelse\nwrite (,2006)\nendif\n2002 format(' Comparison of RMS-norms of solution error')\n2006 format(' RMS-norms of solution error')\n\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(, 2015) m, xce(m)\nelse if ((.not.ieee_is_nan(xcedif(m))) .and. &\n& xcedif(m) .le. epsilon) then\nwrite (,2011) m,xce(m),xceref(m),xcedif(m)\nelse\nverified = .false.\nwrite (,2010) m,xce(m),xceref(m),xcedif(m)\nendif\nenddo\n\n2010 format(' FAILURE: ', i2, E20.13, E20.13, E20.13)\n2011 format(' ', i2, E20.13, E20.13, E20.13)\n2015 format(' ', i2, E20.13)\n\nif (class .eq. 'U') then\nwrite(, 2022)\nwrite(, 2023)\n2022 format(' No reference values provided')\n2023 format(' No verification performed')\nelse if (verified) then\nwrite(, 2020)\n2020 format(' Verification Successful')\nelse\nwrite(, 2021)\n2021 format(' Verification failed')\nendif\n\nreturn\n\n\nend
void add(){\nint i, j, k, m;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_ADD);}\n#pragma omp for\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++){\nu[k][j][i][m]=u[k][j][i][m]+rhs[k][j][i][m];\n}\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_ADD);}\n}	subroutine add\n\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m\n\nif (timeron) call timer_start(t_add)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nu(m,i,j,k) = u(m,i,j,k) + rhs(m,i,j,k)\nenddo\nenddo\nenddo\nenddo\nif (timeron) call timer_stop(t_add)\n\nreturn\nend
void z_solve(){\nint i, j, k, k1, k2, m;\ndouble ru1, fac1, fac2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_ZSOLVE);}\n#pragma omp for\nfor(j=1; j<=ny2; j++){\ndouble cv[PROBLEM_SIZE], rhos[PROBLEM_SIZE];\ndouble lhs[IMAXP+1][IMAXP+1][5];\ndouble lhsp[IMAXP+1][IMAXP+1][5];\ndouble lhsm[IMAXP+1][IMAXP+1][5];\n\nfor(i=1; i<=nx2; i++){\nfor(m=0; m<5; m++){\nlhs[0][i][m]=0.0;\nlhsp[0][i][m]=0.0;\nlhsm[0][i][m]=0.0;\nlhs[nz2+1][i][m]=0.0;\nlhsp[nz2+1][i][m]=0.0;\nlhsm[nz2+1][i][m]=0.0;\n}\nlhs[0][i][2]=1.0;\nlhsp[0][i][2]=1.0;\nlhsm[0][i][2]=1.0;\nlhs[nz2+1][i][2]=1.0;\nlhsp[nz2+1][i][2]=1.0;\nlhsm[nz2+1][i][2]=1.0;\n}\n\n\nfor(i=1; i<=nx2; i++){\nfor(k=0; k<=nz2+1; k++){\nru1=c3c4rho_i[k][j][i];\ncv[k]=ws[k][j][i];\nrhos[k]=max(max(dz4+con43ru1, dz5+c1c5ru1), max(dzmax+ru1, dz1));\n}\nfor(k=1; k<=nz2; k++){\nlhs[k][i][0]=0.0;\nlhs[k][i][1]=-dttz2cv[k-1]-dttz1rhos[k-1];\nlhs[k][i][2]=1.0+c2dttz1rhos[k];\nlhs[k][i][3]=dttz2cv[k+1]-dttz1rhos[k+1];\nlhs[k][i][4]=0.0;\n}\n}\n\nfor(i=1; i<=nx2; i++){\nk=1;\nlhs[k][i][2]=lhs[k][i][2]+comz5;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nlhs[k][i][4]=lhs[k][i][4]+comz1;\nk=2;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz6;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nlhs[k][i][4]=lhs[k][i][4]+comz1;\n}\nfor(k=3; k<=nz2-2; k++){\nfor(i=1; i<=nx2; i++){\nlhs[k][i][0]=lhs[k][i][0]+comz1;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz6;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nlhs[k][i][4]=lhs[k][i][4]+comz1;\n}\n}\nfor(i=1; i<=nx2; i++){\nk=nz2-1;\nlhs[k][i][0]=lhs[k][i][0]+comz1;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz6;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nk=nz2;\nlhs[k][i][0]=lhs[k][i][0]+comz1;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz5;\n}\n\nfor(k=1; k<=nz2; k++){\nfor(i=1; i<=nx2; i++){\nlhsp[k][i][0]=lhs[k][i][0];\nlhsp[k][i][1]=lhs[k][i][1]-dttz2speed[k-1][j][i];\nlhsp[k][i][2]=lhs[k][i][2];\nlhsp[k][i][3]=lhs[k][i][3]+dttz2speed[k+1][j][i];\nlhsp[k][i][4]=lhs[k][i][4];\nlhsm[k][i][0]=lhs[k][i][0];\nlhsm[k][i][1]=lhs[k][i][1]+dttz2speed[k-1][j][i];\nlhsm[k][i][2]=lhs[k][i][2];\nlhsm[k][i][3]=lhs[k][i][3]-dttz2speed[k+1][j][i];\nlhsm[k][i][4]=lhs[k][i][4];\n}\n}\n\nfor(k=0; k<=grid_points[2]-3; k++){\nk1=k+1;\nk2=k+2;\nfor(i=1; i<=nx2; i++){\nfac1=1.0/lhs[k][i][2];\nlhs[k][i][3]=fac1lhs[k][i][3];\nlhs[k][i][4]=fac1lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\n}\nlhs[k1][i][2]=lhs[k1][i][2]-lhs[k1][i][1]lhs[k][i][3];\nlhs[k1][i][3]=lhs[k1][i][3]-lhs[k1][i][1]lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhs[k1][i][1]rhs[k][j][i][m];\n}\nlhs[k2][i][1]=lhs[k2][i][1]-lhs[k2][i][0]lhs[k][i][3];\nlhs[k2][i][2]=lhs[k2][i][2]-lhs[k2][i][0]lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k2][j][i][m]=rhs[k2][j][i][m]-lhs[k2][i][0]rhs[k][j][i][m];\n}\n}\n}\n\nk=grid_points[2]-2;\nk1=grid_points[2]-1;\nfor(i=1; i<=nx2; i++){\nfac1=1.0/lhs[k][i][2];\nlhs[k][i][3]=fac1lhs[k][i][3];\nlhs[k][i][4]=fac1lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\n}\nlhs[k1][i][2]=lhs[k1][i][2]-lhs[k1][i][1]lhs[k][i][3];\nlhs[k1][i][3]=lhs[k1][i][3]-lhs[k1][i][1]lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhs[k1][i][1]rhs[k][j][i][m];\n}\n\nfac2=1.0/lhs[k1][i][2];\nfor(m=0; m<3; m++){\nrhs[k1][j][i][m]=fac2rhs[k1][j][i][m];\n}\n}\n\nfor(k=0; k<=grid_points[2]-3; k++){\nk1=k+1;\nk2=k+2;\nfor(i=1; i<=nx2; i++){\nm=3;\nfac1=1.0/lhsp[k][i][2];\nlhsp[k][i][3]=fac1lhsp[k][i][3];\nlhsp[k][i][4]=fac1lhsp[k][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsp[k1][i][2]=lhsp[k1][i][2]-lhsp[k1][i][1]lhsp[k][i][3];\nlhsp[k1][i][3]=lhsp[k1][i][3]-lhsp[k1][i][1]lhsp[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsp[k1][i][1]rhs[k][j][i][m];\nlhsp[k2][i][1]=lhsp[k2][i][1]-lhsp[k2][i][0]lhsp[k][i][3];\nlhsp[k2][i][2]=lhsp[k2][i][2]-lhsp[k2][i][0]lhsp[k][i][4];\nrhs[k2][j][i][m]=rhs[k2][j][i][m]-lhsp[k2][i][0]rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[k][i][2];\nlhsm[k][i][3]=fac1lhsm[k][i][3];\nlhsm[k][i][4]=fac1lhsm[k][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsm[k1][i][2]=lhsm[k1][i][2]-lhsm[k1][i][1]lhsm[k][i][3];\nlhsm[k1][i][3]=lhsm[k1][i][3]-lhsm[k1][i][1]lhsm[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsm[k1][i][1]rhs[k][j][i][m];\nlhsm[k2][i][1]=lhsm[k2][i][1]-lhsm[k2][i][0]lhsm[k][i][3];\nlhsm[k2][i][2]=lhsm[k2][i][2]-lhsm[k2][i][0]lhsm[k][i][4];\nrhs[k2][j][i][m]=rhs[k2][j][i][m]-lhsm[k2][i][0]rhs[k][j][i][m];\n}\n}\n\nk=grid_points[2]-2;\nk1=grid_points[2]-1;\nfor(i=1; i<=nx2; i++){\nm=3;\nfac1=1.0/lhsp[k][i][2];\nlhsp[k][i][3]=fac1lhsp[k][i][3];\nlhsp[k][i][4]=fac1lhsp[k][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsp[k1][i][2]=lhsp[k1][i][2]-lhsp[k1][i][1]lhsp[k][i][3];\nlhsp[k1][i][3]=lhsp[k1][i][3]-lhsp[k1][i][1]lhsp[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsp[k1][i][1]rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[k][i][2];\nlhsm[k][i][3]=fac1lhsm[k][i][3];\nlhsm[k][i][4]=fac1lhsm[k][i][4];\nrhs[k][j][i][m]=fac1rhs[k][j][i][m];\nlhsm[k1][i][2]=lhsm[k1][i][2]-lhsm[k1][i][1]lhsm[k][i][3];\nlhsm[k1][i][3]=lhsm[k1][i][3]-lhsm[k1][i][1]lhsm[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsm[k1][i][1]rhs[k][j][i][m];\n\nrhs[k1][j][i][3]=rhs[k1][j][i][3]/lhsp[k1][i][2];\nrhs[k1][j][i][4]=rhs[k1][j][i][4]/lhsm[k1][i][2];\n}\n\nk=grid_points[2]-2;\nk1=grid_points[2]-1;\nfor(i=1; i<=nx2; i++){\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[k][i][3]rhs[k1][j][i][m];\n}\nrhs[k][j][i][3]=rhs[k][j][i][3]-lhsp[k][i][3]rhs[k1][j][i][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-lhsm[k][i][3]rhs[k1][j][i][4];\n}\n\nfor(k=grid_points[2]-3; k>=0; k--){\nk1=k+1;\nk2=k+2;\nfor(i=1; i<=nx2; i++){\nfor (m = 0; m < 3; m++) {\nrhs[k][j][i][m]=rhs[k][j][i][m]-\nlhs[k][i][3]rhs[k1][j][i][m]-\nlhs[k][i][4]rhs[k2][j][i][m];\n}\n\nrhs[k][j][i][3]=rhs[k][j][i][3]-\nlhsp[k][i][3]rhs[k1][j][i][3]-\nlhsp[k][i][4]rhs[k2][j][i][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-\nlhsm[k][i][3]rhs[k1][j][i][4]-\nlhsm[k][i][4]*rhs[k2][j][i][4];\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_ZSOLVE);}\ntzetar();\n}	subroutine z_solve\n\n\n\nuse sp_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, k1, k2, m\ndouble precision ru1, fac1, fac2\n\n\n\n\nif (timeron) call timer_start(t_zsolve)\ndo j = 1, ny2\ndo i = 1, nx2\n\ncall lhsinit(nz2+1, lhs, lhsp, lhsm)\n\n\n\ndo k = 0, nz2 + 1\nru1 = c3c4rho_i(i,j,k)\ncv(k) = ws(i,j,k)\nrhov(k) = dmax1(dz4 + con43 ru1, &\n& dz5 + c1c5 * ru1, &\n& dzmax + ru1, &\n& dz1)\nend do\n\ndo k = 1, nz2\nlhs(1,k) = 0.0d0\nlhs(2,k) = -dttz2 * cv(k-1) - dttz1 * rhov(k-1)\nlhs(3,k) = 1.0 + c2dttz1 * rhov(k)\nlhs(4,k) = dttz2 * cv(k+1) - dttz1 * rhov(k+1)\nlhs(5,k) = 0.0d0\nend do\n\n\nk = 1\nlhs(3,k) = lhs(3,k) + comz5\nlhs(4,k) = lhs(4,k) - comz4\nlhs(5,k) = lhs(5,k) + comz1\n\nk = 2\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz6\nlhs(4,k) = lhs(4,k) - comz4\nlhs(5,k) = lhs(5,k) + comz1\n\ndo k = 3, nz2-2\nlhs(1,k) = lhs(1,k) + comz1\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz6\nlhs(4,k) = lhs(4,k) - comz4\nlhs(5,k) = lhs(5,k) + comz1\nend do\n\nk = nz2-1\nlhs(1,k) = lhs(1,k) + comz1\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz6\nlhs(4,k) = lhs(4,k) - comz4\n\nk = nz2\nlhs(1,k) = lhs(1,k) + comz1\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz5\n\n\ndo k = 1, nz2\nlhsp(1,k) = lhs(1,k)\nlhsp(2,k) = lhs(2,k) - &\n& dttz2 * speed(i,j,k-1)\nlhsp(3,k) = lhs(3,k)\nlhsp(4,k) = lhs(4,k) + &\n& dttz2 * speed(i,j,k+1)\nlhsp(5,k) = lhs(5,k)\nlhsm(1,k) = lhs(1,k)\nlhsm(2,k) = lhs(2,k) + &\n& dttz2 * speed(i,j,k-1)\nlhsm(3,k) = lhs(3,k)\nlhsm(4,k) = lhs(4,k) - &\n& dttz2 * speed(i,j,k+1)\nlhsm(5,k) = lhs(5,k)\nend do\n\n\n\ndo k = 0, grid_points(3)-3\nk1 = k + 1\nk2 = k + 2\nfac1 = 1.d0/lhs(3,k)\nlhs(4,k) = fac1lhs(4,k)\nlhs(5,k) = fac1lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nend do\nlhs(3,k1) = lhs(3,k1) - &\n& lhs(2,k1)lhs(4,k)\nlhs(4,k1) = lhs(4,k1) - &\n& lhs(2,k1)lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhs(2,k1)rhs(m,i,j,k)\nend do\nlhs(2,k2) = lhs(2,k2) - &\n& lhs(1,k2)lhs(4,k)\nlhs(3,k2) = lhs(3,k2) - &\n& lhs(1,k2)lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k2) = rhs(m,i,j,k2) - &\n& lhs(1,k2)rhs(m,i,j,k)\nend do\nend do\n\nk = grid_points(3)-2\nk1 = grid_points(3)-1\nfac1 = 1.d0/lhs(3,k)\nlhs(4,k) = fac1lhs(4,k)\nlhs(5,k) = fac1lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nend do\nlhs(3,k1) = lhs(3,k1) - &\n& lhs(2,k1)lhs(4,k)\nlhs(4,k1) = lhs(4,k1) - &\n& lhs(2,k1)lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhs(2,k1)rhs(m,i,j,k)\nend do\nfac2 = 1.d0/lhs(3,k1)\ndo m = 1, 3\nrhs(m,i,j,k1) = fac2rhs(m,i,j,k1)\nend do\n\ndo k = 0, grid_points(3)-3\nk1 = k + 1\nk2 = k + 2\nm = 4\nfac1 = 1.d0/lhsp(3,k)\nlhsp(4,k) = fac1lhsp(4,k)\nlhsp(5,k) = fac1lhsp(5,k)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsp(3,k1) = lhsp(3,k1) - &\n& lhsp(2,k1)lhsp(4,k)\nlhsp(4,k1) = lhsp(4,k1) - &\n& lhsp(2,k1)lhsp(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsp(2,k1)rhs(m,i,j,k)\nlhsp(2,k2) = lhsp(2,k2) - &\n& lhsp(1,k2)lhsp(4,k)\nlhsp(3,k2) = lhsp(3,k2) - &\n& lhsp(1,k2)lhsp(5,k)\nrhs(m,i,j,k2) = rhs(m,i,j,k2) - &\n& lhsp(1,k2)rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,k)\nlhsm(4,k) = fac1lhsm(4,k)\nlhsm(5,k) = fac1lhsm(5,k)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsm(3,k1) = lhsm(3,k1) - &\n& lhsm(2,k1)lhsm(4,k)\nlhsm(4,k1) = lhsm(4,k1) - &\n& lhsm(2,k1)lhsm(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsm(2,k1)rhs(m,i,j,k)\nlhsm(2,k2) = lhsm(2,k2) - &\n& lhsm(1,k2)lhsm(4,k)\nlhsm(3,k2) = lhsm(3,k2) - &\n& lhsm(1,k2)lhsm(5,k)\nrhs(m,i,j,k2) = rhs(m,i,j,k2) - &\n& lhsm(1,k2)rhs(m,i,j,k)\nend do\n\nk = grid_points(3)-2\nk1 = grid_points(3)-1\nm = 4\nfac1 = 1.d0/lhsp(3,k)\nlhsp(4,k) = fac1lhsp(4,k)\nlhsp(5,k) = fac1lhsp(5,k)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsp(3,k1) = lhsp(3,k1) - &\n& lhsp(2,k1)lhsp(4,k)\nlhsp(4,k1) = lhsp(4,k1) - &\n& lhsp(2,k1)lhsp(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsp(2,k1)rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,k)\nlhsm(4,k) = fac1lhsm(4,k)\nlhsm(5,k) = fac1lhsm(5,k)\nrhs(m,i,j,k) = fac1rhs(m,i,j,k)\nlhsm(3,k1) = lhsm(3,k1) - &\n& lhsm(2,k1)lhsm(4,k)\nlhsm(4,k1) = lhsm(4,k1) - &\n& lhsm(2,k1)lhsm(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsm(2,k1)rhs(m,i,j,k)\nrhs(4,i,j,k1) = rhs(4,i,j,k1)/lhsp(3,k1)\nrhs(5,i,j,k1) = rhs(5,i,j,k1)/lhsm(3,k1)\n\n\n\nk = grid_points(3)-2\nk1 = grid_points(3)-1\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,k)rhs(m,i,j,k1)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,k)rhs(4,i,j,k1)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,k)rhs(5,i,j,k1)\n\n\ndo k = grid_points(3)-3, 0, -1\nk1 = k + 1\nk2 = k + 2\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,k)rhs(m,i,j,k1) - &\n& lhs(5,k)rhs(m,i,j,k2)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,k)rhs(4,i,j,k1) - &\n& lhsp(5,k)rhs(4,i,j,k2)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,k)rhs(5,i,j,k1) - &\n& lhsm(5,k)*rhs(5,i,j,k2)\nend do\n\nend do\nend do\nif (timeron) call timer_stop(t_zsolve)\n\ncall tzetar\n\nreturn\nend
void erhs(){\n\nint i, j, k, m;\ndouble xi, eta, zeta;\ndouble q;\ndouble u21, u31, u41;\ndouble tmp;\ndouble u21i, u31i, u41i, u51i;\ndouble u21j, u31j, u41j, u51j;\ndouble u21k, u31k, u41k, u51k;\ndouble u21im1, u31im1, u41im1, u51im1;\ndouble u21jm1, u31jm1, u41jm1, u51jm1;\ndouble u21km1, u31km1, u41km1, u51km1;\ndouble flux[ISIZ1][5];\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nfor(j=0; j<ny; j++){\nfor(i=0; i<nx; i++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=0.0;\n}\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nzeta=((double)k)/(nz-1);\nfor(j=0; j<ny; j++){\neta=((double)j)/(ny0-1 );\nfor(i=0; i<nx; i++){\nxi=((double)i)/(nx0-1);\nfor(m=0; m<5; m++){\nrsd[k][j][i][m]=ce[0][m]+\n(ce[1][m]+\n(ce[4][m]+\n(ce[7][m]+\nce[10][m]xi)xi)xi)xi+\n(ce[2][m]+\n(ce[5][m]+\n(ce[8][m]+\nce[11][m]eta)eta)eta)eta+\n(ce[3][m]+\n(ce[6][m]+\n(ce[9][m]+\nce[12][m]zeta)zeta)zeta)zeta;\n}\n}\n}\n}\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=0; i<nx; i++){\nflux[i][0]=rsd[k][j][i][1];\nu21=rsd[k][j][i][1]/rsd[k][j][i][0];\nq=0.50(rsd[k][j][i][1]rsd[k][j][i][1]\n+rsd[k][j][i][2]rsd[k][j][i][2]\n+rsd[k][j][i][3]rsd[k][j][i][3])\n/rsd[k][j][i][0];\nflux[i][1]=rsd[k][j][i][1]u21+C2(rsd[k][j][i][4]-q);\nflux[i][2]=rsd[k][j][i][2]u21;\nflux[i][3]=rsd[k][j][i][3]u21;\nflux[i][4]=(C1rsd[k][j][i][4]-C2q)u21;\n}\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-tx2(flux[i+1][m]-flux[i-1][m]);\n}\n}\nfor(i=ist; i<nx; i++){\ntmp=1.0/rsd[k][j][i][0];\nu21i=tmprsd[k][j][i][1];\nu31i=tmprsd[k][j][i][2];\nu41i=tmprsd[k][j][i][3];\nu51i=tmprsd[k][j][i][4];\ntmp=1.0/rsd[k][j][i-1][0];\nu21im1=tmprsd[k][j][i-1][1];\nu31im1=tmprsd[k][j][i-1][2];\nu41im1=tmprsd[k][j][i-1][3];\nu51im1=tmprsd[k][j][i-1][4];\nflux[i][1]=(4.0/3.0)tx3(u21i-u21im1);\nflux[i][2]=tx3(u31i-u31im1);\nflux[i][3]=tx3(u41i-u41im1);\nflux[i][4]=0.50(1.0-C1C5)\ntx3((u21iu21i+u31iu31i+u41iu41i)\n-(u21im1u21im1+u31im1u31im1+u41im1u41im1))\n+(1.0/6.0)\ntx3(u21iu21i-u21im1u21im1)\n+C1C5tx3(u51i-u51im1);\n}\nfor(i=ist; i<iend; i++){\nfrct[k][j][i][0]=frct[k][j][i][0]\n+dx1tx1(rsd[k][j][i-1][0]\n-2.0rsd[k][j][i][0]\n+rsd[k][j][i+1][0]);\nfrct[k][j][i][1]=frct[k][j][i][1]\n+tx3C3C4(flux[i+1][1]-flux[i][1])\n+dx2tx1(rsd[k][j][i-1][1]\n-2.0rsd[k][j][i][1]\n+rsd[k][j][i+1][1]);\nfrct[k][j][i][2]=frct[k][j][i][2]\n+tx3C3C4(flux[i+1][2]-flux[i][2])\n+dx3tx1(rsd[k][j][i-1][2]\n-2.0rsd[k][j][i][2]\n+rsd[k][j][i+1][2]);\nfrct[k][j][i][3]=frct[k][j][i][3]\n+tx3C3C4(flux[i+1][3]-flux[i][3])\n+dx4tx1(rsd[k][j][i-1][3]\n-2.0rsd[k][j][i][3]\n+rsd[k][j][i+1][3]);\nfrct[k][j][i][4]=frct[k][j][i][4]\n+tx3C3C4(flux[i+1][4]-flux[i][4])\n+dx5tx1(rsd[k][j][i-1][4]\n-2.0rsd[k][j][i][4]\n+rsd[k][j][i+1][4]);\n}\n\nfor(m=0; m<5; m++){\nfrct[k][j][1][m]=frct[k][j][1][m]\n-dssp(+5.0rsd[k][j][1][m]\n-4.0rsd[k][j][2][m]\n+rsd[k][j][3][m]);\nfrct[k][j][2][m]=frct[k][j][2][m]\n-dssp(-4.0rsd[k][j][1][m]\n+6.0rsd[k][j][2][m]\n-4.0rsd[k][j][3][m]\n+rsd[k][j][4][m]);\n}\nfor(i=3; i<nx-3; i++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-dssp(rsd[k][j][i-2][m]\n-4.0rsd[k][j][i-1][m]\n+6.0rsd[k][j][i][m]\n-4.0rsd[k][j][i+1][m]\n+rsd[k][j][i+2][m] );\n}\n}\nfor(m=0; m<5; m++){\nfrct[k][j][nx-3][m]=frct[k][j][nx-3][m]\n-dssp(rsd[k][j][nx-5][m]\n-4.0rsd[k][j][nx-4][m]\n+6.0rsd[k][j][nx-3][m]\n-4.0rsd[k][j][nx-2][m] );\nfrct[k][j][nx-2][m]=frct[k][j][nx-2][m]\n-dssp(rsd[k][j][nx-4][m]\n-4.0rsd[k][j][nx-3][m]\n+5.0rsd[k][j][nx-2][m] );\n}\n}\n}\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(i=ist; i<iend; i++){\nfor(j=0; j<ny; j++){\nflux[j][0]=rsd[k][j][i][2];\nu31=rsd[k][j][i][2]/rsd[k][j][i][0];\nq=0.50(rsd[k][j][i][1]rsd[k][j][i][1]\n+rsd[k][j][i][2]rsd[k][j][i][2]\n+rsd[k][j][i][3]rsd[k][j][i][3])\n/rsd[k][j][i][0];\nflux[j][1]=rsd[k][j][i][1]u31;\nflux[j][2]=rsd[k][j][i][2]u31+C2(rsd[k][j][i][4]-q);\nflux[j][3]=rsd[k][j][i][3]u31;\nflux[j][4]=(C1rsd[k][j][i][4]-C2q)u31;\n}\nfor(j=jst; j<jend;j++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-ty2(flux[j+1][m]-flux[j-1][m]);\n}\n}\nfor(j=jst; j<ny; j++){\ntmp=1.0/rsd[k][j][i][0];\nu21j=tmprsd[k][j][i][1];\nu31j=tmprsd[k][j][i][2];\nu41j=tmprsd[k][j][i][3];\nu51j=tmprsd[k][j][i][4];\ntmp=1.0/rsd[k][j-1][i][0];\nu21jm1=tmprsd[k][j-1][i][1];\nu31jm1=tmprsd[k][j-1][i][2];\nu41jm1=tmprsd[k][j-1][i][3];\nu51jm1=tmprsd[k][j-1][i][4];\nflux[j][1]=ty3(u21j-u21jm1);\nflux[j][2]=(4.0/3.0)ty3(u31j-u31jm1);\nflux[j][3]=ty3(u41j-u41jm1);\nflux[j][4]=0.50(1.0-C1C5)\nty3((u21ju21j+u31ju31j+u41ju41j)\n-(u21jm1u21jm1+u31jm1u31jm1+u41jm1u41jm1))\n+(1.0/6.0)\nty3(u31ju31j-u31jm1u31jm1)\n+C1C5ty3(u51j-u51jm1);\n}\nfor(j=jst; j<jend; j++){\nfrct[k][j][i][0]=frct[k][j][i][0]\n+dy1ty1(rsd[k][j-1][i][0]\n-2.0rsd[k][j][i][0]\n+rsd[k][j+1][i][0]);\nfrct[k][j][i][1]=frct[k][j][i][1]\n+ty3C3C4(flux[j+1][1]-flux[j][1])\n+dy2ty1(rsd[k][j-1][i][1]\n-2.0rsd[k][j][i][1]\n+rsd[k][j+1][i][1]);\nfrct[k][j][i][2]=frct[k][j][i][2]\n+ty3C3C4(flux[j+1][2]-flux[j][2])\n+dy3ty1(rsd[k][j-1][i][2]\n-2.0rsd[k][j][i][2]\n+rsd[k][j+1][i][2]);\nfrct[k][j][i][3]=frct[k][j][i][3]\n+ty3C3C4(flux[j+1][3]-flux[j][3])\n+dy4ty1(rsd[k][j-1][i][3]\n-2.0rsd[k][j][i][3]\n+rsd[k][j+1][i][3]);\nfrct[k][j][i][4]=frct[k][j][i][4]\n+ty3C3C4(flux[j+1][4]-flux[j][4])\n+dy5ty1(rsd[k][j-1][i][4]\n-2.0rsd[k][j][i][4]\n+rsd[k][j+1][i][4] );\n}\n\nfor(m=0; m<5; m++){\nfrct[k][1][i][m]=frct[k][1][i][m]\n-dssp(+5.0rsd[k][1][i][m]\n-4.0rsd[k][2][i][m]\n+rsd[k][3][i][m]);\nfrct[k][2][i][m]=frct[k][2][i][m]\n-dssp(-4.0rsd[k][1][i][m]\n+6.0rsd[k][2][i][m]\n-4.0rsd[k][3][i][m]\n+rsd[k][4][i][m]);\n}\nfor(j=3; j<ny-3; j++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-dssp(rsd[k][j-2][i][m]\n-4.0rsd[k][j-1][i][m]\n+6.0rsd[k][j][i][m]\n-4.0rsd[k][j+1][i][m]\n+rsd[k][j+2][i][m]);\n}\n}\nfor(m=0; m<5; m++){\nfrct[k][ny-3][i][m]=frct[k][ny-3][i][m]\n-dssp(rsd[k][ny-5][i][m]\n-4.0rsd[k][ny-4][i][m]\n+6.0rsd[k][ny-3][i][m]\n-4.0rsd[k][ny-2][i][m]);\nfrct[k][ny-2][i][m]=frct[k][ny-2][i][m]\n-dssp(rsd[k][ny-4][i][m]\n-4.0rsd[k][ny-3][i][m]\n+5.0rsd[k][ny-2][i][m]);\n}\n}\n}\n\n#pragma omp for\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(k=0; k<nz; k++){\nflux[k][0]=rsd[k][j][i][3];\nu41=rsd[k][j][i][3]/rsd[k][j][i][0];\nq=0.50(rsd[k][j][i][1]rsd[k][j][i][1]\n+rsd[k][j][i][2]rsd[k][j][i][2]\n+rsd[k][j][i][3]rsd[k][j][i][3])\n/rsd[k][j][i][0];\nflux[k][1]=rsd[k][j][i][1]u41;\nflux[k][2]=rsd[k][j][i][2]u41;\nflux[k][3]=rsd[k][j][i][3]u41+C2(rsd[k][j][i][4]-q);\nflux[k][4]=(C1rsd[k][j][i][4]-C2q)u41;\n}\nfor(k=1; k<nz-1; k++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-tz2(flux[k+1][m]-flux[k-1][m]);\n}\n}\nfor(k=1; k<nz; k++){\ntmp=1.0/rsd[k][j][i][0];\nu21k=tmprsd[k][j][i][1];\nu31k=tmprsd[k][j][i][2];\nu41k=tmprsd[k][j][i][3];\nu51k=tmprsd[k][j][i][4];\ntmp=1.0/rsd[k-1][j][i][0];\nu21km1=tmprsd[k-1][j][i][1];\nu31km1=tmprsd[k-1][j][i][2];\nu41km1=tmprsd[k-1][j][i][3];\nu51km1=tmprsd[k-1][j][i][4];\nflux[k][1]=tz3(u21k-u21km1);\nflux[k][2]=tz3(u31k-u31km1);\nflux[k][3]=(4.0/3.0)tz3(u41k-u41km1);\nflux[k][4]=0.50(1.0-C1C5)\ntz3((u21ku21k+u31ku31k+u41ku41k)\n-(u21km1u21km1+u31km1u31km1+u41km1u41km1))\n+(1.0/6.0)\ntz3(u41ku41k-u41km1u41km1)\n+C1C5tz3(u51k-u51km1);\n}\nfor(k=1; k<nz-1; k++){\nfrct[k][j][i][0]=frct[k][j][i][0]\n+dz1tz1(rsd[k+1][j][i][0]\n-2.0rsd[k][j][i][0]\n+rsd[k-1][j][i][0]);\nfrct[k][j][i][1]=frct[k][j][i][1]\n+tz3C3C4(flux[k+1][1]-flux[k][1])\n+dz2tz1(rsd[k+1][j][i][1]\n-2.0rsd[k][j][i][1]\n+rsd[k-1][j][i][1]);\nfrct[k][j][i][2]=frct[k][j][i][2]\n+tz3C3C4(flux[k+1][2]-flux[k][2])\n+dz3tz1(rsd[k+1][j][i][2]\n-2.0rsd[k][j][i][2]\n+rsd[k-1][j][i][2]);\nfrct[k][j][i][3]=frct[k][j][i][3]\n+tz3C3C4(flux[k+1][3]-flux[k][3])\n+dz4tz1(rsd[k+1][j][i][3]\n-2.0rsd[k][j][i][3]\n+rsd[k-1][j][i][3]);\nfrct[k][j][i][4]=frct[k][j][i][4]\n+tz3C3C4(flux[k+1][4]-flux[k][4])\n+dz5tz1(rsd[k+1][j][i][4]\n-2.0rsd[k][j][i][4]\n+rsd[k-1][j][i][4]);\n}\n\nfor(m=0; m<5; m++){\nfrct[1][j][i][m]=frct[1][j][i][m]\n-dssp(+5.0rsd[1][j][i][m]\n-4.0rsd[2][j][i][m]\n+rsd[3][j][i][m]);\nfrct[2][j][i][m]=frct[2][j][i][m]\n-dssp(-4.0rsd[1][j][i][m]\n+6.0rsd[2][j][i][m]\n-4.0rsd[3][j][i][m]\n+rsd[4][j][i][m]);\n}\nfor(k=3; k<nz-3; k++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-dssp(rsd[k-2][j][i][m]\n-4.0rsd[k-1][j][i][m]\n+6.0rsd[k][j][i][m]\n-4.0rsd[k+1][j][i][m]\n+rsd[k+2][j][i][m]);\n}\n}\nfor(m=0; m<5; m++){\nfrct[nz-3][j][i][m]=frct[nz-3][j][i][m]\n-dssp(rsd[nz-5][j][i][m]\n-4.0rsd[nz-4][j][i][m]\n+6.0rsd[nz-3][j][i][m]\n-4.0rsd[nz-2][j][i][m]);\nfrct[nz-2][j][i][m]=frct[nz-2][j][i][m]\n-dssp(rsd[nz-4][j][i][m]\n-4.0rsd[nz-3][j][i][m]\n+5.0rsd[nz-2][j][i][m]);\n}\n}\n}\n}	subroutine erhs\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision xi, eta, zeta\ndouble precision q\ndouble precision u21, u31, u41\ndouble precision tmp\ndouble precision u21i, u31i, u41i, u51i\ndouble precision u21j, u31j, u41j, u51j\ndouble precision u21k, u31k, u41k, u51k\ndouble precision u21im1, u31im1, u41im1, u51im1\ndouble precision u21jm1, u31jm1, u41jm1, u51jm1\ndouble precision u21km1, u31km1, u41km1, u51km1\n\n\ndo k = 1, nz\ndo j = 1, ny\ndo i = 1, nx\ndo m = 1, 5\nfrct( m, i, j, k ) = 0.0d+00\nend do\nend do\nend do\nend do\n\ndo k = 1, nz\ndo j = 1, ny\nzeta = ( dble(k-1) ) / ( nz - 1 )\neta = ( dble(j-1) ) / ( ny0 - 1 )\ndo i = 1, nx\nxi = ( dble(i-1) ) / ( nx0 - 1 )\ndo m = 1, 5\nrsd(m,i,j,k) = ce(m,1) &\n& + (ce(m,2) &\n& + (ce(m,5) &\n& + (ce(m,8) &\n& + ce(m,11) * xi) * xi) * xi) * xi &\n& + (ce(m,3) &\n& + (ce(m,6) &\n& + (ce(m,9) &\n& + ce(m,12) * eta) * eta) * eta) * eta &\n& + (ce(m,4) &\n& + (ce(m,7) &\n& + (ce(m,10) &\n& + ce(m,13) * zeta) * zeta) * zeta) * zeta\nend do\nend do\nend do\nend do\n\n\ndo k = 2, nz - 1\ndo j = jst, jend\ndo i = 1, nx\nflux(1,i) = rsd(2,i,j,k)\nu21 = rsd(2,i,j,k) / rsd(1,i,j,k)\nq = 0.50d+00 * ( rsd(2,i,j,k) * rsd(2,i,j,k) &\n& + rsd(3,i,j,k) * rsd(3,i,j,k) &\n& + rsd(4,i,j,k) * rsd(4,i,j,k) ) &\n& / rsd(1,i,j,k)\nflux(2,i) = rsd(2,i,j,k) * u21 + c2 * &\n& ( rsd(5,i,j,k) - q )\nflux(3,i) = rsd(3,i,j,k) * u21\nflux(4,i) = rsd(4,i,j,k) * u21\nflux(5,i) = ( c1 * rsd(5,i,j,k) - c2 * q ) * u21\nend do\n\ndo i = ist, iend\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - tx2 * ( flux(m,i+1) - flux(m,i-1) )\nend do\nend do\ndo i = ist, nx\ntmp = 1.0d+00 / rsd(1,i,j,k)\n\nu21i = tmp * rsd(2,i,j,k)\nu31i = tmp * rsd(3,i,j,k)\nu41i = tmp * rsd(4,i,j,k)\nu51i = tmp * rsd(5,i,j,k)\n\ntmp = 1.0d+00 / rsd(1,i-1,j,k)\n\nu21im1 = tmp * rsd(2,i-1,j,k)\nu31im1 = tmp * rsd(3,i-1,j,k)\nu41im1 = tmp * rsd(4,i-1,j,k)\nu51im1 = tmp * rsd(5,i-1,j,k)\n\nflux(2,i) = (4.0d+00/3.0d+00) * tx3 * &\n& ( u21i - u21im1 )\nflux(3,i) = tx3 * ( u31i - u31im1 )\nflux(4,i) = tx3 * ( u41i - u41im1 )\nflux(5,i) = 0.50d+00 * ( 1.0d+00 - c1c5 ) &\n& tx3 * ( ( u21i 2 + u31i 2 + u41i 2 ) &\n& - ( u21im12 + u31im12 + u41im12 ) ) &\n& + (1.0d+00/6.0d+00) &\n& * tx3 * ( u21i2 - u21im12 ) &\n& + c1 * c5 * tx3 * ( u51i - u51im1 )\nend do\n\ndo i = ist, iend\nfrct(1,i,j,k) = frct(1,i,j,k) &\n& + dx1 * tx1 * ( rsd(1,i-1,j,k) &\n& - 2.0d+00 * rsd(1,i,j,k) &\n& + rsd(1,i+1,j,k) )\nfrct(2,i,j,k) = frct(2,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(2,i+1) - flux(2,i) ) &\n& + dx2 * tx1 * ( rsd(2,i-1,j,k) &\n& - 2.0d+00 * rsd(2,i,j,k) &\n& + rsd(2,i+1,j,k) )\nfrct(3,i,j,k) = frct(3,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(3,i+1) - flux(3,i) ) &\n& + dx3 * tx1 * ( rsd(3,i-1,j,k) &\n& - 2.0d+00 * rsd(3,i,j,k) &\n& + rsd(3,i+1,j,k) )\nfrct(4,i,j,k) = frct(4,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(4,i+1) - flux(4,i) ) &\n& + dx4 * tx1 * ( rsd(4,i-1,j,k) &\n& - 2.0d+00 * rsd(4,i,j,k) &\n& + rsd(4,i+1,j,k) )\nfrct(5,i,j,k) = frct(5,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(5,i+1) - flux(5,i) ) &\n& + dx5 * tx1 * ( rsd(5,i-1,j,k) &\n& - 2.0d+00 * rsd(5,i,j,k) &\n& + rsd(5,i+1,j,k) )\nend do\n\ndo m = 1, 5\nfrct(m,2,j,k) = frct(m,2,j,k) &\n& - dssp * ( + 5.0d+00 * rsd(m,2,j,k) &\n& - 4.0d+00 * rsd(m,3,j,k) &\n& + rsd(m,4,j,k) )\nfrct(m,3,j,k) = frct(m,3,j,k) &\n& - dssp * ( - 4.0d+00 * rsd(m,2,j,k) &\n& + 6.0d+00 * rsd(m,3,j,k) &\n& - 4.0d+00 * rsd(m,4,j,k) &\n& + rsd(m,5,j,k) )\nend do\n\ndo i = 4, nx - 3\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - dssp * ( rsd(m,i-2,j,k) &\n& - 4.0d+00 * rsd(m,i-1,j,k) &\n& + 6.0d+00 * rsd(m,i,j,k) &\n& - 4.0d+00 * rsd(m,i+1,j,k) &\n& + rsd(m,i+2,j,k) )\nend do\nend do\n\ndo m = 1, 5\nfrct(m,nx-2,j,k) = frct(m,nx-2,j,k) &\n& - dssp * ( rsd(m,nx-4,j,k) &\n& - 4.0d+00 * rsd(m,nx-3,j,k) &\n& + 6.0d+00 * rsd(m,nx-2,j,k) &\n& - 4.0d+00 * rsd(m,nx-1,j,k) )\nfrct(m,nx-1,j,k) = frct(m,nx-1,j,k) &\n& - dssp * ( rsd(m,nx-3,j,k) &\n& - 4.0d+00 * rsd(m,nx-2,j,k) &\n& + 5.0d+00 * rsd(m,nx-1,j,k) )\nend do\n\nend do\nend do\n\n\ndo k = 2, nz - 1\ndo i = ist, iend\ndo j = 1, ny\nflux(1,j) = rsd(3,i,j,k)\nu31 = rsd(3,i,j,k) / rsd(1,i,j,k)\nq = 0.50d+00 * ( rsd(2,i,j,k) * rsd(2,i,j,k) &\n& + rsd(3,i,j,k) * rsd(3,i,j,k) &\n& + rsd(4,i,j,k) * rsd(4,i,j,k) ) &\n& / rsd(1,i,j,k)\nflux(2,j) = rsd(2,i,j,k) * u31\nflux(3,j) = rsd(3,i,j,k) * u31 + c2 * &\n& ( rsd(5,i,j,k) - q )\nflux(4,j) = rsd(4,i,j,k) * u31\nflux(5,j) = ( c1 * rsd(5,i,j,k) - c2 * q ) * u31\nend do\n\ndo j = jst, jend\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - ty2 * ( flux(m,j+1) - flux(m,j-1) )\nend do\nend do\n\ndo j = jst, ny\ntmp = 1.0d+00 / rsd(1,i,j,k)\n\nu21j = tmp * rsd(2,i,j,k)\nu31j = tmp * rsd(3,i,j,k)\nu41j = tmp * rsd(4,i,j,k)\nu51j = tmp * rsd(5,i,j,k)\n\ntmp = 1.0d+00 / rsd(1,i,j-1,k)\n\nu21jm1 = tmp * rsd(2,i,j-1,k)\nu31jm1 = tmp * rsd(3,i,j-1,k)\nu41jm1 = tmp * rsd(4,i,j-1,k)\nu51jm1 = tmp * rsd(5,i,j-1,k)\n\nflux(2,j) = ty3 * ( u21j - u21jm1 )\nflux(3,j) = (4.0d+00/3.0d+00) * ty3 * &\n& ( u31j - u31jm1 )\nflux(4,j) = ty3 * ( u41j - u41jm1 )\nflux(5,j) = 0.50d+00 * ( 1.0d+00 - c1c5 ) &\n& ty3 * ( ( u21j 2 + u31j 2 + u41j 2 ) &\n& - ( u21jm12 + u31jm12 + u41jm12 ) ) &\n& + (1.0d+00/6.0d+00) &\n& * ty3 * ( u31j2 - u31jm12 ) &\n& + c1 * c5 * ty3 * ( u51j - u51jm1 )\nend do\n\ndo j = jst, jend\nfrct(1,i,j,k) = frct(1,i,j,k) &\n& + dy1 * ty1 * ( rsd(1,i,j-1,k) &\n& - 2.0d+00 * rsd(1,i,j,k) &\n& + rsd(1,i,j+1,k) )\nfrct(2,i,j,k) = frct(2,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(2,j+1) - flux(2,j) ) &\n& + dy2 * ty1 * ( rsd(2,i,j-1,k) &\n& - 2.0d+00 * rsd(2,i,j,k) &\n& + rsd(2,i,j+1,k) )\nfrct(3,i,j,k) = frct(3,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(3,j+1) - flux(3,j) ) &\n& + dy3 * ty1 * ( rsd(3,i,j-1,k) &\n& - 2.0d+00 * rsd(3,i,j,k) &\n& + rsd(3,i,j+1,k) )\nfrct(4,i,j,k) = frct(4,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(4,j+1) - flux(4,j) ) &\n& + dy4 * ty1 * ( rsd(4,i,j-1,k) &\n& - 2.0d+00 * rsd(4,i,j,k) &\n& + rsd(4,i,j+1,k) )\nfrct(5,i,j,k) = frct(5,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(5,j+1) - flux(5,j) ) &\n& + dy5 * ty1 * ( rsd(5,i,j-1,k) &\n& - 2.0d+00 * rsd(5,i,j,k) &\n& + rsd(5,i,j+1,k) )\nend do\n\ndo m = 1, 5\nfrct(m,i,2,k) = frct(m,i,2,k) &\n& - dssp * ( + 5.0d+00 * rsd(m,i,2,k) &\n& - 4.0d+00 * rsd(m,i,3,k) &\n& + rsd(m,i,4,k) )\nfrct(m,i,3,k) = frct(m,i,3,k) &\n& - dssp * ( - 4.0d+00 * rsd(m,i,2,k) &\n& + 6.0d+00 * rsd(m,i,3,k) &\n& - 4.0d+00 * rsd(m,i,4,k) &\n& + rsd(m,i,5,k) )\nend do\n\ndo j = 4, ny - 3\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - dssp * ( rsd(m,i,j-2,k) &\n& - 4.0d+00 * rsd(m,i,j-1,k) &\n& + 6.0d+00 * rsd(m,i,j,k) &\n& - 4.0d+00 * rsd(m,i,j+1,k) &\n& + rsd(m,i,j+2,k) )\nend do\nend do\n\ndo m = 1, 5\nfrct(m,i,ny-2,k) = frct(m,i,ny-2,k) &\n& - dssp * ( rsd(m,i,ny-4,k) &\n& - 4.0d+00 * rsd(m,i,ny-3,k) &\n& + 6.0d+00 * rsd(m,i,ny-2,k) &\n& - 4.0d+00 * rsd(m,i,ny-1,k) )\nfrct(m,i,ny-1,k) = frct(m,i,ny-1,k) &\n& - dssp * ( rsd(m,i,ny-3,k) &\n& - 4.0d+00 * rsd(m,i,ny-2,k) &\n& + 5.0d+00 * rsd(m,i,ny-1,k) )\nend do\n\nend do\nend do\n\ndo j = jst, jend\ndo i = ist, iend\ndo k = 1, nz\nflux(1,k) = rsd(4,i,j,k)\nu41 = rsd(4,i,j,k) / rsd(1,i,j,k)\nq = 0.50d+00 * ( rsd(2,i,j,k) * rsd(2,i,j,k) &\n& + rsd(3,i,j,k) * rsd(3,i,j,k) &\n& + rsd(4,i,j,k) * rsd(4,i,j,k) ) &\n& / rsd(1,i,j,k)\nflux(2,k) = rsd(2,i,j,k) * u41\nflux(3,k) = rsd(3,i,j,k) * u41\nflux(4,k) = rsd(4,i,j,k) * u41 + c2 * &\n& ( rsd(5,i,j,k) - q )\nflux(5,k) = ( c1 * rsd(5,i,j,k) - c2 * q ) * u41\nend do\n\ndo k = 2, nz - 1\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - tz2 * ( flux(m,k+1) - flux(m,k-1) )\nend do\nend do\n\ndo k = 2, nz\ntmp = 1.0d+00 / rsd(1,i,j,k)\n\nu21k = tmp * rsd(2,i,j,k)\nu31k = tmp * rsd(3,i,j,k)\nu41k = tmp * rsd(4,i,j,k)\nu51k = tmp * rsd(5,i,j,k)\n\ntmp = 1.0d+00 / rsd(1,i,j,k-1)\n\nu21km1 = tmp * rsd(2,i,j,k-1)\nu31km1 = tmp * rsd(3,i,j,k-1)\nu41km1 = tmp * rsd(4,i,j,k-1)\nu51km1 = tmp * rsd(5,i,j,k-1)\n\nflux(2,k) = tz3 * ( u21k - u21km1 )\nflux(3,k) = tz3 * ( u31k - u31km1 )\nflux(4,k) = (4.0d+00/3.0d+00) * tz3 * ( u41k &\n& - u41km1 )\nflux(5,k) = 0.50d+00 * ( 1.0d+00 - c1c5 ) &\n& tz3 * ( ( u21k 2 + u31k 2 + u41k 2 ) &\n& - ( u21km12 + u31km12 + u41km12 ) ) &\n& + (1.0d+00/6.0d+00) &\n& * tz3 * ( u41k2 - u41km12 ) &\n& + c1 * c5 * tz3 * ( u51k - u51km1 )\nend do\n\ndo k = 2, nz - 1\nfrct(1,i,j,k) = frct(1,i,j,k) &\n& + dz1 * tz1 * ( rsd(1,i,j,k+1) &\n& - 2.0d+00 * rsd(1,i,j,k) &\n& + rsd(1,i,j,k-1) )\nfrct(2,i,j,k) = frct(2,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(2,k+1) - flux(2,k) ) &\n& + dz2 * tz1 * ( rsd(2,i,j,k+1) &\n& - 2.0d+00 * rsd(2,i,j,k) &\n& + rsd(2,i,j,k-1) )\nfrct(3,i,j,k) = frct(3,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(3,k+1) - flux(3,k) ) &\n& + dz3 * tz1 * ( rsd(3,i,j,k+1) &\n& - 2.0d+00 * rsd(3,i,j,k) &\n& + rsd(3,i,j,k-1) )\nfrct(4,i,j,k) = frct(4,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(4,k+1) - flux(4,k) ) &\n& + dz4 * tz1 * ( rsd(4,i,j,k+1) &\n& - 2.0d+00 * rsd(4,i,j,k) &\n& + rsd(4,i,j,k-1) )\nfrct(5,i,j,k) = frct(5,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(5,k+1) - flux(5,k) ) &\n& + dz5 * tz1 * ( rsd(5,i,j,k+1) &\n& - 2.0d+00 * rsd(5,i,j,k) &\n& + rsd(5,i,j,k-1) )\nend do\n\ndo m = 1, 5\nfrct(m,i,j,2) = frct(m,i,j,2) &\n& - dssp * ( + 5.0d+00 * rsd(m,i,j,2) &\n& - 4.0d+00 * rsd(m,i,j,3) &\n& + rsd(m,i,j,4) )\nfrct(m,i,j,3) = frct(m,i,j,3) &\n& - dssp * (- 4.0d+00 * rsd(m,i,j,2) &\n& + 6.0d+00 * rsd(m,i,j,3) &\n& - 4.0d+00 * rsd(m,i,j,4) &\n& + rsd(m,i,j,5) )\nend do\n\ndo k = 4, nz - 3\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - dssp * ( rsd(m,i,j,k-2) &\n& - 4.0d+00 * rsd(m,i,j,k-1) &\n& + 6.0d+00 * rsd(m,i,j,k) &\n& - 4.0d+00 * rsd(m,i,j,k+1) &\n& + rsd(m,i,j,k+2) )\nend do\nend do\n\ndo m = 1, 5\nfrct(m,i,j,nz-2) = frct(m,i,j,nz-2) &\n& - dssp * ( rsd(m,i,j,nz-4) &\n& - 4.0d+00 * rsd(m,i,j,nz-3) &\n& + 6.0d+00 * rsd(m,i,j,nz-2) &\n& - 4.0d+00 * rsd(m,i,j,nz-1) )\nfrct(m,i,j,nz-1) = frct(m,i,j,nz-1) &\n& - dssp * ( rsd(m,i,j,nz-3) &\n& - 4.0d+00 * rsd(m,i,j,nz-2) &\n& + 5.0d+00 * rsd(m,i,j,nz-1) )\nend do\nend do\nend do\n\nreturn\nend
void txinvr(){\nint i, j, k;\ndouble t1, t2, t3, ac, ru1, uu, vv, ww, r1, r2, r3, r4, r5, ac2inv;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_TXINVR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nru1=rho_i[k][j][i];\nuu=us[k][j][i];\nvv=vs[k][j][i];\nww=ws[k][j][i];\nac=speed[k][j][i];\nac2inv=acac;\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nt1=c2/ac2inv(qs[k][j][i]r1-uur2-vvr3-wwr4+r5);\nt2=btru1(uur1-r2);\nt3=(btru1ac)t1;\nrhs[k][j][i][0]=r1-t1;\nrhs[k][j][i][1]=-ru1(wwr1-r4);\nrhs[k][j][i][2]=ru1(vvr1-r3);\nrhs[k][j][i][3]=-t2+t3;\nrhs[k][j][i][4]=t2+t3;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_TXINVR);}\n}	subroutine txinvr\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision t1, t2, t3, ac, ru1, uu, vv, ww, r1, r2, r3, &\n& r4, r5, ac2inv\n\n\nif (timeron) call timer_start(t_txinvr)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nru1 = rho_i(i,j,k)\nuu = us(i,j,k)\nvv = vs(i,j,k)\nww = ws(i,j,k)\nac = speed(i,j,k)\nac2inv = acac\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nt1 = c2 / ac2inv ( qs(i,j,k)r1 - uur2 - &\n& vvr3 - wwr4 + r5 )\nt2 = bt * ru1 * ( uu * r1 - r2 )\nt3 = ( bt * ru1 * ac ) * t1\n\nrhs(1,i,j,k) = r1 - t1\nrhs(2,i,j,k) = - ru1 * ( wwr1 - r4 )\nrhs(3,i,j,k) = ru1 ( vv*r1 - r3 )\nrhs(4,i,j,k) = - t2 + t3\nrhs(5,i,j,k) = t2 + t3\n\nend do\nend do\nend do\nif (timeron) call timer_stop(t_txinvr)\n\nreturn\nend
void blts(int nx,\nint ny,\nint nz,\nint k,\ndouble omega,\ndouble v[][ISIZ2/22+1][ISIZ1/22+1][5],\ndouble ldz[][ISIZ1/22+1][5][5],\ndouble ldy[][ISIZ1/22+1][5][5],\ndouble ldx[][ISIZ1/22+1][5][5],\ndouble d[][ISIZ1/22+1][5][5],\nint ist,\nint iend,\nint jst,\nint jend,\nint nx0,\nint ny0){\n\nint i, j, m;\ndouble tmp, tmp1;\ndouble tmat[5][5], tv[5];\n\n#pragma omp for nowait schedule(static)\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nv[k][j][i][m]= v[k][j][i][m]\n-omega(ldz[j][i][0][m]v[k-1][j][i][0]\n+ldz[j][i][1][m]v[k-1][j][i][1]\n+ldz[j][i][2][m]v[k-1][j][i][2]\n+ldz[j][i][3][m]v[k-1][j][i][3]\n+ldz[j][i][4][m]v[k-1][j][i][4]);\n}\n}\n}\n\n#pragma omp for nowait schedule(static)\nfor(j=jst; j<jend; j++){\n\nif (j != jst) {\nwhile (flag[j-1] == 0){\n#pragma omp flush\n;\n}\n}\nif (j != jend-1) {\nwhile (flag[j] == 1){\n#pragma omp flush\n;\n}\n}\n\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\ntv[m]=v[k][j][i][m]\n-omega(ldy[j][i][0][m]v[k][j-1][i][0]\n+ldx[j][i][0][m]v[k][j][i-1][0]\n+ldy[j][i][1][m]v[k][j-1][i][1]\n+ldx[j][i][1][m]v[k][j][i-1][1]\n+ldy[j][i][2][m]v[k][j-1][i][2]\n+ldx[j][i][2][m]v[k][j][i-1][2]\n+ldy[j][i][3][m]v[k][j-1][i][3]\n+ldx[j][i][3][m]v[k][j][i-1][3]\n+ldy[j][i][4][m]v[k][j-1][i][4]\n+ldx[j][i][4][m]v[k][j][i-1][4]);\n}\n\nfor(m=0; m<5; m++){\ntmat[0][m]=d[j][i][0][m];\ntmat[1][m]=d[j][i][1][m];\ntmat[2][m]=d[j][i][2][m];\ntmat[3][m]=d[j][i][3][m];\ntmat[4][m]=d[j][i][4][m];\n}\n\ntmp1=1.0/tmat[0][0];\ntmp=tmp1tmat[0][1];\ntmat[1][1]=tmat[1][1]-tmptmat[1][0];\ntmat[2][1]=tmat[2][1]-tmptmat[2][0];\ntmat[3][1]=tmat[3][1]-tmptmat[3][0];\ntmat[4][1]=tmat[4][1]-tmptmat[4][0];\ntv[1]=tv[1]-tv[0]tmp;\n\ntmp=tmp1tmat[0][2];\ntmat[1][2]=tmat[1][2]-tmptmat[1][0];\ntmat[2][2]=tmat[2][2]-tmptmat[2][0];\ntmat[3][2]=tmat[3][2]-tmptmat[3][0];\ntmat[4][2]=tmat[4][2]-tmptmat[4][0];\ntv[2]=tv[2]-tv[0]tmp;\n\ntmp=tmp1tmat[0][3];\ntmat[1][3]=tmat[1][3]-tmptmat[1][0];\ntmat[2][3]=tmat[2][3]-tmptmat[2][0];\ntmat[3][3]=tmat[3][3]-tmptmat[3][0];\ntmat[4][3]=tmat[4][3]-tmptmat[4][0];\ntv[3]=tv[3]-tv[0]tmp;\n\ntmp=tmp1tmat[0][4];\ntmat[1][4]=tmat[1][4]-tmptmat[1][0];\ntmat[2][4]=tmat[2][4]-tmptmat[2][0];\ntmat[3][4]=tmat[3][4]-tmptmat[3][0];\ntmat[4][4]=tmat[4][4]-tmptmat[4][0];\ntv[4]=tv[4]-tv[0]tmp;\n\ntmp1=1.0/tmat[1][1];\ntmp=tmp1tmat[1][2];\ntmat[2][2]=tmat[2][2]-tmptmat[2][1];\ntmat[3][2]=tmat[3][2]-tmptmat[3][1];\ntmat[4][2]=tmat[4][2]-tmptmat[4][1];\ntv[2]=tv[2]-tv[1]tmp;\n\ntmp=tmp1tmat[1][3];\ntmat[2][3]=tmat[2][3]-tmptmat[2][1];\ntmat[3][3]=tmat[3][3]-tmptmat[3][1];\ntmat[4][3]=tmat[4][3]-tmptmat[4][1];\ntv[3]=tv[3]-tv[1]tmp;\n\ntmp=tmp1tmat[1][4];\ntmat[2][4]=tmat[2][4]-tmptmat[2][1];\ntmat[3][4]=tmat[3][4]-tmptmat[3][1];\ntmat[4][4]=tmat[4][4]-tmptmat[4][1];\ntv[4]=tv[4]-tv[1]tmp;\n\ntmp1=1.0/tmat[2][2];\ntmp=tmp1tmat[2][3];\ntmat[3][3]=tmat[3][3]-tmptmat[3][2];\ntmat[4][3]=tmat[4][3]-tmptmat[4][2];\ntv[3]=tv[3]-tv[2]tmp;\n\ntmp=tmp1tmat[2][4];\ntmat[3][4]=tmat[3][4]-tmptmat[3][2];\ntmat[4][4]=tmat[4][4]-tmptmat[4][2];\ntv[4]=tv[4]-tv[2]tmp;\n\ntmp1=1.0/tmat[3][3];\ntmp=tmp1tmat[3][4];\ntmat[4][4]=tmat[4][4]-tmptmat[4][3];\ntv[4]=tv[4]-tv[3]tmp;\n\nv[k][j][i][4]=tv[4]/tmat[4][4];\ntv[3]=tv[3]\n-tmat[4][3]v[k][j][i][4];\nv[k][j][i][3]=tv[3]/tmat[3][3];\ntv[2]=tv[2]\n-tmat[3][2]v[k][j][i][3]\n-tmat[4][2]v[k][j][i][4];\nv[k][j][i][2]=tv[2]/tmat[2][2];\ntv[1]=tv[1]\n-tmat[2][1]v[k][j][i][2]\n-tmat[3][1]v[k][j][i][3]\n-tmat[4][1]v[k][j][i][4];\nv[k][j][i][1]=tv[1]/tmat[1][1];\ntv[0]=tv[0]\n-tmat[1][0]v[k][j][i][1]\n-tmat[2][0]v[k][j][i][2]\n-tmat[3][0]v[k][j][i][3]\n-tmat[4][0]*v[k][j][i][4];\nv[k][j][i][0]=tv[0]/tmat[0][0];\n}\n\nif (j != jend-1) flag[j] = 1;\nif (j != jst) flag[j-1] = 0;\n}\n}	subroutine blts ( ldmx, ldmy, ldmz, &\n& nx, ny, nz, &\n& omega, &\n& v, &\n& ldz, ldy, ldx, d, &\n& ist, iend, j, k )\n\n\n\nimplicit none\n\ninteger ldmx, ldmy, ldmz\ninteger nx, ny, nz\ndouble precision omega\ndouble precision v( 5, ldmx/22+1, ldmy/22+1, ldmz), &\n& ldz( 5, 5, ldmx ), &\n& ldy( 5, 5, ldmx ), &\n& ldx( 5, 5, ldmx ), &\n& d ( 5, 5, ldmx )\ninteger ist, iend, j, k\n\ninteger i, m\ndouble precision tmp, tmp1\ndouble precision tmat(5,5), tv(5)\n\n\ndo i = ist, iend\ndo m = 1, 5\n\ntv( m ) = v( m, i, j, k ) &\n& - omega * ( ldz( m, 1, i ) * v( 1, i, j, k-1 ) &\n& + ldz( m, 2, i ) * v( 2, i, j, k-1 ) &\n& + ldz( m, 3, i ) * v( 3, i, j, k-1 ) &\n& + ldz( m, 4, i ) * v( 4, i, j, k-1 ) &\n& + ldz( m, 5, i ) * v( 5, i, j, k-1 ) )\n\ntv( m ) = tv( m ) &\n& - omega * ( ldy( m, 1, i ) * v( 1, i, j-1, k ) &\n& + ldx( m, 1, i ) * v( 1, i-1, j, k ) &\n& + ldy( m, 2, i ) * v( 2, i, j-1, k ) &\n& + ldx( m, 2, i ) * v( 2, i-1, j, k ) &\n& + ldy( m, 3, i ) * v( 3, i, j-1, k ) &\n& + ldx( m, 3, i ) * v( 3, i-1, j, k ) &\n& + ldy( m, 4, i ) * v( 4, i, j-1, k ) &\n& + ldx( m, 4, i ) * v( 4, i-1, j, k ) &\n& + ldy( m, 5, i ) * v( 5, i, j-1, k ) &\n& + ldx( m, 5, i ) * v( 5, i-1, j, k ) )\n\nend do\n\ndo m = 1, 5\ntmat( m, 1 ) = d( m, 1, i )\ntmat( m, 2 ) = d( m, 2, i )\ntmat( m, 3 ) = d( m, 3, i )\ntmat( m, 4 ) = d( m, 4, i )\ntmat( m, 5 ) = d( m, 5, i )\nend do\n\ntmp1 = 1.0d+00 / tmat( 1, 1 )\ntmp = tmp1 * tmat( 2, 1 )\ntmat( 2, 2 ) = tmat( 2, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 2, 3 ) = tmat( 2, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 2, 4 ) = tmat( 2, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 2, 5 ) = tmat( 2, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 2 ) = tv( 2 ) &\n& - tv( 1 ) * tmp\n\ntmp = tmp1 * tmat( 3, 1 )\ntmat( 3, 2 ) = tmat( 3, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 3, 3 ) = tmat( 3, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 3, 4 ) = tmat( 3, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 3, 5 ) = tmat( 3, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 3 ) = tv( 3 ) &\n& - tv( 1 ) * tmp\n\ntmp = tmp1 * tmat( 4, 1 )\ntmat( 4, 2 ) = tmat( 4, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 4, 3 ) = tmat( 4, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 4, 4 ) = tmat( 4, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 4, 5 ) = tmat( 4, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 4 ) = tv( 4 ) &\n& - tv( 1 ) * tmp\n\ntmp = tmp1 * tmat( 5, 1 )\ntmat( 5, 2 ) = tmat( 5, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 5, 3 ) = tmat( 5, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 5, 4 ) = tmat( 5, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 1 ) * tmp\n\n\n\ntmp1 = 1.0d+00 / tmat( 2, 2 )\ntmp = tmp1 * tmat( 3, 2 )\ntmat( 3, 3 ) = tmat( 3, 3 ) &\n& - tmp * tmat( 2, 3 )\ntmat( 3, 4 ) = tmat( 3, 4 ) &\n& - tmp * tmat( 2, 4 )\ntmat( 3, 5 ) = tmat( 3, 5 ) &\n& - tmp * tmat( 2, 5 )\ntv( 3 ) = tv( 3 ) &\n& - tv( 2 ) * tmp\n\ntmp = tmp1 * tmat( 4, 2 )\ntmat( 4, 3 ) = tmat( 4, 3 ) &\n& - tmp * tmat( 2, 3 )\ntmat( 4, 4 ) = tmat( 4, 4 ) &\n& - tmp * tmat( 2, 4 )\ntmat( 4, 5 ) = tmat( 4, 5 ) &\n& - tmp * tmat( 2, 5 )\ntv( 4 ) = tv( 4 ) &\n& - tv( 2 ) * tmp\n\ntmp = tmp1 * tmat( 5, 2 )\ntmat( 5, 3 ) = tmat( 5, 3 ) &\n& - tmp * tmat( 2, 3 )\ntmat( 5, 4 ) = tmat( 5, 4 ) &\n& - tmp * tmat( 2, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 2, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 2 ) * tmp\n\n\n\ntmp1 = 1.0d+00 / tmat( 3, 3 )\ntmp = tmp1 * tmat( 4, 3 )\ntmat( 4, 4 ) = tmat( 4, 4 ) &\n& - tmp * tmat( 3, 4 )\ntmat( 4, 5 ) = tmat( 4, 5 ) &\n& - tmp * tmat( 3, 5 )\ntv( 4 ) = tv( 4 ) &\n& - tv( 3 ) * tmp\n\ntmp = tmp1 * tmat( 5, 3 )\ntmat( 5, 4 ) = tmat( 5, 4 ) &\n& - tmp * tmat( 3, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 3, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 3 ) * tmp\n\n\n\ntmp1 = 1.0d+00 / tmat( 4, 4 )\ntmp = tmp1 * tmat( 5, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 4, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 4 ) * tmp\n\nv( 5, i, j, k ) = tv( 5 ) &\n& / tmat( 5, 5 )\n\ntv( 4 ) = tv( 4 ) &\n& - tmat( 4, 5 ) * v( 5, i, j, k )\nv( 4, i, j, k ) = tv( 4 ) &\n& / tmat( 4, 4 )\n\ntv( 3 ) = tv( 3 ) &\n& - tmat( 3, 4 ) * v( 4, i, j, k ) &\n& - tmat( 3, 5 ) * v( 5, i, j, k )\nv( 3, i, j, k ) = tv( 3 ) &\n& / tmat( 3, 3 )\n\ntv( 2 ) = tv( 2 ) &\n& - tmat( 2, 3 ) * v( 3, i, j, k ) &\n& - tmat( 2, 4 ) * v( 4, i, j, k ) &\n& - tmat( 2, 5 ) * v( 5, i, j, k )\nv( 2, i, j, k ) = tv( 2 ) &\n& / tmat( 2, 2 )\n\ntv( 1 ) = tv( 1 ) &\n& - tmat( 1, 2 ) * v( 2, i, j, k ) &\n& - tmat( 1, 3 ) * v( 3, i, j, k ) &\n& - tmat( 1, 4 ) * v( 4, i, j, k ) &\n& - tmat( 1, 5 ) * v( 5, i, j, k )\nv( 1, i, j, k ) = tv( 1 ) &\n& / tmat( 1, 1 )\n\n\nenddo\n\n\nreturn\nend
static void cffts2(int is,\nint d1,\nint d2,\nint d3,\nvoid* pointer_x,\nvoid* pointer_xout,\ndcomplex y1[][FFTBLOCKPAD],\ndcomplex y2[][FFTBLOCKPAD]){\ndcomplex (x)[NY][NX] = (dcomplex()[NY][NX])pointer_x;\ndcomplex (xout)[NY][NX] = (dcomplex()[NY][NX])pointer_xout;\n\nint logd2;\nint i, j, k, ii;\n\nlogd2 = ilog2(d2);\n\nif(timers_enabled){\n#pragma omp master\ntimer_start(T_FFTY);\n}\n\n#pragma omp for\nfor(k=0; k<d3; k++){\nfor(ii=0; ii<=d1-FFTBLOCK; ii+=FFTBLOCK){\nfor(j=0; j<d2; j++){\nfor(i=0; i<FFTBLOCK; i++){\ny1[j][i] = x[k][j][i+ii];\n}\n}\ncfftz(is, logd2, d2, y1, y2);\nfor(j=0; j<d2; j++){\nfor(i=0; i<FFTBLOCK; i++){\nxout[k][j][i+ii] = y1[j][i];\n}\n}\n}\n}\n\nif(timers_enabled){\n#pragma omp master\ntimer_stop(T_FFTY);\n}\n}	subroutine cffts2(is, d1, d2, d3, x, xout, y1, y2)\n\n\nuse ft_data\nimplicit none\n\ninteger is, d1, d2, d3, logd2\ndouble complex x(d1+1,d2,d3)\ndouble complex xout(d1+1,d2,d3)\ndouble complex y1(fftblockpad, d2), y2(fftblockpad, d2)\ninteger i, j, k, ii, in\n\nlogd2 = ilog2(d2)\n\nif (timers_enabled) call timer_start(T_ffty)\ndo k = 1, d3\ndo in = 0, d1/fftblock - 1\nii = in*fftblock\ndo j = 1, d2\ndo i = 1, fftblock\ny1(i,j) = x(i+ii,j,k)\nenddo\nenddo\n\ncall cfftz (is, logd2, d2, y1, y2)\n\ndo j = 1, d2\ndo i = 1, fftblock\nxout(i+ii,j,k) = y1(i,j)\nenddo\nenddo\nenddo\nenddo\nif (timers_enabled) call timer_stop(T_ffty)\n\nreturn\nend
void setbv(){\n\nint i, j, k, m;\ndouble temp1[5], temp2[5];\n\n#pragma omp for\nfor(j=0; j<ny; j++){\nfor(i=0; i<nx; i++){\nexact(i, j, 0, temp1);\nexact(i, j, nz-1, temp2);\nfor(m=0; m<5; m++){\nu[0][j][i][m]=temp1[m];\nu[nz-1][j][i][m]=temp2[m];\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nfor(i=0; i<nx; i++){\nexact(i, 0, k, temp1);\nexact(i, ny-1, k, temp2);\nfor(m=0; m<5; m++){\nu[k][0][i][m]=temp1[m];\nu[k][ny-1][i][m]=temp2[m];\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nfor(j=0; j<ny; j++){\nexact(0, j, k, temp1);\nexact(nx-1, j, k, temp2);\nfor(m=0; m<5; m++){\nu[k][j][0][m]=temp1[m];\nu[k][j][nx-1][m]=temp2[m];\n}\n}\n}\n}	subroutine setbv\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision temp1(5), temp2(5)\n\ndo j = 1, ny\ndo i = 1, nx\ncall exact( i, j, 1, temp1 )\ncall exact( i, j, nz, temp2 )\ndo m = 1, 5\nu( m, i, j, 1 ) = temp1(m)\nu( m, i, j, nz ) = temp2(m)\nend do\nend do\nend do\n\ndo k = 1, nz\ndo i = 1, nx\ncall exact( i, 1, k, temp1 )\ncall exact( i, ny, k, temp2 )\ndo m = 1, 5\nu( m, i, 1, k ) = temp1(m)\nu( m, i, ny, k ) = temp2(m)\nend do\nend do\nend do\n\ndo k = 1, nz\ndo j = 1, ny\ncall exact( 1, j, k, temp1 )\ncall exact( nx, j, k, temp2 )\ndo m = 1, 5\nu( m, 1, j, k ) = temp1(m)\nu( m, nx, j, k ) = temp2(m)\nend do\nend do\nend do\n\nreturn\nend
void adi(){\ncompute_rhs();\nx_solve();\ny_solve();\nz_solve();\nadd();\n}	subroutine adi\n\n\ncall compute_rhs\n\ncall x_solve\n\ncall y_solve\n\ncall z_solve\n\ncall add\n\nreturn\nend
void exact_rhs(){\ndouble dtemp[5], xi, eta, zeta, dtpp;\nint m, i, j, k, ip1, im1, jp1, jm1, km1, kp1;\n\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<= grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=0.0;\n}\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)kdnzm1;\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)jdnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)idnxm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][i]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][i]=dtppdtemp[m];\n}\ncuf[i]=buf[1][i]buf[1][i];\nbuf[0][i]=cuf[i]+buf[2][i]buf[2][i]+buf[3][i]buf[3][i];\nq[i]=0.5(buf[1][i]ue[1][i]+buf[2][i]ue[2][i]+\nbuf[3][i]ue[3][i]);\n}\nfor(i=1; i<=grid_points[0]-2; i++){\nim1=i-1;\nip1=i+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntx2(ue[1][ip1]-ue[1][im1])+\ndx1tx1(ue[0][ip1]-2.0ue[0][i]+ue[0][im1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tx2(\n(ue[1][ip1]buf[1][ip1]+c2(ue[4][ip1]-q[ip1]))-\n(ue[1][im1]buf[1][im1]+c2(ue[4][im1]-q[im1])))+\nxxcon1(buf[1][ip1]-2.0buf[1][i]+buf[1][im1])+\ndx2tx1(ue[1][ip1]-2.0ue[1][i]+ue[1][im1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tx2(\nue[2][ip1]buf[1][ip1]-ue[2][im1]buf[1][im1])+\nxxcon2(buf[2][ip1]-2.0buf[2][i]+buf[2][im1])+\ndx3tx1(ue[2][ip1]-2.0ue[2][i]+ue[2][im1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tx2(\nue[3][ip1]buf[1][ip1]-ue[3][im1]buf[1][im1])+\nxxcon2(buf[3][ip1]-2.0buf[3][i]+buf[3][im1])+\ndx4tx1(ue[3][ip1]-2.0ue[3][i]+ue[3][im1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tx2(\nbuf[1][ip1](c1ue[4][ip1]-c2q[ip1])-\nbuf[1][im1](c1ue[4][im1]-c2q[im1]))+\n0.5xxcon3(buf[0][ip1]-2.0buf[0][i]+buf[0][im1])+\nxxcon4(cuf[ip1]-2.0cuf[i]+cuf[im1])+\nxxcon5(buf[4][ip1]-2.0buf[4][i]+buf[4][im1])+\ndx5tx1(ue[4][ip1]-2.0ue[4][i]+ue[4][im1]);\n}\n\nfor(m=0; m<5; m++){\ni=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(5.0ue[m][i]-4.0ue[m][i+1]+ue[m][i+2]);\ni=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(-4.0ue[m][i-1]+6.0ue[m][i]-\n4.0ue[m][i+1]+ue[m][i+2]);\n}\nfor(m=0; m<5; m++){\nfor(i=3; i<=grid_points[0]-4; i++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][i-2]-4.0ue[m][i-1]+\n6.0ue[m][i]-4.0ue[m][i+1]+ue[m][i+2]);\n}\n}\nfor(m=0; m<5; m++){\ni=grid_points[0]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][i-2]-4.0ue[m][i-1]+\n6.0ue[m][i]-4.0ue[m][i+1]);\ni=grid_points[0]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][i-2]-4.0ue[m][i-1]+5.0ue[m][i]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)kdnzm1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)idnxm1;\nfor(j=0;j<=grid_points[1]-1;j++){\neta=(double)jdnym1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][j]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][j]=dtppdtemp[m];\n}\ncuf[j]=buf[2][j]buf[2][j];\nbuf[0][j]=cuf[j]+buf[1][j]buf[1][j]+buf[3][j]buf[3][j];\nq[j]=0.5(buf[1][j]ue[1][j]+buf[2][j]ue[2][j]+\nbuf[3][j]ue[3][j]);\n}\nfor(j=1; j<=grid_points[1]-2; j++){\njm1=j-1;\njp1=j+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\nty2(ue[2][jp1]-ue[2][jm1])+\ndy1ty1(ue[0][jp1]-2.0ue[0][j]+ue[0][jm1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-ty2(\nue[1][jp1]buf[2][jp1]-ue[1][jm1]buf[2][jm1])+\nyycon2(buf[1][jp1]-2.0buf[1][j]+buf[1][jm1])+\ndy2ty1(ue[1][jp1]-2.0ue[1][j]+ue[1][jm1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-ty2(\n(ue[2][jp1]buf[2][jp1]+c2(ue[4][jp1]-q[jp1]))-\n(ue[2][jm1]buf[2][jm1]+c2(ue[4][jm1]-q[jm1])))+\nyycon1(buf[2][jp1]-2.0buf[2][j]+buf[2][jm1])+\ndy3ty1(ue[2][jp1]-2.0ue[2][j]+ue[2][jm1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-ty2(\nue[3][jp1]buf[2][jp1]-ue[3][jm1]buf[2][jm1])+\nyycon2(buf[3][jp1]-2.0buf[3][j]+buf[3][jm1])+\ndy4ty1(ue[3][jp1]-2.0ue[3][j]+ue[3][jm1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-ty2(\nbuf[2][jp1](c1ue[4][jp1]-c2q[jp1])-\nbuf[2][jm1](c1ue[4][jm1]-c2q[jm1]))+\n0.5yycon3(buf[0][jp1]-2.0buf[0][j]+\nbuf[0][jm1])+\nyycon4(cuf[jp1]-2.0cuf[j]+cuf[jm1])+\nyycon5(buf[4][jp1]-2.0buf[4][j]+buf[4][jm1])+\ndy5ty1(ue[4][jp1]-2.0ue[4][j]+ue[4][jm1]);\n}\n\nfor(m=0; m<5; m++){\nj=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(5.0ue[m][j]-4.0ue[m][j+1]+ue[m][j+2]);\nj=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(-4.0ue[m][j-1]+6.0ue[m][j]-\n4.0ue[m][j+1]+ue[m][j+2]);\n}\nfor(m=0; m<5; m++){\nfor(j=3; j<=grid_points[1]-4; j++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][j-2]-4.0ue[m][j-1]+\n6.0ue[m][j]-4.0ue[m][j+1]+ue[m][j+2]);\n}\n}\nfor(m=0; m<5; m++){\nj=grid_points[1]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][j-2]-4.0ue[m][j-1]+\n6.0ue[m][j]-4.0ue[m][j+1]);\nj=grid_points[1]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][j-2]-4.0ue[m][j-1]+5.0ue[m][j]);\n}\n}\n}\n\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)jdnym1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)idnxm1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)kdnzm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][k]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][k]=dtppdtemp[m];\n}\ncuf[k]=buf[3][k]buf[3][k];\nbuf[0][k]=cuf[k]+buf[1][k]buf[1][k]+buf[2][k]buf[2][k];\nq[k]=0.5(buf[1][k]ue[1][k]+buf[2][k]ue[2][k]+\nbuf[3][k]ue[3][k]);\n}\nfor(k=1; k<=grid_points[2]-2; k++){\nkm1=k-1;\nkp1=k+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntz2(ue[3][kp1]-ue[3][km1])+\ndz1tz1(ue[0][kp1]-2.0ue[0][k]+ue[0][km1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tz2(\nue[1][kp1]buf[3][kp1]-ue[1][km1]buf[3][km1])+\nzzcon2(buf[1][kp1]-2.0buf[1][k]+buf[1][km1])+\ndz2tz1(ue[1][kp1]-2.0ue[1][k]+ue[1][km1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tz2(\nue[2][kp1]buf[3][kp1]-ue[2][km1]buf[3][km1])+\nzzcon2(buf[2][kp1]-2.0buf[2][k]+buf[2][km1])+\ndz3tz1(ue[2][kp1]-2.0ue[2][k]+ue[2][km1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tz2(\n(ue[3][kp1]buf[3][kp1]+c2(ue[4][kp1]-q[kp1]))-\n(ue[3][km1]buf[3][km1]+c2(ue[4][km1]-q[km1])))+\nzzcon1(buf[3][kp1]-2.0buf[3][k]+buf[3][km1])+\ndz4tz1(ue[3][kp1]-2.0ue[3][k]+ue[3][km1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tz2(\nbuf[3][kp1](c1ue[4][kp1]-c2q[kp1])-\nbuf[3][km1](c1ue[4][km1]-c2q[km1]))+\n0.5zzcon3(buf[0][kp1]-2.0buf[0][k]+buf[0][km1])+\nzzcon4(cuf[kp1]-2.0cuf[k]+cuf[km1])+\nzzcon5(buf[4][kp1]-2.0buf[4][k]+buf[4][km1])+\ndz5tz1(ue[4][kp1]-2.0ue[4][k]+ue[4][km1]);\n}\n\nfor(m=0; m<5; m++){\nk=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(5.0ue[m][k]-4.0ue[m][k+1]+ue[m][k+2]);\nk=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(-4.0ue[m][k-1]+6.0ue[m][k]-\n4.0ue[m][k+1]+ue[m][k+2]);\n}\nfor(m=0; m<5; m++){\nfor(k=3; k<=grid_points[2]-4; k++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][k-2]-4.0ue[m][k-1]+\n6.0ue[m][k]-4.0ue[m][k+1]+ue[m][k+2]);\n}\n}\nfor(m=0; m<5; m++){\nk=grid_points[2]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][k-2]-4.0ue[m][k-1]+\n6.0ue[m][k]-4.0ue[m][k+1]);\nk=grid_points[2]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp\n(ue[m][k-2]-4.0ue[m][k-1]+5.0ue[m][k]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=-1.0forcing[k][j][i][m];\n}\n}\n}\n}\n}	subroutine exact_rhs\n\n\n\nuse sp_data\nimplicit none\n\ndouble precision dtemp(5), xi, eta, zeta, dtpp\ninteger m, i, j, k, ip1, im1, jp1, &\n& jm1, km1, kp1\n\ndo k= 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nforcing(m,i,j,k) = 0.0d0\nend do\nend do\nend do\nend do\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\n\ndo i=0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(i,m) = dtemp(m)\nend do\n\ndtpp = 1.0d0 / dtemp(1)\n\ndo m = 2, 5\nbuf(i,m) = dtpp * dtemp(m)\nend do\n\ncuf(i) = buf(i,2) * buf(i,2)\nbuf(i,1) = cuf(i) + buf(i,3) * buf(i,3) + &\n& buf(i,4) * buf(i,4)\nq(i) = 0.5d0(buf(i,2)ue(i,2) + buf(i,3)ue(i,3) + &\n& buf(i,4)ue(i,4))\n\nend do\n\ndo i = 1, grid_points(1)-2\nim1 = i-1\nip1 = i+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tx2( ue(ip1,2)-ue(im1,2) )+ &\n& dx1tx1(ue(ip1,1)-2.0d0ue(i,1)+ue(im1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tx2 ( &\n& (ue(ip1,2)buf(ip1,2)+c2(ue(ip1,5)-q(ip1)))- &\n& (ue(im1,2)buf(im1,2)+c2(ue(im1,5)-q(im1))))+ &\n& xxcon1(buf(ip1,2)-2.0d0buf(i,2)+buf(im1,2))+ &\n& dx2tx1( ue(ip1,2)-2.0d0 ue(i,2)+ue(im1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tx2 * ( &\n& ue(ip1,3)buf(ip1,2)-ue(im1,3)buf(im1,2))+ &\n& xxcon2(buf(ip1,3)-2.0d0buf(i,3)+buf(im1,3))+ &\n& dx3tx1( ue(ip1,3)-2.0d0ue(i,3) +ue(im1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tx2( &\n& ue(ip1,4)buf(ip1,2)-ue(im1,4)buf(im1,2))+ &\n& xxcon2(buf(ip1,4)-2.0d0buf(i,4)+buf(im1,4))+ &\n& dx4tx1( ue(ip1,4)-2.0d0* ue(i,4)+ ue(im1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tx2( &\n& buf(ip1,2)(c1ue(ip1,5)-c2q(ip1))- &\n& buf(im1,2)(c1ue(im1,5)-c2q(im1)))+ &\n& 0.5d0xxcon3(buf(ip1,1)-2.0d0buf(i,1)+ &\n& buf(im1,1))+ &\n& xxcon4(cuf(ip1)-2.0d0cuf(i)+cuf(im1))+ &\n& xxcon5(buf(ip1,5)-2.0d0buf(i,5)+buf(im1,5))+ &\n& dx5tx1( ue(ip1,5)-2.0d0 ue(i,5)+ ue(im1,5))\nend do\n\ndo m = 1, 5\ni = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0ue(i,m) - 4.0d0ue(i+1,m) +ue(i+2,m))\ni = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0ue(i-1,m) + 6.0d0ue(i,m) - &\n& 4.0d0ue(i+1,m) + ue(i+2,m))\nend do\n\ndo m = 1, 5\ndo i = 3, grid_points(1)-4\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(i-2,m) - 4.0d0ue(i-1,m) + &\n& 6.0d0ue(i,m) - 4.0d0ue(i+1,m) + ue(i+2,m))\nend do\nend do\n\ndo m = 1, 5\ni = grid_points(1)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(i-2,m) - 4.0d0ue(i-1,m) + &\n& 6.0d0ue(i,m) - 4.0d0ue(i+1,m))\ni = grid_points(1)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(i-2,m) - 4.0d0ue(i-1,m) + 5.0d0ue(i,m))\nend do\n\nend do\nend do\n\ndo k = 1, grid_points(3)-2\ndo i=1, grid_points(1)-2\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\n\ndo j=0, grid_points(2)-1\neta = dble(j) * dnym1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(j,m) = dtemp(m)\nend do\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(j,m) = dtpp * dtemp(m)\nend do\n\ncuf(j) = buf(j,3) * buf(j,3)\nbuf(j,1) = cuf(j) + buf(j,2) * buf(j,2) + &\n& buf(j,4) * buf(j,4)\nq(j) = 0.5d0(buf(j,2)ue(j,2) + buf(j,3)ue(j,3) + &\n& buf(j,4)ue(j,4))\nend do\n\ndo j = 1, grid_points(2)-2\njm1 = j-1\njp1 = j+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& ty2( ue(jp1,3)-ue(jm1,3) )+ &\n& dy1ty1(ue(jp1,1)-2.0d0ue(j,1)+ue(jm1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - ty2( &\n& ue(jp1,2)buf(jp1,3)-ue(jm1,2)buf(jm1,3))+ &\n& yycon2(buf(jp1,2)-2.0d0buf(j,2)+buf(jm1,2))+ &\n& dy2ty1( ue(jp1,2)-2.0 ue(j,2)+ ue(jm1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - ty2( &\n& (ue(jp1,3)buf(jp1,3)+c2(ue(jp1,5)-q(jp1)))- &\n& (ue(jm1,3)buf(jm1,3)+c2(ue(jm1,5)-q(jm1))))+ &\n& yycon1(buf(jp1,3)-2.0d0buf(j,3)+buf(jm1,3))+ &\n& dy3ty1( ue(jp1,3)-2.0d0ue(j,3) +ue(jm1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - ty2( &\n& ue(jp1,4)buf(jp1,3)-ue(jm1,4)buf(jm1,3))+ &\n& yycon2(buf(jp1,4)-2.0d0buf(j,4)+buf(jm1,4))+ &\n& dy4ty1( ue(jp1,4)-2.0d0ue(j,4)+ ue(jm1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - ty2( &\n& buf(jp1,3)(c1ue(jp1,5)-c2q(jp1))- &\n& buf(jm1,3)(c1ue(jm1,5)-c2q(jm1)))+ &\n& 0.5d0yycon3(buf(jp1,1)-2.0d0buf(j,1)+ &\n& buf(jm1,1))+ &\n& yycon4(cuf(jp1)-2.0d0cuf(j)+cuf(jm1))+ &\n& yycon5(buf(jp1,5)-2.0d0buf(j,5)+buf(jm1,5))+ &\n& dy5ty1(ue(jp1,5)-2.0d0ue(j,5)+ue(jm1,5))\nend do\n\ndo m = 1, 5\nj = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0ue(j,m) - 4.0d0ue(j+1,m) +ue(j+2,m))\nj = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0ue(j-1,m) + 6.0d0ue(j,m) - &\n& 4.0d0ue(j+1,m) + ue(j+2,m))\nend do\n\ndo m = 1, 5\ndo j = 3, grid_points(2)-4\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(j-2,m) - 4.0d0ue(j-1,m) + &\n& 6.0d0ue(j,m) - 4.0d0ue(j+1,m) + ue(j+2,m))\nend do\nend do\n\ndo m = 1, 5\nj = grid_points(2)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(j-2,m) - 4.0d0ue(j-1,m) + &\n& 6.0d0ue(j,m) - 4.0d0ue(j+1,m))\nj = grid_points(2)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(j-2,m) - 4.0d0ue(j-1,m) + 5.0d0ue(j,m))\n\nend do\n\nend do\nend do\n\ndo j=1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\neta = dble(j) * dnym1\nxi = dble(i) * dnxm1\n\ndo k=0, grid_points(3)-1\nzeta = dble(k) * dnzm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(k,m) = dtemp(m)\nend do\n\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(k,m) = dtpp * dtemp(m)\nend do\n\ncuf(k) = buf(k,4) * buf(k,4)\nbuf(k,1) = cuf(k) + buf(k,2) * buf(k,2) + &\n& buf(k,3) * buf(k,3)\nq(k) = 0.5d0(buf(k,2)ue(k,2) + buf(k,3)ue(k,3) + &\n& buf(k,4)ue(k,4))\nend do\n\ndo k=1, grid_points(3)-2\nkm1 = k-1\nkp1 = k+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tz2( ue(kp1,4)-ue(km1,4) )+ &\n& dz1tz1(ue(kp1,1)-2.0d0ue(k,1)+ue(km1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tz2 ( &\n& ue(kp1,2)buf(kp1,4)-ue(km1,2)buf(km1,4))+ &\n& zzcon2(buf(kp1,2)-2.0d0buf(k,2)+buf(km1,2))+ &\n& dz2tz1( ue(kp1,2)-2.0d0 ue(k,2)+ ue(km1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tz2 * ( &\n& ue(kp1,3)buf(kp1,4)-ue(km1,3)buf(km1,4))+ &\n& zzcon2(buf(kp1,3)-2.0d0buf(k,3)+buf(km1,3))+ &\n& dz3tz1(ue(kp1,3)-2.0d0ue(k,3)+ue(km1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tz2 * ( &\n& (ue(kp1,4)buf(kp1,4)+c2(ue(kp1,5)-q(kp1)))- &\n& (ue(km1,4)buf(km1,4)+c2(ue(km1,5)-q(km1))))+ &\n& zzcon1(buf(kp1,4)-2.0d0buf(k,4)+buf(km1,4))+ &\n& dz4tz1( ue(kp1,4)-2.0d0ue(k,4) +ue(km1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tz2 * ( &\n& buf(kp1,4)(c1ue(kp1,5)-c2q(kp1))- &\n& buf(km1,4)(c1ue(km1,5)-c2q(km1)))+ &\n& 0.5d0zzcon3(buf(kp1,1)-2.0d0buf(k,1) &\n& +buf(km1,1))+ &\n& zzcon4(cuf(kp1)-2.0d0cuf(k)+cuf(km1))+ &\n& zzcon5(buf(kp1,5)-2.0d0buf(k,5)+buf(km1,5))+ &\n& dz5tz1( ue(kp1,5)-2.0d0ue(k,5)+ ue(km1,5))\nend do\n\ndo m = 1, 5\nk = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (5.0d0ue(k,m) - 4.0d0ue(k+1,m) +ue(k+2,m))\nk = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0ue(k-1,m) + 6.0d0ue(k,m) - &\n& 4.0d0ue(k+1,m) + ue(k+2,m))\nend do\n\ndo m = 1, 5\ndo k = 3, grid_points(3)-4\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(k-2,m) - 4.0d0ue(k-1,m) + &\n& 6.0d0ue(k,m) - 4.0d0ue(k+1,m) + ue(k+2,m))\nend do\nend do\n\ndo m = 1, 5\nk = grid_points(3)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(k-2,m) - 4.0d0ue(k-1,m) + &\n& 6.0d0ue(k,m) - 4.0d0ue(k+1,m))\nk = grid_points(3)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp &\n& (ue(k-2,m) - 4.0d0ue(k-1,m) + 5.0d0ue(k,m))\nend do\n\nend do\nend do\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nforcing(m,i,j,k) = -1.d0 * forcing(m,i,j,k)\nend do\nend do\nend do\nend do\n\nreturn\nend
static void vecset(int n, double v[], int iv[], int* nzv, int i, double val){\nint k;\nboolean set;\n\nset = FALSE;\nfor(k = 0; k < nzv; k++){\nif(iv[k] == i){\nv[k] = val;\nset = TRUE;\n}\n}\nif(set == FALSE){\nv[nzv] = val;\niv[nzv] = i;\nnzv = *nzv + 1;\n}\n}	subroutine vecset(n, v, iv, nzv, i, val)\n\nimplicit none\n\ninteger n, iv(), nzv, i, k\ndouble precision v(), val\n\n\nlogical set\n\nset = .false.\ndo k = 1, nzv\nif (iv(k) .eq. i) then\nv(k) = val\nset = .true.\nendif\nenddo\nif (.not. set) then\nnzv = nzv + 1\nv(nzv) = val\niv(nzv) = i\nendif\nreturn\nend
void error_norm(double rms[5]){\nint i, j, k, m, d;\ndouble xi, eta, zeta, u_exact[5], add;\nfor(m=0;m<5;m++){rms[m]=0.0;}\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)dnxm1;\nexact_solution(xi, eta, zeta, u_exact);\nfor(m=0; m<5; m++){\nadd=u[k][j][i][m]-u_exact[m];\nrms[m]=rms[m]+addadd;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}	subroutine error_norm(rms)\n\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m, d\ndouble precision xi, eta, zeta, u_exact(5), rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, u_exact)\n\ndo m = 1, 5\nadd = u(m,i,j,k)-u_exact(m)\nrms(m) = rms(m) + addadd\nenddo\nenddo\nenddo\nenddo\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nenddo\nrms(m) = dsqrt(rms(m))\nenddo\n\nreturn\nend\n\n\n\nsubroutine rhs_norm(rms)\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, d, m\ndouble precision rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nadd = rhs(m,i,j,k)\nrms(m) = rms(m) + addadd\nenddo\nenddo\nenddo\nenddo\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nenddo\nrms(m) = dsqrt(rms(m))\nenddo\n\nreturn\nend
static void bubble(double ten[][MM], int j1[][MM], int j2[][MM], int j3[][MM], int m, int ind){\ndouble temp;\nint i, j_temp;\n\nif(ind == 1){\nfor(i = 0; i < m-1; i++){\nif(ten[ind][i] > ten[ind][i+1]){\ntemp = ten[ind][i+1];\nten[ind][i+1] = ten[ind][i];\nten[ind][i] = temp;\n\nj_temp = j1[ind][i+1];\nj1[ind][i+1] = j1[ind][i];\nj1[ind][i] = j_temp;\n\nj_temp = j2[ind][i+1];\nj2[ind][i+1] = j2[ind][i];\nj2[ind][i] = j_temp;\n\nj_temp = j3[ind][i+1];\nj3[ind][i+1] = j3[ind][i];\nj3[ind][i] = j_temp;\n}else{\nreturn;\n}\n}\n}else{\nfor(i = 0; i < m-1; i++){\nif(ten[ind][i] < ten[ind][i+1]){\ntemp = ten[ind][i+1];\nten[ind][i+1] = ten[ind][i];\nten[ind][i] = temp;\n\nj_temp = j1[ind][i+1];\nj1[ind][i+1] = j1[ind][i];\nj1[ind][i] = j_temp;\n\nj_temp = j2[ind][i+1];\nj2[ind][i+1] = j2[ind][i];\nj2[ind][i] = j_temp;\n\nj_temp = j3[ind][i+1];\nj3[ind][i+1] = j3[ind][i];\nj3[ind][i] = j_temp;\n}else{\nreturn;\n}\n}\n}\n}	subroutine bubble( ten, j1, j2, j3, m, ind )\n\n\nimplicit none\n\n\ninteger m, ind, j1( m, 0:1 ), j2( m, 0:1 ), j3( m, 0:1 )\ndouble precision ten( m, 0:1 )\ndouble precision temp\ninteger i, j_temp\n\nif( ind .eq. 1 )then\n\ndo i=1,m-1\nif( ten(i,ind) .gt. ten(i+1,ind) )then\n\ntemp = ten( i+1, ind )\nten( i+1, ind ) = ten( i, ind )\nten( i, ind ) = temp\n\nj_temp = j1( i+1, ind )\nj1( i+1, ind ) = j1( i, ind )\nj1( i, ind ) = j_temp\n\nj_temp = j2( i+1, ind )\nj2( i+1, ind ) = j2( i, ind )\nj2( i, ind ) = j_temp\n\nj_temp = j3( i+1, ind )\nj3( i+1, ind ) = j3( i, ind )\nj3( i, ind ) = j_temp\n\nelse\nreturn\nendif\nenddo\n\nelse\n\ndo i=1,m-1\nif( ten(i,ind) .lt. ten(i+1,ind) )then\n\ntemp = ten( i+1, ind )\nten( i+1, ind ) = ten( i, ind )\nten( i, ind ) = temp\n\nj_temp = j1( i+1, ind )\nj1( i+1, ind ) = j1( i, ind )\nj1( i, ind ) = j_temp\n\nj_temp = j2( i+1, ind )\nj2( i+1, ind ) = j2( i, ind )\nj2( i, ind ) = j_temp\n\nj_temp = j3( i+1, ind )\nj3( i+1, ind ) = j3( i, ind )\nj3( i, ind ) = j_temp\n\nelse\nreturn\nendif\nenddo\n\nendif\n\nreturn\nend

#include <omp.h>\n#include <stdio.h>\n\nint main()\n{\n int numThreads=0 ; \n#pragma omp parallel\n {\n if ( omp_get_thread_num()==0 ) {\n numThreads = omp_get_num_threads();\n }\n }\n printf ("numThreads=%d\n", numThreads);\n return 0;\n}\n

program DRB051_getthreadnum_orig_no\n use omp_lib\n implicit none\n\n integer :: numThreads\n\n !$omp parallel\n if (omp_get_thread_num() == 0) then\n numThreads = omp_get_num_threads()\n end if\n !$omp end parallel\n\n print 100, numThreads\n 100 format ('numThreads =',i3)\nend program

#include <stdio.h>\n#include <assert.h>\n\nint sum0=0, sum1=0;\n#pragma omp threadprivate(sum0)\n\nvoid foo (int i)\n{\n sum0=sum0+i;\n}\n\nint main()\n{\n int len=1000;\n int i, sum=0;\n#pragma omp parallel copyin(sum0)\n {\n#pragma omp for\n for (i=0;i<len;i++)\n {\n foo (i);\n } \n#pragma omp critical\n {\n sum= sum+sum0;\n } \n } \n/* reference calculation */\n for (i=0;i<len;i++)\n {\n sum1=sum1+i;\n }\n printf("sum=%d; sum1=%d\n",sum,sum1);\n assert(sum==sum1);\n return 0;\n}\n\n

program DRB085_threadprivate_orig_no\n use omp_lib\n use DRB085\n implicit none\n\n integer :: len\n integer (kind=8) :: i, sum\n len = 1000\n sum = 0\n\n !$omp parallel copyin(sum0)\n !$omp do\n do i = 1, len\n call foo(i)\n end do\n !$omp end do\n !$omp critical\n sum = sum+sum0\n !$omp end critical\n !$omp end parallel\n\n do i = 1, len\n sum1=sum1+i\n end do\n\n print*,'sum = ',sum,'sum1 =',sum1\nend program

#include <assert.h>\n#include <stdio.h>\n#include <stdlib.h>\n\n#define N 180\nint indexSet[N] = {\n521, 523, 525, 533, 529, 531, // 521+12=533\n547, 549, 551, 553, 555, 557,\n573, 575, 577, 579, 581, 583,\n599, 601, 603, 605, 607, 609,\n625, 627, 629, 631, 633, 635,\n\n651, 653, 655, 657, 659, 661,\n859, 861, 863, 865, 867, 869,\n885, 887, 889, 891, 893, 895,\n911, 913, 915, 917, 919, 921, \n937, 939, 941, 943, 945, 947,\n\n963, 965, 967, 969, 971, 973,\n989, 991, 993, 995, 997, 999, \n1197, 1199, 1201, 1203, 1205, 1207,\n1223, 1225, 1227, 1229, 1231, 1233,\n1249, 1251, 1253, 1255, 1257, 1259,\n\n1275, 1277, 1279, 1281, 1283, 1285,\n1301, 1303, 1305, 1307, 1309, 1311,\n1327, 1329, 1331, 1333, 1335, 1337,\n1535, 1537, 1539, 1541, 1543, 1545,\n1561, 1563, 1565, 1567, 1569, 1571,\n\n1587, 1589, 1591, 1593, 1595, 1597,\n1613, 1615, 1617, 1619, 1621, 1623,\n1639, 1641, 1643, 1645, 1647, 1649,\n1665, 1667, 1669, 1671, 1673, 1675,\n1873, 1875, 1877, 1879, 1881, 1883,\n\n1899, 1901, 1903, 1905, 1907, 1909,\n1925, 1927, 1929, 1931, 1933, 1935,\n1951, 1953, 1955, 1957, 1959, 1961,\n1977, 1979, 1981, 1983, 1985, 1987,\n2003, 2005, 2007, 2009, 2011, 2013};\n\nint main (int argc, char* argv[])\n{\n double * base = (double*) malloc(sizeof(double)* (2013+12+1));\n if (base == 0)\n {\n printf ("Error in malloc(). Aborting ...\n");\n return 1; \n }\n\n double * xa1 = base;\n double * xa2 = xa1 + 12;\n int i;\n\n // initialize segments touched by indexSet\n for (i =521; i<= 2025; ++i)\n {\n base[i]=0.5*i;\n }\n\n#pragma omp parallel for // default static even scheduling may not trigger data race!\n for (i =0; i< N; ++i) \n {\n int idx = indexSet[i];\n xa1[idx]+= 1.0;\n xa2[idx]+= 3.0;\n }\n printf("x1[999]=%f xa2[1285]=%f\n", xa1[999], xa2[1285]);\n free (base);\n return 0;\n}\n\n

program DRB007_indirectaccess3_orig_yes\n use omp_lib\n use DRB007\n implicit none\n\n integer :: i, idx1, idx2\n integer, parameter :: dp = kind(1.0d0)\n real(dp), dimension(:), pointer :: xa1=>NULL(), xa2=>NULL()\n real(dp), dimension(2025), target :: base\n\n allocate (xa1(2025))\n allocate (xa2(2025))\n\n xa1 => base(1:2025)\n xa2 => base(1:2025)\n\n n=180\n\n indexSet = (/ 521, 523, 525, 533, 529, 531, 547, 549, &\n 551, 553, 555, 557, 573, 575, 577, 579, 581, 583, 599, &\n 601, 603, 605, 607, 609, 625, 627, 629, 631, 633, 635, &\n 651, 653, 655, 657, 659, 661, 859, 861, 863, 865, 867, &\n 869, 885, 887, 889, 891, 893, 895, 911, 913, 915, 917, &\n 919, 921, 937, 939, 941, 943, 945, 947, 963, 965, 967, &\n 969, 971, 973, 989, 991, 993, 995, 997, 999, 1197, 1199, &\n 1201, 1203, 1205, 1207, 1223, 1225, 1227, 1229, 1231, &\n 1233, 1249, 1251, 1253, 1255, 1257, 1259, 1275, 1277, &\n 1279, 1281, 1283, 1285, 1301, 1303, 1305, 1307, 1309, &\n 1311, 1327, 1329, 1331, 1333, 1335, 1337, 1535, 1537, &\n 1539, 1541, 1543, 1545, 1561, 1563, 1565, 1567, 1569, &\n 1571, 1587, 1589, 1591, 1593, 1595, 1597, 1613, 1615, &\n 1617, 1619, 1621, 1623, 1639, 1641, 1643, 1645, 1647, &\n 1649, 1665, 1667, 1669, 1671, 1673, 1675, 1873, 1875, &\n 1877, 1879, 1881, 1883, 1899, 1901, 1903, 1905, 1907, &\n 1909, 1925, 1927, 1929, 1931, 1933, 1935, 1951, 1953, &\n 1955, 1957, 1959, 1961, 1977, 1979, 1981, 1983, 1985, &\n 1987, 2003, 2005, 2007, 2009, 2011, 2013 /)\n\n do i = 521, 2025\n base(i) = 0.5*i\n end do\n\n !$omp parallel do\n do i = 1, n\n idx1 = indexSet(i)\n idx2 = indexSet(i)+12\n base(idx1) = base(idx1)+1.0\n base(idx2) = base(idx2)+3.0\n end do\n !$omp end parallel do\n\n print*,'xa1(999) =',base(999),' xa2(1285) =',base(1285)\n\n nullify(xa1,xa2)\nend program

#include <stdio.h>\n#define N 100\n#define M 100 \n#define K 100\ndouble a[N][M],b[M][K],c[N][K];\n \nint mmm() \n{ \n int i,j,k;\n#pragma omp parallel for private(j,k)\n for (i = 0; i < N; i++) \n for (k = 0; k < K; k++) \n for (j = 0; j < M; j++)\n c[i][j]= c[i][j]+a[i][k]*b[k][j];\n return 0; \n} \n\nint main()\n{\n mmm();\n return 0;\n} \n

program DRB060_matrixmultiply_orig_no\n use omp_lib\n implicit none\n\n integer :: N,M,K, len, i, j, l\n real, dimension(:,:), allocatable :: a, b, c\n\n len = 100\n N=len\n M=len\n K=len\n\n allocate (a(N,M))\n allocate (b(M,K))\n allocate (c(K,N))\n\n !$omp parallel do private(j, l)\n do i = 1, N\n do l = 1, K\n do j = 1, M\n c(i,j) = c(i,j)+a(i,l)*b(l,j)\n end do\n end do\n end do\n !$omp end parallel do\n\n deallocate(a,b,c)\nend program

#include <stdio.h> \nint main()\n{\n int i=0;\n#pragma omp parallel sections\n {\n#pragma omp section\n i = 1; \n#pragma omp section\n i = 2; \n }\n printf("i=%d\n",i);\n return 0;\n} \n

program DRB023_sections1_orig_yes\n use omp_lib\n implicit none\n\n integer :: i\n i = 0\n\n !$omp parallel sections\n !$omp section\n i=1\n !$omp section\n i=2\n !$omp end parallel sections\n\n print 100, i\n 100 format ("i=",i3)\n\nend program

#include <stdio.h>\n \nfloat x=0.0;\nint y=0;\n#pragma omp threadprivate(x,y)\n\nint main (int argc, char * argv[])\n{\n#pragma omp parallel\n {\n#pragma omp single copyprivate(x,y)\n {\n x=1.0;\n y=1;\n }\n }\n printf ("x=%f y=%d\n", x, y);\n return 0;\n}\n

program DRB102_copyprivate_orig_no\n use omp_lib\n use DRB102\n implicit none\n\n !$omp parallel\n !$omp single\n x=1.0\n y=1\n !$omp end single copyprivate(x,y)\n !$omp end parallel\n\n print 100, x, y\n 100 format ('x =',F3.1,2x,'y =',i3)\n\nend program

#include <stdio.h>\n#include <omp.h>\n#include <stdlib.h>\n#define N 100\n\nint main(){\n\n int var[N];\n\n for(int i=0; i<N; i++){\n var[i]=0;\n }\n\n #pragma omp target map(tofrom:var[0:N]) device(0)\n #pragma omp parallel for ordered\n for (int i=1; i<N; i++){\n #pragma omp ordered\n {\n var[i]=var[i-1]+1;\n }\n }\n\n for(int i=0; i<N; i++){\n if(var[i]!=i){\n printf("Data Race Present");\n return 0;\n }\n }\n\n return 0;\n}\n

program DRB155_missingordered_orig_gpu_no\n use omp_lib\n implicit none\n\n integer :: var(100)\n integer :: i\n\n do i = 1, 100\n var(i) = 1\n end do\n\n !$omp target map(tofrom:var) device(0)\n !$omp parallel do ordered\n do i = 2, 100\n !$omp ordered\n var(i) = var(i-1)+1\n !$omp end ordered\n end do\n !$omp end parallel do\n !$omp end target\n\n do i = 1, 100\n if (var(i)/=i) then\n print*,"Data Race Present"\n end if\n end do\n\nend program

#include <stdio.h>\n/*\n * loop missing the linear clause\n * Data race pairs (race on j allows wrong indexing of c): \n j@70:7:R vs. j@71:5:W\n j@71:5:W vs. j@71:5:W \n c[j]@70:5:W vs. c[j]@70:5:W\n*/\nint main()\n{\n int len=100;\n double a[len], b[len], c[len];\n int i,j=0;\n\n for (i=0;i<len;i++)\n {\n a[i]=((double)i)/2.0; \n b[i]=((double)i)/3.0; \n c[i]=((double)i)/7.0; \n }\n\n#pragma omp parallel for \n for (i=0;i<len;i++)\n {\n c[j]+=a[i]*b[i];\n j++;\n }\n\n printf ("c[50]=%f\n",c[50]);\n return 0;\n}\n

program DRB111_linearmissing_orig_yes\n use omp_lib\n implicit none\n\n integer len, i, j\n integer, parameter :: dp = kind(1.0d0)\n real(dp), dimension(:), allocatable :: a,b,c\n\n len = 100\n i = 0\n j = 0\n\n allocate (a(len))\n allocate (b(len))\n allocate (c(len))\n\n do i = 1, len\n a(i) = (real(i,dp))/2.0\n b(i) = (real(i,dp))/3.0\n c(i) = (real(i,dp))/7.0\n end do\n\n !$omp parallel do\n do i = 1, len\n c(j) = c(j)+a(i)*b(i)\n j = j+1\n end do\n !$omp end parallel do\n\n print*,'c(50) =',c(50)\n\n if(allocated(a))deallocate(a)\n if(allocated(b))deallocate(b)\n \nend program

#include <stdio.h>\n#define N 100\n\ndouble a[N][N],v[N],v_out[N];\nint mv()\n{ \n int i,j;\n#pragma omp parallel for private (i,j)\n for (i = 0; i < N; i++)\n { \n float sum = 0.0;\n for (j = 0; j < N; j++)\n { \n sum += a[i][j]*v[j];\n } \n v_out[i] = sum;\n } \n return 0; \n}\n\nint main()\n{\n mv();\n return 0;\n}\n\n

program DRB061_matrixvector1_orig_no\n use omp_lib\n implicit none\n call foo\ncontains\n subroutine foo()\n integer :: i, j, N\n real :: sum\n real, dimension(:,:), allocatable :: a\n real, dimension(:), allocatable :: v, v_out\n\n N = 100\n allocate (a(N,N))\n allocate (v(N))\n allocate (v_out(N))\n\n !$omp parallel do private (i,j,sum)\n do i = 1, N\n do j = 1, N\n sum = sum + a(i,j)*v(j)\n end do\n v_out(i) = sum\n end do\n !$omp end parallel do\n\n end subroutine foo\nend program

#include <stdio.h>\n#include <omp.h>\n#define N 100\n\nint main(){\n int var = 0;\n\n #pragma omp target map(tofrom:var) device(0)\n #pragma omp teams num_teams(1)\n #pragma omp distribute parallel for\n for (int i=0; i<N; i++){\n var++;\n }\n\n printf("%d\n ",var);\n return 0;\n}\n

program DRB153_missinglock2_orig_gpu_yes\n use omp_lib\n implicit none\n\n integer :: var, i\n var = 0\n\n !$omp target map(tofrom:var) device(0)\n !$omp teams num_teams(1)\n !$omp distribute parallel do\n do i = 1, 100\n var = var + 1\n end do\n !$omp end distribute parallel do\n !$omp end teams\n !$omp end target\n\n print*, var\nend program

#include <stdlib.h>\n#include <stdio.h>\nint main(int argc, char* argv[])\n{\n int i;\n\n int a[2000];\n\n for (i=0; i<2000; i++)\n a[i]=i; \n\n#pragma omp parallel for\n for (i=0;i<1000;i++)\n a[2*i+1]=a[i]+1;\n\n printf("a[1001]=%d\n", a[1001]); \n return 0;\n}\n\n

program DRB033_truedeplinear_orig_yes\n use omp_lib\n implicit none\n\n integer :: i, len\n integer, dimension(:), allocatable :: a\n\n len = 2000\n allocate (a(len))\n\n do i = 1, len\n a(i) = i\n end do\n\n !$omp parallel do\n do i = 1, 1000\n a(2*i) = a(i) + 1\n end do\n !$omp end parallel do\n\n print 100, a(1002)\n 100 format ('a(1002) =',i3)\n\n deallocate(a)\nend program

#include <stdio.h>\n#define N 20\n#define C 8\n\nint main(){\n int var[C];\n\n for(int i=0; i<C; i++){\n var[i] = 0;\n }\n\n #pragma omp target map(tofrom:var) device(0)\n #pragma omp teams num_teams(1) thread_limit(1048) \n #pragma omp distribute parallel for reduction(+:var)\n for (int i=0; i<N; i++){\n #pragma omp simd\n for(int i=0; i<C; i++){\n var[i]++;\n }\n }\n\n for(int i=0; i<C; i++){\n if(var[i]!=N) printf("%d\n ",var[i]);\n }\n\n return 0;\n}\n

program DRB162_nolocksimd_orig_gpu_no\n use omp_lib\n implicit none\n\n integer :: var(8)\n integer :: i,j\n\n do i = 1, 8\n var(i) = 0\n end do\n\n !$omp target map(tofrom:var) device(0)\n !$omp teams num_teams(1) thread_limit(1048)\n !$omp distribute parallel do reduction(+:var)\n do i = 1, 20\n !$omp simd\n do j = 1, 8\n var(j) = var(j)+1\n end do\n !$omp end simd\n end do\n !$omp end distribute parallel do\n !$omp end teams\n !$omp end target\n\n do i = 1, 8\n if (var(i) /= 20) then\n print*,var(i)\n end if\n end do\n\nend program

#include <omp.h>\n#include <stdio.h>\n\nint main()\n{\n int k;\n\n#pragma omp parallel\n {\n#pragma omp master\n {\n k = omp_get_num_threads();\n printf ("Number of Threads requested = %i\n",k);\n }\n }\n return 0;\n}\n

program DRB103_master_orig_no\n use omp_lib\n implicit none\n\n integer k\n\n !$omp parallel\n !$omp master\n k = omp_get_num_threads()\n print 100, k\n 100 format ('Number of threads requested =',3i8)\n !$omp end master\n !$omp end parallel\n\nend program

#include <stdio.h>\n#include <omp.h>\n\nvoid foo(){\n int x = 0, y = 2;\n\n #pragma omp task depend(inout: x) shared(x)\n x++; // 1st child task\n\n #pragma omp task depend(in: x) depend(inout: y) shared(x, y)\n y = y-x; //2nd child task\n\n #pragma omp taskwait depend(in: x) // 1st taskwait\n\n printf("x=%d\n",x);\n\n #pragma omp taskwait // 2nd taskwait\n\n printf("y=%d\n",y);\n}\n\nint main(){\n #pragma omp parallel\n #pragma omp single\n foo();\n\n return 0;\n}\n\n

program DRB167_taskdep5_orig_no_omp50\n use omp_lib\n implicit none\n\n !$omp parallel\n !$omp single\n call foo()\n !$omp end single\n !$omp end parallel\ncontains\n subroutine foo()\n implicit none\n integer :: x, y\n x = 0\n y = 2\n\n !$omp task depend(inout: x) shared(x)\n x = x+1 !!1st Child Task\n !$omp end task\n\n !$omp task shared(y)\n y = y-x !!2nd child task\n !$omp end task\n\n !$omp taskwait depend(in: x) !!1st taskwait\n\n print*, "x=", x\n\n !$omp taskwait !!2nd taskwait\n\n print*, "y=", y\n\n end subroutine\nend program

#include<stdio.h>\n#include<stdlib.h>\n\nint* counter; \n//#pragma omp threadprivate(counter)\n\nint main()\n{ \n counter = (int*) malloc(sizeof(int));\n if (counter== NULL)\n {\n fprintf(stderr, "malloc() fails\n");\n exit(1);\n }\n *counter = 0; \n #pragma omp parallel \n {\n (*counter)++; \n }\n printf("%d \n", *counter);\n free (counter);\n return 0; \n}\n\n

program DRB088_dynamic_storage_orig_yes\n use omp_lib\n implicit none\n integer, pointer :: counter\n\n allocate(counter)\n\n counter = 0\n\n !$omp parallel\n counter = counter+1\n !$omp end parallel\n\n print*,counter\n\n deallocate(counter)\n\nend program

#include <stdio.h>\n#define min(x, y) (((x) < (y)) ? (x) : (y))\n\n/*\nuse of omp target + teams + distribute + parallel for\n*/\nint main(int argc, char* argv[])\n{\n int i, i2;\n int len = 2560;\n double sum =0.0, sum2=0.0;\n double a[len], b[len];\n /*Initialize with some values*/\n for (i=0; i<len; i++)\n {\n a[i]= ((double)i)/2.0;\n b[i]= ((double)i)/3.0;\n }\n\n#pragma omp target map(to: a[0:len], b[0:len]) map(tofrom: sum)\n#pragma omp teams num_teams(10) thread_limit(256) reduction (+:sum) \n#pragma omp distribute\n for (i2=0; i2< len; i2+=256) \n#pragma omp parallel for reduction (+:sum)\n for (i=i2;i< min(i2+256, len); i++)\n sum += a[i]*b[i];\n\n/* CPU reference computation */ \n#pragma omp parallel for reduction (+:sum2)\n for (i=0;i< len; i++)\n sum2 += a[i]*b[i];\n printf ("sum=%f sum2=%f\n", sum, sum2);\n return 0;\n}\n

program DRB097_target_teams_distribute_orig_no\n use omp_lib\n use ISO_C_Binding\n implicit none\n integer, parameter :: dp = kind(1.0d0)\n integer, parameter :: double_kind = c_double\n integer (kind=8) :: i, i2, len, l_limit, tmp\n real(dp) :: sum, sum2\n real(dp), dimension(:), allocatable :: a, b\n\n len = 2560\n sum = real(0.0,dp)\n sum2 = real(0.0,dp)\n\n allocate (a(len))\n allocate (b(len))\n\n do i = 1, len\n a(i) = real(i,dp)/real(2.0,dp)\n b(i) = real(i,dp)/real(3.0,dp)\n end do\n\n !$omp target map(to: a(0:len), b(0:len)) map(tofrom: sum)\n !$omp teams num_teams(10) thread_limit(256) reduction (+:sum)\n !$omp distribute\n do i2 = 1, len, 256\n !$omp parallel do reduction (+:sum)\n do i = i2+1, merge(i2+256,len,i2+256<len)\n sum = sum+a(i)*b(i)\n end do\n !$omp end parallel do\n end do\n !$omp end distribute\n !$omp end teams\n !$omp end target\n\n !$omp parallel do reduction (+:sum2)\n do i = 1, len\n sum2 = sum2+a(i)*b(i)\n end do\n !$omp end parallel do\n\n print*,'sum =',int(sum),'; sum2 =',int(sum2)\n\n deallocate(a,b)\nend program

#include<stdio.h>\n#include<assert.h>\n/* argument pass-by-value */\nvoid f1(int q)\n{\n q += 1;\n}\n\nint main()\n{\n int i=0;\n #pragma omp parallel \n {\n f1(i);\n }\n assert (i==0);\n printf ("i=%d\n",i);\n return 0;\n}\n\n

program DRB080_func_arg_orig_yes\n use omp_lib\n use global\n implicit none\n\n integer :: i\n i = 0\n\n !$omp parallel\n call f1(i)\n !$omp end parallel\n\n if (i /= 0) then\n print 100, i\n 100 format ('i =',i3)\n end if\nend program

#include <assert.h> \nint main()\n{\n int i=0;\n#pragma omp parallel\n#pragma omp single\n {\n#pragma omp task depend (out:i)\n i = 1; \n#pragma omp task depend (in:i)\n i = 2; \n }\n\n assert (i==2);\n return 0;\n} \n

program DRB072_taskdep1_orig_no\n use omp_lib\n implicit none\n\n integer :: i\n i = 0\n\n !$omp parallel\n !$omp single\n !$omp task depend (out:i)\n i = 1\n !$omp end task\n !$omp task depend (in:i)\n i = 2\n !$omp end task\n !$omp end single\n !$omp end parallel\n\n if (i/=2) then\n print*,'i is not equal to 2'\n end if\nend program

#include <stdio.h>\n#if (_OPENMP<201511)\n#error "An OpenMP 4.5 compiler is needed to compile this test."\n#endif\n#include <stdio.h>\nint a[100][100];\nint main()\n{\n int i, j;\n#pragma omp parallel for ordered(2)\n for (i = 0; i < 100; i++)\n for (j = 0; j < 100; j++)\n {\n a[i][j] = a[i][j] + 1;\n#pragma omp ordered depend(sink:i-1,j) depend (sink:i,j-1)\n printf ("test i=%d j=%d\n",i,j);\n#pragma omp ordered depend(source)\n }\n return 0;\n}\n\n

program DRB094_doall2_ordered_orig_no\n use omp_lib\n use DRB094\n implicit none\n\n integer :: len, i, j\n len = 100\n\n allocate (a(len,len))\n\n !$omp parallel do ordered(2)\n do i = 1, len\n do j = 1, len\n a(i,j) = a(i,j)+1\n !$omp ordered depend(sink:i-1,j) depend (sink:i,j-1)\n print*,'test i =',i,' j =',j\n !$omp ordered depend(source)\n end do\n end do\n !$omp end parallel do\n\n\nend program

#include <stdlib.h> \n#include <stdio.h>\nint main(int argc, char* argv[]) \n{\n int i;\n int len=100;\n\n int numNodes=len, numNodes2=0; \n int x[100]; \n\n // initialize x[]\n for (i=0; i< len; i++)\n {\n if (i%2==0)\n x[i]=5;\n else\n x[i]= -5;\n }\n\n#pragma omp parallel for\n for (i=numNodes-1 ; i>-1 ; --i) {\n if (x[i]<=0) {\n numNodes2-- ;\n }\n }\n printf ("numNodes2 = %d\n", numNodes2);\n return 0;\n} \n

program DRB011_minusminus_orig_yes\n use omp_lib\n implicit none\n\n integer :: i, len, numNodes, numNodes2\n integer :: x(100)\n len = 100\n numNodes=len\n numNodes2=0\n\n do i = 1, len\n if (MOD(i,2) == 0) then\n x(i) = 5\n else\n x(i) = -5\n end if\n end do\n\n !$omp parallel do\n do i = numNodes, 1, -1\n if (x(i) <= 0) then\n numNodes2 = numNodes2-1\n end if\n end do\n !$omp end parallel do\n\n print*,"numNodes2 =", numNodes2\nend program

#include <stdlib.h>\nint main (int argc, char* argv[])\n{\n int len=1000;\n int i; \n\n if (argc>1)\n len = atoi(argv[1]);\n int a[len];\n a[0] = 2;\n\n#pragma omp parallel for\n for (i=0;i<len;i++)\n a[i]=a[i]+a[0];\n\n return 0;\n}\n

program DRB040_truedepsingleelement_var_yes\n use omp_lib\n implicit none\n\n integer :: len, i, argCount, allocStatus, rdErr, ix\n character(len=80), dimension(:), allocatable :: args\n integer, dimension(:), allocatable :: a\n\n len = 1000\n\n argCount = command_argument_count()\n if (argCount == 0) then\n write (*,'(a)') "No command line arguments provided."\n end if\n\n allocate(args(argCount), stat=allocStatus)\n if (allocStatus > 0) then\n write (*,'(a)') "Allocation error, program terminated."\n stop\n end if\n\n do ix = 1, argCount\n call get_command_argument(ix,args(ix))\n end do\n\n if (argCount >= 1) then\n read (args(1), '(i10)', iostat=rdErr) len\n if (rdErr /= 0 ) then\n write (*,'(a)') "Error, invalid integer value."\n end if\n end if\n\n allocate (a(len))\n\n a(1) = 2\n\n !$omp parallel do\n do i = 1, len\n a(i) = a(i)+a(1)\n end do\n !$omp end parallel do\n\n print 100, a(0)\n 100 format ('a(0) =',i3)\n\n deallocate(args,a)\nend program

#include <stdio.h>\nvoid foo(int * a, int n, int g)\n{\n int i;\n#pragma omp parallel for firstprivate (g)\n for (i=0;i<n;i++)\n {\n a[i] = a[i]+g;\n }\n}\n\nint a[100];\nint main()\n{\n foo(a, 100, 7);\n return 0;\n} \n

program DRB048_firstprivate_orig_no\n use omp_lib\n use DRB048\n implicit none\n\n allocate (a(100))\n call foo(a, 100, 7)\n print*,a(50)\nend program

#include <stdio.h>\n#include <omp.h>\n#define N 100\n#define C 64\n\nint main(){\n\n int var[C];\n\n for(int i=0; i<C; i++){\n var[i]=0;\n }\n\n #pragma omp target map(tofrom:var[0:C]) device(0)\n #pragma omp teams distribute parallel for\n for (int i=0; i<N; i++){\n #pragma omp simd\n for(int i=0; i<C; i++){\n var[i]++;\n }\n }\n\n printf("%d\n",var[63]);\n\n return 0;\n}\n

program DRB163_simdmissinglock1_orig_gpu_no\n use omp_lib\n use DRB163\n implicit none\n\n do i = 1, 16\n var(i) = 0\n end do\n\n !$omp target map(tofrom:var) device(0)\n !$omp teams distribute parallel do\n do i = 1, 20\n !$omp simd\n do j = 1, 16\n var(j) = var(j)+1\n end do\n !$omp end simd\n end do\n !$omp end teams distribute parallel do\n !$omp end target\n\n print*,var(16)\n\nend program

#include <stdlib.h>\n#include <stdio.h>\ndouble b[1000][1000];\n\nint main(int argc, char* argv[]) \n{\n int i,j;\n int n=1000, m=1000;\n for (i=0;i<n;i++)\n#pragma omp parallel for\n for (j=1;j<m;j++)\n b[i][j]=b[i][j-1];\n\n printf("b[500][500]=%f\n", b[500][500]);\n return 0;\n}\n\n

program DRB037_truedepseconddimension_orig_yes\n use omp_lib\n implicit none\n\n integer i, j, n, m, len\n real, dimension(:,:), allocatable :: b\n\n len = 1000\n n = len\n m = len\n\n allocate (b(len,len))\n\n do i = 1, n\n !$omp parallel do\n do j = 2, m\n b(i,j) = b(i,j-1)\n end do\n !$omp end parallel do\n end do\n\n print 100, b(500,500)\n 100 format ('b(500,500) =', F20.6)\n\n deallocate(b)\nend program

#include <stdio.h>\nvoid foo()\n{\n int q=0; \n q += 1;\n}\n\nint main()\n{ \n #pragma omp parallel \n {\n foo();\n }\n return 0; \n}\n\n

program DRB083_declared_in_func_orig_no\n use omp_lib\n use DRB083\n implicit none\n\n !$omp parallel\n call foo()\n !$omp end parallel\nend program

#include <stdio.h>\nint main()\n{\n int i,j;\n int n=100, m=100;\n double b[n][m];\n\n for(i=0;i<n; i++) \n for(j=0;j<n; j++) \n b[i][j]=(double)(i*j);\n\n for (i=1;i<n;i++)\n#pragma omp parallel for\n for (j=1;j<m;j++)\n b[i][j]=b[i-1][j-1];\n return 0;\n}\n

program DRB054_inneronly2_orig_no\n use omp_lib\n implicit none\n\n integer i,j,n,m\n real, dimension(:,:), allocatable :: b\n\n n = 100\n m = 100\n\n allocate (b(n,m))\n\n do i = 1, n\n do j = 1, m\n b(i,j) = i*j\n end do\n end do\n\n do i = 2, n\n !$omp parallel do\n do j =2, m\n b(i,j)=b(i-1,j-1)\n end do\n !$omp end parallel do\n end do\n\n deallocate(b)\nend program

#include <stdlib.h>\nvoid setup(int N)\n{\n double * m_pdv_sum = (double* ) malloc (sizeof (double) * N );\n double * m_nvol = (double* ) malloc (sizeof (double) * N );\n\n#pragma omp parallel for schedule(static)\n for (int i=0; i < N; ++i ) \n { \n m_pdv_sum[ i ] = 0.0;\n m_nvol[ i ] = i*2.5;\n }\n\n free(m_pdv_sum);\n free(m_nvol);\n}\n\nint main()\n{\n int N =1000;\n setup(N);\n}\n \n

program DRB066_pointernoaliasing_orig_no\n use omp_lib\n use DRB066\n implicit none\n\n integer :: N\n N = 1000\n\n call setup(N)\n\nend program

#include <stdio.h>\nint main(int argc, char* argv[])\n{ \n int i;\n int len = 1000;\n\n int a[1000];\n\n for (i=0; i<len; i++)\n a[i]= i; \n\n#pragma omp parallel for\n for (i=0;i< len -1 ;i++)\n a[i]=a[i+1]+1;\n\n printf ("a[500]=%d\n", a[500] );\n return 0;\n} \n

program DRB001_antidep1_orig_yes\nuse omp_lib\n implicit none\n integer :: i, len\n integer :: a(1000)\n\n len = 1000\n\n do i = 1, len\n a(i) = i\n end do\n\n !$omp parallel do\n do i = 1, len-1\n a(i) = a(i+1) + 1\n end do\n !$omp end parallel do\n\n print 100, a(500)\n 100 format ('a(500)=',i3)\nend program

#include <stdio.h>\n#include <math.h>\n\n#define MSIZE 200\nint n=MSIZE, m=MSIZE;\ndouble alpha = 0.0543;\ndouble u[MSIZE][MSIZE], f[MSIZE][MSIZE], uold[MSIZE][MSIZE];\ndouble dx, dy;\n\nvoid\ninitialize ()\n{\n int i, j, xx, yy;\n\n dx = 2.0 / (n - 1);\n dy = 2.0 / (m - 1);\n\n /* Initialize initial condition and RHS */\n#pragma omp parallel for private(i,j,xx,yy)\n for (i = 0; i < n; i++)\n for (j = 0; j < m; j++)\n {\n xx = (int) (-1.0 + dx * (i - 1)); /* -1 < x < 1 */\n yy = (int) (-1.0 + dy * (j - 1)); /* -1 < y < 1 */\n u[i][j] = 0.0;\n f[i][j] = -1.0 * alpha * (1.0 - xx * xx) * (1.0 - yy * yy)\n - 2.0 * (1.0 - xx * xx) - 2.0 * (1.0 - yy * yy);\n\n }\n}\n\nint main()\n{\n initialize();\n return 0;\n}\n

module DRB057\nuse omp_lib\nimplicit none\n\ninteger :: MSIZE\ninteger :: n,m,mits\ninteger, parameter :: dp = kind(1.0d0)\nreal(dp), dimension(:,:), pointer :: u,f,uold\nreal(dp) :: dx,dy,tol,relax,alpha\n\ncontains\nsubroutine initialize()\ninteger :: i,j,xx,yy\n\nMSIZE = 200\nmits = 1000\nrelax = 1.0\nalpha = 0.0543\nn = MSIZE\nm = MSIZE\nallocate(u(MSIZE,MSIZE))\nallocate(f(MSIZE,MSIZE))\nallocate(uold(MSIZE,MSIZE))\n\ndx = 2.0D0 / DBLE(n-1)\ndy = 2.0D0 / DBLE(m-1)\n\n!Initialize initial condition and RHS\n!$omp parallel do private(i,j,xx,yy)\ndo i = 1, n\ndo j = 1, m\nxx = int(-1.0 + dx * (i-1))\nyy = int(-1.0 + dy * (i-1))\nu(i,j) = 0.0\nf(i,j) = -1.0 * alpha * (1.0-xx*xx) * (1.0-yy*yy) - 2.0* (1.0-xx*xx) -2.0 * (1.0-yy*yy)\nend do\nend do\n!$omp end parallel do\n\nend subroutine\nend module program DRB057_jacobiinitialize_orig_no\n use omp_lib\n use DRB057\n implicit none\n\n call initialize()\nend program

#include <stdio.h>\n#include <assert.h>\n#include <unistd.h>\n\nint main()\n{\n int result = 0;\n#pragma omp parallel\n {\n#pragma omp single\n {\n#pragma omp taskgroup\n {\n#pragma omp task\n {\n sleep(3);\n result = 1; \n }\n }\n#pragma omp task\n {\n result = 2; \n }\n }\n }\n printf ("result=%d\n", result);\n assert (result==2);\n return 0;\n}\n

program DRB107_taskgroup_orig_no\n use omp_lib\n implicit none\n\n integer result\n result = 0\n\n !$omp parallel\n !$omp single\n !$omp taskgroup\n !$omp task\n call sleep(3)\n result = 1\n !$omp end task\n !$omp end taskgroup\n !$omp task\n result = 2\n !$omp end task\n !$omp end single\n !$omp end parallel\n\n print 100, result\n 100 format ('result =',3i8)\n\nend program

#include <omp.h>\n#include <stdio.h>\n\nint main(){\n int section_count = 0;\n omp_set_dynamic(0);\n \n omp_set_num_threads(1);\n\n #pragma omp parallel\n #pragma omp sections firstprivate( section_count )\n {\n #pragma omp section\n {\n section_count++;\n printf("%d\n",section_count);\n }\n #pragma omp section\n {\n section_count++;\n printf("%d\n",section_count);\n }\n }\n return 0;\n}\n

program DRB126_firstprivatesections_orig_no\n use omp_lib\n implicit none\n\n integer :: section_count\n\n section_count = 0\n\n call omp_set_dynamic(.FALSE.)\n call omp_set_num_threads(1)\n\n !$omp parallel\n !$omp sections firstprivate( section_count )\n !$omp section\n section_count = section_count+1\n print 100, section_count\n 100 format ('section_count =',3i8)\n\n !$omp section\n section_count = section_count+1\n print 101, section_count\n 101 format ('section_count =',3i8)\n !$omp end sections\n !$omp end parallel\nend program

#include<stdio.h>\n#include<stdlib.h>\n\nint* counter; \n\nvoid foo()\n{\n (*counter)++; \n}\n\nint main()\n{ \n counter = (int*) malloc(sizeof(int));\n if (counter== NULL)\n {\n fprintf(stderr, "malloc() fails\n");\n exit(1);\n }\n *counter = 0; \n #pragma omp parallel \n {\n foo();\n }\n printf("%d \n", *counter);\n free (counter);\n return 0; \n}\n\n

program DRB088_dynamic_storage_orig_yes\n use omp_lib\n use DRB088\n implicit none\n\n allocate(counter)\n\n counter = 0\n\n !$omp parallel\n call foo()\n !$omp end parallel\n\n print*,counter\n\n deallocate(counter)\n\nend program

#include <omp.h>\n#include <stdio.h>\n\n\nint main(){\n int x = 2;\n\n #pragma omp task mergeable\n {\n x++;\n }\n #pragma omp taskwait\n\n printf("%d\n",x);\n return 0;\n}\n

program DRB129_mergeable_taskwait_orig_yes\n use omp_lib\n implicit none\n\n integer :: x\n x = 2\n\n !$omp task mergeable\n x = x+1\n !$omp end task\n\n print 100, x\n 100 format ('x =',3i8)\nend program

#include <stdio.h>\n#include <stdlib.h>\n\nint main(){\n\n int a[4];\n int psum[2];\n int sum;\n\n #pragma omp parallel num_threads(2)\n {\n #pragma omp for schedule(dynamic, 1)\n for (int i=0; i < 4; ++i){\n a[i] = i;\n int s;\n s = (- 3 - 3) / - 3;\n }\n\n #pragma omp single\n {\n #pragma omp task\n {\n #pragma omp task\n {\n psum[1] = a[2] + a[3];\n }\n psum[0] = a[0] + a[1];\n }\n\n #pragma omp taskwait\n sum = psum[1] + psum[0];\n }\n }\n\n printf("sum = %d\n", sum);\n return 0;\n }\n

program DRB117_taskwait_waitonlychild_orig_yes\n use omp_lib\n implicit none\n\n integer, dimension(:), allocatable :: a, psum\n integer :: sum, i\n\n allocate(a(4))\n allocate(psum(4))\n\n !$omp parallel num_threads(2)\n !$omp do schedule(dynamic, 1)\n do i = 1, 4\n a(i) = i\n end do\n !$omp end do\n\n !$omp single\n !$omp task\n !$omp task\n psum(2) = a(3)+a(4)\n !$omp end task\n psum(1) = a(1)+a(2)\n !$omp end task\n !$omp taskwait\n sum = psum(2)+psum(1)\n !$omp end single\n !$omp end parallel\n\n print*,'sum =',sum\n\n deallocate(a,psum)\nend program

#include<stdio.h>\n\nint main(int argc, char* argv[])\n{\n int i;\n int len=100;\n int a[len], b[len];\n\n for (i=0;i<len;i++)\n { a[i]=i; b[i]=i;} \n/* static storage for a local variable */\n#pragma omp parallel \n {\n static int tmp;\n#pragma omp for\n for (i=0;i<len;i++)\n {\n tmp = a[i]+i;\n a[i] = tmp;\n }\n }\n\n/* automatic storage for a local variable */\n#pragma omp parallel \n {\n int tmp;\n#pragma omp for\n for (i=0;i<len;i++)\n {\n tmp = b[i]+i;\n b[i] = tmp;\n }\n }\n\n printf("a[50]=%d b[50]=%d\n", a[50], b[50]);\n \n return 0;\n}\n

program DRB090_static_local_orig_yes\n use omp_lib\n implicit none\n\n integer :: i, len\n integer, dimension(:), allocatable :: a, b\n integer, save :: tmp\n integer :: tmp2\n\n len = 100\n allocate (a(len))\n allocate (b(len))\n\n do i = 1, len\n a(i) = i\n b(i) = i\n end do\n\n !$omp parallel\n !$omp do\n do i = 1, len\n tmp = a(i)+i\n a(i) = tmp\n end do\n !$omp end do\n !$omp end parallel\n\n !$omp parallel\n !$omp do\n do i = 1, len\n tmp2 = b(i)+i\n b(i) = tmp2\n end do\n !$omp end do\n !$omp end parallel\n\n print 100, a(50), b(50)\n 100 format (i3,3x,i3)\n\n deallocate(a,b)\n\nend program

#include <stdio.h>\n\nint main()\n{\n int count=0;\n\n#pragma omp parallel shared(count) \n {\n#pragma omp single\n count += 1;\n }\n\n printf ("count= %d\n", count);\n return 0;\n}\n

program DRB077_single_orig_no\n use omp_lib\n implicit none\n\n integer :: count\n count = 0\n\n !$omp parallel shared(count)\n !$omp single\n count = count + 1\n !$omp end single\n !$omp end parallel\n\n print 100, count\n 100 format ('count =',i3)\nend program

#include <omp.h>\n#include <stdio.h>\n#include <stdlib.h>\n\ntypedef struct {\n int a, b;\n omp_nest_lock_t lck;\n} pair;\n\nvoid incr_a(pair *p){\n p->a += 1;\n}\n\nvoid incr_b(pair *p){\n p->b += 1;\n}\n\n\nint main(int argc, char* argv[])\n{\n pair p[1];\n p->a = 0;\n p->b = 0;\n omp_init_nest_lock(&p->lck);\n\n #pragma omp parallel sections\n {\n #pragma omp section\n {\n omp_set_nest_lock(&p->lck);\n incr_b(p);\n incr_a(p);\n omp_unset_nest_lock(&p->lck);\n }\n #pragma omp section\n incr_b(p);\n }\n\n omp_destroy_nest_lock(&p->lck);\n\n printf("%d\n",p->b);\n return 0;\n}\n

program DRB118_nestlock_orig_no\n use omp_lib\n use DRB118\n implicit none\n\n integer :: a, b\n\n type(pair) :: p\n p%a = 0\n p%b = 0\n call omp_init_nest_lock(p%lck);\n\n !$omp parallel sections\n !$omp section\n call omp_set_nest_lock(p%lck)\n call incr_b(p, a)\n call incr_a(p, b)\n call omp_unset_nest_lock(p%lck)\n\n !$omp section\n call incr_b(p, b);\n\n !$omp end parallel sections\n\n call omp_destroy_nest_lock(p%lck)\n\n print*,p%b\n\nend program

#include <omp.h>\n#include <stdio.h>\n\nint main(int argc, char* argv[])\n{\n int var = 0, i, res;\n int sum1 = 0;\n int sum2 = 0;\n\n res = omp_get_max_threads();\n\n #pragma omp parallel reduction(+: var)\n {\n #pragma omp for schedule(static) reduction(+: sum1)\n for (i=0; i<5; i++)\n sum1+=i;\n #pragma omp for schedule(static) reduction(+: sum2)\n for (i=0; i<5; i++)\n sum2+=i;\n\n var = sum1 + sum2;\n }\n\n int error = (var != 20*res);\n if (error) printf("%d %d\n",var,20*res);\n return error;\n}\n

program DRB121_reduction_orig_no\n use omp_lib\n implicit none\n\n integer :: var, i, sum1, sum2\n\n var = 0\n sum1 = 0\n sum2 = 0\n\n !$omp parallel reduction(+: var)\n !$omp do schedule(static) reduction(+: sum1)\n do i = 1, 5\n sum1 = sum1+i\n end do\n !$omp end do\n\n !$omp do schedule(static) reduction(+: sum2)\n do i = 1, 5\n sum2 = sum2+i\n end do\n !$omp end do\n\n var = sum1 + sum2\n !$omp end parallel\n\n print 100, var\n 100 format ('var =',3i8)\nend program

#include <stdio.h>\n/*\nuse of omp target + map + array sections derived from pointers\n*/\nvoid foo (double* a, double* b, int N)\n{\n int i; \n#pragma omp target map(to:a[0:N]) map(from:b[0:N])\n#pragma omp parallel for\n for (i=0;i< N ;i++)\n b[i]=a[i]*(double)i;\n}\n\nint main(int argc, char* argv[])\n{\n int i;\n int len = 1000;\n double a[len], b[len];\n for (i=0; i<len; i++)\n {\n a[i]= ((double)i)/2.0;\n b[i]=0.0;\n }\n\n foo(a, b, len);\n\n printf("b[50]=%f\n",b[50]);\n return 0;\n}\n

program DRB099_targetparallelfor2_orig_no\n use omp_lib\n use DRB099\n implicit none\n\n integer :: i, len\n integer, parameter :: dp = kind(1.0d0)\n real(dp), dimension(:), allocatable :: a,b\n real :: x\n\n len = 1000\n\n allocate(a(len))\n allocate(b(len))\n\n do i = 1, len\n a(i) = (real(i,dp))/2.0\n b(i) = 0.0\n end do\n\n x=foo(a,b,len)\n print*,'b(50) =',b(50)\n \n deallocate(a,b)\nend program

#include <omp.h>\n#include <stdio.h>\n#include <stdlib.h>\n\ntypedef struct {\n int a, b;\n omp_nest_lock_t lck;\n} pair;\n\nvoid incr_a(pair *p){\n p->a += 1;\n}\nvoid incr_b(pair *p){\n omp_set_nest_lock(&p->lck);\n p->b += 1;\n omp_unset_nest_lock(&p->lck);\n}\n\n\nint main(int argc, char* argv[])\n{\n pair p[1];\n p->a = 0;\n p->b = 0;\n omp_init_nest_lock(&p->lck);\n\n #pragma omp parallel sections\n {\n #pragma omp section\n {\n omp_set_nest_lock(&p->lck);\n incr_b(p);\n incr_a(p);\n omp_unset_nest_lock(&p->lck);\n }\n #pragma omp section\n incr_b(p);\n }\n\n omp_destroy_nest_lock(&p->lck);\n\n printf("%d\n",p->b);\n return 0;\n}\n

program DRB118_nestlock_orig_no\n use omp_lib\n use DRB118\n implicit none\n\n integer :: a, b\n\n type(pair) :: p\n p%a = 0\n p%b = 0\n call omp_init_nest_lock(p%lck);\n\n !$omp parallel sections\n !$omp section\n call omp_set_nest_lock(p%lck)\n call incr_b(p, a)\n call incr_a(p, b)\n call omp_unset_nest_lock(p%lck)\n\n !$omp section\n call incr_b(p, b);\n\n !$omp end parallel sections\n\n call omp_destroy_nest_lock(p%lck)\n\n print*,p%b\n\nend program

#include <stdlib.h>\nint main(int argc, char* argv[])\n{\n int i;\n int len=2000;\n\n if (argc>1)\n len = atoi(argv[1]);\n int a[len];\n\n for (i=0; i<len; i++)\n a[i]=i; \n\n#pragma omp parallel for\n for (i=0;i<len/2;i++)\n a[2*i+1]=a[i]+1;\n\n return 0;\n}\n\n

program DRB034_truedeplinear_var_yes\n use omp_lib\n implicit none\n\n integer :: i, len, uLen, argCount, allocStatus, rdErr, ix\n character(len=80), dimension(:), allocatable :: args\n integer, dimension(:), allocatable :: a\n\n len = 2000\n\n argCount = command_argument_count()\n if (argCount == 0) then\n write (*,'(a)') "No command line arguments provided."\n end if\n\n allocate(args(argCount), stat=allocStatus)\n if (allocStatus > 0) then\n write (*,'(a)') "Allocation error, program terminated."\n stop\n end if\n\n do ix = 1, argCount\n call get_command_argument(ix,args(ix))\n end do\n\n if (argCount >= 1) then\n read (args(1), '(i10)', iostat=rdErr) len\n if (rdErr /= 0 ) then\n write (*,'(a)') "Error, invalid integer value."\n end if\n end if\n\n allocate (a(len))\n\n do i = 1, len\n a(i) = i\n end do\n\n uLen = len/2\n\n !$omp parallel do\n do i = 1, uLen\n a(2*i) = a(i) + 1\n end do\n !$omp end parallel do\n\n deallocate(args,a)\nend program

#include <stdio.h>\n#include <assert.h>\n\nint sum0=0, sum1=0;\n#pragma omp threadprivate(sum0)\n\nint main()\n{\n int len=1000;\n int i, sum=0;\n#pragma omp parallel copyin(sum0)\n {\n#pragma omp for\n for (i=0;i<len;i++)\n {\n sum0=sum0+i;\n } \n#pragma omp critical\n {\n sum= sum+sum0;\n } \n } \n /* reference calculation */\n for (i=0;i<len;i++)\n {\n sum1=sum1+i;\n }\n printf("sum=%d; sum1=%d\n",sum,sum1);\n assert(sum==sum1);\n return 0;\n}\n\n

program DRB091_threadprivate2_orig_no\n use omp_lib\n use DRB091\n implicit none\n\n integer :: len, i, sum\n len = 1000\n sum = 0\n\n !$omp parallel copyin(sum0)\n !$omp do\n do i = 1, len\n sum0 = sum0+i\n end do\n !$omp end do\n !$omp critical\n sum = sum+sum0\n !$omp end critical\n !$omp end parallel\n\n do i = 1, len\n sum1 = sum1+i\n end do\n\n print*,'sum =',sum,'sum1 =',sum1\n\nend program

#include <stdio.h>\n/* This is a program based on a test contributed by Yizi Gu@Rice Univ.\n * Classic Fibonacci calculation using task but missing taskwait. \n * Data races pairs: i@61:5:W vs. i@65:14:R\n * j@63:5:W vs. j@65:16:R\n * */\nunsigned int input = 10;\nint fib(unsigned int n)\n{\n if (n<2)\n return n;\n else\n {\n int i, j;\n#pragma omp task shared(i)\n i=fib(n-1);\n#pragma omp task shared(j)\n j=fib(n-2);\n\n int res= i+j; \n/* We move the original taskwait to a location after i+j to \n * simulate the missing taskwait mistake.\n * Directly removing the taskwait may cause a child task to write to i or j\n * within the stack of a parent task which may already be gone, causing seg fault.\n * This change is suggested by Joachim Protze @RWTH-Aachen. \n * */\n#pragma omp taskwait\n return res;\n }\n}\nint main()\n{\n int result = 0;\n#pragma omp parallel\n {\n #pragma omp single\n {\n result = fib(input);\n }\n }\n printf ("Fib(%d)=%d (correct answer should be 55)\n", input, result);\n return 0;\n}\n

module DRB106\n implicit none\n integer (kind=4) input\n\ncontains\n recursive function fib(n) result(r)\n use omp_lib\n implicit none\n integer (kind=4) :: n, i, j, r\n\n if (n<2) then\n r = n\n else\n !$omp task shared(i)\n i = fib(n-1)\n !$omp end task\n !$omp task shared(j)\n j = fib(n-2)\n !$omp end task\n r = i+j\n end if\n !$omp taskwait\n end function\nend module\n\nprogram DRB106_taskwaitmissing_orig_yes\n use omp_lib\n use DRB106\n implicit none\n\n integer :: result\n input = 30\n\n !$omp parallel\n !$omp single\n result = fib(input)\n !$omp end single\n !$omp end parallel\n\n print*,'Fib for ',input,' =',result\n\nend program

#include <stdio.h>\n#define N 1000\ndouble a[N][N],v[N],v_out[N];\n\nvoid mv()\n{ \n int i,j;\n for (i = 0; i < N; i++)\n { \n float sum = 0.0;\n#pragma omp parallel for reduction(+:sum)\n for (j = 0; j < N; j++)\n { \n sum += a[i][j]*v[j];\n } \n v_out[i] = sum;\n } \n}\n\nint main()\n{\n mv();\n return 0;\n}\n

program DRB062_matrixvector2_orig_no\n use omp_lib\n implicit none\n\n call foo\ncontains\n subroutine foo()\n integer :: i, j, N\n real :: sum\n real, dimension(:,:), allocatable :: a\n real, dimension(:), allocatable :: v, v_out\n\n N = 1000\n allocate (a(N,N))\n allocate (v(N))\n allocate (v_out(N))\n\n do i = 1, N\n sum = 0.0\n !$omp parallel do reduction(+:sum)\n do j = 1, N\n sum = sum + a(i,j)*v(j)\n print*,sum\n end do\n !$omp end parallel do\n v_out(i) = sum\n end do\n\n end subroutine foo\nend program

#include <stdio.h>\n#include <stdlib.h>\n\nint main(int argc, char* argv[])\n{\n int len=100; \n\n if (argc>1)\n len = atoi(argv[1]);\n\n int a[len];\n int i,x=10;\n\n#pragma omp parallel for \n for (i=0;i<len;i++)\n {\n a[i] = x;\n x=i;\n }\n printf("x=%d, a[0]=%d\n",x,a[0]); \n return 0;\n} \n\n

program DRB017_outputdep_var_yes\n use omp_lib\n implicit none\n\n integer len, i, x, argCount, allocStatus, rdErr, ix\n character(len=80), dimension(:), allocatable :: args\n integer, dimension (:), allocatable :: a\n\n len = 100\n x = 10\n\n argCount = command_argument_count()\n if (argCount == 0) then\n write (*,'(a)') "No command line arguments provided."\n end if\n\n allocate(args(argCount), stat=allocStatus)\n if (allocStatus > 0) then\n write (*,'(a)') "Allocation error, program terminated."\n stop\n end if\n\n do ix = 1, argCount\n call get_command_argument(ix,args(ix))\n end do\n\n if (argCount >= 1) then\n read (args(1), '(i10)', iostat=rdErr) len\n if (rdErr /= 0 ) then\n write (*,'(a)') "Error, invalid integer value."\n end if\n end if\n\n allocate (a(len))\n !$omp parallel do\n do i = 1, len\n a(i) = x\n x = i\n end do\n !$omp end parallel do\n\n print 100, x, a(0)\n 100 format ("x=",i3,2x,"a(0)=",i3)\n\n deallocate(args,a)\nend program

#include <omp.h>\n#include <stdio.h>\nint main()\n{\n int numThreads=0 ; \n#pragma omp parallel\n {\n if ( omp_get_thread_num()==0 ) {\n numThreads = omp_get_num_threads();\n }\n else\n {\n printf("numThreads=%d\n", numThreads);\n }\n }\n return 0;\n}\n

program DRB075_getthreadnum_orig_yes\n use omp_lib\n implicit none\n\n integer :: numThreads\n numThreads = 0\n\n !$omp parallel\n if ( omp_get_thread_num()==0 ) then\n numThreads = omp_get_num_threads();\n else\n print*,'numThreads =',numThreads\n end if\n !$omp endparallel\nend program

void error_norm(double rms[]){\nint i, j, k, m, d;\ndouble xi, eta, zeta, u_exact[5], add;\nfor(m=0; m<5; m++){rms[m]=0.0;}\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)j*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nexact_solution(xi, eta, zeta, u_exact);\nfor(m=0; m<5; m++){\nadd=u[k][j][i][m]-u_exact[m];\nrms[m]=rms[m]+add*add;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}

subroutine error_norm(rms)\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, m, d\ndouble precision xi, eta, zeta, u_exact(5), rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, u_exact)\n\ndo m = 1, 5\nadd = u(m,i,j,k)-u_exact(m)\nrms(m) = rms(m) + add*add\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nend do\nrms(m) = dsqrt(rms(m))\nend do\n\nreturn\nend\n\n\n\nsubroutine rhs_norm(rms)\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, d, m\ndouble precision rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\ndo m = 1, 5\nadd = rhs(m,i,j,k)\nrms(m) = rms(m) + add*add\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nend do\nrms(m) = dsqrt(rms(m))\nend do\n\nreturn\nend

void set_constants(){\nce[0][0]=2.0;\nce[1][0]=0.0;\nce[2][0]=0.0;\nce[3][0]=4.0;\nce[4][0]=5.0;\nce[5][0]=3.0;\nce[6][0]=0.5;\nce[7][0]=0.02;\nce[8][0]=0.01;\nce[9][0]=0.03;\nce[10][0]=0.5;\nce[11][0]=0.4;\nce[12][0]=0.3;\n\nce[0][1]=1.0;\nce[1][1]=0.0;\nce[2][1]=0.0;\nce[3][1]=0.0;\nce[4][1]=1.0;\nce[5][1]=2.0;\nce[6][1]=3.0;\nce[7][1]=0.01;\nce[8][1]=0.03;\nce[9][1]=0.02;\nce[10][1]=0.4;\nce[11][1]=0.3;\nce[12][1]=0.5;\n\nce[0][2]=2.0;\nce[1][2]=2.0;\nce[2][2]=0.0;\nce[3][2]=0.0;\nce[4][2]=0.0;\nce[5][2]=2.0;\nce[6][2]=3.0;\nce[7][2]=0.04;\nce[8][2]=0.03;\nce[9][2]=0.05;\nce[10][2]=0.3;\nce[11][2]=0.5;\nce[12][2]=0.4;\n\nce[0][3]=2.0;\nce[1][3]=2.0;\nce[2][3]=0.0;\nce[3][3]=0.0;\nce[4][3]=0.0;\nce[5][3]=2.0;\nce[6][3]=3.0;\nce[7][3]=0.03;\nce[8][3]=0.05;\nce[9][3]=0.04;\nce[10][3]=0.2;\nce[11][3]=0.1;\nce[12][3]=0.3;\n\nce[0][4]=5.0;\nce[1][4]=4.0;\nce[2][4]=3.0;\nce[3][4]=2.0;\nce[4][4]=0.1;\nce[5][4]=0.4;\nce[6][4]=0.3;\nce[7][4]=0.05;\nce[8][4]=0.04;\nce[9][4]=0.03;\nce[10][4]=0.1;\nce[11][4]=0.3;\nce[12][4]=0.2;\n\nc1=1.4;\nc2=0.4;\nc3=0.1;\nc4=1.0;\nc5=1.4;\ndnxm1=1.0/(double)(grid_points[0]-1);\ndnym1=1.0/(double)(grid_points[1]-1);\ndnzm1=1.0/(double)(grid_points[2]-1);\nc1c2=c1*c2;\nc1c5=c1*c5;\nc3c4=c3*c4;\nc1345=c1c5*c3c4;\nconz1=(1.0-c1c5);\ntx1=1.0/(dnxm1*dnxm1);\ntx2=1.0/(2.0*dnxm1);\ntx3=1.0/dnxm1;\nty1=1.0/(dnym1*dnym1);\nty2=1.0/(2.0*dnym1);\nty3=1.0/dnym1;\ntz1=1.0/(dnzm1*dnzm1);\ntz2=1.0/(2.0*dnzm1);\ntz3=1.0/dnzm1;\ndx1=0.75;\ndx2=0.75;\ndx3=0.75;\ndx4=0.75;\ndx5=0.75;\ndy1=0.75;\ndy2=0.75;\ndy3=0.75;\ndy4=0.75;\ndy5=0.75;\ndz1=1.0;\ndz2=1.0;\ndz3=1.0;\ndz4=1.0;\ndz5=1.0;\ndxmax=max(dx3, dx4);\ndymax=max(dy2, dy4);\ndzmax=max(dz2, dz3);\ndssp=0.25*max(dx1, max(dy1, dz1));\nc4dssp=4.0*dssp;\nc5dssp=5.0*dssp;\ndttx1=dt*tx1;\ndttx2=dt*tx2;\ndtty1=dt*ty1;\ndtty2=dt*ty2;\ndttz1=dt*tz1;\ndttz2=dt*tz2;\nc2dttx1=2.0*dttx1;\nc2dtty1=2.0*dtty1;\nc2dttz1=2.0*dttz1;\ndtdssp=dt*dssp;\ncomz1=dtdssp;\ncomz4=4.0*dtdssp;\ncomz5=5.0*dtdssp;\ncomz6=6.0*dtdssp;\nc3c4tx3=c3c4*tx3;\nc3c4ty3=c3c4*ty3;\nc3c4tz3=c3c4*tz3;\ndx1tx1=dx1*tx1;\ndx2tx1=dx2*tx1;\ndx3tx1=dx3*tx1;\ndx4tx1=dx4*tx1;\ndx5tx1=dx5*tx1;\ndy1ty1=dy1*ty1;\ndy2ty1=dy2*ty1;\ndy3ty1=dy3*ty1;\ndy4ty1=dy4*ty1;\ndy5ty1=dy5*ty1;\ndz1tz1=dz1*tz1;\ndz2tz1=dz2*tz1;\ndz3tz1=dz3*tz1;\ndz4tz1=dz4*tz1;\ndz5tz1=dz5*tz1;\nc2iv=2.5;\ncon43=4.0/3.0;\ncon16=1.0/6.0;\nxxcon1=c3c4tx3*con43*tx3;\nxxcon2=c3c4tx3*tx3;\nxxcon3=c3c4tx3*conz1*tx3;\nxxcon4=c3c4tx3*con16*tx3;\nxxcon5=c3c4tx3*c1c5*tx3;\nyycon1=c3c4ty3*con43*ty3;\nyycon2=c3c4ty3*ty3;\nyycon3=c3c4ty3*conz1*ty3;\nyycon4=c3c4ty3*con16*ty3;\nyycon5=c3c4ty3*c1c5*ty3;\nzzcon1=c3c4tz3*con43*tz3;\nzzcon2=c3c4tz3*tz3;\nzzcon3=c3c4tz3*conz1*tz3;\nzzcon4=c3c4tz3*con16*tz3;\nzzcon5=c3c4tz3*c1c5*tz3;\n}

subroutine set_constants\n\n\nuse bt_data\nimplicit none\n\nce(1,1) = 2.0d0\nce(1,2) = 0.0d0\nce(1,3) = 0.0d0\nce(1,4) = 4.0d0\nce(1,5) = 5.0d0\nce(1,6) = 3.0d0\nce(1,7) = 0.5d0\nce(1,8) = 0.02d0\nce(1,9) = 0.01d0\nce(1,10) = 0.03d0\nce(1,11) = 0.5d0\nce(1,12) = 0.4d0\nce(1,13) = 0.3d0\n\nce(2,1) = 1.0d0\nce(2,2) = 0.0d0\nce(2,3) = 0.0d0\nce(2,4) = 0.0d0\nce(2,5) = 1.0d0\nce(2,6) = 2.0d0\nce(2,7) = 3.0d0\nce(2,8) = 0.01d0\nce(2,9) = 0.03d0\nce(2,10) = 0.02d0\nce(2,11) = 0.4d0\nce(2,12) = 0.3d0\nce(2,13) = 0.5d0\n\nce(3,1) = 2.0d0\nce(3,2) = 2.0d0\nce(3,3) = 0.0d0\nce(3,4) = 0.0d0\nce(3,5) = 0.0d0\nce(3,6) = 2.0d0\nce(3,7) = 3.0d0\nce(3,8) = 0.04d0\nce(3,9) = 0.03d0\nce(3,10) = 0.05d0\nce(3,11) = 0.3d0\nce(3,12) = 0.5d0\nce(3,13) = 0.4d0\n\nce(4,1) = 2.0d0\nce(4,2) = 2.0d0\nce(4,3) = 0.0d0\nce(4,4) = 0.0d0\nce(4,5) = 0.0d0\nce(4,6) = 2.0d0\nce(4,7) = 3.0d0\nce(4,8) = 0.03d0\nce(4,9) = 0.05d0\nce(4,10) = 0.04d0\nce(4,11) = 0.2d0\nce(4,12) = 0.1d0\nce(4,13) = 0.3d0\n\nce(5,1) = 5.0d0\nce(5,2) = 4.0d0\nce(5,3) = 3.0d0\nce(5,4) = 2.0d0\nce(5,5) = 0.1d0\nce(5,6) = 0.4d0\nce(5,7) = 0.3d0\nce(5,8) = 0.05d0\nce(5,9) = 0.04d0\nce(5,10) = 0.03d0\nce(5,11) = 0.1d0\nce(5,12) = 0.3d0\nce(5,13) = 0.2d0\n\nc1 = 1.4d0\nc2 = 0.4d0\nc3 = 0.1d0\nc4 = 1.0d0\nc5 = 1.4d0\n\ndnxm1 = 1.0d0 / dble(grid_points(1)-1)\ndnym1 = 1.0d0 / dble(grid_points(2)-1)\ndnzm1 = 1.0d0 / dble(grid_points(3)-1)\n\nc1c2 = c1 * c2\nc1c5 = c1 * c5\nc3c4 = c3 * c4\nc1345 = c1c5 * c3c4\n\nconz1 = (1.0d0-c1c5)\n\ntx1 = 1.0d0 / (dnxm1 * dnxm1)\ntx2 = 1.0d0 / (2.0d0 * dnxm1)\ntx3 = 1.0d0 / dnxm1\n\nty1 = 1.0d0 / (dnym1 * dnym1)\nty2 = 1.0d0 / (2.0d0 * dnym1)\nty3 = 1.0d0 / dnym1\n\ntz1 = 1.0d0 / (dnzm1 * dnzm1)\ntz2 = 1.0d0 / (2.0d0 * dnzm1)\ntz3 = 1.0d0 / dnzm1\n\ndx1 = 0.75d0\ndx2 = 0.75d0\ndx3 = 0.75d0\ndx4 = 0.75d0\ndx5 = 0.75d0\n\ndy1 = 0.75d0\ndy2 = 0.75d0\ndy3 = 0.75d0\ndy4 = 0.75d0\ndy5 = 0.75d0\n\ndz1 = 1.0d0\ndz2 = 1.0d0\ndz3 = 1.0d0\ndz4 = 1.0d0\ndz5 = 1.0d0\n\ndxmax = dmax1(dx3, dx4)\ndymax = dmax1(dy2, dy4)\ndzmax = dmax1(dz2, dz3)\n\ndssp = 0.25d0 * dmax1(dx1, dmax1(dy1, dz1) )\n\nc4dssp = 4.0d0 * dssp\nc5dssp = 5.0d0 * dssp\n\ndttx1 = dt*tx1\ndttx2 = dt*tx2\ndtty1 = dt*ty1\ndtty2 = dt*ty2\ndttz1 = dt*tz1\ndttz2 = dt*tz2\n\nc2dttx1 = 2.0d0*dttx1\nc2dtty1 = 2.0d0*dtty1\nc2dttz1 = 2.0d0*dttz1\n\ndtdssp = dt*dssp\n\ncomz1 = dtdssp\ncomz4 = 4.0d0*dtdssp\ncomz5 = 5.0d0*dtdssp\ncomz6 = 6.0d0*dtdssp\n\nc3c4tx3 = c3c4*tx3\nc3c4ty3 = c3c4*ty3\nc3c4tz3 = c3c4*tz3\n\ndx1tx1 = dx1*tx1\ndx2tx1 = dx2*tx1\ndx3tx1 = dx3*tx1\ndx4tx1 = dx4*tx1\ndx5tx1 = dx5*tx1\n\ndy1ty1 = dy1*ty1\ndy2ty1 = dy2*ty1\ndy3ty1 = dy3*ty1\ndy4ty1 = dy4*ty1\ndy5ty1 = dy5*ty1\n\ndz1tz1 = dz1*tz1\ndz2tz1 = dz2*tz1\ndz3tz1 = dz3*tz1\ndz4tz1 = dz4*tz1\ndz5tz1 = dz5*tz1\n\nc2iv = 2.5d0\ncon43 = 4.0d0/3.0d0\ncon16 = 1.0d0/6.0d0\n\nxxcon1 = c3c4tx3*con43*tx3\nxxcon2 = c3c4tx3*tx3\nxxcon3 = c3c4tx3*conz1*tx3\nxxcon4 = c3c4tx3*con16*tx3\nxxcon5 = c3c4tx3*c1c5*tx3\n\nyycon1 = c3c4ty3*con43*ty3\nyycon2 = c3c4ty3*ty3\nyycon3 = c3c4ty3*conz1*ty3\nyycon4 = c3c4ty3*con16*ty3\nyycon5 = c3c4ty3*c1c5*ty3\n\nzzcon1 = c3c4tz3*con43*tz3\nzzcon2 = c3c4tz3*tz3\nzzcon3 = c3c4tz3*conz1*tz3\nzzcon4 = c3c4tz3*con16*tz3\nzzcon5 = c3c4tz3*c1c5*tz3\n\nreturn\nend

void rhs_norm(double rms[]){\nint i, j, k, d, m;\ndouble add;\nfor(m=0;m<5;m++){rms[m]=0.0;}\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nfor(m=0; m<5; m++){\nadd=rhs[k][j][i][m];\nrms[m]=rms[m]+add*add;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}

subroutine compute_rhs\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision aux, rho_inv, uijk, up1, um1, vijk, vp1, vm1, &\n& wijk, wp1, wm1\n\n\nif (timeron) call timer_start(t_rhs)\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\nrho_inv = 1.0d0/u(1,i,j,k)\nrho_i(i,j,k) = rho_inv\nus(i,j,k) = u(2,i,j,k) * rho_inv\nvs(i,j,k) = u(3,i,j,k) * rho_inv\nws(i,j,k) = u(4,i,j,k) * rho_inv\nsquare(i,j,k) = 0.5d0* ( &\n& u(2,i,j,k)*u(2,i,j,k) + &\n& u(3,i,j,k)*u(3,i,j,k) + &\n& u(4,i,j,k)*u(4,i,j,k) ) * rho_inv\nqs(i,j,k) = square(i,j,k) * rho_inv\naux = c1c2*rho_inv* (u(5,i,j,k) - square(i,j,k))\nspeed(i,j,k) = dsqrt(aux)\nend do\nend do\nend do\n\n\ndo k = 0, nz2+1\ndo j = 0, ny2+1\ndo i = 0, nx2+1\ndo m = 1, 5\nrhs(m,i,j,k) = forcing(m,i,j,k)\nend do\nend do\nend do\nend do\n\nif (timeron) call timer_start(t_rhsx)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\nuijk = us(i,j,k)\nup1 = us(i+1,j,k)\num1 = us(i-1,j,k)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dx1tx1 * &\n& (u(1,i+1,j,k) - 2.0d0*u(1,i,j,k) + &\n& u(1,i-1,j,k)) - &\n& tx2 * (u(2,i+1,j,k) - u(2,i-1,j,k))\n\nrhs(2,i,j,k) = rhs(2,i,j,k) + dx2tx1 * &\n& (u(2,i+1,j,k) - 2.0d0*u(2,i,j,k) + &\n& u(2,i-1,j,k)) + &\n& xxcon2*con43 * (up1 - 2.0d0*uijk + um1) - &\n& tx2 * (u(2,i+1,j,k)*up1 - &\n& u(2,i-1,j,k)*um1 + &\n& (u(5,i+1,j,k)- square(i+1,j,k)- &\n& u(5,i-1,j,k)+ square(i-1,j,k))* &\n& c2)\n\nrhs(3,i,j,k) = rhs(3,i,j,k) + dx3tx1 * &\n& (u(3,i+1,j,k) - 2.0d0*u(3,i,j,k) + &\n& u(3,i-1,j,k)) + &\n& xxcon2 * (vs(i+1,j,k) - 2.0d0*vs(i,j,k) + &\n& vs(i-1,j,k)) - &\n& tx2 * (u(3,i+1,j,k)*up1 - &\n& u(3,i-1,j,k)*um1)\n\nrhs(4,i,j,k) = rhs(4,i,j,k) + dx4tx1 * &\n& (u(4,i+1,j,k) - 2.0d0*u(4,i,j,k) + &\n& u(4,i-1,j,k)) + &\n& xxcon2 * (ws(i+1,j,k) - 2.0d0*ws(i,j,k) + &\n& ws(i-1,j,k)) - &\n& tx2 * (u(4,i+1,j,k)*up1 - &\n& u(4,i-1,j,k)*um1)\n\nrhs(5,i,j,k) = rhs(5,i,j,k) + dx5tx1 * &\n& (u(5,i+1,j,k) - 2.0d0*u(5,i,j,k) + &\n& u(5,i-1,j,k)) + &\n& xxcon3 * (qs(i+1,j,k) - 2.0d0*qs(i,j,k) + &\n& qs(i-1,j,k)) + &\n& xxcon4 * (up1*up1 - 2.0d0*uijk*uijk + &\n& um1*um1) + &\n& xxcon5 * (u(5,i+1,j,k)*rho_i(i+1,j,k) - &\n& 2.0d0*u(5,i,j,k)*rho_i(i,j,k) + &\n& u(5,i-1,j,k)*rho_i(i-1,j,k)) - &\n& tx2 * ( (c1*u(5,i+1,j,k) - &\n& c2*square(i+1,j,k))*up1 - &\n& (c1*u(5,i-1,j,k) - &\n& c2*square(i-1,j,k))*um1 )\nend do\n\ni = 1\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0*u(m,i,j,k) - 4.0d0*u(m,i+1,j,k) + &\n& u(m,i+2,j,k))\nend do\n\ni = 2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0*u(m,i-1,j,k) + 6.0d0*u(m,i,j,k) - &\n& 4.0d0*u(m,i+1,j,k) + u(m,i+2,j,k))\nend do\n\ndo i = 3, nx2-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i-2,j,k) - 4.0d0*u(m,i-1,j,k) + &\n& 6.0*u(m,i,j,k) - 4.0d0*u(m,i+1,j,k) + &\n& u(m,i+2,j,k) )\nend do\nend do\n\ni = nx2-1\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i-2,j,k) - 4.0d0*u(m,i-1,j,k) + &\n& 6.0d0*u(m,i,j,k) - 4.0d0*u(m,i+1,j,k) )\nend do\n\ni = nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i-2,j,k) - 4.d0*u(m,i-1,j,k) + &\n& 5.d0*u(m,i,j,k) )\nend do\nend do\nend do\nif (timeron) call timer_stop(t_rhsx)\n\nif (timeron) call timer_start(t_rhsy)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\nvijk = vs(i,j,k)\nvp1 = vs(i,j+1,k)\nvm1 = vs(i,j-1,k)\nrhs(1,i,j,k) = rhs(1,i,j,k) + dy1ty1 * &\n& (u(1,i,j+1,k) - 2.0d0*u(1,i,j,k) + &\n& u(1,i,j-1,k)) - &\n& ty2 * (u(3,i,j+1,k) - u(3,i,j-1,k))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dy2ty1 * &\n& (u(2,i,j+1,k) - 2.0d0*u(2,i,j,k) + &\n& u(2,i,j-1,k)) + &\n& yycon2 * (us(i,j+1,k) - 2.0d0*us(i,j,k) + &\n& us(i,j-1,k)) - &\n& ty2 * (u(2,i,j+1,k)*vp1 - &\n& u(2,i,j-1,k)*vm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dy3ty1 * &\n& (u(3,i,j+1,k) - 2.0d0*u(3,i,j,k) + &\n& u(3,i,j-1,k)) + &\n& yycon2*con43 * (vp1 - 2.0d0*vijk + vm1) - &\n& ty2 * (u(3,i,j+1,k)*vp1 - &\n& u(3,i,j-1,k)*vm1 + &\n& (u(5,i,j+1,k) - square(i,j+1,k) - &\n& u(5,i,j-1,k) + square(i,j-1,k)) &\n& *c2)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dy4ty1 * &\n& (u(4,i,j+1,k) - 2.0d0*u(4,i,j,k) + &\n& u(4,i,j-1,k)) + &\n& yycon2 * (ws(i,j+1,k) - 2.0d0*ws(i,j,k) + &\n& ws(i,j-1,k)) - &\n& ty2 * (u(4,i,j+1,k)*vp1 - &\n& u(4,i,j-1,k)*vm1)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dy5ty1 * &\n& (u(5,i,j+1,k) - 2.0d0*u(5,i,j,k) + &\n& u(5,i,j-1,k)) + &\n& yycon3 * (qs(i,j+1,k) - 2.0d0*qs(i,j,k) + &\n& qs(i,j-1,k)) + &\n& yycon4 * (vp1*vp1 - 2.0d0*vijk*vijk + &\n& vm1*vm1) + &\n& yycon5 * (u(5,i,j+1,k)*rho_i(i,j+1,k) - &\n& 2.0d0*u(5,i,j,k)*rho_i(i,j,k) + &\n& u(5,i,j-1,k)*rho_i(i,j-1,k)) - &\n& ty2 * ((c1*u(5,i,j+1,k) - &\n& c2*square(i,j+1,k)) * vp1 - &\n& (c1*u(5,i,j-1,k) - &\n& c2*square(i,j-1,k)) * vm1)\nend do\n\n\n\nif (j .eq. 1) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j+1,k) + &\n& u(m,i,j+2,k))\nend do\nend do\n\nelse if (j .eq. 2) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0*u(m,i,j-1,k) + 6.0d0*u(m,i,j,k) - &\n& 4.0d0*u(m,i,j+1,k) + u(m,i,j+2,k))\nend do\nend do\n\nelse if (j .eq. ny2-1) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.0d0*u(m,i,j-1,k) + &\n& 6.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j+1,k) )\nend do\nend do\n\nelse if (j .eq. ny2) then\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.d0*u(m,i,j-1,k) + &\n& 5.d0*u(m,i,j,k) )\nend do\nend do\n\nelse !do j = 3, ny2-2\ndo i = 1,nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.0d0*u(m,i,j-1,k) + &\n& 6.0*u(m,i,j,k) - 4.0d0*u(m,i,j+1,k) + &\n& u(m,i,j+2,k) )\nend do\nend do\nendif\nend do\nend do\nif (timeron) call timer_stop(t_rhsy)\n\nif (timeron) call timer_start(t_rhsz)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nwijk = ws(i,j,k)\nwp1 = ws(i,j,k+1)\nwm1 = ws(i,j,k-1)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dz1tz1 * &\n& (u(1,i,j,k+1) - 2.0d0*u(1,i,j,k) + &\n& u(1,i,j,k-1)) - &\n& tz2 * (u(4,i,j,k+1) - u(4,i,j,k-1))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dz2tz1 * &\n& (u(2,i,j,k+1) - 2.0d0*u(2,i,j,k) + &\n& u(2,i,j,k-1)) + &\n& zzcon2 * (us(i,j,k+1) - 2.0d0*us(i,j,k) + &\n& us(i,j,k-1)) - &\n& tz2 * (u(2,i,j,k+1)*wp1 - &\n& u(2,i,j,k-1)*wm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dz3tz1 * &\n& (u(3,i,j,k+1) - 2.0d0*u(3,i,j,k) + &\n& u(3,i,j,k-1)) + &\n& zzcon2 * (vs(i,j,k+1) - 2.0d0*vs(i,j,k) + &\n& vs(i,j,k-1)) - &\n& tz2 * (u(3,i,j,k+1)*wp1 - &\n& u(3,i,j,k-1)*wm1)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dz4tz1 * &\n& (u(4,i,j,k+1) - 2.0d0*u(4,i,j,k) + &\n& u(4,i,j,k-1)) + &\n& zzcon2*con43 * (wp1 - 2.0d0*wijk + wm1) - &\n& tz2 * (u(4,i,j,k+1)*wp1 - &\n& u(4,i,j,k-1)*wm1 + &\n& (u(5,i,j,k+1) - square(i,j,k+1) - &\n& u(5,i,j,k-1) + square(i,j,k-1)) &\n& *c2)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dz5tz1 * &\n& (u(5,i,j,k+1) - 2.0d0*u(5,i,j,k) + &\n& u(5,i,j,k-1)) + &\n& zzcon3 * (qs(i,j,k+1) - 2.0d0*qs(i,j,k) + &\n& qs(i,j,k-1)) + &\n& zzcon4 * (wp1*wp1 - 2.0d0*wijk*wijk + &\n& wm1*wm1) + &\n& zzcon5 * (u(5,i,j,k+1)*rho_i(i,j,k+1) - &\n& 2.0d0*u(5,i,j,k)*rho_i(i,j,k) + &\n& u(5,i,j,k-1)*rho_i(i,j,k-1)) - &\n& tz2 * ( (c1*u(5,i,j,k+1) - &\n& c2*square(i,j,k+1))*wp1 - &\n& (c1*u(5,i,j,k-1) - &\n& c2*square(i,j,k-1))*wm1)\nend do\n\n\nif (k .eq. 1) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j,k+1) + &\n& u(m,i,j,k+2))\nend do\nend do\n\nelse if (k .eq. 2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0*u(m,i,j,k-1) + 6.0d0*u(m,i,j,k) - &\n& 4.0d0*u(m,i,j,k+1) + u(m,i,j,k+2))\nend do\nend do\n\nelse if (k .eq. grid_points(3)-3) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.0d0*u(m,i,j,k-1) + &\n& 6.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j,k+1) )\nend do\nend do\n\nelse if (k .eq. grid_points(3)-2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.d0*u(m,i,j,k-1) + &\n& 5.d0*u(m,i,j,k) )\nend do\nend do\n\nelse !do k = 3, grid_points(3)-4\ndo i = 1,grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.0d0*u(m,i,j,k-1) + &\n& 6.0*u(m,i,j,k) - 4.0d0*u(m,i,j,k+1) + &\n& u(m,i,j,k+2) )\nend do\nend do\nendif\nend do\nend do\nif (timeron) call timer_stop(t_rhsz)\n\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) * dt\nend do\nend do\nend do\nend do\nif (timeron) call timer_stop(t_rhs)\n\nreturn\nend

void set_constants(){\nce[0][0]=2.0;\nce[1][0]=0.0;\nce[2][0]=0.0;\nce[3][0]=4.0;\nce[4][0]=5.0;\nce[5][0]=3.0;\nce[6][0]=0.5;\nce[7][0]=0.02;\nce[8][0]=0.01;\nce[9][0]=0.03;\nce[10][0]=0.5;\nce[11][0]=0.4;\nce[12][0]=0.3;\n\nce[0][1]=1.0;\nce[1][1]=0.0;\nce[2][1]=0.0;\nce[3][1]=0.0;\nce[4][1]=1.0;\nce[5][1]=2.0;\nce[6][1]=3.0;\nce[7][1]=0.01;\nce[8][1]=0.03;\nce[9][1]=0.02;\nce[10][1]=0.4;\nce[11][1]=0.3;\nce[12][1]=0.5;\n\nce[0][2]=2.0;\nce[1][2]=2.0;\nce[2][2]=0.0;\nce[3][2]=0.0;\nce[4][2]=0.0;\nce[5][2]=2.0;\nce[6][2]=3.0;\nce[7][2]=0.04;\nce[8][2]=0.03;\nce[9][2]=0.05;\nce[10][2]=0.3;\nce[11][2]=0.5;\nce[12][2]=0.4;\n\nce[0][3]=2.0;\nce[1][3]=2.0;\nce[2][3]=0.0;\nce[3][3]=0.0;\nce[4][3]=0.0;\nce[5][3]=2.0;\nce[6][3]=3.0;\nce[7][3]=0.03;\nce[8][3]=0.05;\nce[9][3]=0.04;\nce[10][3]=0.2;\nce[11][3]=0.1;\nce[12][3]=0.3;\n\nce[0][4]=5.0;\nce[1][4]=4.0;\nce[2][4]=3.0;\nce[3][4]=2.0;\nce[4][4]=0.1;\nce[5][4]=0.4;\nce[6][4]=0.3;\nce[7][4]=0.05;\nce[8][4]=0.04;\nce[9][4]=0.03;\nce[10][4]=0.1;\nce[11][4]=0.3;\nce[12][4]=0.2;\n\nc1=1.4;\nc2=0.4;\nc3=0.1;\nc4=1.0;\nc5=1.4;\n\nbt=sqrt(0.5);\n\ndnxm1=1.0/(double)(grid_points[0]-1);\ndnym1=1.0/(double)(grid_points[1]-1);\ndnzm1=1.0/(double)(grid_points[2]-1);\n\nc1c2=c1*c2;\nc1c5=c1*c5;\nc3c4=c3*c4;\nc1345=c1c5*c3c4;\n\nconz1=(1.0-c1c5);\n\ntx1=1.0/(dnxm1*dnxm1);\ntx2=1.0/(2.0*dnxm1);\ntx3=1.0/dnxm1;\n\nty1=1.0/(dnym1*dnym1);\nty2=1.0/(2.0*dnym1);\nty3=1.0/dnym1;\n\ntz1=1.0/(dnzm1*dnzm1);\ntz2=1.0/(2.0*dnzm1);\ntz3=1.0/dnzm1;\n\ndx1=0.75;\ndx2=0.75;\ndx3=0.75;\ndx4=0.75;\ndx5=0.75;\n\ndy1=0.75;\ndy2=0.75;\ndy3=0.75;\ndy4=0.75;\ndy5=0.75;\n\ndz1=1.0;\ndz2=1.0;\ndz3=1.0;\ndz4=1.0;\ndz5=1.0;\n\ndxmax=max(dx3, dx4);\ndymax=max(dy2, dy4);\ndzmax=max(dz2, dz3);\n\ndssp=0.25*max(dx1, max(dy1, dz1));\n\nc4dssp=4.0*dssp;\nc5dssp=5.0*dssp;\n\ndttx1=dt*tx1;\ndttx2=dt*tx2;\ndtty1=dt*ty1;\ndtty2=dt*ty2;\ndttz1=dt*tz1;\ndttz2=dt*tz2;\n\nc2dttx1=2.0*dttx1;\nc2dtty1=2.0*dtty1;\nc2dttz1=2.0*dttz1;\n\ndtdssp=dt*dssp;\n\ncomz1=dtdssp;\ncomz4=4.0*dtdssp;\ncomz5=5.0*dtdssp;\ncomz6=6.0*dtdssp;\n\nc3c4tx3=c3c4*tx3;\nc3c4ty3=c3c4*ty3;\nc3c4tz3=c3c4*tz3;\n\ndx1tx1=dx1*tx1;\ndx2tx1=dx2*tx1;\ndx3tx1=dx3*tx1;\ndx4tx1=dx4*tx1;\ndx5tx1=dx5*tx1;\n\ndy1ty1=dy1*ty1;\ndy2ty1=dy2*ty1;\ndy3ty1=dy3*ty1;\ndy4ty1=dy4*ty1;\ndy5ty1=dy5*ty1;\n\ndz1tz1=dz1*tz1;\ndz2tz1=dz2*tz1;\ndz3tz1=dz3*tz1;\ndz4tz1=dz4*tz1;\ndz5tz1=dz5*tz1;\n\nc2iv=2.5;\ncon43=4.0/3.0;\ncon16=1.0/6.0;\n\nxxcon1=c3c4tx3*con43*tx3;\nxxcon2=c3c4tx3*tx3;\nxxcon3=c3c4tx3*conz1*tx3;\nxxcon4=c3c4tx3*con16*tx3;\nxxcon5=c3c4tx3*c1c5*tx3;\n\nyycon1=c3c4ty3*con43*ty3;\nyycon2=c3c4ty3*ty3;\nyycon3=c3c4ty3*conz1*ty3;\nyycon4=c3c4ty3*con16*ty3;\nyycon5=c3c4ty3*c1c5*ty3;\n\nzzcon1=c3c4tz3*con43*tz3;\nzzcon2=c3c4tz3*tz3;\nzzcon3=c3c4tz3*conz1*tz3;\nzzcon4=c3c4tz3*con16*tz3;\nzzcon5=c3c4tz3*c1c5*tz3;\n}

subroutine set_constants\n\n\nuse sp_data\nimplicit none\n\nce(1,1) = 2.0d0\nce(1,2) = 0.0d0\nce(1,3) = 0.0d0\nce(1,4) = 4.0d0\nce(1,5) = 5.0d0\nce(1,6) = 3.0d0\nce(1,7) = 0.5d0\nce(1,8) = 0.02d0\nce(1,9) = 0.01d0\nce(1,10) = 0.03d0\nce(1,11) = 0.5d0\nce(1,12) = 0.4d0\nce(1,13) = 0.3d0\n\nce(2,1) = 1.0d0\nce(2,2) = 0.0d0\nce(2,3) = 0.0d0\nce(2,4) = 0.0d0\nce(2,5) = 1.0d0\nce(2,6) = 2.0d0\nce(2,7) = 3.0d0\nce(2,8) = 0.01d0\nce(2,9) = 0.03d0\nce(2,10) = 0.02d0\nce(2,11) = 0.4d0\nce(2,12) = 0.3d0\nce(2,13) = 0.5d0\n\nce(3,1) = 2.0d0\nce(3,2) = 2.0d0\nce(3,3) = 0.0d0\nce(3,4) = 0.0d0\nce(3,5) = 0.0d0\nce(3,6) = 2.0d0\nce(3,7) = 3.0d0\nce(3,8) = 0.04d0\nce(3,9) = 0.03d0\nce(3,10) = 0.05d0\nce(3,11) = 0.3d0\nce(3,12) = 0.5d0\nce(3,13) = 0.4d0\n\nce(4,1) = 2.0d0\nce(4,2) = 2.0d0\nce(4,3) = 0.0d0\nce(4,4) = 0.0d0\nce(4,5) = 0.0d0\nce(4,6) = 2.0d0\nce(4,7) = 3.0d0\nce(4,8) = 0.03d0\nce(4,9) = 0.05d0\nce(4,10) = 0.04d0\nce(4,11) = 0.2d0\nce(4,12) = 0.1d0\nce(4,13) = 0.3d0\n\nce(5,1) = 5.0d0\nce(5,2) = 4.0d0\nce(5,3) = 3.0d0\nce(5,4) = 2.0d0\nce(5,5) = 0.1d0\nce(5,6) = 0.4d0\nce(5,7) = 0.3d0\nce(5,8) = 0.05d0\nce(5,9) = 0.04d0\nce(5,10) = 0.03d0\nce(5,11) = 0.1d0\nce(5,12) = 0.3d0\nce(5,13) = 0.2d0\n\nc1 = 1.4d0\nc2 = 0.4d0\nc3 = 0.1d0\nc4 = 1.0d0\nc5 = 1.4d0\n\nbt = dsqrt(0.5d0)\n\ndnxm1 = 1.0d0 / dble(grid_points(1)-1)\ndnym1 = 1.0d0 / dble(grid_points(2)-1)\ndnzm1 = 1.0d0 / dble(grid_points(3)-1)\n\nc1c2 = c1 * c2\nc1c5 = c1 * c5\nc3c4 = c3 * c4\nc1345 = c1c5 * c3c4\n\nconz1 = (1.0d0-c1c5)\n\ntx1 = 1.0d0 / (dnxm1 * dnxm1)\ntx2 = 1.0d0 / (2.0d0 * dnxm1)\ntx3 = 1.0d0 / dnxm1\n\nty1 = 1.0d0 / (dnym1 * dnym1)\nty2 = 1.0d0 / (2.0d0 * dnym1)\nty3 = 1.0d0 / dnym1\n\ntz1 = 1.0d0 / (dnzm1 * dnzm1)\ntz2 = 1.0d0 / (2.0d0 * dnzm1)\ntz3 = 1.0d0 / dnzm1\n\ndx1 = 0.75d0\ndx2 = 0.75d0\ndx3 = 0.75d0\ndx4 = 0.75d0\ndx5 = 0.75d0\n\ndy1 = 0.75d0\ndy2 = 0.75d0\ndy3 = 0.75d0\ndy4 = 0.75d0\ndy5 = 0.75d0\n\ndz1 = 1.0d0\ndz2 = 1.0d0\ndz3 = 1.0d0\ndz4 = 1.0d0\ndz5 = 1.0d0\n\ndxmax = dmax1(dx3, dx4)\ndymax = dmax1(dy2, dy4)\ndzmax = dmax1(dz2, dz3)\n\ndssp = 0.25d0 * dmax1(dx1, dmax1(dy1, dz1) )\n\nc4dssp = 4.0d0 * dssp\nc5dssp = 5.0d0 * dssp\n\ndttx1 = dt*tx1\ndttx2 = dt*tx2\ndtty1 = dt*ty1\ndtty2 = dt*ty2\ndttz1 = dt*tz1\ndttz2 = dt*tz2\n\nc2dttx1 = 2.0d0*dttx1\nc2dtty1 = 2.0d0*dtty1\nc2dttz1 = 2.0d0*dttz1\n\ndtdssp = dt*dssp\n\ncomz1 = dtdssp\ncomz4 = 4.0d0*dtdssp\ncomz5 = 5.0d0*dtdssp\ncomz6 = 6.0d0*dtdssp\n\nc3c4tx3 = c3c4*tx3\nc3c4ty3 = c3c4*ty3\nc3c4tz3 = c3c4*tz3\n\ndx1tx1 = dx1*tx1\ndx2tx1 = dx2*tx1\ndx3tx1 = dx3*tx1\ndx4tx1 = dx4*tx1\ndx5tx1 = dx5*tx1\n\ndy1ty1 = dy1*ty1\ndy2ty1 = dy2*ty1\ndy3ty1 = dy3*ty1\ndy4ty1 = dy4*ty1\ndy5ty1 = dy5*ty1\n\ndz1tz1 = dz1*tz1\ndz2tz1 = dz2*tz1\ndz3tz1 = dz3*tz1\ndz4tz1 = dz4*tz1\ndz5tz1 = dz5*tz1\n\nc2iv = 2.5d0\ncon43 = 4.0d0/3.0d0\ncon16 = 1.0d0/6.0d0\n\nxxcon1 = c3c4tx3*con43*tx3\nxxcon2 = c3c4tx3*tx3\nxxcon3 = c3c4tx3*conz1*tx3\nxxcon4 = c3c4tx3*con16*tx3\nxxcon5 = c3c4tx3*c1c5*tx3\n\nyycon1 = c3c4ty3*con43*ty3\nyycon2 = c3c4ty3*ty3\nyycon3 = c3c4ty3*conz1*ty3\nyycon4 = c3c4ty3*con16*ty3\nyycon5 = c3c4ty3*c1c5*ty3\n\nzzcon1 = c3c4tz3*con43*tz3\nzzcon2 = c3c4tz3*tz3\nzzcon3 = c3c4tz3*conz1*tz3\nzzcon4 = c3c4tz3*con16*tz3\nzzcon5 = c3c4tz3*c1c5*tz3\n\nreturn\nend

static void makea(int n,\nint nz,\ndouble a[],\nint colidx[],\nint rowstr[],\nint firstrow,\nint lastrow,\nint firstcol,\nint lastcol,\nint arow[],\nint acol[][NONZER+1],\ndouble aelt[][NONZER+1],\nint iv[]){\nint iouter, ivelt, nzv, nn1;\nint ivc[NONZER+1];\ndouble vc[NONZER+1];\n\n\nnn1 = 1;\ndo{\nnn1 = 2 * nn1;\n}while(nn1 < n);\n\n\nfor(iouter = 0; iouter < n; iouter++){\nnzv = NONZER;\nsprnvc(n, nzv, nn1, vc, ivc);\nvecset(n, vc, ivc, &nzv, iouter+1, 0.5);\narow[iouter] = nzv;\nfor(ivelt = 0; ivelt < nzv; ivelt++){\nacol[iouter][ivelt] = ivc[ivelt] - 1;\naelt[iouter][ivelt] = vc[ivelt];\n}\n}\n\n\nsparse(a,\ncolidx,\nrowstr,\nn,\nnz,\nNONZER,\narow,\nacol,\naelt,\nfirstrow,\nlastrow,\niv,\nRCOND,\nSHIFT);\n}

subroutine makea( n, nz, a, colidx, rowstr, &\n& firstrow, lastrow, firstcol, lastcol, &\n& arow, acol, aelt, v, iv )\n\nuse tinfo\nuse cg_data, only : nonzer, rcond, shift\n\nimplicit none\n\ninteger n\ninteger(kz) nz, rowstr(n+1)\ninteger firstrow, lastrow, firstcol, lastcol\ninteger colidx(nz)\ninteger iv(n+nz), arow(n), acol(nonzer+1,n)\ndouble precision aelt(nonzer+1,n), v(nz)\ndouble precision a(nz)\n\n\ninteger i, iouter, ivelt, nzv, nn1\ninteger ivc(nonzer+1)\ndouble precision vc(nonzer+1)\n\n\nexternal sparse, sprnvc, vecset\ninteger work\n\n\n\nnn1 = 1\n50 continue\nnn1 = 2 * nn1\nif (nn1 .lt. n) goto 50\n\nnum_threads = 1\nmyid = 0\nif (num_threads .gt. max_threads) then\nif (myid .eq. 0) write(*,100) num_threads, max_threads\n100 format(' Warning: num_threads',i6, &\n& ' exceeded an internal limit',i6)\nnum_threads = max_threads\nendif\nwork = (n + num_threads - 1)/num_threads\nilow = work * myid + 1\nihigh = ilow + work - 1\nif (ihigh .gt. n) ihigh = n\n\ndo iouter = 1, ihigh\nnzv = nonzer\ncall sprnvc( n, nzv, nn1, vc, ivc )\nif ( iouter .ge. ilow ) then\ncall vecset( n, vc, ivc, nzv, iouter, .5D0 )\narow(iouter) = nzv\ndo ivelt = 1, nzv\nacol(ivelt, iouter) = ivc(ivelt)\naelt(ivelt, iouter) = vc(ivelt)\nenddo\nendif\nenddo\n\ncall sparse( a, colidx, rowstr, n, nz, nonzer, arow, acol, &\n& aelt, firstrow, lastrow, &\n& v, iv(1), iv(nz+1), rcond, shift )\nreturn\n\nend

void initialize(){\nint i, j, k, m, ix, iy, iz;\ndouble xi, eta, zeta, Pface[2][3][5], Pxi, Peta, Pzeta, temp[5];\n\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<=grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nu[k][j][i][0]=1.0;\nu[k][j][i][1]=0.0;\nu[k][j][i][2]=0.0;\nu[k][j][i][3]=0.0;\nu[k][j][i][4]=1.0;\n}\n}\n}\n\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)j*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nfor(ix=0; ix<2; ix++){\nPxi=(double)ix;\nexact_solution(Pxi, eta, zeta, &Pface[ix][0][0]);\n}\nfor(iy=0; iy<2; iy++){\nPeta=(double)iy;\nexact_solution(xi, Peta, zeta, &Pface[iy][1][0]);\n}\nfor(iz=0; iz<2; iz++){\nPzeta=(double)iz;\nexact_solution(xi, eta, Pzeta, &Pface[iz][2][0]);\n}\nfor(m=0; m<5; m++){\nPxi=xi*Pface[1][0][m]+(1.0-xi)*Pface[0][0][m];\nPeta=eta*Pface[1][1][m]+(1.0-eta)*Pface[0][1][m];\nPzeta=zeta*Pface[1][2][m]+(1.0-zeta)*Pface[0][2][m];\nu[k][j][i][m]=Pxi+Peta+Pzeta-\nPxi*Peta-Pxi*Pzeta-Peta*Pzeta+\nPxi*Peta*Pzeta;\n}\n}\n}\n}\n\nxi=0.0;\ni=0;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)j*dnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nxi=1.0;\ni=grid_points[0]-1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)j*dnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\neta=0.0;\nj=0;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\neta=1.0;\nj=grid_points[1]-1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nzeta=0.0;\nk=0;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)j*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nzeta=1.0;\nk=grid_points[2]-1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)j*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n}

subroutine initialize\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k, m, ix, iy, iz\ndouble precision xi, eta, zeta, Pface(5,3,2), Pxi, Peta, &\n& Pzeta, temp(5)\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\nu(1,i,j,k) = 1.0\nu(2,i,j,k) = 0.0\nu(3,i,j,k) = 0.0\nu(4,i,j,k) = 0.0\nu(5,i,j,k) = 1.0\nend do\nend do\nend do\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ndo ix = 1, 2\nPxi = dble(ix-1)\ncall exact_solution(Pxi, eta, zeta, &\n& Pface(1,1,ix))\nend do\n\ndo iy = 1, 2\nPeta = dble(iy-1)\ncall exact_solution(xi, Peta, zeta, &\n& Pface(1,2,iy))\nend do\n\ndo iz = 1, 2\nPzeta = dble(iz-1)\ncall exact_solution(xi, eta, Pzeta, &\n& Pface(1,3,iz))\nend do\n\ndo m = 1, 5\nPxi = xi * Pface(m,1,2) + &\n& (1.0d0-xi) * Pface(m,1,1)\nPeta = eta * Pface(m,2,2) + &\n& (1.0d0-eta) * Pface(m,2,1)\nPzeta = zeta * Pface(m,3,2) + &\n& (1.0d0-zeta) * Pface(m,3,1)\n\nu(m,i,j,k) = Pxi + Peta + Pzeta - &\n& Pxi*Peta - Pxi*Pzeta - Peta*Pzeta + &\n& Pxi*Peta*Pzeta\n\nend do\nend do\nend do\nend do\n\n\n\nxi = 0.0d0\ni = 0\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\nxi = 1.0d0\ni = grid_points(1)-1\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\neta = 0.0d0\nj = 0\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\n\neta = 1.0d0\nj = grid_points(2)-1\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\nzeta = 0.0d0\nk = 0\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) * dnym1\nxi = dble(i) *dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\n\nzeta = 1.0d0\nk = grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) * dnym1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nend do\nend do\nend do\n\nreturn\nend

void read_input(){\n\nFILE* fp; int avoid_warning;\nif((fp=fopen("inputlu.data","r"))!=NULL){\nprintf("Reading from input file inputlu.data\n");\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%d%d",&ipr,&inorm);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%d",&itmax);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%lf",&dt);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%lf",&omega);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%lf%lf%lf%lf%lf",&tolrsd[0],\n&tolrsd[1],\n&tolrsd[2],\n&tolrsd[3],\n&tolrsd[4]);\nwhile(fgetc(fp)!='\n');\nwhile(fgetc(fp)!='\n');\navoid_warning=fscanf(fp,"%d%d%d",&nx0,&ny0,&nz0);\nfclose(fp);\n}else{\nipr=IPR_DEFAULT;\ninorm=INORM_DEFAULT;\nitmax=ITMAX_DEFAULT;\ndt=DT_DEFAULT;\nomega=OMEGA_DEFAULT;\ntolrsd[0]=TOLRSD1_DEF;\ntolrsd[1]=TOLRSD2_DEF;\ntolrsd[2]=TOLRSD3_DEF;\ntolrsd[3]=TOLRSD4_DEF;\ntolrsd[4]=TOLRSD5_DEF;\nnx0=ISIZ1;\nny0=ISIZ2;\nnz0=ISIZ3;\n}\n\nif((nx0<4)||(ny0<4)||(nz0<4)){\nprintf(" PROBLEM SIZE IS TOO SMALL -\n"\n" SET EACH OF NX, NY AND NZ AT LEAST EQUAL TO 5\n");\nexit(EXIT_FAILURE);\n}\nif((nx0>ISIZ1)||(ny0>ISIZ2)||(nz0>ISIZ3)){\nprintf(" PROBLEM SIZE IS TOO LARGE -\n"\n" NX, NY AND NZ SHOULD BE EQUAL TO\n"\n" ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY\n");\nexit(EXIT_FAILURE);\n}\nprintf("\n\nNAS Parallel Benchmarks 4.1 Parallel C++ version with OpenMP - LU Benchmark\n\n");\nprintf(" Size: %4dx%4dx%4d\n",nx0,ny0,nz0);\nprintf(" Iterations: %4d\n",itmax);\nprintf("\n");\n}

subroutine read_input\n\n\nuse lu_data\nimplicit none\n\ninteger fstatus\n\n\n\nwrite(*, 1000)\n\nopen (unit=3,file='inputlu.data',status='old', &\n& access='sequential',form='formatted', iostat=fstatus)\nif (fstatus .eq. 0) then\n\nwrite(*, *) 'Reading from input file inputlu.data'\n\nread (3,*)\nread (3,*)\nread (3,*) ipr, inorm\nread (3,*)\nread (3,*)\nread (3,*) itmax\nread (3,*)\nread (3,*)\nread (3,*) dt\nread (3,*)\nread (3,*)\nread (3,*) omega\nread (3,*)\nread (3,*)\nread (3,*) tolrsd(1),tolrsd(2),tolrsd(3),tolrsd(4),tolrsd(5)\nread (3,*)\nread (3,*)\nread (3,*) nx0, ny0, nz0\nclose(3)\nelse\nipr = ipr_default\ninorm = inorm_default\nitmax = itmax_default\ndt = dt_default\nomega = omega_default\ntolrsd(1) = tolrsd1_def\ntolrsd(2) = tolrsd2_def\ntolrsd(3) = tolrsd3_def\ntolrsd(4) = tolrsd4_def\ntolrsd(5) = tolrsd5_def\nnx0 = isiz1\nny0 = isiz2\nnz0 = isiz3\nendif\n\n\nif ( ( nx0 .lt. 4 ) .or. &\n& ( ny0 .lt. 4 ) .or. &\n& ( nz0 .lt. 4 ) ) then\n\nwrite (*,2001)\n2001 format (5x,'PROBLEM SIZE IS TOO SMALL - ', &\n& /5x,'SET EACH OF NX, NY AND NZ AT LEAST EQUAL TO 5')\nstop\n\nend if\n\nif ( ( nx0 .gt. isiz1 ) .or. &\n& ( ny0 .gt. isiz2 ) .or. &\n& ( nz0 .gt. isiz3 ) ) then\n\nwrite (*,2002)\n2002 format (5x,'PROBLEM SIZE IS TOO LARGE - ', &\n& /5x,'NX, NY AND NZ SHOULD BE EQUAL TO ', &\n& /5x,'ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY')\nstop\n\nend if\n\n\nwrite(*, 1001) nx0, ny0, nz0\nwrite(*, 1002) itmax\nwrite(*, *)\n\n\n1000 format(//,' NAS Parallel Benchmarks (NPB3.4-OMP)', &\n& ' - LU Benchmark', /)\n1001 format(' Size: ', i4, 'x', i4, 'x', i4)\n1002 format(' Iterations: ', i5)\n1003 format(' Number of available threads: ', i5)\n\n\n\nreturn\nend

void ninvr(){\nint i, j, k;\ndouble r1, r2, r3, r4, r5, t1, t2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_NINVR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nt1=bt*r3;\nt2=0.5*(r4+r5);\nrhs[k][j][i][0]=-r2;\nrhs[k][j][i][1]=r1;\nrhs[k][j][i][2]=bt*(r4-r5);\nrhs[k][j][i][3]=-t1+t2;\nrhs[k][j][i][4]=t1+t2;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_NINVR);}\n}

subroutine ninvr\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision r1, r2, r3, r4, r5, t1, t2\n\nif (timeron) call timer_start(t_ninvr)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nt1 = bt * r3\nt2 = 0.5d0 * ( r4 + r5 )\n\nrhs(1,i,j,k) = -r2\nrhs(2,i,j,k) = r1\nrhs(3,i,j,k) = bt * ( r4 - r5 )\nrhs(4,i,j,k) = -t1 + t2\nrhs(5,i,j,k) = t1 + t2\nenddo\nenddo\nenddo\nif (timeron) call timer_stop(t_ninvr)\n\nreturn\nend

void l2norm(int nx0,\nint ny0,\nint nz0,\nint ist,\nint iend,\nint jst,\nint jend,\ndouble v[][ISIZ2/2*2+1][ISIZ1/2*2+1][5],\ndouble sum[]){\n\nint i, j, k, m;\ndouble sum0=0.0, sum1=0.0, sum2=0.0, sum3=0.0, sum4=0.0;\n\n#pragma omp single\nfor (m = 0; m < 5; m++) {\nsum[m] = 0.0;\n}\n\n#pragma omp for nowait\nfor(k=1; k<nz0-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nsum0 = sum0 + v[i][j][k][0] * v[i][j][k][0];\nsum1 = sum1 + v[i][j][k][1] * v[i][j][k][1];\nsum2 = sum2 + v[i][j][k][2] * v[i][j][k][2];\nsum3 = sum3 + v[i][j][k][3] * v[i][j][k][3];\nsum4 = sum4 + v[i][j][k][4] * v[i][j][k][4];\n}\n}\n}\n\n#pragma omp critical\n{\nsum[0] += sum0;\nsum[1] += sum1;\nsum[2] += sum2;\nsum[3] += sum3;\nsum[4] += sum4;\n}\n#pragma omp barrier\n\n#pragma omp single\nfor(m=0; m<5; m++){\nsum[m]=sqrt(sum[m]/((nx0-2)*(ny0-2)*(nz0-2)));\n}\n}

subroutine l2norm ( ldx, ldy, ldz, &\n& nx0, ny0, nz0, &\n& ist, iend, &\n& jst, jend, &\n& v, sum )\n\n\nimplicit none\n\ninteger ldx, ldy, ldz\ninteger nx0, ny0, nz0\ninteger ist, iend\ninteger jst, jend\ndouble precision v(5,ldx/2*2+1,ldy/2*2+1,*), sum(5)\n\ninteger i, j, k, m\n\n\ndo m = 1, 5\nsum(m) = 0.0d+00\nend do\n\ndo k = 2, nz0-1\ndo j = jst, jend\ndo i = ist, iend\ndo m = 1, 5\nsum(m) = sum(m) + v(m,i,j,k)*v(m,i,j,k)\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\nsum(m) = sqrt ( sum(m) / ( dble(nx0-2)*(ny0-2)*(nz0-2) ) )\nend do\n\nreturn\nend

void verify(int no_time_steps, char* class_npb, boolean* verified){\ndouble xcrref[5], xceref[5], xcrdif[5], xcedif[5];\ndouble epsilon, xce[5], xcr[5], dtref=0.0;\nint m;\n\nepsilon=1.0e-08;\n\nerror_norm(xce);\ncompute_rhs();\nrhs_norm(xcr);\nfor(m=0; m<5; m++){\nxcr[m]=xcr[m]/dt;\n}\n*class_npb='U';\n*verified=TRUE;\nfor(m=0; m<5; m++){\nxcrref[m]=1.0;\nxceref[m]=1.0;\n}\n\nif((grid_points[0]==12)&&\n(grid_points[1]==12)&&\n(grid_points[2]==12)&&\n(no_time_steps==60)){\n*class_npb='S';\ndtref=1.0e-2;\n\nxcrref[0]=1.7034283709541311e-01;\nxcrref[1]=1.2975252070034097e-02;\nxcrref[2]=3.2527926989486055e-02;\nxcrref[3]=2.6436421275166801e-02;\nxcrref[4]=1.9211784131744430e-01;\n\nxceref[0]=4.9976913345811579e-04;\nxceref[1]=4.5195666782961927e-05;\nxceref[2]=7.3973765172921357e-05;\nxceref[3]=7.3821238632439731e-05;\nxceref[4]=8.9269630987491446e-04;\n\n}else if((grid_points[0]==24)&&\n(grid_points[1]==24)&&\n(grid_points[2]==24)&&\n(no_time_steps==200)){\n*class_npb='W';\ndtref = 0.8e-3;\n\nxcrref[0]=0.1125590409344e+03;\nxcrref[1]=0.1180007595731e+02;\nxcrref[2]=0.2710329767846e+02;\nxcrref[3]=0.2469174937669e+02;\nxcrref[4]=0.2638427874317e+03;\n\nxceref[0]=0.4419655736008e+01;\nxceref[1]=0.4638531260002e+00;\nxceref[2]=0.1011551749967e+01;\nxceref[3]=0.9235878729944e+00;\nxceref[4]=0.1018045837718e+02;\n\n}else if((grid_points[0]==64)&&\n(grid_points[1]==64)&&\n(grid_points[2]==64)&&\n(no_time_steps==200)){\n*class_npb='A';\ndtref=0.8e-3;\n\nxcrref[0]=1.0806346714637264e+02;\nxcrref[1]=1.1319730901220813e+01;\nxcrref[2]=2.5974354511582465e+01;\nxcrref[3]=2.3665622544678910e+01;\nxcrref[4]=2.5278963211748344e+02;\n\nxceref[0]=4.2348416040525025e+00;\nxceref[1]=4.4390282496995698e-01;\nxceref[2]=9.6692480136345650e-01;\nxceref[3]=8.8302063039765474e-01;\nxceref[4]=9.7379901770829278e+00;\n\n}else if((grid_points[0]==102)&&\n(grid_points[1]==102)&&\n(grid_points[2]==102)&&\n(no_time_steps==200)){\n*class_npb='B';\ndtref=3.0e-4;\n\nxcrref[0]=1.4233597229287254e+03;\nxcrref[1]=9.9330522590150238e+01;\nxcrref[2]=3.5646025644535285e+02;\nxcrref[3]=3.2485447959084092e+02;\nxcrref[4]=3.2707541254659363e+03;\n\nxceref[0]=5.2969847140936856e+01;\nxceref[1]=4.4632896115670668e+00;\nxceref[2]=1.3122573342210174e+01;\nxceref[3]=1.2006925323559144e+01;\nxceref[4]=1.2459576151035986e+02;\n\n}else if((grid_points[0]==162)&&\n(grid_points[1]==162)&&\n(grid_points[2]==162)&&\n(no_time_steps==200)){\n*class_npb='C';\ndtref=1.0e-4;\n\nxcrref[0]=0.62398116551764615e+04;\nxcrref[1]=0.50793239190423964e+03;\nxcrref[2]=0.15423530093013596e+04;\nxcrref[3]=0.13302387929291190e+04;\nxcrref[4]=0.11604087428436455e+05;\n\nxceref[0]=0.16462008369091265e+03;\nxceref[1]=0.11497107903824313e+02;\nxceref[2]=0.41207446207461508e+02;\nxceref[3]=0.37087651059694167e+02;\nxceref[4]=0.36211053051841265e+03;\n\n}else if((grid_points[0]==408)&&\n(grid_points[1]==408)&&\n(grid_points[2]==408)&&\n(no_time_steps==250)){\n*class_npb='D';\ndtref=0.2e-4;\n\nxcrref[0]=0.2533188551738e+05;\nxcrref[1]=0.2346393716980e+04;\nxcrref[2]=0.6294554366904e+04;\nxcrref[3]=0.5352565376030e+04;\nxcrref[4]=0.3905864038618e+05;\n\nxceref[0]=0.3100009377557e+03;\nxceref[1]=0.2424086324913e+02;\nxceref[2]=0.7782212022645e+02;\nxceref[3]=0.6835623860116e+02;\nxceref[4]=0.6065737200368e+03;\n\n}else if((grid_points[0]==1020)&&\n(grid_points[1]==1020)&&\n(grid_points[2]==1020)&&\n(no_time_steps==250)){\n*class_npb='E';\ndtref=0.4e-5;\n\nxcrref[0]=0.9795372484517e+05;\nxcrref[1]=0.9739814511521e+04;\nxcrref[2]=0.2467606342965e+05;\nxcrref[3]=0.2092419572860e+05;\nxcrref[4]=0.1392138856939e+06;\n\nxceref[0]=0.4327562208414e+03;\nxceref[1]=0.3699051964887e+02;\nxceref[2]=0.1089845040954e+03;\nxceref[3]=0.9462517622043e+02;\nxceref[4]=0.7765512765309e+03;\n}else{\n*verified=FALSE;\n}\n\nfor(m=0; m<5; m++){\nxcrdif[m]=fabs((xcr[m]-xcrref[m])/xcrref[m]);\nxcedif[m]=fabs((xce[m]-xceref[m])/xceref[m]);\n}\n\nif(*class_npb!='U'){\nprintf(" Verification being performed for class_npb %c\n",*class_npb);\nprintf(" accuracy setting for epsilon = %20.13E\n",epsilon);\n*verified=(fabs(dt-dtref)<=epsilon);\nif(!(*verified)){\n*class_npb='U';\nprintf(" DT does not match the reference value of %15.8E\n",dtref);\n}\n}else{\nprintf(" Unknown class_npb\n");\n}\nif(*class_npb!='U'){\nprintf(" Comparison of RMS-norms of residual\n");\n}else{\nprintf(" RMS-norms of residual\n");\n}\nfor(m=0; m<5; m++){\nif(*class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xcr[m]);\n}else if(xcrdif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}else{\n*verified=FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}\n}\nif(*class_npb!='U'){\nprintf(" Comparison of RMS-norms of solution error\n");\n}else{\nprintf(" RMS-norms of solution error\n");\n}\nfor(m=0; m<5; m++){\nif(*class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xce[m]);\n}else if(xcedif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}else{\n*verified=FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}\n}\nif(*class_npb=='U'){\nprintf(" No reference values provided\n");\nprintf(" No verification performed\n");\n}else if(*verified){\nprintf(" Verification Successful\n");\n}else{\nprintf(" Verification failed\n");\n}\n}

subroutine verify(no_time_steps, class, verified)\n\n\n\nuse, intrinsic :: ieee_arithmetic, only : ieee_is_nan\n\nuse bt_data\n\nimplicit none\n\ndouble precision xcrref(5),xceref(5),xcrdif(5),xcedif(5), &\n& epsilon, xce(5), xcr(5), dtref\ninteger m, no_time_steps\ncharacter class\nlogical verified\n\nepsilon = 1.0d-08\n\n\ncall error_norm(xce)\ncall compute_rhs\n\ncall rhs_norm(xcr)\n\ndo m = 1, 5\nxcr(m) = xcr(m) / dt\nenddo\n\n\nclass = 'U'\nverified = .true.\n\ndo m = 1,5\nxcrref(m) = 1.0\nxceref(m) = 1.0\nend do\n\nif ( (grid_points(1) .eq. 12 ) .and. &\n& (grid_points(2) .eq. 12 ) .and. &\n& (grid_points(3) .eq. 12 ) .and. &\n& (no_time_steps .eq. 60 )) then\n\nclass = 'S'\ndtref = 1.0d-2\n\nxcrref(1) = 1.7034283709541311d-01\nxcrref(2) = 1.2975252070034097d-02\nxcrref(3) = 3.2527926989486055d-02\nxcrref(4) = 2.6436421275166801d-02\nxcrref(5) = 1.9211784131744430d-01\n\nxceref(1) = 4.9976913345811579d-04\nxceref(2) = 4.5195666782961927d-05\nxceref(3) = 7.3973765172921357d-05\nxceref(4) = 7.3821238632439731d-05\nxceref(5) = 8.9269630987491446d-04\n\nelseif ( (grid_points(1) .eq. 24) .and. &\n& (grid_points(2) .eq. 24) .and. &\n& (grid_points(3) .eq. 24) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'W'\ndtref = 0.8d-3\nxcrref(1) = 0.1125590409344d+03\nxcrref(2) = 0.1180007595731d+02\nxcrref(3) = 0.2710329767846d+02\nxcrref(4) = 0.2469174937669d+02\nxcrref(5) = 0.2638427874317d+03\n\nxceref(1) = 0.4419655736008d+01\nxceref(2) = 0.4638531260002d+00\nxceref(3) = 0.1011551749967d+01\nxceref(4) = 0.9235878729944d+00\nxceref(5) = 0.1018045837718d+02\n\n\nelseif ( (grid_points(1) .eq. 64) .and. &\n& (grid_points(2) .eq. 64) .and. &\n& (grid_points(3) .eq. 64) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'A'\ndtref = 0.8d-3\nxcrref(1) = 1.0806346714637264d+02\nxcrref(2) = 1.1319730901220813d+01\nxcrref(3) = 2.5974354511582465d+01\nxcrref(4) = 2.3665622544678910d+01\nxcrref(5) = 2.5278963211748344d+02\n\nxceref(1) = 4.2348416040525025d+00\nxceref(2) = 4.4390282496995698d-01\nxceref(3) = 9.6692480136345650d-01\nxceref(4) = 8.8302063039765474d-01\nxceref(5) = 9.7379901770829278d+00\n\nelseif ( (grid_points(1) .eq. 102) .and. &\n& (grid_points(2) .eq. 102) .and. &\n& (grid_points(3) .eq. 102) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'B'\ndtref = 3.0d-4\n\nxcrref(1) = 1.4233597229287254d+03\nxcrref(2) = 9.9330522590150238d+01\nxcrref(3) = 3.5646025644535285d+02\nxcrref(4) = 3.2485447959084092d+02\nxcrref(5) = 3.2707541254659363d+03\n\nxceref(1) = 5.2969847140936856d+01\nxceref(2) = 4.4632896115670668d+00\nxceref(3) = 1.3122573342210174d+01\nxceref(4) = 1.2006925323559144d+01\nxceref(5) = 1.2459576151035986d+02\n\nelseif ( (grid_points(1) .eq. 162) .and. &\n& (grid_points(2) .eq. 162) .and. &\n& (grid_points(3) .eq. 162) .and. &\n& (no_time_steps .eq. 200) ) then\n\nclass = 'C'\ndtref = 1.0d-4\n\nxcrref(1) = 0.62398116551764615d+04\nxcrref(2) = 0.50793239190423964d+03\nxcrref(3) = 0.15423530093013596d+04\nxcrref(4) = 0.13302387929291190d+04\nxcrref(5) = 0.11604087428436455d+05\n\nxceref(1) = 0.16462008369091265d+03\nxceref(2) = 0.11497107903824313d+02\nxceref(3) = 0.41207446207461508d+02\nxceref(4) = 0.37087651059694167d+02\nxceref(5) = 0.36211053051841265d+03\n\nelseif ( (grid_points(1) .eq. 408) .and. &\n& (grid_points(2) .eq. 408) .and. &\n& (grid_points(3) .eq. 408) .and. &\n& (no_time_steps .eq. 250) ) then\n\nclass = 'D'\ndtref = 0.2d-4\n\nxcrref(1) = 0.2533188551738d+05\nxcrref(2) = 0.2346393716980d+04\nxcrref(3) = 0.6294554366904d+04\nxcrref(4) = 0.5352565376030d+04\nxcrref(5) = 0.3905864038618d+05\n\n\nxceref(1) = 0.3100009377557d+03\nxceref(2) = 0.2424086324913d+02\nxceref(3) = 0.7782212022645d+02\nxceref(4) = 0.6835623860116d+02\nxceref(5) = 0.6065737200368d+03\n\nelseif ( (grid_points(1) .eq. 1020) .and. &\n& (grid_points(2) .eq. 1020) .and. &\n& (grid_points(3) .eq. 1020) .and. &\n& (no_time_steps .eq. 250) ) then\n\nclass = 'E'\ndtref = 0.4d-5\n\nxcrref(1) = 0.9795372484517d+05\nxcrref(2) = 0.9739814511521d+04\nxcrref(3) = 0.2467606342965d+05\nxcrref(4) = 0.2092419572860d+05\nxcrref(5) = 0.1392138856939d+06\n\n\nxceref(1) = 0.4327562208414d+03\nxceref(2) = 0.3699051964887d+02\nxceref(3) = 0.1089845040954d+03\nxceref(4) = 0.9462517622043d+02\nxceref(5) = 0.7765512765309d+03\n\nelseif ( (grid_points(1) .eq. 2560) .and. &\n& (grid_points(2) .eq. 2560) .and. &\n& (grid_points(3) .eq. 2560) .and. &\n& (no_time_steps .eq. 250) ) then\n\nclass = 'F'\ndtref = 0.6d-6\n\nxcrref(1) = 0.4240735175585d+06\nxcrref(2) = 0.4348701133212d+05\nxcrref(3) = 0.1078114688845d+06\nxcrref(4) = 0.9142160938556d+05\nxcrref(5) = 0.5879842143431d+06\n\n\nxceref(1) = 0.5095577042351d+03\nxceref(2) = 0.4557065541652d+02\nxceref(3) = 0.1286632140581d+03\nxceref(4) = 0.1111419378722d+03\nxceref(5) = 0.8720011709356d+03\n\nelse\nverified = .false.\nendif\n\n\ndo m = 1, 5\n\nxcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))\nxcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))\n\nenddo\n\n\nif (class .ne. 'U') then\nwrite(*, 1990) class\n1990 format(' Verification being performed for class ', a)\nwrite (*,2000) epsilon\n2000 format(' accuracy setting for epsilon = ', E20.13)\nverified = (dabs(dt-dtref) .le. epsilon)\nif (.not.verified) then\nclass = 'U'\nwrite (*,1000) dtref\n1000 format(' DT does not match the reference value of ', &\n& E15.8)\nendif\nelse\nwrite(*, 1995)\n1995 format(' Unknown class')\nendif\n\n\nif (class .ne. 'U') then\nwrite (*, 2001)\nelse\nwrite (*, 2005)\nendif\n\n2001 format(' Comparison of RMS-norms of residual')\n2005 format(' RMS-norms of residual')\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(*, 2015) m, xcr(m)\nelse if ((.not.ieee_is_nan(xcrdif(m))) .and. &\n& xcrdif(m) .le. epsilon) then\nwrite (*,2011) m,xcr(m),xcrref(m),xcrdif(m)\nelse\nverified = .false.\nwrite (*,2010) m,xcr(m),xcrref(m),xcrdif(m)\nendif\nenddo\n\nif (class .ne. 'U') then\nwrite (*,2002)\nelse\nwrite (*,2006)\nendif\n2002 format(' Comparison of RMS-norms of solution error')\n2006 format(' RMS-norms of solution error')\n\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(*, 2015) m, xce(m)\nelse if ((.not.ieee_is_nan(xcedif(m))) .and. &\n& xcedif(m) .le. epsilon) then\nwrite (*,2011) m,xce(m),xceref(m),xcedif(m)\nelse\nverified = .false.\nwrite (*,2010) m,xce(m),xceref(m),xcedif(m)\nendif\nenddo\n\n2010 format(' FAILURE: ', i2, E20.13, E20.13, E20.13)\n2011 format(' ', i2, E20.13, E20.13, E20.13)\n2015 format(' ', i2, E20.13)\n\nif (class .eq. 'U') then\nwrite(*, 2022)\nwrite(*, 2023)\n2022 format(' No reference values provided')\n2023 format(' No verification performed')\nelse if (verified) then\nwrite(*, 2020)\n2020 format(' Verification Successful')\nelse\nwrite(*, 2021)\n2021 format(' Verification failed')\nendif\n\nreturn\n\n\nend

void x_solve(){\nint i, j, k, i1, i2, m;\ndouble ru1, fac1, fac2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_XSOLVE);}\n\n#pragma omp for\nfor(k=1; k<=nz2; k++){\ndouble cv[PROBLEM_SIZE], rhon[PROBLEM_SIZE];\ndouble lhs[IMAXP+1][IMAXP+1][5];\ndouble lhsp[IMAXP+1][IMAXP+1][5];\ndouble lhsm[IMAXP+1][IMAXP+1][5];\n\nfor(j=1; j<=ny2; j++){\nfor(m=0; m<5; m++){\nlhs[j][0][m]=0.0;\nlhsp[j][0][m]=0.0;\nlhsm[j][0][m]=0.0;\nlhs[j][nx2+1][m]=0.0;\nlhsp[j][nx2+1][m]=0.0;\nlhsm[j][nx2+1][m]=0.0;\n}\nlhs[j][0][2]=1.0;\nlhsp[j][0][2]=1.0;\nlhsm[j][0][2]=1.0;\nlhs[j][nx2+1][2]=1.0;\nlhsp[j][nx2+1][2]=1.0;\nlhsm[j][nx2+1][2]=1.0;\n}\n\n\nfor(j=1; j<=ny2; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nru1=c3c4*rho_i[k][j][i];\ncv[i]=us[k][j][i];\nrhon[i]=max(max(dx2+con43*ru1,dx5+c1c5*ru1), max(dxmax+ru1,dx1));\n}\nfor(i=1; i<=nx2; i++){\nlhs[j][i][0]=0.0;\nlhs[j][i][1]=-dttx2*cv[i-1]-dttx1*rhon[i-1];\nlhs[j][i][2]=1.0+c2dttx1*rhon[i];\nlhs[j][i][3]=dttx2*cv[i+1]-dttx1*rhon[i+1];\nlhs[j][i][4]=0.0;\n}\n}\n\nfor(j=1; j<=ny2; j++){\ni=1;\nlhs[j][i][2]=lhs[j][i][2]+comz5;\nlhs[j][i][3]=lhs[j][i][3]-comz4;\nlhs[j][i][4]=lhs[j][i][4]+comz1;\nlhs[j][i+1][1]=lhs[j][i+1][1]-comz4;\nlhs[j][i+1][2]=lhs[j][i+1][2]+comz6;\nlhs[j][i+1][3]=lhs[j][i+1][3]-comz4;\nlhs[j][i+1][4]=lhs[j][i+1][4]+comz1;\n}\nfor(j=1; j<=ny2; j++){\nfor(i=3; i<=grid_points[0]-4; i++){\nlhs[j][i][0]=lhs[j][i][0]+comz1;\nlhs[j][i][1]=lhs[j][i][1]-comz4;\nlhs[j][i][2]=lhs[j][i][2]+comz6;\nlhs[j][i][3]=lhs[j][i][3]-comz4;\nlhs[j][i][4]=lhs[j][i][4]+comz1;\n}\n}\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-3;\nlhs[j][i][0]=lhs[j][i][0]+comz1;\nlhs[j][i][1]=lhs[j][i][1]-comz4;\nlhs[j][i][2]=lhs[j][i][2]+comz6;\nlhs[j][i][3]=lhs[j][i][3]-comz4;\nlhs[j][i+1][0]=lhs[j][i+1][0]+comz1;\nlhs[j][i+1][1]=lhs[j][i+1][1]-comz4;\nlhs[j][i+1][2]=lhs[j][i+1][2]+comz5;\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nlhsp[j][i][0]=lhs[j][i][0];\nlhsp[j][i][1]=lhs[j][i][1]-dttx2*speed[k][j][i-1];\nlhsp[j][i][2]=lhs[j][i][2];\nlhsp[j][i][3]=lhs[j][i][3]+dttx2*speed[k][j][i+1];\nlhsp[j][i][4]=lhs[j][i][4];\nlhsm[j][i][0]=lhs[j][i][0];\nlhsm[j][i][1]=lhs[j][i][1]+dttx2*speed[k][j][i-1];\nlhsm[j][i][2]=lhs[j][i][2];\nlhsm[j][i][3]=lhs[j][i][3]-dttx2*speed[k][j][i+1];\nlhsm[j][i][4]=lhs[j][i][4];\n}\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=0; i<=grid_points[0]-3; i++){\ni1=i+1;\ni2=i+2;\nfac1=1.0/lhs[j][i][2];\nlhs[j][i][3]=fac1*lhs[j][i][3];\nlhs[j][i][4]=fac1*lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\n}\nlhs[j][i1][2]=lhs[j][i1][2]-lhs[j][i1][1]*lhs[j][i][3];\nlhs[j][i1][3]=lhs[j][i1][3]-lhs[j][i1][1]*lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhs[j][i1][1]*rhs[k][j][i][m];\n}\nlhs[j][i2][1]=lhs[j][i2][1]-lhs[j][i2][0]*lhs[j][i][3];\nlhs[j][i2][2]=lhs[j][i2][2]-lhs[j][i2][0]*lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i2][m]=rhs[k][j][i2][m]-lhs[j][i2][0]*rhs[k][j][i][m];\n}\n}\n}\n\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-2;\ni1=grid_points[0]-1;\nfac1=1.0/lhs[j][i][2];\nlhs[j][i][3]=fac1*lhs[j][i][3];\nlhs[j][i][4]=fac1*lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\n}\nlhs[j][i1][2]=lhs[j][i1][2]-lhs[j][i1][1]*lhs[j][i][3];\nlhs[j][i1][3]=lhs[j][i1][3]-lhs[j][i1][1]*lhs[j][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhs[j][i1][1]*rhs[k][j][i][m];\n}\n\nfac2 = 1.0/lhs[j][i1][2];\nfor(m=0; m<3; m++){\nrhs[k][j][i1][m]=fac2*rhs[k][j][i1][m];\n}\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=0; i<=grid_points[0]-3; i++){\ni1=i+1;\ni2=i+2;\nm=3;\nfac1=1.0/lhsp[j][i][2];\nlhsp[j][i][3]=fac1*lhsp[j][i][3];\nlhsp[j][i][4]=fac1*lhsp[j][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsp[j][i1][2]=lhsp[j][i1][2]-lhsp[j][i1][1]*lhsp[j][i][3];\nlhsp[j][i1][3]=lhsp[j][i1][3]-lhsp[j][i1][1]*lhsp[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsp[j][i1][1]*rhs[k][j][i][m];\nlhsp[j][i2][1]=lhsp[j][i2][1]-lhsp[j][i2][0]*lhsp[j][i][3];\nlhsp[j][i2][2]=lhsp[j][i2][2]-lhsp[j][i2][0]*lhsp[j][i][4];\nrhs[k][j][i2][m]=rhs[k][j][i2][m]-lhsp[j][i2][0]*rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[j][i][2];\nlhsm[j][i][3]=fac1*lhsm[j][i][3];\nlhsm[j][i][4]=fac1*lhsm[j][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsm[j][i1][2]=lhsm[j][i1][2]-lhsm[j][i1][1]*lhsm[j][i][3];\nlhsm[j][i1][3]=lhsm[j][i1][3]-lhsm[j][i1][1]*lhsm[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsm[j][i1][1]*rhs[k][j][i][m];\nlhsm[j][i2][1]=lhsm[j][i2][1]-lhsm[j][i2][0]*lhsm[j][i][3];\nlhsm[j][i2][2]=lhsm[j][i2][2]-lhsm[j][i2][0]*lhsm[j][i][4];\nrhs[k][j][i2][m]=rhs[k][j][i2][m]-lhsm[j][i2][0]*rhs[k][j][i][m];\n}\n}\n\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-2;\ni1=grid_points[0]-1;\nm=3;\nfac1=1.0/lhsp[j][i][2];\nlhsp[j][i][3]=fac1*lhsp[j][i][3];\nlhsp[j][i][4]=fac1*lhsp[j][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsp[j][i1][2]=lhsp[j][i1][2]-lhsp[j][i1][1]*lhsp[j][i][3];\nlhsp[j][i1][3]=lhsp[j][i1][3]-lhsp[j][i1][1]*lhsp[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsp[j][i1][1]*rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[j][i][2];\nlhsm[j][i][3]=fac1*lhsm[j][i][3];\nlhsm[j][i][4]=fac1*lhsm[j][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsm[j][i1][2]=lhsm[j][i1][2]-lhsm[j][i1][1]*lhsm[j][i][3];\nlhsm[j][i1][3]=lhsm[j][i1][3]-lhsm[j][i1][1]*lhsm[j][i][4];\nrhs[k][j][i1][m]=rhs[k][j][i1][m]-lhsm[j][i1][1]*rhs[k][j][i][m];\n\nrhs[k][j][i1][3]=rhs[k][j][i1][3]/lhsp[j][i1][2];\nrhs[k][j][i1][4]=rhs[k][j][i1][4]/lhsm[j][i1][2];\n}\n\nfor(j=1; j<=ny2; j++){\ni=grid_points[0]-2;\ni1=grid_points[0]-1;\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[j][i][3]*rhs[k][j][i1][m];\n}\nrhs[k][j][i][3]=rhs[k][j][i][3]-lhsp[j][i][3]*rhs[k][j][i1][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-lhsm[j][i][3]*rhs[k][j][i1][4];\n}\n\nfor(j=1; j<=ny2; j++){\nfor(i=grid_points[0]-3; i>=0; i--){\ni1=i+1;\ni2=i+2;\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-\nlhs[j][i][3]*rhs[k][j][i1][m]-\nlhs[j][i][4]*rhs[k][j][i2][m];\n}\n\nrhs[k][j][i][3]=rhs[k][j][i][3]-\nlhsp[j][i][3]*rhs[k][j][i1][3] -\nlhsp[j][i][4]*rhs[k][j][i2][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-\nlhsm[j][i][3]*rhs[k][j][i1][4]-\nlhsm[j][i][4]*rhs[k][j][i2][4];\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_XSOLVE);}\n\nninvr();\n}

subroutine x_solve\n\n\n\nuse sp_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, i1, i2, m\ndouble precision ru1, fac1, fac2\n\n\n\nif (timeron) call timer_start(t_xsolve)\ndo k = 1, nz2\ndo j = 1, ny2\n\ncall lhsinit(nx2+1, lhs, lhsp, lhsm)\n\n\ndo i = 0, grid_points(1)-1\nru1 = c3c4*rho_i(i,j,k)\ncv(i) = us(i,j,k)\nrhov(i) = dmax1(dx2+con43*ru1, &\n& dx5+c1c5*ru1, &\n& dxmax+ru1, &\n& dx1)\nend do\n\ndo i = 1, nx2\nlhs(1,i) = 0.0d0\nlhs(2,i) = -dttx2 * cv(i-1) - dttx1 * rhov(i-1)\nlhs(3,i) = 1.0d0 + c2dttx1 * rhov(i)\nlhs(4,i) = dttx2 * cv(i+1) - dttx1 * rhov(i+1)\nlhs(5,i) = 0.0d0\nend do\n\n\ni = 1\nlhs(3,i) = lhs(3,i) + comz5\nlhs(4,i) = lhs(4,i) - comz4\nlhs(5,i) = lhs(5,i) + comz1\n\nlhs(2,i+1) = lhs(2,i+1) - comz4\nlhs(3,i+1) = lhs(3,i+1) + comz6\nlhs(4,i+1) = lhs(4,i+1) - comz4\nlhs(5,i+1) = lhs(5,i+1) + comz1\n\ndo i=3, grid_points(1)-4\nlhs(1,i) = lhs(1,i) + comz1\nlhs(2,i) = lhs(2,i) - comz4\nlhs(3,i) = lhs(3,i) + comz6\nlhs(4,i) = lhs(4,i) - comz4\nlhs(5,i) = lhs(5,i) + comz1\nend do\n\ni = grid_points(1)-3\nlhs(1,i) = lhs(1,i) + comz1\nlhs(2,i) = lhs(2,i) - comz4\nlhs(3,i) = lhs(3,i) + comz6\nlhs(4,i) = lhs(4,i) - comz4\n\nlhs(1,i+1) = lhs(1,i+1) + comz1\nlhs(2,i+1) = lhs(2,i+1) - comz4\nlhs(3,i+1) = lhs(3,i+1) + comz5\n\ndo i = 1, nx2\nlhsp(1,i) = lhs(1,i)\nlhsp(2,i) = lhs(2,i) - &\n& dttx2 * speed(i-1,j,k)\nlhsp(3,i) = lhs(3,i)\nlhsp(4,i) = lhs(4,i) + &\n& dttx2 * speed(i+1,j,k)\nlhsp(5,i) = lhs(5,i)\nlhsm(1,i) = lhs(1,i)\nlhsm(2,i) = lhs(2,i) + &\n& dttx2 * speed(i-1,j,k)\nlhsm(3,i) = lhs(3,i)\nlhsm(4,i) = lhs(4,i) - &\n& dttx2 * speed(i+1,j,k)\nlhsm(5,i) = lhs(5,i)\nend do\n\n\n\ndo i = 0, grid_points(1)-3\ni1 = i + 1\ni2 = i + 2\nfac1 = 1.d0/lhs(3,i)\nlhs(4,i) = fac1*lhs(4,i)\nlhs(5,i) = fac1*lhs(5,i)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nend do\nlhs(3,i1) = lhs(3,i1) - &\n& lhs(2,i1)*lhs(4,i)\nlhs(4,i1) = lhs(4,i1) - &\n& lhs(2,i1)*lhs(5,i)\ndo m = 1, 3\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhs(2,i1)*rhs(m,i,j,k)\nend do\nlhs(2,i2) = lhs(2,i2) - &\n& lhs(1,i2)*lhs(4,i)\nlhs(3,i2) = lhs(3,i2) - &\n& lhs(1,i2)*lhs(5,i)\ndo m = 1, 3\nrhs(m,i2,j,k) = rhs(m,i2,j,k) - &\n& lhs(1,i2)*rhs(m,i,j,k)\nend do\nend do\n\n\ni = grid_points(1)-2\ni1 = grid_points(1)-1\nfac1 = 1.d0/lhs(3,i)\nlhs(4,i) = fac1*lhs(4,i)\nlhs(5,i) = fac1*lhs(5,i)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nend do\nlhs(3,i1) = lhs(3,i1) - &\n& lhs(2,i1)*lhs(4,i)\nlhs(4,i1) = lhs(4,i1) - &\n& lhs(2,i1)*lhs(5,i)\ndo m = 1, 3\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhs(2,i1)*rhs(m,i,j,k)\nend do\nfac2 = 1.d0/lhs(3,i1)\ndo m = 1, 3\nrhs(m,i1,j,k) = fac2*rhs(m,i1,j,k)\nend do\n\n\ndo i = 0, grid_points(1)-3\ni1 = i + 1\ni2 = i + 2\nm = 4\nfac1 = 1.d0/lhsp(3,i)\nlhsp(4,i) = fac1*lhsp(4,i)\nlhsp(5,i) = fac1*lhsp(5,i)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsp(3,i1) = lhsp(3,i1) - &\n& lhsp(2,i1)*lhsp(4,i)\nlhsp(4,i1) = lhsp(4,i1) - &\n& lhsp(2,i1)*lhsp(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsp(2,i1)*rhs(m,i,j,k)\nlhsp(2,i2) = lhsp(2,i2) - &\n& lhsp(1,i2)*lhsp(4,i)\nlhsp(3,i2) = lhsp(3,i2) - &\n& lhsp(1,i2)*lhsp(5,i)\nrhs(m,i2,j,k) = rhs(m,i2,j,k) - &\n& lhsp(1,i2)*rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,i)\nlhsm(4,i) = fac1*lhsm(4,i)\nlhsm(5,i) = fac1*lhsm(5,i)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsm(3,i1) = lhsm(3,i1) - &\n& lhsm(2,i1)*lhsm(4,i)\nlhsm(4,i1) = lhsm(4,i1) - &\n& lhsm(2,i1)*lhsm(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsm(2,i1)*rhs(m,i,j,k)\nlhsm(2,i2) = lhsm(2,i2) - &\n& lhsm(1,i2)*lhsm(4,i)\nlhsm(3,i2) = lhsm(3,i2) - &\n& lhsm(1,i2)*lhsm(5,i)\nrhs(m,i2,j,k) = rhs(m,i2,j,k) - &\n& lhsm(1,i2)*rhs(m,i,j,k)\nend do\n\ni = grid_points(1)-2\ni1 = grid_points(1)-1\nm = 4\nfac1 = 1.d0/lhsp(3,i)\nlhsp(4,i) = fac1*lhsp(4,i)\nlhsp(5,i) = fac1*lhsp(5,i)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsp(3,i1) = lhsp(3,i1) - &\n& lhsp(2,i1)*lhsp(4,i)\nlhsp(4,i1) = lhsp(4,i1) - &\n& lhsp(2,i1)*lhsp(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsp(2,i1)*rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,i)\nlhsm(4,i) = fac1*lhsm(4,i)\nlhsm(5,i) = fac1*lhsm(5,i)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsm(3,i1) = lhsm(3,i1) - &\n& lhsm(2,i1)*lhsm(4,i)\nlhsm(4,i1) = lhsm(4,i1) - &\n& lhsm(2,i1)*lhsm(5,i)\nrhs(m,i1,j,k) = rhs(m,i1,j,k) - &\n& lhsm(2,i1)*rhs(m,i,j,k)\nrhs(4,i1,j,k) = rhs(4,i1,j,k)/lhsp(3,i1)\nrhs(5,i1,j,k) = rhs(5,i1,j,k)/lhsm(3,i1)\n\n\n\n\ni = grid_points(1)-2\ni1 = grid_points(1)-1\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,i)*rhs(m,i1,j,k)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,i)*rhs(4,i1,j,k)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,i)*rhs(5,i1,j,k)\n\ndo i = grid_points(1)-3, 0, -1\ni1 = i + 1\ni2 = i + 2\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,i)*rhs(m,i1,j,k) - &\n& lhs(5,i)*rhs(m,i2,j,k)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,i)*rhs(4,i1,j,k) - &\n& lhsp(5,i)*rhs(4,i2,j,k)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,i)*rhs(5,i1,j,k) - &\n& lhsm(5,i)*rhs(5,i2,j,k)\nend do\nend do\n\nend do\nif (timeron) call timer_stop(t_xsolve)\n\ncall ninvr\n\nreturn\nend

static void evolve(void* pointer_u0,\nvoid* pointer_u1,\nvoid* pointer_twiddle,\nint d1,\nint d2,\nint d3){\ndcomplex (*u0)[NY][NX] = (dcomplex(*)[NY][NX])pointer_u0;\ndcomplex (*u1)[NY][NX] = (dcomplex(*)[NY][NX])pointer_u1;\ndouble (*twiddle)[NY][NX] = (double(*)[NY][NX])pointer_twiddle;\n\nint i, j, k;\n#pragma omp for\nfor(k=0; k<d3; k++){\nfor(j=0; j<d2; j++){\nfor(i=0; i<d1; i++){\nu0[k][j][i] = dcomplex_mul2(u0[k][j][i], twiddle[k][j][i]);\nu1[k][j][i] = u0[k][j][i];\n}\n}\n}\n}

subroutine evolve(u0, u1, twiddle, d1, d2, d3)\n\n\n\nuse ft_data\nimplicit none\n\ninteger d1, d2, d3\ndouble complex u0(d1+1,d2,d3)\ndouble complex u1(d1+1,d2,d3)\ndouble precision twiddle(d1+1,d2,d3)\ninteger i, j, k\n\ndo k = 1, d3\ndo j = 1, d2\ndo i = 1, d1\nu0(i,j,k) = u0(i,j,k) * twiddle(i,j,k)\nu1(i,j,k) = u0(i,j,k)\nend do\nend do\nend do\n\nreturn\nend

void domain(){\n\nnx=nx0;\nny=ny0;\nnz=nz0;\n\nif((nx<4)||(ny<4)||(nz<4)){\nprintf(" SUBDOMAIN SIZE IS TOO SMALL -\n"\n" ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS\n"\n" SO THAT NX, NY AND NZ ARE GREATER THAN OR EQUAL\n"\n" TO 4 THEY ARE CURRENTLY%3d%3d%3d\n",nx,ny,nz);\nexit(EXIT_FAILURE);\n}\nif((nx>ISIZ1)||(ny>ISIZ2)||(nz>ISIZ3)){\nprintf(" SUBDOMAIN SIZE IS TOO LARGE -\n"\n" ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS\n"\n" SO THAT NX, NY AND NZ ARE LESS THAN OR EQUAL TO\n"\n" ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY. THEY ARE\n"\n" CURRENTLYi%4d%4d%4d\n", nx, ny, nz);\nexit(EXIT_FAILURE);\n}\n\nist=1;\niend=nx-1;\njst=1;\njend=ny-1;\nii1=1;\nii2=nx0-1;\nji1=1;\nji2=ny0-2;\nki1=2;\nki2=nz0-1;\n}

subroutine domain\n\n\nuse lu_data\nimplicit none\n\n\n\nnx = nx0\nny = ny0\nnz = nz0\n\nif ( ( nx .lt. 4 ) .or. &\n& ( ny .lt. 4 ) .or. &\n& ( nz .lt. 4 ) ) then\nwrite (*,2001) nx, ny, nz\n2001 format (5x,'SUBDOMAIN SIZE IS TOO SMALL - ', &\n& /5x,'ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS', &\n& /5x,'SO THAT NX, NY AND NZ ARE GREATER THAN OR EQUAL', &\n& /5x,'TO 4 THEY ARE CURRENTLY', 3I3)\nstop\nend if\n\nif ( ( nx .gt. isiz1 ) .or. &\n& ( ny .gt. isiz2 ) .or. &\n& ( nz .gt. isiz3 ) ) then\nwrite (*,2002) nx, ny, nz\n2002 format (5x,'SUBDOMAIN SIZE IS TOO LARGE - ', &\n& /5x,'ADJUST PROBLEM SIZE OR NUMBER OF PROCESSORS', &\n& /5x,'SO THAT NX, NY AND NZ ARE LESS THAN OR EQUAL TO ', &\n& /5x,'ISIZ1, ISIZ2 AND ISIZ3 RESPECTIVELY. THEY ARE', &\n& /5x,'CURRENTLY', 3I4)\nstop\nend if\n\nist = 2\niend = nx - 1\n\njst = 2\njend = ny - 1\n\nii1 = 2\nii2 = nx0 - 1\nji1 = 2\nji2 = ny0 - 2\nki1 = 3\nki2 = nz0 - 1\n\nreturn\nend

void tzetar(){\nint i, j, k;\ndouble t1, t2, t3, ac, xvel, yvel, zvel, r1, r2, r3, r4, r5, btuz, ac2u, uzik1;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_TZETAR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nxvel=us[k][j][i];\nyvel=vs[k][j][i];\nzvel=ws[k][j][i];\nac=speed[k][j][i];\nac2u=ac*ac;\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nuzik1=u[k][j][i][0];\nbtuz=bt*uzik1;\nt1=btuz/ac*(r4+r5);\nt2=r3+t1;\nt3=btuz*(r4-r5);\nrhs[k][j][i][0]=t2;\nrhs[k][j][i][1]=-uzik1*r2+xvel*t2;\nrhs[k][j][i][2]=uzik1*r1+yvel*t2;\nrhs[k][j][i][3]=zvel*t2+t3;\nrhs[k][j][i][4]=uzik1*(-xvel*r2+yvel*r1) +\nqs[k][j][i]*t2+c2iv*ac2u*t1+zvel*t3;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_TZETAR);}\n}

subroutine tzetar\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision t1, t2, t3, ac, xvel, yvel, zvel, r1, r2, r3, &\n& r4, r5, btuz, ac2u, uzik1\n\n\nif (timeron) call timer_start(t_tzetar)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nxvel = us(i,j,k)\nyvel = vs(i,j,k)\nzvel = ws(i,j,k)\nac = speed(i,j,k)\n\nac2u = ac*ac\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nuzik1 = u(1,i,j,k)\nbtuz = bt * uzik1\n\nt1 = btuz/ac * (r4 + r5)\nt2 = r3 + t1\nt3 = btuz * (r4 - r5)\n\nrhs(1,i,j,k) = t2\nrhs(2,i,j,k) = -uzik1*r2 + xvel*t2\nrhs(3,i,j,k) = uzik1*r1 + yvel*t2\nrhs(4,i,j,k) = zvel*t2 + t3\nrhs(5,i,j,k) = uzik1*(-xvel*r2 + yvel*r1) + &\n& qs(i,j,k)*t2 + c2iv*ac2u*t1 + zvel*t3\n\nend do\nend do\nend do\nif (timeron) call timer_stop(t_tzetar)\n\nreturn\nend

static void rep_nrm(void* pointer_u, int n1, int n2, int n3, char* title, int kk){\ndouble rnm2, rnmu;\nnorm2u3(pointer_u,n1,n2,n3,&rnm2,&rnmu,nx[kk],ny[kk],nz[kk]);\n#pragma omp master\nprintf(" Level%2d in %8s: norms =%21.14e%21.14e\n", kk, title, rnm2, rnmu);\n}

subroutine rep_nrm(u,n1,n2,n3,title,kk)\n\n\n\nuse mg_data\nimplicit none\n\ninteger n1, n2, n3, kk\ndouble precision u(n1,n2,n3)\ncharacter*8 title\n\ndouble precision rnm2, rnmu\n\n\ncall norm2u3(u,n1,n2,n3,rnm2,rnmu,nx(kk),ny(kk),nz(kk))\nwrite(*,7)kk,title,rnm2,rnmu\n7 format(' Level',i2,' in ',a8,': norms =',D21.14,D21.14)\n\nreturn\nend

void exact_rhs(){\ndouble dtemp[5], xi, eta, zeta, dtpp;\nint m, i, j, k, ip1, im1, jp1, jm1, km1, kp1;\n\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<=grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=0.0;\n}\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)(k)*dnzm1;\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)(j)*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][i]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][i]=dtpp*dtemp[m];\n}\ncuf[i]=buf[1][i]*buf[1][i];\nbuf[0][i]=cuf[i]+buf[2][i]*buf[2][i]+buf[3][i]*buf[3][i];\nq[i]=0.5*(buf[1][i]*ue[1][i]+buf[2][i]*ue[2][i]+\nbuf[3][i]*ue[3][i]);\n}\nfor(i=1; i<=grid_points[0]-2; i++){\nim1=i-1;\nip1=i+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntx2*(ue[1][ip1]-ue[1][im1])+\ndx1tx1*(ue[0][ip1]-2.0*ue[0][i]+ue[0][im1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tx2*(\n(ue[1][ip1]*buf[1][ip1]+c2*(ue[4][ip1]-q[ip1]))-\n(ue[1][im1]*buf[1][im1]+c2*(ue[4][im1]-q[im1])))+\nxxcon1*(buf[1][ip1]-2.0*buf[1][i]+buf[1][im1])+\ndx2tx1*(ue[1][ip1]-2.0*ue[1][i]+ue[1][im1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tx2*(\nue[2][ip1]*buf[1][ip1]-ue[2][im1]*buf[1][im1])+\nxxcon2*(buf[2][ip1]-2.0*buf[2][i]+buf[2][im1])+\ndx3tx1*(ue[2][ip1]-2.0*ue[2][i] +ue[2][im1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tx2*(\nue[3][ip1]*buf[1][ip1]-ue[3][im1]*buf[1][im1])+\nxxcon2*(buf[3][ip1]-2.0*buf[3][i]+buf[3][im1])+\ndx4tx1*(ue[3][ip1]-2.0*ue[3][i]+ue[3][im1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tx2*(\nbuf[1][ip1]*(c1*ue[4][ip1]-c2*q[ip1])-\nbuf[1][im1]*(c1*ue[4][im1]-c2*q[im1]))+\n0.5*xxcon3*(buf[0][ip1]-2.0*buf[0][i]+\nbuf[0][im1])+\nxxcon4*(cuf[ip1]-2.0*cuf[i]+cuf[im1])+\nxxcon5*(buf[4][ip1]-2.0*buf[4][i]+buf[4][im1])+\ndx5tx1*(ue[4][ip1]-2.0*ue[4][i]+ue[4][im1]);\n}\n\nfor(m=0; m<5; m++){\ni=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(5.0*ue[m][i]-4.0*ue[m][i+1]+ue[m][i+2]);\ni=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(-4.0*ue[m][i-1]+6.0*ue[m][i]-\n4.0*ue[m][i+1]+ue[m][i+2]);\n}\nfor(i=3; i<=grid_points[0]-4; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][i-2]-4.0*ue[m][i-1]+\n6.0*ue[m][i]-4.0*ue[m][i+1]+ue[m][i+2]);\n}\n}\nfor(m=0; m<5; m++){\ni=grid_points[0]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][i-2]-4.0*ue[m][i-1]+\n6.0*ue[m][i]-4.0*ue[m][i+1]);\ni=grid_points[0]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][i-2]-4.0*ue[m][i-1]+5.0*ue[m][i]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)(k)*dnzm1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)(i)*dnxm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][j]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][j]=dtpp*dtemp[m];\n}\ncuf[j]=buf[2][j]*buf[2][j];\nbuf[0][j]=cuf[j]+buf[1][j]*buf[1][j]+buf[3][j]*buf[3][j];\nq[j]=0.5*(buf[1][j]*ue[1][j]+buf[2][j]*ue[2][j]+\nbuf[3][j]*ue[3][j]);\n}\nfor(j=1; j<=grid_points[1]-2; j++){\njm1=j-1;\njp1=j+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\nty2*(ue[2][jp1]-ue[2][jm1])+\ndy1ty1*(ue[0][jp1]-2.0*ue[0][j]+ue[0][jm1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-ty2*(\nue[1][jp1]*buf[2][jp1]-ue[1][jm1]*buf[2][jm1])+\nyycon2*(buf[1][jp1]-2.0*buf[1][j]+buf[1][jm1])+\ndy2ty1*(ue[1][jp1]-2.0*ue[1][j]+ue[1][jm1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-ty2*(\n(ue[2][jp1]*buf[2][jp1]+c2*(ue[4][jp1]-q[jp1]))-\n(ue[2][jm1]*buf[2][jm1]+c2*(ue[4][jm1]-q[jm1])))+\nyycon1*(buf[2][jp1]-2.0*buf[2][j]+buf[2][jm1])+\ndy3ty1*(ue[2][jp1]-2.0*ue[2][j]+ue[2][jm1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-ty2*(\nue[3][jp1]*buf[2][jp1]-ue[3][jm1]*buf[2][jm1])+\nyycon2*(buf[3][jp1]-2.0*buf[3][j]+buf[3][jm1])+\ndy4ty1*(ue[3][jp1]-2.0*ue[3][j]+ue[3][jm1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-ty2*(\nbuf[2][jp1]*(c1*ue[4][jp1]-c2*q[jp1])-\nbuf[2][jm1]*(c1*ue[4][jm1]-c2*q[jm1]))+\n0.5*yycon3*(buf[0][jp1]-2.0*buf[0][j]+\nbuf[0][jm1])+\nyycon4*(cuf[jp1]-2.0*cuf[j]+cuf[jm1])+\nyycon5*(buf[4][jp1]-2.0*buf[4][j]+buf[4][jm1])+\ndy5ty1*(ue[4][jp1]-2.0*ue[4][j]+ue[4][jm1]);\n}\n\nfor(m=0; m<5; m++){\nj=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(5.0*ue[m][j]-4.0*ue[m][j+1] +ue[m][j+2]);\nj=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(-4.0*ue[m][j-1]+6.0*ue[m][j]-\n4.0*ue[m][j+1]+ue[m][j+2]);\n}\nfor(j=3; j<=grid_points[1]-4; j++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][j-2]-4.0*ue[m][j-1]+\n6.0*ue[m][j]-4.0*ue[m][j+1]+ue[m][j+2]);\n}\n}\nfor(m=0; m<5; m++){\nj=grid_points[1]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][j-2]-4.0*ue[m][j-1]+\n6.0*ue[m][j]-4.0*ue[m][j+1]);\nj=grid_points[1]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][j-2]-4.0*ue[m][j-1]+5.0*ue[m][j]);\n}\n}\n}\n\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)(j)*dnym1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)(i)*dnxm1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)*dnzm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][k]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][k]=dtpp*dtemp[m];\n}\ncuf[k]=buf[3][k]*buf[3][k];\nbuf[0][k]=cuf[k]+buf[1][k]*buf[1][k]+buf[2][k]*buf[2][k];\nq[k]=0.5*(buf[1][k]*ue[1][k]+buf[2][k]*ue[2][k]+\nbuf[3][k]*ue[3][k]);\n}\nfor(k=1; k<=grid_points[2]-2; k++){\nkm1=k-1;\nkp1=k+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntz2*(ue[3][kp1]-ue[3][km1])+\ndz1tz1*(ue[0][kp1]-2.0*ue[0][k]+ue[0][km1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tz2*(\nue[1][kp1]*buf[3][kp1]-ue[1][km1]*buf[3][km1])+\nzzcon2*(buf[1][kp1]-2.0*buf[1][k]+buf[1][km1])+\ndz2tz1*(ue[1][kp1]-2.0*ue[1][k]+ue[1][km1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tz2*(\nue[2][kp1]*buf[3][kp1]-ue[2][km1]*buf[3][km1])+\nzzcon2*(buf[2][kp1]-2.0*buf[2][k]+buf[2][km1])+\ndz3tz1*(ue[2][kp1]-2.0*ue[2][k]+ue[2][km1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tz2*(\n(ue[3][kp1]*buf[3][kp1]+c2*(ue[4][kp1]-q[kp1]))-\n(ue[3][km1]*buf[3][km1]+c2*(ue[4][km1]-q[km1])))+\nzzcon1*(buf[3][kp1]-2.0*buf[3][k]+buf[3][km1])+\ndz4tz1*(ue[3][kp1]-2.0*ue[3][k]+ue[3][km1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tz2*(\nbuf[3][kp1]*(c1*ue[4][kp1]-c2*q[kp1])-\nbuf[3][km1]*(c1*ue[4][km1]-c2*q[km1]))+\n0.5*zzcon3*(buf[0][kp1]-2.0*buf[0][k]\n+buf[0][km1])+\nzzcon4*(cuf[kp1]-2.0*cuf[k]+cuf[km1])+\nzzcon5*(buf[4][kp1]-2.0*buf[4][k]+buf[4][km1])+\ndz5tz1*(ue[4][kp1]-2.0*ue[4][k]+ue[4][km1]);\n}\n\nfor(m=0; m<5; m++){\nk=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(5.0*ue[m][k]-4.0*ue[m][k+1]+ue[m][k+2]);\nk=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(-4.0*ue[m][k-1]+6.0*ue[m][k]-\n4.0*ue[m][k+1]+ue[m][k+2]);\n}\nfor(k=3; k<=grid_points[2]-4; k++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][k-2]-4.0*ue[m][k-1]+\n6.0*ue[m][k]-4.0*ue[m][k+1]+ue[m][k+2]);\n}\n}\nfor(m=0; m<5; m++){\nk=grid_points[2]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][k-2]-4.0*ue[m][k-1]+\n6.0*ue[m][k]-4.0*ue[m][k+1]);\nk=grid_points[2]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][k-2]-4.0*ue[m][k-1]+5.0*ue[m][k]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=-1.0*forcing[k][j][i][m];\n}\n}\n}\n}\n}

subroutine exact_rhs\n\n\n\nuse bt_data\nimplicit none\n\ndouble precision dtemp(5), xi, eta, zeta, dtpp\ninteger m, i, j, k, ip1, im1, jp1, jm1, km1, kp1\n\ndo k= 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nforcing(m,i,j,k) = 0.0d0\nenddo\nenddo\nenddo\nenddo\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\n\ndo i=0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(i,m) = dtemp(m)\nenddo\n\ndtpp = 1.0d0 / dtemp(1)\n\ndo m = 2, 5\nbuf(i,m) = dtpp * dtemp(m)\nenddo\n\ncuf(i) = buf(i,2) * buf(i,2)\nbuf(i,1) = cuf(i) + buf(i,3) * buf(i,3) + &\n& buf(i,4) * buf(i,4)\nq(i) = 0.5d0*(buf(i,2)*ue(i,2) + buf(i,3)*ue(i,3) + &\n& buf(i,4)*ue(i,4))\n\nenddo\n\ndo i = 1, grid_points(1)-2\nim1 = i-1\nip1 = i+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tx2*( ue(ip1,2)-ue(im1,2) )+ &\n& dx1tx1*(ue(ip1,1)-2.0d0*ue(i,1)+ue(im1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tx2 * ( &\n& (ue(ip1,2)*buf(ip1,2)+c2*(ue(ip1,5)-q(ip1)))- &\n& (ue(im1,2)*buf(im1,2)+c2*(ue(im1,5)-q(im1))))+ &\n& xxcon1*(buf(ip1,2)-2.0d0*buf(i,2)+buf(im1,2))+ &\n& dx2tx1*( ue(ip1,2)-2.0d0* ue(i,2)+ue(im1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tx2 * ( &\n& ue(ip1,3)*buf(ip1,2)-ue(im1,3)*buf(im1,2))+ &\n& xxcon2*(buf(ip1,3)-2.0d0*buf(i,3)+buf(im1,3))+ &\n& dx3tx1*( ue(ip1,3)-2.0d0*ue(i,3) +ue(im1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tx2*( &\n& ue(ip1,4)*buf(ip1,2)-ue(im1,4)*buf(im1,2))+ &\n& xxcon2*(buf(ip1,4)-2.0d0*buf(i,4)+buf(im1,4))+ &\n& dx4tx1*( ue(ip1,4)-2.0d0* ue(i,4)+ ue(im1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tx2*( &\n& buf(ip1,2)*(c1*ue(ip1,5)-c2*q(ip1))- &\n& buf(im1,2)*(c1*ue(im1,5)-c2*q(im1)))+ &\n& 0.5d0*xxcon3*(buf(ip1,1)-2.0d0*buf(i,1)+ &\n& buf(im1,1))+ &\n& xxcon4*(cuf(ip1)-2.0d0*cuf(i)+cuf(im1))+ &\n& xxcon5*(buf(ip1,5)-2.0d0*buf(i,5)+buf(im1,5))+ &\n& dx5tx1*( ue(ip1,5)-2.0d0* ue(i,5)+ ue(im1,5))\nenddo\n\n\ndo m = 1, 5\ni = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0*ue(i,m) - 4.0d0*ue(i+1,m) +ue(i+2,m))\ni = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0*ue(i-1,m) + 6.0d0*ue(i,m) - &\n& 4.0d0*ue(i+1,m) + ue(i+2,m))\nenddo\n\ndo i = 3, grid_points(1)-4\ndo m = 1, 5\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp* &\n& (ue(i-2,m) - 4.0d0*ue(i-1,m) + &\n& 6.0d0*ue(i,m) - 4.0d0*ue(i+1,m) + ue(i+2,m))\nenddo\nenddo\n\ndo m = 1, 5\ni = grid_points(1)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(i-2,m) - 4.0d0*ue(i-1,m) + &\n& 6.0d0*ue(i,m) - 4.0d0*ue(i+1,m))\ni = grid_points(1)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(i-2,m) - 4.0d0*ue(i-1,m) + 5.0d0*ue(i,m))\nenddo\n\nenddo\nenddo\n\ndo k = 1, grid_points(3)-2\ndo i=1, grid_points(1)-2\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\n\ndo j=0, grid_points(2)-1\neta = dble(j) * dnym1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(j,m) = dtemp(m)\nenddo\n\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(j,m) = dtpp * dtemp(m)\nenddo\n\ncuf(j) = buf(j,3) * buf(j,3)\nbuf(j,1) = cuf(j) + buf(j,2) * buf(j,2) + &\n& buf(j,4) * buf(j,4)\nq(j) = 0.5d0*(buf(j,2)*ue(j,2) + buf(j,3)*ue(j,3) + &\n& buf(j,4)*ue(j,4))\nenddo\n\ndo j = 1, grid_points(2)-2\njm1 = j-1\njp1 = j+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& ty2*( ue(jp1,3)-ue(jm1,3) )+ &\n& dy1ty1*(ue(jp1,1)-2.0d0*ue(j,1)+ue(jm1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - ty2*( &\n& ue(jp1,2)*buf(jp1,3)-ue(jm1,2)*buf(jm1,3))+ &\n& yycon2*(buf(jp1,2)-2.0d0*buf(j,2)+buf(jm1,2))+ &\n& dy2ty1*( ue(jp1,2)-2.0* ue(j,2)+ ue(jm1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - ty2*( &\n& (ue(jp1,3)*buf(jp1,3)+c2*(ue(jp1,5)-q(jp1)))- &\n& (ue(jm1,3)*buf(jm1,3)+c2*(ue(jm1,5)-q(jm1))))+ &\n& yycon1*(buf(jp1,3)-2.0d0*buf(j,3)+buf(jm1,3))+ &\n& dy3ty1*( ue(jp1,3)-2.0d0*ue(j,3) +ue(jm1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - ty2*( &\n& ue(jp1,4)*buf(jp1,3)-ue(jm1,4)*buf(jm1,3))+ &\n& yycon2*(buf(jp1,4)-2.0d0*buf(j,4)+buf(jm1,4))+ &\n& dy4ty1*( ue(jp1,4)-2.0d0*ue(j,4)+ ue(jm1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - ty2*( &\n& buf(jp1,3)*(c1*ue(jp1,5)-c2*q(jp1))- &\n& buf(jm1,3)*(c1*ue(jm1,5)-c2*q(jm1)))+ &\n& 0.5d0*yycon3*(buf(jp1,1)-2.0d0*buf(j,1)+ &\n& buf(jm1,1))+ &\n& yycon4*(cuf(jp1)-2.0d0*cuf(j)+cuf(jm1))+ &\n& yycon5*(buf(jp1,5)-2.0d0*buf(j,5)+buf(jm1,5))+ &\n& dy5ty1*(ue(jp1,5)-2.0d0*ue(j,5)+ue(jm1,5))\nenddo\n\ndo m = 1, 5\nj = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0*ue(j,m) - 4.0d0*ue(j+1,m) +ue(j+2,m))\nj = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0*ue(j-1,m) + 6.0d0*ue(j,m) - &\n& 4.0d0*ue(j+1,m) + ue(j+2,m))\nenddo\n\ndo j = 3, grid_points(2)-4\ndo m = 1, 5\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp* &\n& (ue(j-2,m) - 4.0d0*ue(j-1,m) + &\n& 6.0d0*ue(j,m) - 4.0d0*ue(j+1,m) + ue(j+2,m))\nenddo\nenddo\n\ndo m = 1, 5\nj = grid_points(2)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(j-2,m) - 4.0d0*ue(j-1,m) + &\n& 6.0d0*ue(j,m) - 4.0d0*ue(j+1,m))\nj = grid_points(2)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(j-2,m) - 4.0d0*ue(j-1,m) + 5.0d0*ue(j,m))\n\nenddo\n\nenddo\nenddo\n\ndo j=1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\neta = dble(j) * dnym1\nxi = dble(i) * dnxm1\n\ndo k=0, grid_points(3)-1\nzeta = dble(k) * dnzm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(k,m) = dtemp(m)\nenddo\n\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(k,m) = dtpp * dtemp(m)\nenddo\n\ncuf(k) = buf(k,4) * buf(k,4)\nbuf(k,1) = cuf(k) + buf(k,2) * buf(k,2) + &\n& buf(k,3) * buf(k,3)\nq(k) = 0.5d0*(buf(k,2)*ue(k,2) + buf(k,3)*ue(k,3) + &\n& buf(k,4)*ue(k,4))\nenddo\n\ndo k=1, grid_points(3)-2\nkm1 = k-1\nkp1 = k+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tz2*( ue(kp1,4)-ue(km1,4) )+ &\n& dz1tz1*(ue(kp1,1)-2.0d0*ue(k,1)+ue(km1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tz2 * ( &\n& ue(kp1,2)*buf(kp1,4)-ue(km1,2)*buf(km1,4))+ &\n& zzcon2*(buf(kp1,2)-2.0d0*buf(k,2)+buf(km1,2))+ &\n& dz2tz1*( ue(kp1,2)-2.0d0* ue(k,2)+ ue(km1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tz2 * ( &\n& ue(kp1,3)*buf(kp1,4)-ue(km1,3)*buf(km1,4))+ &\n& zzcon2*(buf(kp1,3)-2.0d0*buf(k,3)+buf(km1,3))+ &\n& dz3tz1*(ue(kp1,3)-2.0d0*ue(k,3)+ue(km1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tz2 * ( &\n& (ue(kp1,4)*buf(kp1,4)+c2*(ue(kp1,5)-q(kp1)))- &\n& (ue(km1,4)*buf(km1,4)+c2*(ue(km1,5)-q(km1))))+ &\n& zzcon1*(buf(kp1,4)-2.0d0*buf(k,4)+buf(km1,4))+ &\n& dz4tz1*( ue(kp1,4)-2.0d0*ue(k,4) +ue(km1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tz2 * ( &\n& buf(kp1,4)*(c1*ue(kp1,5)-c2*q(kp1))- &\n& buf(km1,4)*(c1*ue(km1,5)-c2*q(km1)))+ &\n& 0.5d0*zzcon3*(buf(kp1,1)-2.0d0*buf(k,1) &\n& +buf(km1,1))+ &\n& zzcon4*(cuf(kp1)-2.0d0*cuf(k)+cuf(km1))+ &\n& zzcon5*(buf(kp1,5)-2.0d0*buf(k,5)+buf(km1,5))+ &\n& dz5tz1*( ue(kp1,5)-2.0d0*ue(k,5)+ ue(km1,5))\nenddo\n\ndo m = 1, 5\nk = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0*ue(k,m) - 4.0d0*ue(k+1,m) +ue(k+2,m))\nk = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0*ue(k-1,m) + 6.0d0*ue(k,m) - &\n& 4.0d0*ue(k+1,m) + ue(k+2,m))\nenddo\n\ndo k = 3, grid_points(3)-4\ndo m = 1, 5\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp* &\n& (ue(k-2,m) - 4.0d0*ue(k-1,m) + &\n& 6.0d0*ue(k,m) - 4.0d0*ue(k+1,m) + ue(k+2,m))\nenddo\nenddo\n\ndo m = 1, 5\nk = grid_points(3)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(k-2,m) - 4.0d0*ue(k-1,m) + &\n& 6.0d0*ue(k,m) - 4.0d0*ue(k+1,m))\nk = grid_points(3)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(k-2,m) - 4.0d0*ue(k-1,m) + 5.0d0*ue(k,m))\nenddo\n\nenddo\nenddo\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nforcing(m,i,j,k) = -1.d0 * forcing(m,i,j,k)\nenddo\nenddo\nenddo\nenddo\n\nreturn\nend

void pinvr(){\nint i, j, k;\ndouble r1, r2, r3, r4, r5, t1, t2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_PINVR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nt1=bt*r1;\nt2=0.5*(r4+r5);\nrhs[k][j][i][0]=bt*(r4-r5);\nrhs[k][j][i][1]=-r3;\nrhs[k][j][i][2]=r2;\nrhs[k][j][i][3]=-t1+t2;\nrhs[k][j][i][4]=t1+t2;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_PINVR);}\n}

subroutine pinvr\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision r1, r2, r3, r4, r5, t1, t2\n\nif (timeron) call timer_start(t_pinvr)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nt1 = bt * r1\nt2 = 0.5d0 * ( r4 + r5 )\n\nrhs(1,i,j,k) = bt * ( r4 - r5 )\nrhs(2,i,j,k) = -r3\nrhs(3,i,j,k) = r2\nrhs(4,i,j,k) = -t1 + t2\nrhs(5,i,j,k) = t1 + t2\nend do\nend do\nend do\nif (timeron) call timer_stop(t_pinvr)\n\nreturn\nend

static void cffts1(int is,\nint d1,\nint d2,\nint d3,\nvoid* pointer_x,\nvoid* pointer_xout,\ndcomplex y1[][FFTBLOCKPAD],\ndcomplex y2[][FFTBLOCKPAD]){\ndcomplex (*x)[NY][NX] = (dcomplex(*)[NY][NX])pointer_x;\ndcomplex (*xout)[NY][NX] = (dcomplex(*)[NY][NX])pointer_xout;\n\nint logd1;\nint i, j, k, jj;\n\nlogd1 = ilog2(d1);\n\n\nif(timers_enabled){\n#pragma omp master\ntimer_start(T_FFTX);\n}\n\n#pragma omp for\nfor(k=0; k<d3; k++){\nfor(jj=0; jj<=d2-FFTBLOCK; jj+=FFTBLOCK){\nfor(j=0; j<FFTBLOCK; j++){\nfor(i=0; i<d1; i++){\ny1[i][j] = x[k][j+jj][i];\n}\n}\ncfftz(is, logd1, d1, y1, y2);\nfor(j=0; j<FFTBLOCK; j++){\nfor(i=0; i<d1; i++){\nxout[k][j+jj][i] = y1[i][j];\n}\n}\n}\n}\n\nif(timers_enabled){\n#pragma omp master\ntimer_stop(T_FFTX);\n}\n}

subroutine cffts1(is, d1, d2, d3, x, xout, y1, y2)\n\n\nuse ft_data\nimplicit none\n\ninteger is, d1, d2, d3, logd1\ndouble complex x(d1+1,d2,d3)\ndouble complex xout(d1+1,d2,d3)\ndouble complex y1(fftblockpad, d1), y2(fftblockpad, d1)\ninteger i, j, k, jj, jn\n\nlogd1 = ilog2(d1)\n\nif (timers_enabled) call timer_start(T_fftx)\ndo k = 1, d3\ndo jn = 0, d2/fftblock - 1\njj = jn*fftblock\ndo j = 1, fftblock\ndo i = 1, d1\ny1(j,i) = x(i,j+jj,k)\nenddo\nenddo\n\ncall cfftz (is, logd1, d1, y1, y2)\n\n\ndo j = 1, fftblock\ndo i = 1, d1\nxout(i,j+jj,k) = y1(j,i)\nenddo\nenddo\nenddo\nenddo\nif (timers_enabled) call timer_stop(T_fftx)\n\nreturn\nend

void error(){\n\nint i, j, k, m;\ndouble tmp;\ndouble u000ijk[5];\nfor(m=0;m<5;m++){errnm[m]=0.0;}\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nexact(i, j, k, u000ijk);\nfor(m=0; m<5; m++){\ntmp=(u000ijk[m]-u[k][j][i][m]);\nerrnm[m]=errnm[m]+tmp*tmp;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nerrnm[m]=sqrt(errnm[m]/((nx0-2)*(ny0-2)*(nz0-2)));\n}\n}

subroutine error\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision tmp\ndouble precision u000ijk(5)\n\n\ndo m = 1, 5\nerrnm(m) = 0.0d+00\nend do\n\ndo k = 2, nz-1\ndo j = jst, jend\ndo i = ist, iend\ncall exact( i, j, k, u000ijk )\ndo m = 1, 5\ntmp = ( u000ijk(m) - u(m,i,j,k) )\nerrnm(m) = errnm(m) + tmp * tmp\nend do\nend do\nend do\nend do\n\ndo m = 1, 5\nerrnm(m) = sqrt ( errnm(m) / ( dble(nx0-2)*(ny0-2)*(nz0-2) ) )\nend do\n\n\n1002 format (1x/1x,'RMS-norm of error in soln. to ', &\n& 'first pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'second pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'third pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'fourth pde = ',1pe12.5/, &\n& 1x,'RMS-norm of error in soln. to ', &\n& 'fifth pde = ',1pe12.5)\n\nreturn\nend

static void cffts3(int is,\nint d1,\nint d2,\nint d3,\nvoid* pointer_x,\nvoid* pointer_xout,\ndcomplex y1[][FFTBLOCKPAD],\ndcomplex y2[][FFTBLOCKPAD]){\ndcomplex (*x)[NY][NX] = (dcomplex(*)[NY][NX])pointer_x;\ndcomplex (*xout)[NY][NX] = (dcomplex(*)[NY][NX])pointer_xout;\n\nint logd3;\nint i, j, k, ii;\n\nlogd3 = ilog2(d3);\n\nif(timers_enabled){\n#pragma omp master\ntimer_start(T_FFTZ);\n}\n\n#pragma omp for\nfor(j=0; j<d2; j++){\nfor(ii=0; ii<=d1-FFTBLOCK; ii+=FFTBLOCK){\nfor(k=0; k<d3; k++){\nfor(i=0; i<FFTBLOCK; i++){\ny1[k][i] = x[k][j][i+ii];\n}\n}\ncfftz(is, logd3, d3, y1, y2);\nfor(k=0; k<d3; k++){\nfor(i=0; i<FFTBLOCK; i++){\nxout[k][j][i+ii] = y1[k][i];\n}\n}\n}\n}\n\nif(timers_enabled){\n#pragma omp master\ntimer_stop(T_FFTZ);\n}\n}

subroutine cffts3(is, d1, d2, d3, x, xout, y1, y2)\n\n\nuse ft_data\nimplicit none\n\ninteger is, d1, d2, d3, logd3\ndouble complex x(d1+1,d2,d3)\ndouble complex xout(d1+1,d2,d3)\ndouble complex y1(fftblockpad, d3), y2(fftblockpad, d3)\ninteger i, j, k, ii, in\n\nlogd3 = ilog2(d3)\n\nif (timers_enabled) call timer_start(T_fftz)\ndo j = 1, d2\ndo in = 0, d1/fftblock - 1\nii = in*fftblock\ndo k = 1, d3\ndo i = 1, fftblock\ny1(i,k) = x(i+ii,j,k)\nenddo\nenddo\n\ncall cfftz (is, logd3, d3, y1, y2)\n\ndo k = 1, d3\ndo i = 1, fftblock\nxout(i+ii,j,k) = y1(i,k)\nenddo\nenddo\nenddo\nenddo\nif (timers_enabled) call timer_stop(T_fftz)\n\nreturn\nend

void setcoeff(){\n\ndxi=1.0/(nx0-1);\ndeta=1.0/(ny0-1);\ndzeta=1.0/(nz0-1);\ntx1=1.0/(dxi*dxi);\ntx2=1.0/(2.0*dxi);\ntx3=1.0/dxi;\nty1=1.0/(deta*deta);\nty2=1.0/(2.0*deta);\nty3=1.0/deta;\ntz1=1.0/(dzeta*dzeta);\ntz2=1.0/(2.0*dzeta);\ntz3=1.0/dzeta;\n\ndx1=0.75;\ndx2=dx1;\ndx3=dx1;\ndx4=dx1;\ndx5=dx1;\ndy1=0.75;\ndy2=dy1;\ndy3=dy1;\ndy4=dy1;\ndy5=dy1;\ndz1=1.00;\ndz2=dz1;\ndz3=dz1;\ndz4=dz1;\ndz5=dz1;\n\ndssp=(max(max(dx1,dy1),dz1))/4.0;\n\nce[0][0]=2.0;\nce[1][0]=0.0;\nce[2][0]=0.0;\nce[3][0]=4.0;\nce[4][0]=5.0;\nce[5][0]=3.0;\nce[6][0]=5.0e-01;\nce[7][0]=2.0e-02;\nce[8][0]=1.0e-02;\nce[9][0]=3.0e-02;\nce[10][0]=5.0e-01;\nce[11][0]=4.0e-01;\nce[12][0]=3.0e-01;\n\nce[0][1]=1.0;\nce[1][1]=0.0;\nce[2][1]=0.0;\nce[3][1]=0.0;\nce[4][1]=1.0;\nce[5][1]=2.0;\nce[6][1]=3.0;\nce[7][1]=1.0e-02;\nce[8][1]=3.0e-02;\nce[9][1]=2.0e-02;\nce[10][1]=4.0e-01;\nce[11][1]=3.0e-01;\nce[12][1]=5.0e-01;\n\nce[0][2]=2.0;\nce[1][2]=2.0;\nce[2][2]=0.0;\nce[3][2]=0.0;\nce[4][2]=0.0;\nce[5][2]=2.0;\nce[6][2]=3.0;\nce[7][2]=4.0e-02;\nce[8][2]=3.0e-02;\nce[9][2]=5.0e-02;\nce[10][2]=3.0e-01;\nce[11][2]=5.0e-01;\nce[12][2]=4.0e-01;\n\nce[0][3]=2.0;\nce[1][3]=2.0;\nce[2][3]=0.0;\nce[3][3]=0.0;\nce[4][3]=0.0;\nce[5][3]=2.0;\nce[6][3]=3.0;\nce[7][3]=3.0e-02;\nce[8][3]=5.0e-02;\nce[9][3]=4.0e-02;\nce[10][3]=2.0e-01;\nce[11][3]=1.0e-01;\nce[12][3]=3.0e-01;\n\nce[0][4]=5.0;\nce[1][4]=4.0;\nce[2][4]=3.0;\nce[3][4]=2.0;\nce[4][4]=1.0e-01;\nce[5][4]=4.0e-01;\nce[6][4]=3.0e-01;\nce[7][4]=5.0e-02;\nce[8][4]=4.0e-02;\nce[9][4]=3.0e-02;\nce[10][4]=1.0e-01;\nce[11][4]=3.0e-01;\nce[12][4]=2.0e-01;\n}

subroutine setcoeff\n\n\nuse lu_data\nimplicit none\n\n\n\ndxi = 1.0d+00 / ( nx0 - 1 )\ndeta = 1.0d+00 / ( ny0 - 1 )\ndzeta = 1.0d+00 / ( nz0 - 1 )\n\ntx1 = 1.0d+00 / ( dxi * dxi )\ntx2 = 1.0d+00 / ( 2.0d+00 * dxi )\ntx3 = 1.0d+00 / dxi\n\nty1 = 1.0d+00 / ( deta * deta )\nty2 = 1.0d+00 / ( 2.0d+00 * deta )\nty3 = 1.0d+00 / deta\n\ntz1 = 1.0d+00 / ( dzeta * dzeta )\ntz2 = 1.0d+00 / ( 2.0d+00 * dzeta )\ntz3 = 1.0d+00 / dzeta\n\ndx1 = 0.75d+00\ndx2 = dx1\ndx3 = dx1\ndx4 = dx1\ndx5 = dx1\n\ndy1 = 0.75d+00\ndy2 = dy1\ndy3 = dy1\ndy4 = dy1\ndy5 = dy1\n\ndz1 = 1.00d+00\ndz2 = dz1\ndz3 = dz1\ndz4 = dz1\ndz5 = dz1\n\ndssp = ( max (dx1, dy1, dz1 ) ) / 4.0d+00\n\nce(1,1) = 2.0d+00\nce(1,2) = 0.0d+00\nce(1,3) = 0.0d+00\nce(1,4) = 4.0d+00\nce(1,5) = 5.0d+00\nce(1,6) = 3.0d+00\nce(1,7) = 5.0d-01\nce(1,8) = 2.0d-02\nce(1,9) = 1.0d-02\nce(1,10) = 3.0d-02\nce(1,11) = 5.0d-01\nce(1,12) = 4.0d-01\nce(1,13) = 3.0d-01\n\nce(2,1) = 1.0d+00\nce(2,2) = 0.0d+00\nce(2,3) = 0.0d+00\nce(2,4) = 0.0d+00\nce(2,5) = 1.0d+00\nce(2,6) = 2.0d+00\nce(2,7) = 3.0d+00\nce(2,8) = 1.0d-02\nce(2,9) = 3.0d-02\nce(2,10) = 2.0d-02\nce(2,11) = 4.0d-01\nce(2,12) = 3.0d-01\nce(2,13) = 5.0d-01\n\nce(3,1) = 2.0d+00\nce(3,2) = 2.0d+00\nce(3,3) = 0.0d+00\nce(3,4) = 0.0d+00\nce(3,5) = 0.0d+00\nce(3,6) = 2.0d+00\nce(3,7) = 3.0d+00\nce(3,8) = 4.0d-02\nce(3,9) = 3.0d-02\nce(3,10) = 5.0d-02\nce(3,11) = 3.0d-01\nce(3,12) = 5.0d-01\nce(3,13) = 4.0d-01\n\nce(4,1) = 2.0d+00\nce(4,2) = 2.0d+00\nce(4,3) = 0.0d+00\nce(4,4) = 0.0d+00\nce(4,5) = 0.0d+00\nce(4,6) = 2.0d+00\nce(4,7) = 3.0d+00\nce(4,8) = 3.0d-02\nce(4,9) = 5.0d-02\nce(4,10) = 4.0d-02\nce(4,11) = 2.0d-01\nce(4,12) = 1.0d-01\nce(4,13) = 3.0d-01\n\nce(5,1) = 5.0d+00\nce(5,2) = 4.0d+00\nce(5,3) = 3.0d+00\nce(5,4) = 2.0d+00\nce(5,5) = 1.0d-01\nce(5,6) = 4.0d-01\nce(5,7) = 3.0d-01\nce(5,8) = 5.0d-02\nce(5,9) = 4.0d-02\nce(5,10) = 3.0d-02\nce(5,11) = 1.0d-01\nce(5,12) = 3.0d-01\nce(5,13) = 2.0d-01\n\nreturn\nend

void y_solve(){\nint i, j, k, m, n, jsize;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_YSOLVE);}\n\njsize=grid_points[1]-1;\n\n#pragma omp for\nfor(k=1; k<=grid_points[2]-2; k++){\ndouble fjac[PROBLEM_SIZE+1][5][5];\ndouble njac[PROBLEM_SIZE+1][5][5];\ndouble lhs[PROBLEM_SIZE+1][3][5][5];\ndouble tmp1, tmp2, tmp3;\n\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(j=0; j<=jsize; j++){\ntmp1=rho_i[k][j][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nfjac[j][0][0]=0.0;\nfjac[j][1][0]=0.0;\nfjac[j][2][0]=1.0;\nfjac[j][3][0]=0.0;\nfjac[j][4][0]=0.0;\nfjac[j][0][1]=-(u[k][j][i][1]*u[k][j][i][2])*tmp2;\nfjac[j][1][1]=u[k][j][i][2]*tmp1;\nfjac[j][2][1]=u[k][j][i][1]*tmp1;\nfjac[j][3][1]=0.0;\nfjac[j][4][1]=0.0;\nfjac[j][0][2]=-(u[k][j][i][2]*u[k][j][i][2]*tmp2)+c2*qs[k][j][i];\nfjac[j][1][2]=-c2*u[k][j][i][1]*tmp1;\nfjac[j][2][2]=(2.0-c2)*u[k][j][i][2]*tmp1;\nfjac[j][3][2]=-c2*u[k][j][i][3]*tmp1;\nfjac[j][4][2]=c2;\nfjac[j][0][3]=-(u[k][j][i][2]*u[k][j][i][3])*tmp2;\nfjac[j][1][3]=0.0;\nfjac[j][2][3]=u[k][j][i][3]*tmp1;\nfjac[j][3][3]=u[k][j][i][2]*tmp1;\nfjac[j][4][3]=0.0;\nfjac[j][0][4]=(c2*2.0*square[k][j][i]-c1*u[k][j][i][4])*u[k][j][i][2]*tmp2;\nfjac[j][1][4]=-c2*u[k][j][i][1]*u[k][j][i][2]*tmp2;\nfjac[j][2][4]=c1*u[k][j][i][4]*tmp1-c2*(qs[k][j][i]+u[k][j][i][2]*u[k][j][i][2]*tmp2);\nfjac[j][3][4]=-c2*(u[k][j][i][2]*u[k][j][i][3])*tmp2;\nfjac[j][4][4]=c1*u[k][j][i][2]*tmp1;\nnjac[j][0][0]=0.0;\nnjac[j][1][0]=0.0;\nnjac[j][2][0]=0.0;\nnjac[j][3][0]=0.0;\nnjac[j][4][0]=0.0;\nnjac[j][0][1]=-c3c4*tmp2*u[k][j][i][1];\nnjac[j][1][1]=c3c4*tmp1;\nnjac[j][2][1]=0.0;\nnjac[j][3][1]=0.0;\nnjac[j][4][1]=0.0;\nnjac[j][0][2]=-con43*c3c4*tmp2*u[k][j][i][2];\nnjac[j][1][2]=0.0;\nnjac[j][2][2]=con43*c3c4*tmp1;\nnjac[j][3][2]=0.0;\nnjac[j][4][2]=0.0;\nnjac[j][0][3]=-c3c4*tmp2*u[k][j][i][3];\nnjac[j][1][3]=0.0;\nnjac[j][2][3]=0.0;\nnjac[j][3][3]=c3c4*tmp1;\nnjac[j][4][3]=0.0;\nnjac[j][0][4]=-(c3c4-c1345)*tmp3*(u[k][j][i][1]*u[k][j][i][1])\n-(con43*c3c4-c1345)*tmp3*(u[k][j][i][2]*u[k][j][i][2])\n-(c3c4-c1345)*tmp3*(u[k][j][i][3]*u[k][j][i][3])\n-c1345*tmp2*u[k][j][i][4];\nnjac[j][1][4]=(c3c4-c1345)*tmp2*u[k][j][i][1];\nnjac[j][2][4]=(con43*c3c4-c1345)*tmp2*u[k][j][i][2];\nnjac[j][3][4]=(c3c4-c1345)*tmp2*u[k][j][i][3];\nnjac[j][4][4]=(c1345)*tmp1;\n}\n\nlhsinit(lhs, jsize);\nfor(j=1; j<=jsize-1; j++){\ntmp1=dt*ty1;\ntmp2=dt*ty2;\nlhs[j][AA][0][0]=-tmp2*fjac[j-1][0][0]\n-tmp1*njac[j-1][0][0]\n-tmp1*dy1;\nlhs[j][AA][1][0]=-tmp2*fjac[j-1][1][0]\n-tmp1*njac[j-1][1][0];\nlhs[j][AA][2][0]=-tmp2*fjac[j-1][2][0]\n-tmp1*njac[j-1][2][0];\nlhs[j][AA][3][0]=-tmp2*fjac[j-1][3][0]\n-tmp1*njac[j-1][3][0];\nlhs[j][AA][4][0]=-tmp2*fjac[j-1][4][0]\n-tmp1*njac[j-1][4][0];\nlhs[j][AA][0][1]=-tmp2*fjac[j-1][0][1]\n-tmp1*njac[j-1][0][1];\nlhs[j][AA][1][1]=-tmp2*fjac[j-1][1][1]\n-tmp1*njac[j-1][1][1]\n-tmp1*dy2;\nlhs[j][AA][2][1]=-tmp2*fjac[j-1][2][1]\n-tmp1*njac[j-1][2][1];\nlhs[j][AA][3][1]=-tmp2*fjac[j-1][3][1]\n-tmp1*njac[j-1][3][1];\nlhs[j][AA][4][1]=-tmp2*fjac[j-1][4][1]\n-tmp1*njac[j-1][4][1];\nlhs[j][AA][0][2]=-tmp2*fjac[j-1][0][2]\n-tmp1*njac[j-1][0][2];\nlhs[j][AA][1][2]=-tmp2*fjac[j-1][1][2]\n-tmp1*njac[j-1][1][2];\nlhs[j][AA][2][2]=-tmp2*fjac[j-1][2][2]\n-tmp1*njac[j-1][2][2]\n-tmp1*dy3;\nlhs[j][AA][3][2]=-tmp2*fjac[j-1][3][2]\n-tmp1*njac[j-1][3][2];\nlhs[j][AA][4][2]=-tmp2*fjac[j-1][4][2]\n-tmp1*njac[j-1][4][2];\nlhs[j][AA][0][3]=-tmp2*fjac[j-1][0][3]\n-tmp1*njac[j-1][0][3];\nlhs[j][AA][1][3]=-tmp2*fjac[j-1][1][3]\n-tmp1*njac[j-1][1][3];\nlhs[j][AA][2][3]=-tmp2*fjac[j-1][2][3]\n-tmp1*njac[j-1][2][3];\nlhs[j][AA][3][3]=-tmp2*fjac[j-1][3][3]\n-tmp1*njac[j-1][3][3]\n-tmp1*dy4;\nlhs[j][AA][4][3]=-tmp2*fjac[j-1][4][3]\n-tmp1*njac[j-1][4][3];\nlhs[j][AA][0][4]=-tmp2*fjac[j-1][0][4]\n-tmp1*njac[j-1][0][4];\nlhs[j][AA][1][4]=-tmp2*fjac[j-1][1][4]\n-tmp1*njac[j-1][1][4];\nlhs[j][AA][2][4]=-tmp2*fjac[j-1][2][4]\n-tmp1*njac[j-1][2][4];\nlhs[j][AA][3][4]=-tmp2*fjac[j-1][3][4]\n-tmp1*njac[j-1][3][4];\nlhs[j][AA][4][4]=-tmp2*fjac[j-1][4][4]\n-tmp1*njac[j-1][4][4]\n-tmp1*dy5;\nlhs[j][BB][0][0]=1.0\n+tmp1*2.0*njac[j][0][0]\n+tmp1*2.0*dy1;\nlhs[j][BB][1][0]=tmp1*2.0*njac[j][1][0];\nlhs[j][BB][2][0]=tmp1*2.0*njac[j][2][0];\nlhs[j][BB][3][0]=tmp1*2.0*njac[j][3][0];\nlhs[j][BB][4][0]=tmp1*2.0*njac[j][4][0];\nlhs[j][BB][0][1]=tmp1*2.0*njac[j][0][1];\nlhs[j][BB][1][1]=1.0\n+tmp1*2.0*njac[j][1][1]\n+tmp1*2.0*dy2;\nlhs[j][BB][2][1]=tmp1*2.0*njac[j][2][1];\nlhs[j][BB][3][1]=tmp1*2.0*njac[j][3][1];\nlhs[j][BB][4][1]=tmp1*2.0*njac[j][4][1];\nlhs[j][BB][0][2]=tmp1*2.0*njac[j][0][2];\nlhs[j][BB][1][2]=tmp1*2.0*njac[j][1][2];\nlhs[j][BB][2][2]=1.0\n+tmp1*2.0*njac[j][2][2]\n+tmp1*2.0*dy3;\nlhs[j][BB][3][2]=tmp1*2.0*njac[j][3][2];\nlhs[j][BB][4][2]=tmp1*2.0*njac[j][4][2];\nlhs[j][BB][0][3]=tmp1*2.0*njac[j][0][3];\nlhs[j][BB][1][3]=tmp1*2.0*njac[j][1][3];\nlhs[j][BB][2][3]=tmp1*2.0*njac[j][2][3];\nlhs[j][BB][3][3]=1.0\n+tmp1*2.0*njac[j][3][3]\n+tmp1*2.0*dy4;\nlhs[j][BB][4][3]=tmp1*2.0*njac[j][4][3];\nlhs[j][BB][0][4]=tmp1*2.0*njac[j][0][4];\nlhs[j][BB][1][4]=tmp1*2.0*njac[j][1][4];\nlhs[j][BB][2][4]=tmp1*2.0*njac[j][2][4];\nlhs[j][BB][3][4]=tmp1*2.0*njac[j][3][4];\nlhs[j][BB][4][4]=1.0\n+tmp1*2.0*njac[j][4][4]\n+tmp1*2.0*dy5;\nlhs[j][CC][0][0]=tmp2*fjac[j+1][0][0]\n-tmp1*njac[j+1][0][0]\n-tmp1*dy1;\nlhs[j][CC][1][0]=tmp2*fjac[j+1][1][0]\n-tmp1*njac[j+1][1][0];\nlhs[j][CC][2][0]=tmp2*fjac[j+1][2][0]\n-tmp1*njac[j+1][2][0];\nlhs[j][CC][3][0]=tmp2*fjac[j+1][3][0]\n-tmp1*njac[j+1][3][0];\nlhs[j][CC][4][0]=tmp2*fjac[j+1][4][0]\n-tmp1*njac[j+1][4][0];\nlhs[j][CC][0][1]=tmp2*fjac[j+1][0][1]\n-tmp1*njac[j+1][0][1];\nlhs[j][CC][1][1]=tmp2*fjac[j+1][1][1]\n-tmp1*njac[j+1][1][1]\n-tmp1*dy2;\nlhs[j][CC][2][1]=tmp2*fjac[j+1][2][1]\n-tmp1*njac[j+1][2][1];\nlhs[j][CC][3][1]=tmp2*fjac[j+1][3][1]\n-tmp1*njac[j+1][3][1];\nlhs[j][CC][4][1]=tmp2*fjac[j+1][4][1]\n-tmp1*njac[j+1][4][1];\nlhs[j][CC][0][2]=tmp2*fjac[j+1][0][2]\n-tmp1*njac[j+1][0][2];\nlhs[j][CC][1][2]=tmp2*fjac[j+1][1][2]\n-tmp1*njac[j+1][1][2];\nlhs[j][CC][2][2]=tmp2*fjac[j+1][2][2]\n-tmp1*njac[j+1][2][2]\n-tmp1*dy3;\nlhs[j][CC][3][2]=tmp2*fjac[j+1][3][2]\n-tmp1*njac[j+1][3][2];\nlhs[j][CC][4][2]=tmp2*fjac[j+1][4][2]\n-tmp1*njac[j+1][4][2];\nlhs[j][CC][0][3]=tmp2*fjac[j+1][0][3]\n-tmp1*njac[j+1][0][3];\nlhs[j][CC][1][3]=tmp2*fjac[j+1][1][3]\n-tmp1*njac[j+1][1][3];\nlhs[j][CC][2][3]=tmp2*fjac[j+1][2][3]\n-tmp1*njac[j+1][2][3];\nlhs[j][CC][3][3]=tmp2*fjac[j+1][3][3]\n-tmp1*njac[j+1][3][3]\n-tmp1*dy4;\nlhs[j][CC][4][3]=tmp2*fjac[j+1][4][3]\n-tmp1*njac[j+1][4][3];\nlhs[j][CC][0][4]=tmp2*fjac[j+1][0][4]\n-tmp1*njac[j+1][0][4];\nlhs[j][CC][1][4]=tmp2*fjac[j+1][1][4]\n-tmp1*njac[j+1][1][4];\nlhs[j][CC][2][4]=tmp2*fjac[j+1][2][4]\n-tmp1*njac[j+1][2][4];\nlhs[j][CC][3][4]=tmp2*fjac[j+1][3][4]\n-tmp1*njac[j+1][3][4];\nlhs[j][CC][4][4]=tmp2*fjac[j+1][4][4]\n-tmp1*njac[j+1][4][4]\n-tmp1*dy5;\n}\n\nbinvcrhs(lhs[0][BB], lhs[0][CC], rhs[k][0][i]);\n\nfor(j=1; j<=jsize-1; j++){\n\nmatvec_sub(lhs[j][AA], rhs[k][j-1][i], rhs[k][j][i]);\n\nmatmul_sub(lhs[j][AA], lhs[j-1][CC], lhs[j][BB]);\n\nbinvcrhs(lhs[j][BB], lhs[j][CC], rhs[k][j][i]);\n}\n\nmatvec_sub(lhs[jsize][AA], rhs[k][jsize-1][i], rhs[k][jsize][i]);\n\nmatmul_sub(lhs[jsize][AA], lhs[jsize-1][CC], lhs[jsize][BB]);\n\nbinvrhs(lhs[jsize][BB], rhs[k][jsize][i]);\n\nfor(j=jsize-1; j>=0; j--){\nfor(m=0; m<BLOCK_SIZE; m++){\nfor(n=0; n<BLOCK_SIZE; n++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[j][CC][n][m]*rhs[k][j+1][i][n];\n}\n}\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_YSOLVE);}\n}

subroutine y_solve\n\n\n\nuse bt_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, m, n, jsize\ndouble precision tmp1, tmp2, tmp3\n\n\nif (timeron) call timer_start(t_ysolve)\n\n\n\njsize = grid_points(2)-1\n\ndo k = 1, grid_points(3)-2\ndo i = 1, grid_points(1)-2\ndo j = 0, jsize\n\ntmp1 = rho_i(i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nfjac(1,1,j) = 0.0d+00\nfjac(1,2,j) = 0.0d+00\nfjac(1,3,j) = 1.0d+00\nfjac(1,4,j) = 0.0d+00\nfjac(1,5,j) = 0.0d+00\n\nfjac(2,1,j) = - ( u(2,i,j,k)*u(3,i,j,k) ) &\n& * tmp2\nfjac(2,2,j) = u(3,i,j,k) * tmp1\nfjac(2,3,j) = u(2,i,j,k) * tmp1\nfjac(2,4,j) = 0.0d+00\nfjac(2,5,j) = 0.0d+00\n\nfjac(3,1,j) = - ( u(3,i,j,k)*u(3,i,j,k)*tmp2) &\n& + c2 * qs(i,j,k)\nfjac(3,2,j) = - c2 * u(2,i,j,k) * tmp1\nfjac(3,3,j) = ( 2.0d+00 - c2 ) &\n& * u(3,i,j,k) * tmp1\nfjac(3,4,j) = - c2 * u(4,i,j,k) * tmp1\nfjac(3,5,j) = c2\n\nfjac(4,1,j) = - ( u(3,i,j,k)*u(4,i,j,k) ) &\n& * tmp2\nfjac(4,2,j) = 0.0d+00\nfjac(4,3,j) = u(4,i,j,k) * tmp1\nfjac(4,4,j) = u(3,i,j,k) * tmp1\nfjac(4,5,j) = 0.0d+00\n\nfjac(5,1,j) = ( c2 * 2.0d0 * square(i,j,k) &\n& - c1 * u(5,i,j,k) ) &\n& * u(3,i,j,k) * tmp2\nfjac(5,2,j) = - c2 * u(2,i,j,k)*u(3,i,j,k) &\n& * tmp2\nfjac(5,3,j) = c1 * u(5,i,j,k) * tmp1 &\n& - c2 &\n& * ( qs(i,j,k) &\n& + u(3,i,j,k)*u(3,i,j,k) * tmp2 )\nfjac(5,4,j) = - c2 * ( u(3,i,j,k)*u(4,i,j,k) ) &\n& * tmp2\nfjac(5,5,j) = c1 * u(3,i,j,k) * tmp1\n\nnjac(1,1,j) = 0.0d+00\nnjac(1,2,j) = 0.0d+00\nnjac(1,3,j) = 0.0d+00\nnjac(1,4,j) = 0.0d+00\nnjac(1,5,j) = 0.0d+00\n\nnjac(2,1,j) = - c3c4 * tmp2 * u(2,i,j,k)\nnjac(2,2,j) = c3c4 * tmp1\nnjac(2,3,j) = 0.0d+00\nnjac(2,4,j) = 0.0d+00\nnjac(2,5,j) = 0.0d+00\n\nnjac(3,1,j) = - con43 * c3c4 * tmp2 * u(3,i,j,k)\nnjac(3,2,j) = 0.0d+00\nnjac(3,3,j) = con43 * c3c4 * tmp1\nnjac(3,4,j) = 0.0d+00\nnjac(3,5,j) = 0.0d+00\n\nnjac(4,1,j) = - c3c4 * tmp2 * u(4,i,j,k)\nnjac(4,2,j) = 0.0d+00\nnjac(4,3,j) = 0.0d+00\nnjac(4,4,j) = c3c4 * tmp1\nnjac(4,5,j) = 0.0d+00\n\nnjac(5,1,j) = - ( c3c4 &\n& - c1345 ) * tmp3 * (u(2,i,j,k)**2) &\n& - ( con43 * c3c4 &\n& - c1345 ) * tmp3 * (u(3,i,j,k)**2) &\n& - ( c3c4 - c1345 ) * tmp3 * (u(4,i,j,k)**2) &\n& - c1345 * tmp2 * u(5,i,j,k)\n\nnjac(5,2,j) = ( c3c4 - c1345 ) * tmp2 * u(2,i,j,k)\nnjac(5,3,j) = ( con43 * c3c4 &\n& - c1345 ) * tmp2 * u(3,i,j,k)\nnjac(5,4,j) = ( c3c4 - c1345 ) * tmp2 * u(4,i,j,k)\nnjac(5,5,j) = ( c1345 ) * tmp1\n\nenddo\n\ncall lhsinit(lhs, jsize)\ndo j = 1, jsize-1\n\ntmp1 = dt * ty1\ntmp2 = dt * ty2\n\nlhs(1,1,aa,j) = - tmp2 * fjac(1,1,j-1) &\n& - tmp1 * njac(1,1,j-1) &\n& - tmp1 * dy1\nlhs(1,2,aa,j) = - tmp2 * fjac(1,2,j-1) &\n& - tmp1 * njac(1,2,j-1)\nlhs(1,3,aa,j) = - tmp2 * fjac(1,3,j-1) &\n& - tmp1 * njac(1,3,j-1)\nlhs(1,4,aa,j) = - tmp2 * fjac(1,4,j-1) &\n& - tmp1 * njac(1,4,j-1)\nlhs(1,5,aa,j) = - tmp2 * fjac(1,5,j-1) &\n& - tmp1 * njac(1,5,j-1)\n\nlhs(2,1,aa,j) = - tmp2 * fjac(2,1,j-1) &\n& - tmp1 * njac(2,1,j-1)\nlhs(2,2,aa,j) = - tmp2 * fjac(2,2,j-1) &\n& - tmp1 * njac(2,2,j-1) &\n& - tmp1 * dy2\nlhs(2,3,aa,j) = - tmp2 * fjac(2,3,j-1) &\n& - tmp1 * njac(2,3,j-1)\nlhs(2,4,aa,j) = - tmp2 * fjac(2,4,j-1) &\n& - tmp1 * njac(2,4,j-1)\nlhs(2,5,aa,j) = - tmp2 * fjac(2,5,j-1) &\n& - tmp1 * njac(2,5,j-1)\n\nlhs(3,1,aa,j) = - tmp2 * fjac(3,1,j-1) &\n& - tmp1 * njac(3,1,j-1)\nlhs(3,2,aa,j) = - tmp2 * fjac(3,2,j-1) &\n& - tmp1 * njac(3,2,j-1)\nlhs(3,3,aa,j) = - tmp2 * fjac(3,3,j-1) &\n& - tmp1 * njac(3,3,j-1) &\n& - tmp1 * dy3\nlhs(3,4,aa,j) = - tmp2 * fjac(3,4,j-1) &\n& - tmp1 * njac(3,4,j-1)\nlhs(3,5,aa,j) = - tmp2 * fjac(3,5,j-1) &\n& - tmp1 * njac(3,5,j-1)\n\nlhs(4,1,aa,j) = - tmp2 * fjac(4,1,j-1) &\n& - tmp1 * njac(4,1,j-1)\nlhs(4,2,aa,j) = - tmp2 * fjac(4,2,j-1) &\n& - tmp1 * njac(4,2,j-1)\nlhs(4,3,aa,j) = - tmp2 * fjac(4,3,j-1) &\n& - tmp1 * njac(4,3,j-1)\nlhs(4,4,aa,j) = - tmp2 * fjac(4,4,j-1) &\n& - tmp1 * njac(4,4,j-1) &\n& - tmp1 * dy4\nlhs(4,5,aa,j) = - tmp2 * fjac(4,5,j-1) &\n& - tmp1 * njac(4,5,j-1)\n\nlhs(5,1,aa,j) = - tmp2 * fjac(5,1,j-1) &\n& - tmp1 * njac(5,1,j-1)\nlhs(5,2,aa,j) = - tmp2 * fjac(5,2,j-1) &\n& - tmp1 * njac(5,2,j-1)\nlhs(5,3,aa,j) = - tmp2 * fjac(5,3,j-1) &\n& - tmp1 * njac(5,3,j-1)\nlhs(5,4,aa,j) = - tmp2 * fjac(5,4,j-1) &\n& - tmp1 * njac(5,4,j-1)\nlhs(5,5,aa,j) = - tmp2 * fjac(5,5,j-1) &\n& - tmp1 * njac(5,5,j-1) &\n& - tmp1 * dy5\n\nlhs(1,1,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(1,1,j) &\n& + tmp1 * 2.0d+00 * dy1\nlhs(1,2,bb,j) = tmp1 * 2.0d+00 * njac(1,2,j)\nlhs(1,3,bb,j) = tmp1 * 2.0d+00 * njac(1,3,j)\nlhs(1,4,bb,j) = tmp1 * 2.0d+00 * njac(1,4,j)\nlhs(1,5,bb,j) = tmp1 * 2.0d+00 * njac(1,5,j)\n\nlhs(2,1,bb,j) = tmp1 * 2.0d+00 * njac(2,1,j)\nlhs(2,2,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(2,2,j) &\n& + tmp1 * 2.0d+00 * dy2\nlhs(2,3,bb,j) = tmp1 * 2.0d+00 * njac(2,3,j)\nlhs(2,4,bb,j) = tmp1 * 2.0d+00 * njac(2,4,j)\nlhs(2,5,bb,j) = tmp1 * 2.0d+00 * njac(2,5,j)\n\nlhs(3,1,bb,j) = tmp1 * 2.0d+00 * njac(3,1,j)\nlhs(3,2,bb,j) = tmp1 * 2.0d+00 * njac(3,2,j)\nlhs(3,3,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(3,3,j) &\n& + tmp1 * 2.0d+00 * dy3\nlhs(3,4,bb,j) = tmp1 * 2.0d+00 * njac(3,4,j)\nlhs(3,5,bb,j) = tmp1 * 2.0d+00 * njac(3,5,j)\n\nlhs(4,1,bb,j) = tmp1 * 2.0d+00 * njac(4,1,j)\nlhs(4,2,bb,j) = tmp1 * 2.0d+00 * njac(4,2,j)\nlhs(4,3,bb,j) = tmp1 * 2.0d+00 * njac(4,3,j)\nlhs(4,4,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(4,4,j) &\n& + tmp1 * 2.0d+00 * dy4\nlhs(4,5,bb,j) = tmp1 * 2.0d+00 * njac(4,5,j)\n\nlhs(5,1,bb,j) = tmp1 * 2.0d+00 * njac(5,1,j)\nlhs(5,2,bb,j) = tmp1 * 2.0d+00 * njac(5,2,j)\nlhs(5,3,bb,j) = tmp1 * 2.0d+00 * njac(5,3,j)\nlhs(5,4,bb,j) = tmp1 * 2.0d+00 * njac(5,4,j)\nlhs(5,5,bb,j) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(5,5,j) &\n& + tmp1 * 2.0d+00 * dy5\n\nlhs(1,1,cc,j) = tmp2 * fjac(1,1,j+1) &\n& - tmp1 * njac(1,1,j+1) &\n& - tmp1 * dy1\nlhs(1,2,cc,j) = tmp2 * fjac(1,2,j+1) &\n& - tmp1 * njac(1,2,j+1)\nlhs(1,3,cc,j) = tmp2 * fjac(1,3,j+1) &\n& - tmp1 * njac(1,3,j+1)\nlhs(1,4,cc,j) = tmp2 * fjac(1,4,j+1) &\n& - tmp1 * njac(1,4,j+1)\nlhs(1,5,cc,j) = tmp2 * fjac(1,5,j+1) &\n& - tmp1 * njac(1,5,j+1)\n\nlhs(2,1,cc,j) = tmp2 * fjac(2,1,j+1) &\n& - tmp1 * njac(2,1,j+1)\nlhs(2,2,cc,j) = tmp2 * fjac(2,2,j+1) &\n& - tmp1 * njac(2,2,j+1) &\n& - tmp1 * dy2\nlhs(2,3,cc,j) = tmp2 * fjac(2,3,j+1) &\n& - tmp1 * njac(2,3,j+1)\nlhs(2,4,cc,j) = tmp2 * fjac(2,4,j+1) &\n& - tmp1 * njac(2,4,j+1)\nlhs(2,5,cc,j) = tmp2 * fjac(2,5,j+1) &\n& - tmp1 * njac(2,5,j+1)\n\nlhs(3,1,cc,j) = tmp2 * fjac(3,1,j+1) &\n& - tmp1 * njac(3,1,j+1)\nlhs(3,2,cc,j) = tmp2 * fjac(3,2,j+1) &\n& - tmp1 * njac(3,2,j+1)\nlhs(3,3,cc,j) = tmp2 * fjac(3,3,j+1) &\n& - tmp1 * njac(3,3,j+1) &\n& - tmp1 * dy3\nlhs(3,4,cc,j) = tmp2 * fjac(3,4,j+1) &\n& - tmp1 * njac(3,4,j+1)\nlhs(3,5,cc,j) = tmp2 * fjac(3,5,j+1) &\n& - tmp1 * njac(3,5,j+1)\n\nlhs(4,1,cc,j) = tmp2 * fjac(4,1,j+1) &\n& - tmp1 * njac(4,1,j+1)\nlhs(4,2,cc,j) = tmp2 * fjac(4,2,j+1) &\n& - tmp1 * njac(4,2,j+1)\nlhs(4,3,cc,j) = tmp2 * fjac(4,3,j+1) &\n& - tmp1 * njac(4,3,j+1)\nlhs(4,4,cc,j) = tmp2 * fjac(4,4,j+1) &\n& - tmp1 * njac(4,4,j+1) &\n& - tmp1 * dy4\nlhs(4,5,cc,j) = tmp2 * fjac(4,5,j+1) &\n& - tmp1 * njac(4,5,j+1)\n\nlhs(5,1,cc,j) = tmp2 * fjac(5,1,j+1) &\n& - tmp1 * njac(5,1,j+1)\nlhs(5,2,cc,j) = tmp2 * fjac(5,2,j+1) &\n& - tmp1 * njac(5,2,j+1)\nlhs(5,3,cc,j) = tmp2 * fjac(5,3,j+1) &\n& - tmp1 * njac(5,3,j+1)\nlhs(5,4,cc,j) = tmp2 * fjac(5,4,j+1) &\n& - tmp1 * njac(5,4,j+1)\nlhs(5,5,cc,j) = tmp2 * fjac(5,5,j+1) &\n& - tmp1 * njac(5,5,j+1) &\n& - tmp1 * dy5\n\nenddo\n\n\n\nif (timeron) call timer_start(t_solsub)\ncall binvcrhs( lhs(1,1,bb,0), &\n& lhs(1,1,cc,0), &\n& rhs(1,i,0,k) )\n\ndo j=1,jsize-1\n\ncall matvec_sub(lhs(1,1,aa,j), &\n& rhs(1,i,j-1,k),rhs(1,i,j,k))\n\ncall matmul_sub(lhs(1,1,aa,j), &\n& lhs(1,1,cc,j-1), &\n& lhs(1,1,bb,j))\n\ncall binvcrhs( lhs(1,1,bb,j), &\n& lhs(1,1,cc,j), &\n& rhs(1,i,j,k) )\n\nenddo\n\n\ncall matvec_sub(lhs(1,1,aa,jsize), &\n& rhs(1,i,jsize-1,k),rhs(1,i,jsize,k))\n\ncall matmul_sub(lhs(1,1,aa,jsize), &\n& lhs(1,1,cc,jsize-1), &\n& lhs(1,1,bb,jsize))\n\ncall binvrhs( lhs(1,1,bb,jsize), &\n& rhs(1,i,jsize,k) )\nif (timeron) call timer_stop(t_solsub)\n\n\n\ndo j=jsize-1,0,-1\ndo m=1,BLOCK_SIZE\ndo n=1,BLOCK_SIZE\nrhs(m,i,j,k) = rhs(m,i,j,k) &\n& - lhs(m,n,cc,j)*rhs(n,i,j+1,k)\nenddo\nenddo\nenddo\n\nenddo\nenddo\nif (timeron) call timer_stop(t_ysolve)\n\nreturn\nend

void initialize(){\nint i, j, k, m, ix, iy, iz;\ndouble xi, eta, zeta, Pface[2][3][5], Pxi, Peta, Pzeta, temp[5];\n\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<=grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nfor(m=0; m<5; m++){\nu[k][j][i][m]=1.0;\n}\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)* dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nfor(ix=0; ix<2; ix++){\nexact_solution((double)ix, eta, zeta, &Pface[ix][0][0]);\n}\nfor(iy=0; iy<2; iy++){\nexact_solution(xi, (double)iy , zeta, &Pface[iy][1][0]);\n}\nfor(iz=0; iz<2; iz++){\nexact_solution(xi, eta, (double)iz, &Pface[iz][2][0]);\n}\nfor(m=0; m<5; m++){\nPxi=xi*Pface[1][0][m]+(1.0-xi)*Pface[0][0][m];\nPeta=eta*Pface[1][1][m]+(1.0-eta)*Pface[0][1][m];\nPzeta=zeta*Pface[1][2][m]+(1.0-zeta)*Pface[0][2][m];\nu[k][j][i][m]=Pxi+Peta+Pzeta-\nPxi*Peta-Pxi*Pzeta-Peta*Pzeta+\nPxi*Peta*Pzeta;\n}\n}\n}\n}\n\ni=0;\nxi=0.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\ni=grid_points[0]-1;\nxi=1.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nj=0;\neta=0.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)*dnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nj=grid_points[1]-1;\neta=1.0;\n#pragma omp for\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)*dnzm1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nk=0;\nzeta=0.0;\n#pragma omp for\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n\nk=grid_points[2]-1;\nzeta=1.0;\n#pragma omp for\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, temp);\nfor(m=0; m<5; m++){\nu[k][j][i][m]=temp[m];\n}\n}\n}\n}

subroutine initialize\n\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m, ix, iy, iz\ndouble precision xi, eta, zeta, Pface(5,3,2), Pxi, Peta, &\n& Pzeta, temp(5)\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nu(m,i,j,k) = 1.0\nend do\nend do\nend do\nend do\n\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ndo ix = 1, 2\ncall exact_solution(dble(ix-1), eta, zeta, &\n& Pface(1,1,ix))\nenddo\n\ndo iy = 1, 2\ncall exact_solution(xi, dble(iy-1) , zeta, &\n& Pface(1,2,iy))\nenddo\n\ndo iz = 1, 2\ncall exact_solution(xi, eta, dble(iz-1), &\n& Pface(1,3,iz))\nenddo\n\ndo m = 1, 5\nPxi = xi * Pface(m,1,2) + &\n& (1.0d0-xi) * Pface(m,1,1)\nPeta = eta * Pface(m,2,2) + &\n& (1.0d0-eta) * Pface(m,2,1)\nPzeta = zeta * Pface(m,3,2) + &\n& (1.0d0-zeta) * Pface(m,3,1)\n\nu(m,i,j,k) = Pxi + Peta + Pzeta - &\n& Pxi*Peta - Pxi*Pzeta - Peta*Pzeta + &\n& Pxi*Peta*Pzeta\n\nenddo\nenddo\nenddo\nenddo\n\n\ni = 0\nxi = 0.0d0\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\n\ni = grid_points(1)-1\nxi = 1.0d0\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nj = 0\neta = 0.0d0\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\n\nj = grid_points(2)-1\neta = 1.0d0\ndo k = 0, grid_points(3)-1\ndo i = 0, grid_points(1)-1\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nk = 0\nzeta = 0.0d0\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) * dnym1\nxi = dble(i) *dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nk = grid_points(3)-1\nzeta = 1.0d0\ndo j = 0, grid_points(2)-1\ndo i =0, grid_points(1)-1\neta = dble(j) * dnym1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, temp)\ndo m = 1, 5\nu(m,i,j,k) = temp(m)\nenddo\nenddo\nenddo\n\nreturn\nend

static void conj_grad(int colidx[],\nint rowstr[],\ndouble x[],\ndouble z[],\ndouble a[],\ndouble p[],\ndouble q[],\ndouble r[],\ndouble* rnorm){\nint j, k;\nint cgit, cgitmax;\ndouble alpha, beta, suml;\nstatic double d, sum, rho, rho0;\n\ncgitmax = 25;\n#pragma omp single nowait\n{\n\nrho = 0.0;\nsum = 0.0;\n}\n\n#pragma omp for\nfor(j = 0; j < naa+1; j++){\nq[j] = 0.0;\nz[j] = 0.0;\nr[j] = x[j];\np[j] = r[j];\n}\n\n\n#pragma omp for reduction(+:rho)\nfor(j = 0; j < lastcol - firstcol + 1; j++){\nrho += r[j]*r[j];\n}\n\n\nfor(cgit = 1; cgit <= cgitmax; cgit++){\n\n\n#pragma omp single nowait\n{\nd = 0.0;\n\nrho0 = rho;\nrho = 0.0;\n}\n\n#pragma omp for nowait\nfor(j = 0; j < lastrow - firstrow + 1; j++){\nsuml = 0.0;\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\nsuml += a[k]*p[colidx[k]];\n}\nq[j] = suml;\n}\n\n\n\n#pragma omp for reduction(+:d)\nfor (j = 0; j < lastcol - firstcol + 1; j++) {\nd += p[j]*q[j];\n}\n\n\nalpha = rho0 / d;\n\n\n\n#pragma omp for reduction(+:rho)\nfor(j = 0; j < lastcol - firstcol + 1; j++){\nz[j] += alpha*p[j];\nr[j] -= alpha*q[j];\n\n\nrho += r[j]*r[j];\n}\n\n\nbeta = rho / rho0;\n\n\n#pragma omp for\nfor(j = 0; j < lastcol - firstcol + 1; j++){\np[j] = r[j] + beta*p[j];\n}\n} \n\n\n#pragma omp for nowait\nfor(j = 0; j < lastrow - firstrow + 1; j++){\nsuml = 0.0;\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\nsuml += a[k]*z[colidx[k]];\n}\nr[j] = suml;\n}\n\n\n#pragma omp for reduction(+:sum)\nfor(j = 0; j < lastcol-firstcol+1; j++){\nsuml = x[j] - r[j];\nsum += suml*suml;\n}\n#pragma omp single\n*rnorm = sqrt(sum);\n}

subroutine conj_grad ( rnorm )\n\n\nuse cg_data\nimplicit none\n\ninteger j\ninteger cgit, cgitmax\ninteger(kz) k\n\ndouble precision d, sum, rho, rho0, alpha, beta, rnorm, suml\n\ndata cgitmax / 25 /\n\n\nrho = 0.0d0\nsum = 0.0d0\n\n\ndo j=1,naa+1\nq(j) = 0.0d0\nz(j) = 0.0d0\nr(j) = x(j)\np(j) = r(j)\nenddo\n\n\ndo j=1, lastcol-firstcol+1\nrho = rho + r(j)*r(j)\nenddo\n\ndo cgit = 1, cgitmax\n\nrho0 = rho\nd = 0.d0\nrho = 0.d0\n\ndo j=1,lastrow-firstrow+1\nsuml = 0.d0\ndo k=rowstr(j),rowstr(j+1)-1\nsuml = suml + a(k)*p(colidx(k))\nenddo\nq(j) = suml\nenddo\n\n\n\n\ndo j=1, lastcol-firstcol+1\nd = d + p(j)*q(j)\nenddo\n\n\nalpha = rho0 / d\n\ndo j=1, lastcol-firstcol+1\nz(j) = z(j) + alpha*p(j)\nr(j) = r(j) - alpha*q(j)\n\nrho = rho + r(j)*r(j)\nenddo\n\nbeta = rho / rho0\n\ndo j=1, lastcol-firstcol+1\np(j) = r(j) + beta*p(j)\nenddo\n\n\nenddo ! end of do cgit=1,cgitmax\n\n\ndo j=1,lastrow-firstrow+1\nsuml = 0.d0\ndo k=rowstr(j),rowstr(j+1)-1\nsuml = suml + a(k)*z(colidx(k))\nenddo\nr(j) = suml\nenddo\n\n\ndo j=1, lastcol-firstcol+1\nsuml = x(j) - r(j)\nsum = sum + suml*suml\nenddo\n\nrnorm = sqrt( sum )\n\n\n\nreturn\nend

static void sparse(double a[],\nint colidx[],\nint rowstr[],\nint n,\nint nz,\nint nozer,\nint arow[],\nint acol[][NONZER+1],\ndouble aelt[][NONZER+1],\nint firstrow,\nint lastrow,\nint nzloc[],\ndouble rcond,\ndouble shift){\nint nrows;\n\n\nint i, j, j1, j2, nza, k, kk, nzrow, jcol;\ndouble size, scale, ratio, va;\nboolean goto_40;\n\n\nnrows = lastrow - firstrow + 1;\n\n\nfor(j = 0; j < nrows+1; j++){\nrowstr[j] = 0;\n}\nfor(i = 0; i < n; i++){\nfor(nza = 0; nza < arow[i]; nza++){\nj = acol[i][nza] + 1;\nrowstr[j] = rowstr[j] + arow[i];\n}\n}\nrowstr[0] = 0;\nfor(j = 1; j < nrows+1; j++){\nrowstr[j] = rowstr[j] + rowstr[j-1];\n}\nnza = rowstr[nrows] - 1;\n\n\nif(nza > nz){\nprintf("Space for matrix elements exceeded in sparse\n");\nprintf("nza, nzmax = %d, %d\n", nza, nz);\nexit(EXIT_FAILURE);\n}\n\n\nfor(j = 0; j < nrows; j++){\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\na[k] = 0.0;\ncolidx[k] = -1;\n}\nnzloc[j] = 0;\n}\n\n\nsize = 1.0;\nratio = pow(rcond, (1.0 / (double)(n)));\nfor(i = 0; i < n; i++){\nfor(nza = 0; nza < arow[i]; nza++){\nj = acol[i][nza];\n\nscale = size * aelt[i][nza];\nfor(nzrow = 0; nzrow < arow[i]; nzrow++){\njcol = acol[i][nzrow];\nva = aelt[i][nzrow] * scale;\n\n\nif(jcol == j && j == i){\nva = va + rcond - shift;\n}\n\ngoto_40 = FALSE;\nfor(k = rowstr[j]; k < rowstr[j+1]; k++){\nif(colidx[k] > jcol){\n\nfor(kk = rowstr[j+1]-2; kk >= k; kk--){\nif(colidx[kk] > -1){\na[kk+1] = a[kk];\ncolidx[kk+1] = colidx[kk];\n}\n}\ncolidx[k] = jcol;\na[k] = 0.0;\ngoto_40 = TRUE;\nbreak;\n}else if(colidx[k] == -1){\ncolidx[k] = jcol;\ngoto_40 = TRUE;\nbreak;\n}else if(colidx[k] == jcol){\n\nnzloc[j] = nzloc[j] + 1;\ngoto_40 = TRUE;\nbreak;\n}\n}\nif(goto_40 == FALSE){\nprintf("internal error in sparse: i=%d\n", i);\nexit(EXIT_FAILURE);\n}\na[k] = a[k] + va;\n}\n}\nsize = size * ratio;\n}\n\n\nfor(j = 1; j < nrows; j++){\nnzloc[j] = nzloc[j] + nzloc[j-1];\n}\n\nfor(j = 0; j < nrows; j++){\nif(j > 0){\nj1 = rowstr[j] - nzloc[j-1];\n}else{\nj1 = 0;\n}\nj2 = rowstr[j+1] - nzloc[j];\nnza = rowstr[j];\nfor(k = j1; k < j2; k++){\na[k] = a[nza];\ncolidx[k] = colidx[nza];\nnza = nza + 1;\n}\n}\nfor(j = 1; j < nrows+1; j++){\nrowstr[j] = rowstr[j] - nzloc[j-1];\n}\nnza = rowstr[nrows] - 1;\n}

subroutine sparse( a, colidx, rowstr, n, nz, nonzer, arow, acol, &\n& aelt, firstrow, lastrow, &\n& v, iv, nzloc, rcond, shift )\n\nuse tinfo\n\nimplicit none\n\ninteger colidx(*), iv(*)\ninteger firstrow, lastrow\ninteger n, nonzer, arow(*), acol(nonzer+1,*)\ninteger(kz) nz, rowstr(*)\ndouble precision a(*), aelt(nonzer+1,*), v(*), rcond, shift\n\ninteger nzloc(n), nrows\n\n\ninteger i, j, jcol\ninteger(kz) j1, j2, nza, k, kk, nzrow\ndouble precision xi, size, scale, ratio, va\n\nnrows = lastrow - firstrow + 1\nj1 = ilow + 1\nj2 = ihigh + 1\n\ndo j = j1, j2\nrowstr(j) = 0\nenddo\n\ndo i = 1, n\ndo nza = 1, arow(i)\nj = acol(nza, i)\nif (j.ge.ilow .and. j.le.ihigh) then\nj = j + 1\nrowstr(j) = rowstr(j) + arow(i)\nendif\nend do\nend do\n\nif (myid .eq. 0) then\nrowstr(1) = 1\nj1 = 1\nendif\ndo j = j1+1, j2\nrowstr(j) = rowstr(j) + rowstr(j-1)\nenddo\nif (myid .lt. num_threads) last_n(myid) = rowstr(j2)\n\nnzrow = 0\nif (myid .lt. num_threads) then\ndo i = 0, myid-1\nnzrow = nzrow + last_n(i)\nend do\nendif\nif (nzrow .gt. 0) then\ndo j = j1, j2\nrowstr(j) = rowstr(j) + nzrow\nenddo\nendif\nnza = rowstr(nrows+1) - 1\n\n\nif (nza .gt. nz) then\nwrite(*,*) 'Space for matrix elements exceeded in sparse'\nwrite(*,*) 'nza, nzmax = ',nza, nz\nstop\nendif\n\n\ndo j = ilow, ihigh\ndo k = rowstr(j), rowstr(j+1)-1\nv(k) = 0.d0\niv(k) = 0\nenddo\nnzloc(j) = 0\nenddo\n\n\nsize = 1.0D0\nratio = rcond ** (1.0D0 / dfloat(n))\n\ndo i = 1, n\ndo nza = 1, arow(i)\nj = acol(nza, i)\n\nif (j .lt. ilow .or. j .gt. ihigh) goto 60\n\nscale = size * aelt(nza, i)\ndo nzrow = 1, arow(i)\njcol = acol(nzrow, i)\nva = aelt(nzrow, i) * scale\n\nif (jcol .eq. j .and. j .eq. i) then\nva = va + rcond - shift\nendif\n\ndo k = rowstr(j), rowstr(j+1)-1\nif (iv(k) .gt. jcol) then\ndo kk = rowstr(j+1)-2, k, -1\nif (iv(kk) .gt. 0) then\nv(kk+1) = v(kk)\niv(kk+1) = iv(kk)\nendif\nenddo\niv(k) = jcol\nv(k) = 0.d0\ngoto 40\nelse if (iv(k) .eq. 0) then\niv(k) = jcol\ngoto 40\nelse if (iv(k) .eq. jcol) then\nnzloc(j) = nzloc(j) + 1\ngoto 40\nendif\nenddo\nprint *,'internal error in sparse: i=',i\nstop\n40 continue\nv(k) = v(k) + va\nenddo\n60 continue\nenddo\nsize = size * ratio\nenddo\n\n\ndo j = ilow+1, ihigh\nnzloc(j) = nzloc(j) + nzloc(j-1)\nenddo\nif (myid .lt. num_threads) last_n(myid) = nzloc(ihigh)\n\nnzrow = 0\nif (myid .lt. num_threads) then\ndo i = 0, myid-1\nnzrow = nzrow + last_n(i)\nend do\nendif\nif (nzrow .gt. 0) then\ndo j = ilow, ihigh\nnzloc(j) = nzloc(j) + nzrow\nenddo\nendif\n\ndo j = 1, nrows\nif (j .gt. 1) then\nj1 = rowstr(j) - nzloc(j-1)\nelse\nj1 = 1\nendif\nj2 = rowstr(j+1) - nzloc(j) - 1\nnza = rowstr(j)\ndo k = j1, j2\na(k) = v(nza)\ncolidx(k) = iv(nza)\nnza = nza + 1\nenddo\nenddo\ndo j = 2, nrows+1\nrowstr(j) = rowstr(j) - nzloc(j-1)\nenddo\nnza = rowstr(nrows+1) - 1\n\n\nreturn\n11000 format ( //,'final nonzero count in sparse ', &\n& /,'number of nonzeros = ', i16 )\nend

void rhs_norm(double rms[5]){\nint i, j, k, d, m;\ndouble add;\nfor(m=0; m<5; m++){\nrms[m]=0.0;\n}\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++) {\nadd=rhs[k][j][i][m];\nrms[m]=rms[m]+add*add;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}

subroutine compute_rhs\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision rho_inv, uijk, up1, um1, vijk, vp1, vm1, &\n& wijk, wp1, wm1\n\n\nif (timeron) call timer_start(t_rhs)\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\nrho_inv = 1.0d0/u(1,i,j,k)\nrho_i(i,j,k) = rho_inv\nus(i,j,k) = u(2,i,j,k) * rho_inv\nvs(i,j,k) = u(3,i,j,k) * rho_inv\nws(i,j,k) = u(4,i,j,k) * rho_inv\nsquare(i,j,k) = 0.5d0* ( &\n& u(2,i,j,k)*u(2,i,j,k) + &\n& u(3,i,j,k)*u(3,i,j,k) + &\n& u(4,i,j,k)*u(4,i,j,k) ) * rho_inv\nqs(i,j,k) = square(i,j,k) * rho_inv\nenddo\nenddo\nenddo\n\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nrhs(m,i,j,k) = forcing(m,i,j,k)\nenddo\nenddo\nenddo\nenddo\n\n\nif (timeron) call timer_start(t_rhsx)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nuijk = us(i,j,k)\nup1 = us(i+1,j,k)\num1 = us(i-1,j,k)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dx1tx1 * &\n& (u(1,i+1,j,k) - 2.0d0*u(1,i,j,k) + &\n& u(1,i-1,j,k)) - &\n& tx2 * (u(2,i+1,j,k) - u(2,i-1,j,k))\n\nrhs(2,i,j,k) = rhs(2,i,j,k) + dx2tx1 * &\n& (u(2,i+1,j,k) - 2.0d0*u(2,i,j,k) + &\n& u(2,i-1,j,k)) + &\n& xxcon2*con43 * (up1 - 2.0d0*uijk + um1) - &\n& tx2 * (u(2,i+1,j,k)*up1 - &\n& u(2,i-1,j,k)*um1 + &\n& (u(5,i+1,j,k)- square(i+1,j,k)- &\n& u(5,i-1,j,k)+ square(i-1,j,k))* &\n& c2)\n\nrhs(3,i,j,k) = rhs(3,i,j,k) + dx3tx1 * &\n& (u(3,i+1,j,k) - 2.0d0*u(3,i,j,k) + &\n& u(3,i-1,j,k)) + &\n& xxcon2 * (vs(i+1,j,k) - 2.0d0*vs(i,j,k) + &\n& vs(i-1,j,k)) - &\n& tx2 * (u(3,i+1,j,k)*up1 - &\n& u(3,i-1,j,k)*um1)\n\nrhs(4,i,j,k) = rhs(4,i,j,k) + dx4tx1 * &\n& (u(4,i+1,j,k) - 2.0d0*u(4,i,j,k) + &\n& u(4,i-1,j,k)) + &\n& xxcon2 * (ws(i+1,j,k) - 2.0d0*ws(i,j,k) + &\n& ws(i-1,j,k)) - &\n& tx2 * (u(4,i+1,j,k)*up1 - &\n& u(4,i-1,j,k)*um1)\n\nrhs(5,i,j,k) = rhs(5,i,j,k) + dx5tx1 * &\n& (u(5,i+1,j,k) - 2.0d0*u(5,i,j,k) + &\n& u(5,i-1,j,k)) + &\n& xxcon3 * (qs(i+1,j,k) - 2.0d0*qs(i,j,k) + &\n& qs(i-1,j,k)) + &\n& xxcon4 * (up1*up1 - 2.0d0*uijk*uijk + &\n& um1*um1) + &\n& xxcon5 * (u(5,i+1,j,k)*rho_i(i+1,j,k) - &\n& 2.0d0*u(5,i,j,k)*rho_i(i,j,k) + &\n& u(5,i-1,j,k)*rho_i(i-1,j,k)) - &\n& tx2 * ( (c1*u(5,i+1,j,k) - &\n& c2*square(i+1,j,k))*up1 - &\n& (c1*u(5,i-1,j,k) - &\n& c2*square(i-1,j,k))*um1 )\nenddo\n\ni = 1\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0*u(m,i,j,k) - 4.0d0*u(m,i+1,j,k) + &\n& u(m,i+2,j,k))\nenddo\n\ni = 2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0*u(m,i-1,j,k) + 6.0d0*u(m,i,j,k) - &\n& 4.0d0*u(m,i+1,j,k) + u(m,i+2,j,k))\nenddo\n\ndo i = 3,grid_points(1)-4\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i-2,j,k) - 4.0d0*u(m,i-1,j,k) + &\n& 6.0*u(m,i,j,k) - 4.0d0*u(m,i+1,j,k) + &\n& u(m,i+2,j,k) )\nenddo\nenddo\n\ni = grid_points(1)-3\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i-2,j,k) - 4.0d0*u(m,i-1,j,k) + &\n& 6.0d0*u(m,i,j,k) - 4.0d0*u(m,i+1,j,k) )\nenddo\n\ni = grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i-2,j,k) - 4.d0*u(m,i-1,j,k) + &\n& 5.d0*u(m,i,j,k) )\nenddo\nenddo\nenddo\nif (timeron) call timer_stop(t_rhsx)\n\nif (timeron) call timer_start(t_rhsy)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nvijk = vs(i,j,k)\nvp1 = vs(i,j+1,k)\nvm1 = vs(i,j-1,k)\nrhs(1,i,j,k) = rhs(1,i,j,k) + dy1ty1 * &\n& (u(1,i,j+1,k) - 2.0d0*u(1,i,j,k) + &\n& u(1,i,j-1,k)) - &\n& ty2 * (u(3,i,j+1,k) - u(3,i,j-1,k))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dy2ty1 * &\n& (u(2,i,j+1,k) - 2.0d0*u(2,i,j,k) + &\n& u(2,i,j-1,k)) + &\n& yycon2 * (us(i,j+1,k) - 2.0d0*us(i,j,k) + &\n& us(i,j-1,k)) - &\n& ty2 * (u(2,i,j+1,k)*vp1 - &\n& u(2,i,j-1,k)*vm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dy3ty1 * &\n& (u(3,i,j+1,k) - 2.0d0*u(3,i,j,k) + &\n& u(3,i,j-1,k)) + &\n& yycon2*con43 * (vp1 - 2.0d0*vijk + vm1) - &\n& ty2 * (u(3,i,j+1,k)*vp1 - &\n& u(3,i,j-1,k)*vm1 + &\n& (u(5,i,j+1,k) - square(i,j+1,k) - &\n& u(5,i,j-1,k) + square(i,j-1,k)) &\n& *c2)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dy4ty1 * &\n& (u(4,i,j+1,k) - 2.0d0*u(4,i,j,k) + &\n& u(4,i,j-1,k)) + &\n& yycon2 * (ws(i,j+1,k) - 2.0d0*ws(i,j,k) + &\n& ws(i,j-1,k)) - &\n& ty2 * (u(4,i,j+1,k)*vp1 - &\n& u(4,i,j-1,k)*vm1)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dy5ty1 * &\n& (u(5,i,j+1,k) - 2.0d0*u(5,i,j,k) + &\n& u(5,i,j-1,k)) + &\n& yycon3 * (qs(i,j+1,k) - 2.0d0*qs(i,j,k) + &\n& qs(i,j-1,k)) + &\n& yycon4 * (vp1*vp1 - 2.0d0*vijk*vijk + &\n& vm1*vm1) + &\n& yycon5 * (u(5,i,j+1,k)*rho_i(i,j+1,k) - &\n& 2.0d0*u(5,i,j,k)*rho_i(i,j,k) + &\n& u(5,i,j-1,k)*rho_i(i,j-1,k)) - &\n& ty2 * ((c1*u(5,i,j+1,k) - &\n& c2*square(i,j+1,k)) * vp1 - &\n& (c1*u(5,i,j-1,k) - &\n& c2*square(i,j-1,k)) * vm1)\nenddo\n\nif (j .eq. 1) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j+1,k) + &\n& u(m,i,j+2,k))\nenddo\nenddo\n\nelse if (j .eq. 2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0*u(m,i,j-1,k) + 6.0d0*u(m,i,j,k) - &\n& 4.0d0*u(m,i,j+1,k) + u(m,i,j+2,k))\nenddo\nenddo\n\nelse if (j .eq. grid_points(2)-3) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.0d0*u(m,i,j-1,k) + &\n& 6.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j+1,k) )\nenddo\nenddo\n\nelse if (j .eq. grid_points(2)-2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.d0*u(m,i,j-1,k) + &\n& 5.d0*u(m,i,j,k) )\nenddo\nenddo\n\nelse\ndo i = 1,grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j-2,k) - 4.0d0*u(m,i,j-1,k) + &\n& 6.0*u(m,i,j,k) - 4.0d0*u(m,i,j+1,k) + &\n& u(m,i,j+2,k) )\nenddo\nenddo\nendif\nenddo\nenddo\nif (timeron) call timer_stop(t_rhsy)\n\nif (timeron) call timer_start(t_rhsz)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nwijk = ws(i,j,k)\nwp1 = ws(i,j,k+1)\nwm1 = ws(i,j,k-1)\n\nrhs(1,i,j,k) = rhs(1,i,j,k) + dz1tz1 * &\n& (u(1,i,j,k+1) - 2.0d0*u(1,i,j,k) + &\n& u(1,i,j,k-1)) - &\n& tz2 * (u(4,i,j,k+1) - u(4,i,j,k-1))\nrhs(2,i,j,k) = rhs(2,i,j,k) + dz2tz1 * &\n& (u(2,i,j,k+1) - 2.0d0*u(2,i,j,k) + &\n& u(2,i,j,k-1)) + &\n& zzcon2 * (us(i,j,k+1) - 2.0d0*us(i,j,k) + &\n& us(i,j,k-1)) - &\n& tz2 * (u(2,i,j,k+1)*wp1 - &\n& u(2,i,j,k-1)*wm1)\nrhs(3,i,j,k) = rhs(3,i,j,k) + dz3tz1 * &\n& (u(3,i,j,k+1) - 2.0d0*u(3,i,j,k) + &\n& u(3,i,j,k-1)) + &\n& zzcon2 * (vs(i,j,k+1) - 2.0d0*vs(i,j,k) + &\n& vs(i,j,k-1)) - &\n& tz2 * (u(3,i,j,k+1)*wp1 - &\n& u(3,i,j,k-1)*wm1)\nrhs(4,i,j,k) = rhs(4,i,j,k) + dz4tz1 * &\n& (u(4,i,j,k+1) - 2.0d0*u(4,i,j,k) + &\n& u(4,i,j,k-1)) + &\n& zzcon2*con43 * (wp1 - 2.0d0*wijk + wm1) - &\n& tz2 * (u(4,i,j,k+1)*wp1 - &\n& u(4,i,j,k-1)*wm1 + &\n& (u(5,i,j,k+1) - square(i,j,k+1) - &\n& u(5,i,j,k-1) + square(i,j,k-1)) &\n& *c2)\nrhs(5,i,j,k) = rhs(5,i,j,k) + dz5tz1 * &\n& (u(5,i,j,k+1) - 2.0d0*u(5,i,j,k) + &\n& u(5,i,j,k-1)) + &\n& zzcon3 * (qs(i,j,k+1) - 2.0d0*qs(i,j,k) + &\n& qs(i,j,k-1)) + &\n& zzcon4 * (wp1*wp1 - 2.0d0*wijk*wijk + &\n& wm1*wm1) + &\n& zzcon5 * (u(5,i,j,k+1)*rho_i(i,j,k+1) - &\n& 2.0d0*u(5,i,j,k)*rho_i(i,j,k) + &\n& u(5,i,j,k-1)*rho_i(i,j,k-1)) - &\n& tz2 * ( (c1*u(5,i,j,k+1) - &\n& c2*square(i,j,k+1))*wp1 - &\n& (c1*u(5,i,j,k-1) - &\n& c2*square(i,j,k-1))*wm1)\nenddo\n\nif (k.eq.1) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k)- dssp * &\n& ( 5.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j,k+1) + &\n& u(m,i,j,k+2))\nenddo\nenddo\n\nelse if (k.eq.2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& (-4.0d0*u(m,i,j,k-1) + 6.0d0*u(m,i,j,k) - &\n& 4.0d0*u(m,i,j,k+1) + u(m,i,j,k+2))\nenddo\nenddo\n\nelse if (k.eq.grid_points(3)-3) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.0d0*u(m,i,j,k-1) + &\n& 6.0d0*u(m,i,j,k) - 4.0d0*u(m,i,j,k+1) )\nenddo\nenddo\n\nelse if (k.eq.grid_points(3)-2) then\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.d0*u(m,i,j,k-1) + &\n& 5.d0*u(m,i,j,k) )\nenddo\nenddo\n\nelse\ndo i = 1,grid_points(1)-2\ndo m = 1, 5\nrhs(m,i,j,k) = rhs(m,i,j,k) - dssp * &\n& ( u(m,i,j,k-2) - 4.0d0*u(m,i,j,k-1) + &\n& 6.0*u(m,i,j,k) - 4.0d0*u(m,i,j,k+1) + &\n& u(m,i,j,k+2) )\nenddo\nenddo\nendif\nenddo\nenddo\nif (timeron) call timer_stop(t_rhsz)\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\nrhs(1,i,j,k) = rhs(1,i,j,k) * dt\nrhs(2,i,j,k) = rhs(2,i,j,k) * dt\nrhs(3,i,j,k) = rhs(3,i,j,k) * dt\nrhs(4,i,j,k) = rhs(4,i,j,k) * dt\nrhs(5,i,j,k) = rhs(5,i,j,k) * dt\nenddo\nenddo\nenddo\n\n\nif (timeron) call timer_stop(t_rhs)\n\nreturn\nend

void exact_solution(double xi, double eta, double zeta, double dtemp[5]){\nint m;\nfor(m=0; m<5; m++){\ndtemp[m]=ce[0][m]+\nxi*(ce[1][m]+\nxi*(ce[4][m]+\nxi*(ce[7][m]+\nxi*ce[10][m])))+\neta*(ce[2][m]+\neta*(ce[5][m]+\neta*(ce[8][m]+\neta*ce[11][m])))+\nzeta*(ce[3][m]+\nzeta*(ce[6][m]+\nzeta*(ce[9][m]+\nzeta*ce[12][m])));\n}\n}

subroutine exact_solution(xi,eta,zeta,dtemp)\n\n\n\nuse bt_data\nimplicit none\n\ndouble precision xi, eta, zeta, dtemp(5)\ninteger m\n\ndo m = 1, 5\ndtemp(m) = ce(m,1) + &\n& xi*(ce(m,2) + xi*(ce(m,5) + xi*(ce(m,8) + xi*ce(m,11)))) + &\n& eta*(ce(m,3) + eta*(ce(m,6) + eta*(ce(m,9) + eta*ce(m,12))))+ &\n& zeta*(ce(m,4) + zeta*(ce(m,7) + zeta*(ce(m,10) + &\n& zeta*ce(m,13))))\nenddo\n\nreturn\nend

void jacu(int k){\n\nint i, j;\ndouble r43;\ndouble c1345;\ndouble c34;\ndouble tmp1, tmp2, tmp3;\nr43=(4.0/3.0);\nc1345=C1*C3*C4*C5;\nc34=C3*C4;\n\n#pragma omp for nowait schedule(static)\nfor (j=jend-1; j>=jst; j--) {\nfor (i=iend-1; i>=ist; i--) {\n\ntmp1=rho_i[k][j][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nd[j][i][0][0]=1.0+dt*2.0*(tx1*dx1+ty1*dy1+tz1*dz1);\nd[j][i][1][0]=0.0;\nd[j][i][2][0]=0.0;\nd[j][i][3][0]=0.0;\nd[j][i][4][0]=0.0;\nd[j][i][0][1]=dt*2.0\n*(-tx1*r43-ty1-tz1)\n*(c34*tmp2*u[k][j][i][1]);\nd[j][i][1][1]=1.0\n+dt*2.0*c34*tmp1\n*(tx1*r43+ty1+tz1)\n+dt*2.0*(tx1*dx2+ty1*dy2+tz1*dz2);\nd[j][i][2][1]=0.0;\nd[j][i][3][1]=0.0;\nd[j][i][4][1]=0.0;\nd[j][i][0][2]=dt*2.0\n*(-tx1-ty1*r43-tz1)\n*(c34*tmp2*u[k][j][i][2]);\nd[j][i][1][2]=0.0;\nd[j][i][2][2]=1.0\n+dt*2.0*c34*tmp1\n*(tx1+ty1*r43+tz1)\n+dt*2.0*(tx1*dx3+ty1*dy3+tz1*dz3);\nd[j][i][3][2]=0.0;\nd[j][i][4][2]=0.0;\nd[j][i][0][3]=dt*2.0\n*(-tx1-ty1-tz1*r43)\n*(c34*tmp2*u[k][j][i][3]);\nd[j][i][1][3]=0.0;\nd[j][i][2][3]=0.0;\nd[j][i][3][3]=1.0\n+dt*2.0*c34*tmp1\n*(tx1+ty1+tz1*r43)\n+dt*2.0*(tx1*dx4+ty1*dy4+tz1*dz4);\nd[j][i][4][3]=0.0;\nd[j][i][0][4]=-dt*2.0\n*(((tx1*(r43*c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(c34-c1345))*(u[k][j][i][1]*u[k][j][i][1])\n+(tx1*(c34-c1345)\n+ty1*(r43*c34-c1345)\n+tz1*(c34-c1345))*(u[k][j][i][2]*u[k][j][i][2])\n+(tx1*(c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(r43*c34-c1345))*(u[k][j][i][3]*u[k][j][i][3])\n)*tmp3\n+(tx1+ty1+tz1)*c1345*tmp2*u[k][j][i][4]);\nd[j][i][1][4]=dt*2.0\n*(tx1*(r43*c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(c34-c1345))*tmp2*u[k][j][i][1];\nd[j][i][2][4]=dt*2.0\n*(tx1*(c34-c1345)\n+ty1*(r43*c34-c1345)\n+tz1*(c34-c1345))*tmp2*u[k][j][i][2];\nd[j][i][3][4]=dt*2.0\n*(tx1*(c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(r43*c34-c1345))*tmp2*u[k][j][i][3];\nd[j][i][4][4]=1.0\n+dt*2.0*(tx1+ty1+tz1)*c1345*tmp1\n+dt*2.0*(tx1*dx5+ty1*dy5+tz1*dz5);\n\ntmp1=rho_i[k][j][i+1];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\na[j][i][0][0]=-dt*tx1*dx1;\na[j][i][1][0]=dt*tx2;\na[j][i][2][0]=0.0;\na[j][i][3][0]=0.0;\na[j][i][4][0]=0.0;\na[j][i][0][1]=dt*tx2\n*(-(u[k][j][i+1][1]*tmp1)*(u[k][j][i+1][1]*tmp1)\n+C2*qs[k][j][i+1]*tmp1)\n-dt*tx1*(-r43*c34*tmp2*u[k][j][i+1][1]);\na[j][i][1][1]=dt*tx2\n*((2.0-C2)*(u[k][j][i+1][1]*tmp1))\n-dt*tx1*(r43*c34*tmp1)\n-dt*tx1*dx2;\na[j][i][2][1]=dt*tx2\n*(-C2*(u[k][j][i+1][2]*tmp1));\na[j][i][3][1]=dt*tx2\n*(-C2*(u[k][j][i+1][3]*tmp1));\na[j][i][4][1]=dt*tx2*C2;\na[j][i][0][2]=dt*tx2\n*(-(u[k][j][i+1][1]*u[k][j][i+1][2])*tmp2)\n-dt*tx1*(-c34*tmp2*u[k][j][i+1][2]);\na[j][i][1][2]=dt*tx2*(u[k][j][i+1][2]*tmp1);\na[j][i][2][2]=dt*tx2*(u[k][j][i+1][1]*tmp1)\n-dt*tx1*(c34*tmp1)\n-dt*tx1*dx3;\na[j][i][3][2]=0.0;\na[j][i][4][2]=0.0;\na[j][i][0][3]=dt*tx2\n*(-(u[k][j][i+1][1]*u[k][j][i+1][3])*tmp2)\n-dt*tx1*(-c34*tmp2*u[k][j][i+1][3]);\na[j][i][1][3]=dt*tx2*(u[k][j][i+1][3]*tmp1);\na[j][i][2][3]=0.0;\na[j][i][3][3]=dt*tx2*(u[k][j][i+1][1]*tmp1)\n-dt*tx1*(c34*tmp1)\n-dt*tx1*dx4;\na[j][i][4][3]=0.0;\na[j][i][0][4]=dt*tx2\n*((C2*2.0*qs[k][j][i+1]\n-C1*u[k][j][i+1][4])\n*(u[k][j][i+1][1]*tmp2))\n-dt*tx1\n*(-(r43*c34-c1345)*tmp3*(u[k][j][i+1][1]*u[k][j][i+1][1])\n-(c34-c1345)*tmp3*(u[k][j][i+1][2]*u[k][j][i+1][2])\n-(c34-c1345)*tmp3*( u[k][j][i+1][3]*u[k][j][i+1][3])\n-c1345*tmp2*u[k][j][i+1][4]);\na[j][i][1][4]=dt*tx2\n*(C1*(u[k][j][i+1][4]*tmp1)\n-C2\n*(u[k][j][i+1][1]*u[k][j][i+1][1]*tmp2\n+qs[k][j][i+1]*tmp1))\n-dt*tx1\n*(r43*c34-c1345)*tmp2*u[k][j][i+1][1];\na[j][i][2][4]=dt*tx2\n*(-C2*(u[k][j][i+1][2]*u[k][j][i+1][1])*tmp2)\n-dt*tx1\n*(c34-c1345)*tmp2*u[k][j][i+1][2];\na[j][i][3][4]=dt*tx2\n*(-C2*(u[k][j][i+1][3]*u[k][j][i+1][1])*tmp2)\n-dt*tx1\n*(c34-c1345)*tmp2*u[k][j][i+1][3];\na[j][i][4][4]=dt*tx2\n*(C1*(u[k][j][i+1][1]*tmp1))\n-dt*tx1*c1345*tmp1\n-dt*tx1*dx5;\n\ntmp1=rho_i[k][j+1][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nb[j][i][0][0]=-dt*ty1*dy1;\nb[j][i][1][0]=0.0;\nb[j][i][2][0]=dt*ty2;\nb[j][i][3][0]=0.0;\nb[j][i][4][0]=0.0;\nb[j][i][0][1]=dt*ty2\n*(-(u[k][j+1][i][1]*u[k][j+1][i][2])*tmp2)\n-dt*ty1*(-c34*tmp2*u[k][j+1][i][1]);\nb[j][i][1][1]=dt*ty2*(u[k][j+1][i][2]*tmp1)\n-dt*ty1*(c34*tmp1)\n-dt*ty1*dy2;\nb[j][i][2][1]=dt*ty2*(u[k][j+1][i][1]*tmp1);\nb[j][i][3][1]=0.0;\nb[j][i][4][1]=0.0;\nb[j][i][0][2]=dt*ty2\n*(-(u[k][j+1][i][2]*tmp1)*(u[k][j+1][i][2]*tmp1)\n+C2*(qs[k][j+1][i]*tmp1))\n-dt*ty1*(-r43*c34*tmp2*u[k][j+1][i][2]);\nb[j][i][1][2]=dt*ty2\n*(-C2*(u[k][j+1][i][1]*tmp1));\nb[j][i][2][2]=dt*ty2*((2.0-C2)\n*(u[k][j+1][i][2]*tmp1))\n-dt*ty1*(r43*c34*tmp1)\n-dt*ty1*dy3;\nb[j][i][3][2]=dt*ty2\n*(-C2*(u[k][j+1][i][3]*tmp1));\nb[j][i][4][2]=dt*ty2*C2;\nb[j][i][0][3]=dt*ty2\n*(-(u[k][j+1][i][2]*u[k][j+1][i][3])*tmp2)\n-dt*ty1*(-c34*tmp2*u[k][j+1][i][3]);\nb[j][i][1][3]=0.0;\nb[j][i][2][3]=dt*ty2*(u[k][j+1][i][3]*tmp1);\nb[j][i][3][3]=dt*ty2*(u[k][j+1][i][2]*tmp1)\n-dt*ty1*(c34*tmp1)\n-dt*ty1*dy4;\nb[j][i][4][3]=0.0;\nb[j][i][0][4]=dt*ty2\n*((C2*2.0*qs[k][j+1][i]\n-C1*u[k][j+1][i][4])\n*(u[k][j+1][i][2]*tmp2))\n-dt*ty1\n*(-(c34-c1345)*tmp3*(u[k][j+1][i][1]*u[k][j+1][i][1])\n-(r43*c34-c1345)*tmp3*(u[k][j+1][i][2]*u[k][j+1][i][2])\n-(c34-c1345)*tmp3*(u[k][j+1][i][3]*u[k][j+1][i][3])\n-c1345*tmp2*u[k][j+1][i][4]);\nb[j][i][1][4]=dt*ty2\n*(-C2*(u[k][j+1][i][1]*u[k][j+1][i][2])*tmp2)\n-dt*ty1\n*(c34-c1345)*tmp2*u[k][j+1][i][1];\nb[j][i][2][4]=dt*ty2\n*(C1*(u[k][j+1][i][4]*tmp1)\n-C2\n*(qs[k][j+1][i]*tmp1\n+u[k][j+1][i][2]*u[k][j+1][i][2]*tmp2))\n-dt*ty1\n*(r43*c34-c1345)*tmp2*u[k][j+1][i][2];\nb[j][i][3][4]=dt*ty2\n*(-C2*(u[k][j+1][i][2]*u[k][j+1][i][3])*tmp2)\n-dt*ty1*(c34-c1345)*tmp2*u[k][j+1][i][3];\nb[j][i][4][4]=dt*ty2\n*(C1*(u[k][j+1][i][2]*tmp1))\n-dt*ty1*c1345*tmp1\n-dt*ty1*dy5;\n\ntmp1=rho_i[k+1][j][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nc[j][i][0][0]=-dt*tz1*dz1;\nc[j][i][1][0]=0.0;\nc[j][i][2][0]=0.0;\nc[j][i][3][0]=dt*tz2;\nc[j][i][4][0]=0.0;\nc[j][i][0][1]=dt*tz2\n*(-(u[k+1][j][i][1]*u[k+1][j][i][3])*tmp2)\n-dt*tz1*(-c34*tmp2*u[k+1][j][i][1]);\nc[j][i][1][1]=dt*tz2*(u[k+1][j][i][3]*tmp1)\n-dt*tz1*c34*tmp1\n-dt*tz1*dz2;\nc[j][i][2][1]=0.0;\nc[j][i][3][1]=dt*tz2*(u[k+1][j][i][1]*tmp1);\nc[j][i][4][1]=0.0;\nc[j][i][0][2]=dt*tz2\n*(-(u[k+1][j][i][2]*u[k+1][j][i][3])*tmp2)\n-dt*tz1*(-c34*tmp2*u[k+1][j][i][2]);\nc[j][i][1][2]=0.0;\nc[j][i][2][2]=dt*tz2*(u[k+1][j][i][3]*tmp1)\n-dt*tz1*(c34*tmp1)\n-dt*tz1*dz3;\nc[j][i][3][2]=dt*tz2*(u[k+1][j][i][2]*tmp1);\nc[j][i][4][2]=0.0;\nc[j][i][0][3]=dt*tz2\n*(-(u[k+1][j][i][3]*tmp1)*(u[k+1][j][i][3]*tmp1)\n+C2*(qs[k+1][j][i]*tmp1))\n-dt*tz1*(-r43*c34*tmp2*u[k+1][j][i][3]);\nc[j][i][1][3]=dt*tz2\n*(-C2*(u[k+1][j][i][1]*tmp1));\nc[j][i][2][3]=dt*tz2\n*(-C2*(u[k+1][j][i][2]*tmp1));\nc[j][i][3][3]=dt*tz2*(2.0-C2)\n*(u[k+1][j][i][3]*tmp1)\n-dt*tz1*(r43*c34*tmp1)\n-dt*tz1*dz4;\nc[j][i][4][3]=dt*tz2*C2;\nc[j][i][0][4]=dt*tz2\n*((C2*2.0*qs[k+1][j][i]\n-C1*u[k+1][j][i][4])\n*(u[k+1][j][i][3]*tmp2))\n-dt*tz1\n*(-(c34-c1345)*tmp3*(u[k+1][j][i][1]*u[k+1][j][i][1])\n-(c34-c1345)*tmp3*(u[k+1][j][i][2]*u[k+1][j][i][2])\n-(r43*c34-c1345)*tmp3*(u[k+1][j][i][3]*u[k+1][j][i][3])\n-c1345*tmp2*u[k+1][j][i][4]);\nc[j][i][1][4]=dt*tz2\n*(-C2*(u[k+1][j][i][1]*u[k+1][j][i][3])*tmp2)\n-dt*tz1*(c34-c1345)*tmp2*u[k+1][j][i][1];\nc[j][i][2][4]=dt*tz2\n*(-C2*(u[k+1][j][i][2]*u[k+1][j][i][3])*tmp2)\n-dt*tz1*(c34-c1345)*tmp2*u[k+1][j][i][2];\nc[j][i][3][4]=dt*tz2\n*(C1*(u[k+1][j][i][4]*tmp1)\n-C2\n*(qs[k+1][j][i]*tmp1\n+u[k+1][j][i][3]*u[k+1][j][i][3]*tmp2))\n-dt*tz1*(r43*c34-c1345)*tmp2*u[k+1][j][i][3];\nc[j][i][4][4]=dt*tz2\n*(C1*(u[k+1][j][i][3]*tmp1))\n-dt*tz1*c1345*tmp1\n-dt*tz1*dz5;\n}\n}\n}

subroutine jacu(j, k)\n\n\n\nuse lu_data\nimplicit none\n\ninteger j, k\n\ninteger i\ndouble precision r43\ndouble precision c1345\ndouble precision c34\ndouble precision tmp1, tmp2, tmp3\n\n\n\nr43 = ( 4.0d+00 / 3.0d+00 )\nc1345 = c1 * c3 * c4 * c5\nc34 = c3 * c4\n\ndo i = iend, ist, -1\n\ntmp1 = rho_i(i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nd(1,1,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 * dx1 &\n& + ty1 * dy1 &\n& + tz1 * dz1 )\nd(1,2,i) = 0.0d+00\nd(1,3,i) = 0.0d+00\nd(1,4,i) = 0.0d+00\nd(1,5,i) = 0.0d+00\n\nd(2,1,i) = dt * 2.0d+00 &\n& * ( - tx1 * r43 - ty1 - tz1 ) &\n& * ( c34 * tmp2 * u(2,i,j,k) )\nd(2,2,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 * r43 + ty1 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx2 &\n& + ty1 * dy2 &\n& + tz1 * dz2 )\nd(2,3,i) = 0.0d+00\nd(2,4,i) = 0.0d+00\nd(2,5,i) = 0.0d+00\n\nd(3,1,i) = dt * 2.0d+00 &\n& * ( - tx1 - ty1 * r43 - tz1 ) &\n& * ( c34 * tmp2 * u(3,i,j,k) )\nd(3,2,i) = 0.0d+00\nd(3,3,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 * r43 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx3 &\n& + ty1 * dy3 &\n& + tz1 * dz3 )\nd(3,4,i) = 0.0d+00\nd(3,5,i) = 0.0d+00\n\nd(4,1,i) = dt * 2.0d+00 &\n& * ( - tx1 - ty1 - tz1 * r43 ) &\n& * ( c34 * tmp2 * u(4,i,j,k) )\nd(4,2,i) = 0.0d+00\nd(4,3,i) = 0.0d+00\nd(4,4,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 + tz1 * r43 ) &\n& + dt * 2.0d+00 * ( tx1 * dx4 &\n& + ty1 * dy4 &\n& + tz1 * dz4 )\nd(4,5,i) = 0.0d+00\n\nd(5,1,i) = -dt * 2.0d+00 &\n& * ( ( ( tx1 * ( r43*c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * ( u(2,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43*c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * ( u(3,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43*c34 - c1345 ) ) * ( u(4,i,j,k) ** 2 ) &\n& ) * tmp3 &\n& + ( tx1 + ty1 + tz1 ) * c1345 * tmp2 * u(5,i,j,k) )\n\nd(5,2,i) = dt * 2.0d+00 &\n& * ( tx1 * ( r43*c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * tmp2 * u(2,i,j,k)\nd(5,3,i) = dt * 2.0d+00 &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43*c34 -c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * tmp2 * u(3,i,j,k)\nd(5,4,i) = dt * 2.0d+00 &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43*c34 - c1345 ) ) * tmp2 * u(4,i,j,k)\nd(5,5,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 + ty1 + tz1 ) * c1345 * tmp1 &\n& + dt * 2.0d+00 * ( tx1 * dx5 &\n& + ty1 * dy5 &\n& + tz1 * dz5 )\n\ntmp1 = rho_i(i+1,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\na(1,1,i) = - dt * tx1 * dx1\na(1,2,i) = dt * tx2\na(1,3,i) = 0.0d+00\na(1,4,i) = 0.0d+00\na(1,5,i) = 0.0d+00\n\na(2,1,i) = dt * tx2 &\n& * ( - ( u(2,i+1,j,k) * tmp1 ) ** 2 &\n& + c2 * qs(i+1,j,k) * tmp1 ) &\n& - dt * tx1 * ( - r43 * c34 * tmp2 * u(2,i+1,j,k) )\na(2,2,i) = dt * tx2 &\n& * ( ( 2.0d+00 - c2 ) * ( u(2,i+1,j,k) * tmp1 ) ) &\n& - dt * tx1 * ( r43 * c34 * tmp1 ) &\n& - dt * tx1 * dx2\na(2,3,i) = dt * tx2 &\n& * ( - c2 * ( u(3,i+1,j,k) * tmp1 ) )\na(2,4,i) = dt * tx2 &\n& * ( - c2 * ( u(4,i+1,j,k) * tmp1 ) )\na(2,5,i) = dt * tx2 * c2\n\na(3,1,i) = dt * tx2 &\n& * ( - ( u(2,i+1,j,k) * u(3,i+1,j,k) ) * tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(3,i+1,j,k) )\na(3,2,i) = dt * tx2 * ( u(3,i+1,j,k) * tmp1 )\na(3,3,i) = dt * tx2 * ( u(2,i+1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx3\na(3,4,i) = 0.0d+00\na(3,5,i) = 0.0d+00\n\na(4,1,i) = dt * tx2 &\n& * ( - ( u(2,i+1,j,k)*u(4,i+1,j,k) ) * tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(4,i+1,j,k) )\na(4,2,i) = dt * tx2 * ( u(4,i+1,j,k) * tmp1 )\na(4,3,i) = 0.0d+00\na(4,4,i) = dt * tx2 * ( u(2,i+1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx4\na(4,5,i) = 0.0d+00\n\na(5,1,i) = dt * tx2 &\n& * ( ( c2 * 2.0d0 * qs(i+1,j,k) &\n& - c1 * u(5,i+1,j,k) ) &\n& * ( u(2,i+1,j,k) * tmp2 ) ) &\n& - dt * tx1 &\n& * ( - ( r43*c34 - c1345 ) * tmp3 * ( u(2,i+1,j,k)**2 ) &\n& - ( c34 - c1345 ) * tmp3 * ( u(3,i+1,j,k)**2 ) &\n& - ( c34 - c1345 ) * tmp3 * ( u(4,i+1,j,k)**2 ) &\n& - c1345 * tmp2 * u(5,i+1,j,k) )\na(5,2,i) = dt * tx2 &\n& * ( c1 * ( u(5,i+1,j,k) * tmp1 ) &\n& - c2 &\n& * ( u(2,i+1,j,k)*u(2,i+1,j,k) * tmp2 &\n& + qs(i+1,j,k) * tmp1 ) ) &\n& - dt * tx1 &\n& * ( r43*c34 - c1345 ) * tmp2 * u(2,i+1,j,k)\na(5,3,i) = dt * tx2 &\n& * ( - c2 * ( u(3,i+1,j,k)*u(2,i+1,j,k) ) * tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(3,i+1,j,k)\na(5,4,i) = dt * tx2 &\n& * ( - c2 * ( u(4,i+1,j,k)*u(2,i+1,j,k) ) * tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(4,i+1,j,k)\na(5,5,i) = dt * tx2 &\n& * ( c1 * ( u(2,i+1,j,k) * tmp1 ) ) &\n& - dt * tx1 * c1345 * tmp1 &\n& - dt * tx1 * dx5\n\ntmp1 = rho_i(i,j+1,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nb(1,1,i) = - dt * ty1 * dy1\nb(1,2,i) = 0.0d+00\nb(1,3,i) = dt * ty2\nb(1,4,i) = 0.0d+00\nb(1,5,i) = 0.0d+00\n\nb(2,1,i) = dt * ty2 &\n& * ( - ( u(2,i,j+1,k)*u(3,i,j+1,k) ) * tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(2,i,j+1,k) )\nb(2,2,i) = dt * ty2 * ( u(3,i,j+1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy2\nb(2,3,i) = dt * ty2 * ( u(2,i,j+1,k) * tmp1 )\nb(2,4,i) = 0.0d+00\nb(2,5,i) = 0.0d+00\n\nb(3,1,i) = dt * ty2 &\n& * ( - ( u(3,i,j+1,k) * tmp1 ) ** 2 &\n& + c2 * ( qs(i,j+1,k) * tmp1 ) ) &\n& - dt * ty1 * ( - r43 * c34 * tmp2 * u(3,i,j+1,k) )\nb(3,2,i) = dt * ty2 &\n& * ( - c2 * ( u(2,i,j+1,k) * tmp1 ) )\nb(3,3,i) = dt * ty2 * ( ( 2.0d+00 - c2 ) &\n& * ( u(3,i,j+1,k) * tmp1 ) ) &\n& - dt * ty1 * ( r43 * c34 * tmp1 ) &\n& - dt * ty1 * dy3\nb(3,4,i) = dt * ty2 &\n& * ( - c2 * ( u(4,i,j+1,k) * tmp1 ) )\nb(3,5,i) = dt * ty2 * c2\n\nb(4,1,i) = dt * ty2 &\n& * ( - ( u(3,i,j+1,k)*u(4,i,j+1,k) ) * tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(4,i,j+1,k) )\nb(4,2,i) = 0.0d+00\nb(4,3,i) = dt * ty2 * ( u(4,i,j+1,k) * tmp1 )\nb(4,4,i) = dt * ty2 * ( u(3,i,j+1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy4\nb(4,5,i) = 0.0d+00\n\nb(5,1,i) = dt * ty2 &\n& * ( ( c2 * 2.0d0 * qs(i,j+1,k) &\n& - c1 * u(5,i,j+1,k) ) &\n& * ( u(3,i,j+1,k) * tmp2 ) ) &\n& - dt * ty1 &\n& * ( - ( c34 - c1345 )*tmp3*(u(2,i,j+1,k)**2) &\n& - ( r43*c34 - c1345 )*tmp3*(u(3,i,j+1,k)**2) &\n& - ( c34 - c1345 )*tmp3*(u(4,i,j+1,k)**2) &\n& - c1345*tmp2*u(5,i,j+1,k) )\nb(5,2,i) = dt * ty2 &\n& * ( - c2 * ( u(2,i,j+1,k)*u(3,i,j+1,k) ) * tmp2 ) &\n& - dt * ty1 &\n& * ( c34 - c1345 ) * tmp2 * u(2,i,j+1,k)\nb(5,3,i) = dt * ty2 &\n& * ( c1 * ( u(5,i,j+1,k) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j+1,k) * tmp1 &\n& + u(3,i,j+1,k)*u(3,i,j+1,k) * tmp2 ) ) &\n& - dt * ty1 &\n& * ( r43*c34 - c1345 ) * tmp2 * u(3,i,j+1,k)\nb(5,4,i) = dt * ty2 &\n& * ( - c2 * ( u(3,i,j+1,k)*u(4,i,j+1,k) ) * tmp2 ) &\n& - dt * ty1 * ( c34 - c1345 ) * tmp2 * u(4,i,j+1,k)\nb(5,5,i) = dt * ty2 &\n& * ( c1 * ( u(3,i,j+1,k) * tmp1 ) ) &\n& - dt * ty1 * c1345 * tmp1 &\n& - dt * ty1 * dy5\n\ntmp1 = rho_i(i,j,k+1)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nc(1,1,i) = - dt * tz1 * dz1\nc(1,2,i) = 0.0d+00\nc(1,3,i) = 0.0d+00\nc(1,4,i) = dt * tz2\nc(1,5,i) = 0.0d+00\n\nc(2,1,i) = dt * tz2 &\n& * ( - ( u(2,i,j,k+1)*u(4,i,j,k+1) ) * tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(2,i,j,k+1) )\nc(2,2,i) = dt * tz2 * ( u(4,i,j,k+1) * tmp1 ) &\n& - dt * tz1 * c34 * tmp1 &\n& - dt * tz1 * dz2\nc(2,3,i) = 0.0d+00\nc(2,4,i) = dt * tz2 * ( u(2,i,j,k+1) * tmp1 )\nc(2,5,i) = 0.0d+00\n\nc(3,1,i) = dt * tz2 &\n& * ( - ( u(3,i,j,k+1)*u(4,i,j,k+1) ) * tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(3,i,j,k+1) )\nc(3,2,i) = 0.0d+00\nc(3,3,i) = dt * tz2 * ( u(4,i,j,k+1) * tmp1 ) &\n& - dt * tz1 * ( c34 * tmp1 ) &\n& - dt * tz1 * dz3\nc(3,4,i) = dt * tz2 * ( u(3,i,j,k+1) * tmp1 )\nc(3,5,i) = 0.0d+00\n\nc(4,1,i) = dt * tz2 &\n& * ( - ( u(4,i,j,k+1) * tmp1 ) ** 2 &\n& + c2 * ( qs(i,j,k+1) * tmp1 ) ) &\n& - dt * tz1 * ( - r43 * c34 * tmp2 * u(4,i,j,k+1) )\nc(4,2,i) = dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k+1) * tmp1 ) )\nc(4,3,i) = dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k+1) * tmp1 ) )\nc(4,4,i) = dt * tz2 * ( 2.0d+00 - c2 ) &\n& * ( u(4,i,j,k+1) * tmp1 ) &\n& - dt * tz1 * ( r43 * c34 * tmp1 ) &\n& - dt * tz1 * dz4\nc(4,5,i) = dt * tz2 * c2\n\nc(5,1,i) = dt * tz2 &\n& * ( ( c2 * 2.0d0 * qs(i,j,k+1) &\n& - c1 * u(5,i,j,k+1) ) &\n& * ( u(4,i,j,k+1) * tmp2 ) ) &\n& - dt * tz1 &\n& * ( - ( c34 - c1345 ) * tmp3 * (u(2,i,j,k+1)**2) &\n& - ( c34 - c1345 ) * tmp3 * (u(3,i,j,k+1)**2) &\n& - ( r43*c34 - c1345 )* tmp3 * (u(4,i,j,k+1)**2) &\n& - c1345 * tmp2 * u(5,i,j,k+1) )\nc(5,2,i) = dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k+1)*u(4,i,j,k+1) ) * tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(2,i,j,k+1)\nc(5,3,i) = dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k+1)*u(4,i,j,k+1) ) * tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(3,i,j,k+1)\nc(5,4,i) = dt * tz2 &\n& * ( c1 * ( u(5,i,j,k+1) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j,k+1) * tmp1 &\n& + u(4,i,j,k+1)*u(4,i,j,k+1) * tmp2 ) ) &\n& - dt * tz1 * ( r43*c34 - c1345 ) * tmp2 * u(4,i,j,k+1)\nc(5,5,i) = dt * tz2 &\n& * ( c1 * ( u(4,i,j,k+1) * tmp1 ) ) &\n& - dt * tz1 * c1345 * tmp1 &\n& - dt * tz1 * dz5\n\nend do\n\n\nreturn\nend

void exact(int i, int j, int k, double u000ijk[]){\n\nint m;\ndouble xi, eta, zeta;\nxi=((double)i)/(nx0-1);\neta=((double)j)/(ny0-1);\nzeta=((double)k)/(nz-1);\nfor(m=0; m<5; m++){\nu000ijk[m]=ce[0][m]+\n(ce[1][m]+\n(ce[4][m]+\n(ce[7][m]+\nce[10][m]*xi)*xi)*xi)*xi+\n(ce[2][m]+\n(ce[5][m]+\n(ce[8][m]+\nce[11][m]*eta)*eta)*eta)*eta+\n(ce[3][m]+\n(ce[6][m]+\n(ce[9][m]+\nce[12][m]*zeta)*zeta)*zeta)*zeta;\n}\n}

subroutine exact( i, j, k, u000ijk )\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k\ndouble precision u000ijk(*)\n\ninteger m\ndouble precision xi, eta, zeta\n\nxi = ( dble ( i - 1 ) ) / ( nx0 - 1 )\neta = ( dble ( j - 1 ) ) / ( ny0 - 1 )\nzeta = ( dble ( k - 1 ) ) / ( nz - 1 )\n\n\ndo m = 1, 5\nu000ijk(m) = ce(m,1) &\n& + (ce(m,2) &\n& + (ce(m,5) &\n& + (ce(m,8) &\n& + ce(m,11) * xi) * xi) * xi) * xi &\n& + (ce(m,3) &\n& + (ce(m,6) &\n& + (ce(m,9) &\n& + ce(m,12) * eta) * eta) * eta) * eta &\n& + (ce(m,4) &\n& + (ce(m,7) &\n& + (ce(m,10) &\n& + ce(m,13) * zeta) * zeta) * zeta) * zeta\nend do\n\nreturn\nend

void z_solve(){\nint i, j, k, m, n, ksize;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_ZSOLVE);}\n\nksize = grid_points[2]-1;\n\n#pragma omp for\nfor(j=1; j<=grid_points[1]-2; j++){\ndouble fjac[PROBLEM_SIZE+1][5][5];\ndouble njac[PROBLEM_SIZE+1][5][5];\ndouble lhs[PROBLEM_SIZE+1][3][5][5];\ndouble tmp1, tmp2, tmp3;\n\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(k=0; k<=ksize; k++){\ntmp1=1.0/u[k][j][i][0];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nfjac[k][0][0]=0.0;\nfjac[k][1][0]=0.0;\nfjac[k][2][0]=0.0;\nfjac[k][3][0]=1.0;\nfjac[k][4][0]=0.0;\nfjac[k][0][1]=-(u[k][j][i][1]*u[k][j][i][3])*tmp2;\nfjac[k][1][1]=u[k][j][i][3]*tmp1;\nfjac[k][2][1]=0.0;\nfjac[k][3][1]=u[k][j][i][1]*tmp1;\nfjac[k][4][1]=0.0;\nfjac[k][0][2]=-(u[k][j][i][2]*u[k][j][i][3])*tmp2;\nfjac[k][1][2]=0.0;\nfjac[k][2][2]=u[k][j][i][3]*tmp1;\nfjac[k][3][2]=u[k][j][i][2]*tmp1;\nfjac[k][4][2]=0.0;\nfjac[k][0][3]=-(u[k][j][i][3]*u[k][j][i][3]*tmp2)+c2*qs[k][j][i];\nfjac[k][1][3]=-c2*u[k][j][i][1]*tmp1;\nfjac[k][2][3]=-c2*u[k][j][i][2]*tmp1;\nfjac[k][3][3]=(2.0-c2)*u[k][j][i][3]*tmp1;\nfjac[k][4][3]=c2;\nfjac[k][0][4]=(c2*2.0*square[k][j][i]-c1*u[k][j][i][4])*u[k][j][i][3]*tmp2;\nfjac[k][1][4]=-c2*(u[k][j][i][1]*u[k][j][i][3])*tmp2;\nfjac[k][2][4]=-c2*(u[k][j][i][2]*u[k][j][i][3])*tmp2;\nfjac[k][3][4]=c1*(u[k][j][i][4]*tmp1)-c2*(qs[k][j][i]+u[k][j][i][3]*u[k][j][i][3]*tmp2);\nfjac[k][4][4]=c1*u[k][j][i][3]*tmp1;\nnjac[k][0][0]=0.0;\nnjac[k][1][0]=0.0;\nnjac[k][2][0]=0.0;\nnjac[k][3][0]=0.0;\nnjac[k][4][0]=0.0;\nnjac[k][0][1]=-c3c4*tmp2*u[k][j][i][1];\nnjac[k][1][1]=c3c4*tmp1;\nnjac[k][2][1]=0.0;\nnjac[k][3][1]=0.0;\nnjac[k][4][1]=0.0;\nnjac[k][0][2]=-c3c4*tmp2*u[k][j][i][2];\nnjac[k][1][2]=0.0;\nnjac[k][2][2]=c3c4*tmp1;\nnjac[k][3][2]=0.0;\nnjac[k][4][2]=0.0;\nnjac[k][0][3]=-con43*c3c4*tmp2*u[k][j][i][3];\nnjac[k][1][3]=0.0;\nnjac[k][2][3]=0.0;\nnjac[k][3][3]=con43*c3*c4*tmp1;\nnjac[k][4][3]=0.0;\nnjac[k][0][4]=-(c3c4-c1345)*tmp3*(u[k][j][i][1]*u[k][j][i][1])\n-(c3c4-c1345)*tmp3*(u[k][j][i][2]*u[k][j][i][2])\n-(con43*c3c4-c1345)*tmp3*(u[k][j][i][3]*u[k][j][i][3])\n-c1345*tmp2*u[k][j][i][4];\nnjac[k][1][4]=(c3c4-c1345)*tmp2*u[k][j][i][1];\nnjac[k][2][4]=(c3c4-c1345)*tmp2*u[k][j][i][2];\nnjac[k][3][4]=(con43*c3c4-c1345)*tmp2*u[k][j][i][3];\nnjac[k][4][4]=(c1345)*tmp1;\n}\n\nlhsinit(lhs, ksize);\nfor(k=1; k<=ksize-1; k++){\ntmp1=dt*tz1;\ntmp2=dt*tz2;\nlhs[k][AA][0][0]=-tmp2*fjac[k-1][0][0]\n-tmp1*njac[k-1][0][0]\n-tmp1*dz1;\nlhs[k][AA][1][0]=-tmp2*fjac[k-1][1][0]\n-tmp1*njac[k-1][1][0];\nlhs[k][AA][2][0]=-tmp2*fjac[k-1][2][0]\n-tmp1*njac[k-1][2][0];\nlhs[k][AA][3][0]=-tmp2*fjac[k-1][3][0]\n-tmp1*njac[k-1][3][0];\nlhs[k][AA][4][0]=-tmp2*fjac[k-1][4][0]\n-tmp1*njac[k-1][4][0];\nlhs[k][AA][0][1]=-tmp2*fjac[k-1][0][1]\n-tmp1*njac[k-1][0][1];\nlhs[k][AA][1][1]=-tmp2*fjac[k-1][1][1]\n-tmp1*njac[k-1][1][1]\n-tmp1*dz2;\nlhs[k][AA][2][1]=-tmp2*fjac[k-1][2][1]\n-tmp1*njac[k-1][2][1];\nlhs[k][AA][3][1]=-tmp2*fjac[k-1][3][1]\n-tmp1*njac[k-1][3][1];\nlhs[k][AA][4][1]=-tmp2*fjac[k-1][4][1]\n-tmp1*njac[k-1][4][1];\nlhs[k][AA][0][2]=-tmp2*fjac[k-1][0][2]\n-tmp1*njac[k-1][0][2];\nlhs[k][AA][1][2]=-tmp2*fjac[k-1][1][2]\n-tmp1*njac[k-1][1][2];\nlhs[k][AA][2][2]=-tmp2*fjac[k-1][2][2]\n-tmp1*njac[k-1][2][2]\n-tmp1*dz3;\nlhs[k][AA][3][2]=-tmp2*fjac[k-1][3][2]\n-tmp1*njac[k-1][3][2];\nlhs[k][AA][4][2]=-tmp2*fjac[k-1][4][2]\n-tmp1*njac[k-1][4][2];\nlhs[k][AA][0][3]=-tmp2*fjac[k-1][0][3]\n-tmp1*njac[k-1][0][3];\nlhs[k][AA][1][3]=-tmp2*fjac[k-1][1][3]\n-tmp1*njac[k-1][1][3];\nlhs[k][AA][2][3]=-tmp2*fjac[k-1][2][3]\n-tmp1*njac[k-1][2][3];\nlhs[k][AA][3][3]=-tmp2*fjac[k-1][3][3]\n-tmp1*njac[k-1][3][3]\n-tmp1*dz4;\nlhs[k][AA][4][3]=-tmp2*fjac[k-1][4][3]\n-tmp1*njac[k-1][4][3];\nlhs[k][AA][0][4]=-tmp2*fjac[k-1][0][4]\n-tmp1*njac[k-1][0][4];\nlhs[k][AA][1][4]=-tmp2*fjac[k-1][1][4]\n-tmp1*njac[k-1][1][4];\nlhs[k][AA][2][4]=-tmp2*fjac[k-1][2][4]\n-tmp1*njac[k-1][2][4];\nlhs[k][AA][3][4]=-tmp2*fjac[k-1][3][4]\n-tmp1*njac[k-1][3][4];\nlhs[k][AA][4][4]=-tmp2*fjac[k-1][4][4]\n-tmp1*njac[k-1][4][4]\n-tmp1*dz5;\nlhs[k][BB][0][0]=1.0\n+tmp1*2.0*njac[k][0][0]\n+tmp1*2.0*dz1;\nlhs[k][BB][1][0]=tmp1*2.0*njac[k][1][0];\nlhs[k][BB][2][0]=tmp1*2.0*njac[k][2][0];\nlhs[k][BB][3][0]=tmp1*2.0*njac[k][3][0];\nlhs[k][BB][4][0]=tmp1*2.0*njac[k][4][0];\nlhs[k][BB][0][1]=tmp1*2.0*njac[k][0][1];\nlhs[k][BB][1][1]=1.0\n+tmp1*2.0*njac[k][1][1]\n+tmp1*2.0*dz2;\nlhs[k][BB][2][1]=tmp1*2.0*njac[k][2][1];\nlhs[k][BB][3][1]=tmp1*2.0*njac[k][3][1];\nlhs[k][BB][4][1]=tmp1*2.0*njac[k][4][1];\nlhs[k][BB][0][2]=tmp1*2.0*njac[k][0][2];\nlhs[k][BB][1][2]=tmp1*2.0*njac[k][1][2];\nlhs[k][BB][2][2]=1.0\n+tmp1*2.0*njac[k][2][2]\n+tmp1*2.0*dz3;\nlhs[k][BB][3][2]=tmp1*2.0*njac[k][3][2];\nlhs[k][BB][4][2]=tmp1*2.0*njac[k][4][2];\nlhs[k][BB][0][3]=tmp1*2.0*njac[k][0][3];\nlhs[k][BB][1][3]=tmp1*2.0*njac[k][1][3];\nlhs[k][BB][2][3]=tmp1*2.0*njac[k][2][3];\nlhs[k][BB][3][3]=1.0\n+tmp1*2.0*njac[k][3][3]\n+tmp1*2.0*dz4;\nlhs[k][BB][4][3]=tmp1*2.0*njac[k][4][3];\nlhs[k][BB][0][4]=tmp1*2.0*njac[k][0][4];\nlhs[k][BB][1][4]=tmp1*2.0*njac[k][1][4];\nlhs[k][BB][2][4]=tmp1*2.0*njac[k][2][4];\nlhs[k][BB][3][4]=tmp1*2.0*njac[k][3][4];\nlhs[k][BB][4][4]=1.0\n+tmp1*2.0*njac[k][4][4]\n+tmp1*2.0*dz5;\nlhs[k][CC][0][0]=tmp2*fjac[k+1][0][0]\n-tmp1*njac[k+1][0][0]\n-tmp1*dz1;\nlhs[k][CC][1][0]=tmp2*fjac[k+1][1][0]\n-tmp1*njac[k+1][1][0];\nlhs[k][CC][2][0]=tmp2*fjac[k+1][2][0]\n-tmp1*njac[k+1][2][0];\nlhs[k][CC][3][0]=tmp2*fjac[k+1][3][0]\n-tmp1*njac[k+1][3][0];\nlhs[k][CC][4][0]=tmp2*fjac[k+1][4][0]\n-tmp1*njac[k+1][4][0];\nlhs[k][CC][0][1]=tmp2*fjac[k+1][0][1]\n-tmp1*njac[k+1][0][1];\nlhs[k][CC][1][1]=tmp2*fjac[k+1][1][1]\n-tmp1*njac[k+1][1][1]\n-tmp1*dz2;\nlhs[k][CC][2][1]=tmp2*fjac[k+1][2][1]\n-tmp1*njac[k+1][2][1];\nlhs[k][CC][3][1]=tmp2*fjac[k+1][3][1]\n-tmp1*njac[k+1][3][1];\nlhs[k][CC][4][1]=tmp2*fjac[k+1][4][1]\n-tmp1*njac[k+1][4][1];\nlhs[k][CC][0][2]=tmp2*fjac[k+1][0][2]\n-tmp1*njac[k+1][0][2];\nlhs[k][CC][1][2]= tmp2*fjac[k+1][1][2]\n-tmp1*njac[k+1][1][2];\nlhs[k][CC][2][2]=tmp2*fjac[k+1][2][2]\n-tmp1*njac[k+1][2][2]\n-tmp1*dz3;\nlhs[k][CC][3][2]=tmp2*fjac[k+1][3][2]\n-tmp1*njac[k+1][3][2];\nlhs[k][CC][4][2]=tmp2*fjac[k+1][4][2]\n-tmp1*njac[k+1][4][2];\nlhs[k][CC][0][3]=tmp2*fjac[k+1][0][3]\n-tmp1*njac[k+1][0][3];\nlhs[k][CC][1][3]=tmp2*fjac[k+1][1][3]\n-tmp1*njac[k+1][1][3];\nlhs[k][CC][2][3]=tmp2*fjac[k+1][2][3]\n-tmp1*njac[k+1][2][3];\nlhs[k][CC][3][3]=tmp2*fjac[k+1][3][3]\n-tmp1*njac[k+1][3][3]\n-tmp1*dz4;\nlhs[k][CC][4][3]=tmp2*fjac[k+1][4][3]\n-tmp1*njac[k+1][4][3];\nlhs[k][CC][0][4]=tmp2*fjac[k+1][0][4]\n-tmp1*njac[k+1][0][4];\nlhs[k][CC][1][4]=tmp2*fjac[k+1][1][4]\n-tmp1*njac[k+1][1][4];\nlhs[k][CC][2][4]=tmp2*fjac[k+1][2][4]\n-tmp1*njac[k+1][2][4];\nlhs[k][CC][3][4]=tmp2*fjac[k+1][3][4]\n-tmp1*njac[k+1][3][4];\nlhs[k][CC][4][4]=tmp2*fjac[k+1][4][4]\n-tmp1*njac[k+1][4][4]\n-tmp1*dz5;\n}\n\nbinvcrhs(lhs[0][BB], lhs[0][CC], rhs[0][j][i]);\n\nfor(k=1; k<=ksize-1; k++){\n\nmatvec_sub(lhs[k][AA], rhs[k-1][j][i], rhs[k][j][i]);\n\nmatmul_sub(lhs[k][AA], lhs[k-1][CC], lhs[k][BB]);\n\nbinvcrhs(lhs[k][BB], lhs[k][CC], rhs[k][j][i]);\n}\n\nmatvec_sub(lhs[ksize][AA], rhs[ksize-1][j][i], rhs[ksize][j][i]);\n\nmatmul_sub(lhs[ksize][AA], lhs[ksize-1][CC], lhs[ksize][BB]);\n\nbinvrhs(lhs[ksize][BB], rhs[ksize][j][i]);\n\nfor(k=ksize-1; k>=0; k--){\nfor(m=0; m<BLOCK_SIZE; m++){\nfor(n=0; n<BLOCK_SIZE; n++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[k][CC][n][m]*rhs[k+1][j][i][n];\n}\n}\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_ZSOLVE);}\n}

subroutine z_solve\n\n\n\nuse bt_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, m, n, ksize\ndouble precision tmp1, tmp2, tmp3\n\n\nif (timeron) call timer_start(t_zsolve)\n\n\n\nksize = grid_points(3)-1\n\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo k = 0, ksize\n\ntmp1 = 1.0d+00 / u(1,i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nfjac(1,1,k) = 0.0d+00\nfjac(1,2,k) = 0.0d+00\nfjac(1,3,k) = 0.0d+00\nfjac(1,4,k) = 1.0d+00\nfjac(1,5,k) = 0.0d+00\n\nfjac(2,1,k) = - ( u(2,i,j,k)*u(4,i,j,k) ) &\n& * tmp2\nfjac(2,2,k) = u(4,i,j,k) * tmp1\nfjac(2,3,k) = 0.0d+00\nfjac(2,4,k) = u(2,i,j,k) * tmp1\nfjac(2,5,k) = 0.0d+00\n\nfjac(3,1,k) = - ( u(3,i,j,k)*u(4,i,j,k) ) &\n& * tmp2\nfjac(3,2,k) = 0.0d+00\nfjac(3,3,k) = u(4,i,j,k) * tmp1\nfjac(3,4,k) = u(3,i,j,k) * tmp1\nfjac(3,5,k) = 0.0d+00\n\nfjac(4,1,k) = - (u(4,i,j,k)*u(4,i,j,k) * tmp2 ) &\n& + c2 * qs(i,j,k)\nfjac(4,2,k) = - c2 * u(2,i,j,k) * tmp1\nfjac(4,3,k) = - c2 * u(3,i,j,k) * tmp1\nfjac(4,4,k) = ( 2.0d+00 - c2 ) &\n& * u(4,i,j,k) * tmp1\nfjac(4,5,k) = c2\n\nfjac(5,1,k) = ( c2 * 2.0d0 * square(i,j,k) &\n& - c1 * u(5,i,j,k) ) &\n& * u(4,i,j,k) * tmp2\nfjac(5,2,k) = - c2 * ( u(2,i,j,k)*u(4,i,j,k) ) &\n& * tmp2\nfjac(5,3,k) = - c2 * ( u(3,i,j,k)*u(4,i,j,k) ) &\n& * tmp2\nfjac(5,4,k) = c1 * ( u(5,i,j,k) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j,k) &\n& + u(4,i,j,k)*u(4,i,j,k) * tmp2 )\nfjac(5,5,k) = c1 * u(4,i,j,k) * tmp1\n\nnjac(1,1,k) = 0.0d+00\nnjac(1,2,k) = 0.0d+00\nnjac(1,3,k) = 0.0d+00\nnjac(1,4,k) = 0.0d+00\nnjac(1,5,k) = 0.0d+00\n\nnjac(2,1,k) = - c3c4 * tmp2 * u(2,i,j,k)\nnjac(2,2,k) = c3c4 * tmp1\nnjac(2,3,k) = 0.0d+00\nnjac(2,4,k) = 0.0d+00\nnjac(2,5,k) = 0.0d+00\n\nnjac(3,1,k) = - c3c4 * tmp2 * u(3,i,j,k)\nnjac(3,2,k) = 0.0d+00\nnjac(3,3,k) = c3c4 * tmp1\nnjac(3,4,k) = 0.0d+00\nnjac(3,5,k) = 0.0d+00\n\nnjac(4,1,k) = - con43 * c3c4 * tmp2 * u(4,i,j,k)\nnjac(4,2,k) = 0.0d+00\nnjac(4,3,k) = 0.0d+00\nnjac(4,4,k) = con43 * c3 * c4 * tmp1\nnjac(4,5,k) = 0.0d+00\n\nnjac(5,1,k) = - ( c3c4 &\n& - c1345 ) * tmp3 * (u(2,i,j,k)**2) &\n& - ( c3c4 - c1345 ) * tmp3 * (u(3,i,j,k)**2) &\n& - ( con43 * c3c4 &\n& - c1345 ) * tmp3 * (u(4,i,j,k)**2) &\n& - c1345 * tmp2 * u(5,i,j,k)\n\nnjac(5,2,k) = ( c3c4 - c1345 ) * tmp2 * u(2,i,j,k)\nnjac(5,3,k) = ( c3c4 - c1345 ) * tmp2 * u(3,i,j,k)\nnjac(5,4,k) = ( con43 * c3c4 &\n& - c1345 ) * tmp2 * u(4,i,j,k)\nnjac(5,5,k) = ( c1345 )* tmp1\n\nenddo\n\ncall lhsinit(lhs, ksize)\ndo k = 1, ksize-1\n\ntmp1 = dt * tz1\ntmp2 = dt * tz2\n\nlhs(1,1,aa,k) = - tmp2 * fjac(1,1,k-1) &\n& - tmp1 * njac(1,1,k-1) &\n& - tmp1 * dz1\nlhs(1,2,aa,k) = - tmp2 * fjac(1,2,k-1) &\n& - tmp1 * njac(1,2,k-1)\nlhs(1,3,aa,k) = - tmp2 * fjac(1,3,k-1) &\n& - tmp1 * njac(1,3,k-1)\nlhs(1,4,aa,k) = - tmp2 * fjac(1,4,k-1) &\n& - tmp1 * njac(1,4,k-1)\nlhs(1,5,aa,k) = - tmp2 * fjac(1,5,k-1) &\n& - tmp1 * njac(1,5,k-1)\n\nlhs(2,1,aa,k) = - tmp2 * fjac(2,1,k-1) &\n& - tmp1 * njac(2,1,k-1)\nlhs(2,2,aa,k) = - tmp2 * fjac(2,2,k-1) &\n& - tmp1 * njac(2,2,k-1) &\n& - tmp1 * dz2\nlhs(2,3,aa,k) = - tmp2 * fjac(2,3,k-1) &\n& - tmp1 * njac(2,3,k-1)\nlhs(2,4,aa,k) = - tmp2 * fjac(2,4,k-1) &\n& - tmp1 * njac(2,4,k-1)\nlhs(2,5,aa,k) = - tmp2 * fjac(2,5,k-1) &\n& - tmp1 * njac(2,5,k-1)\n\nlhs(3,1,aa,k) = - tmp2 * fjac(3,1,k-1) &\n& - tmp1 * njac(3,1,k-1)\nlhs(3,2,aa,k) = - tmp2 * fjac(3,2,k-1) &\n& - tmp1 * njac(3,2,k-1)\nlhs(3,3,aa,k) = - tmp2 * fjac(3,3,k-1) &\n& - tmp1 * njac(3,3,k-1) &\n& - tmp1 * dz3\nlhs(3,4,aa,k) = - tmp2 * fjac(3,4,k-1) &\n& - tmp1 * njac(3,4,k-1)\nlhs(3,5,aa,k) = - tmp2 * fjac(3,5,k-1) &\n& - tmp1 * njac(3,5,k-1)\n\nlhs(4,1,aa,k) = - tmp2 * fjac(4,1,k-1) &\n& - tmp1 * njac(4,1,k-1)\nlhs(4,2,aa,k) = - tmp2 * fjac(4,2,k-1) &\n& - tmp1 * njac(4,2,k-1)\nlhs(4,3,aa,k) = - tmp2 * fjac(4,3,k-1) &\n& - tmp1 * njac(4,3,k-1)\nlhs(4,4,aa,k) = - tmp2 * fjac(4,4,k-1) &\n& - tmp1 * njac(4,4,k-1) &\n& - tmp1 * dz4\nlhs(4,5,aa,k) = - tmp2 * fjac(4,5,k-1) &\n& - tmp1 * njac(4,5,k-1)\n\nlhs(5,1,aa,k) = - tmp2 * fjac(5,1,k-1) &\n& - tmp1 * njac(5,1,k-1)\nlhs(5,2,aa,k) = - tmp2 * fjac(5,2,k-1) &\n& - tmp1 * njac(5,2,k-1)\nlhs(5,3,aa,k) = - tmp2 * fjac(5,3,k-1) &\n& - tmp1 * njac(5,3,k-1)\nlhs(5,4,aa,k) = - tmp2 * fjac(5,4,k-1) &\n& - tmp1 * njac(5,4,k-1)\nlhs(5,5,aa,k) = - tmp2 * fjac(5,5,k-1) &\n& - tmp1 * njac(5,5,k-1) &\n& - tmp1 * dz5\n\nlhs(1,1,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(1,1,k) &\n& + tmp1 * 2.0d+00 * dz1\nlhs(1,2,bb,k) = tmp1 * 2.0d+00 * njac(1,2,k)\nlhs(1,3,bb,k) = tmp1 * 2.0d+00 * njac(1,3,k)\nlhs(1,4,bb,k) = tmp1 * 2.0d+00 * njac(1,4,k)\nlhs(1,5,bb,k) = tmp1 * 2.0d+00 * njac(1,5,k)\n\nlhs(2,1,bb,k) = tmp1 * 2.0d+00 * njac(2,1,k)\nlhs(2,2,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(2,2,k) &\n& + tmp1 * 2.0d+00 * dz2\nlhs(2,3,bb,k) = tmp1 * 2.0d+00 * njac(2,3,k)\nlhs(2,4,bb,k) = tmp1 * 2.0d+00 * njac(2,4,k)\nlhs(2,5,bb,k) = tmp1 * 2.0d+00 * njac(2,5,k)\n\nlhs(3,1,bb,k) = tmp1 * 2.0d+00 * njac(3,1,k)\nlhs(3,2,bb,k) = tmp1 * 2.0d+00 * njac(3,2,k)\nlhs(3,3,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(3,3,k) &\n& + tmp1 * 2.0d+00 * dz3\nlhs(3,4,bb,k) = tmp1 * 2.0d+00 * njac(3,4,k)\nlhs(3,5,bb,k) = tmp1 * 2.0d+00 * njac(3,5,k)\n\nlhs(4,1,bb,k) = tmp1 * 2.0d+00 * njac(4,1,k)\nlhs(4,2,bb,k) = tmp1 * 2.0d+00 * njac(4,2,k)\nlhs(4,3,bb,k) = tmp1 * 2.0d+00 * njac(4,3,k)\nlhs(4,4,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(4,4,k) &\n& + tmp1 * 2.0d+00 * dz4\nlhs(4,5,bb,k) = tmp1 * 2.0d+00 * njac(4,5,k)\n\nlhs(5,1,bb,k) = tmp1 * 2.0d+00 * njac(5,1,k)\nlhs(5,2,bb,k) = tmp1 * 2.0d+00 * njac(5,2,k)\nlhs(5,3,bb,k) = tmp1 * 2.0d+00 * njac(5,3,k)\nlhs(5,4,bb,k) = tmp1 * 2.0d+00 * njac(5,4,k)\nlhs(5,5,bb,k) = 1.0d+00 &\n& + tmp1 * 2.0d+00 * njac(5,5,k) &\n& + tmp1 * 2.0d+00 * dz5\n\nlhs(1,1,cc,k) = tmp2 * fjac(1,1,k+1) &\n& - tmp1 * njac(1,1,k+1) &\n& - tmp1 * dz1\nlhs(1,2,cc,k) = tmp2 * fjac(1,2,k+1) &\n& - tmp1 * njac(1,2,k+1)\nlhs(1,3,cc,k) = tmp2 * fjac(1,3,k+1) &\n& - tmp1 * njac(1,3,k+1)\nlhs(1,4,cc,k) = tmp2 * fjac(1,4,k+1) &\n& - tmp1 * njac(1,4,k+1)\nlhs(1,5,cc,k) = tmp2 * fjac(1,5,k+1) &\n& - tmp1 * njac(1,5,k+1)\n\nlhs(2,1,cc,k) = tmp2 * fjac(2,1,k+1) &\n& - tmp1 * njac(2,1,k+1)\nlhs(2,2,cc,k) = tmp2 * fjac(2,2,k+1) &\n& - tmp1 * njac(2,2,k+1) &\n& - tmp1 * dz2\nlhs(2,3,cc,k) = tmp2 * fjac(2,3,k+1) &\n& - tmp1 * njac(2,3,k+1)\nlhs(2,4,cc,k) = tmp2 * fjac(2,4,k+1) &\n& - tmp1 * njac(2,4,k+1)\nlhs(2,5,cc,k) = tmp2 * fjac(2,5,k+1) &\n& - tmp1 * njac(2,5,k+1)\n\nlhs(3,1,cc,k) = tmp2 * fjac(3,1,k+1) &\n& - tmp1 * njac(3,1,k+1)\nlhs(3,2,cc,k) = tmp2 * fjac(3,2,k+1) &\n& - tmp1 * njac(3,2,k+1)\nlhs(3,3,cc,k) = tmp2 * fjac(3,3,k+1) &\n& - tmp1 * njac(3,3,k+1) &\n& - tmp1 * dz3\nlhs(3,4,cc,k) = tmp2 * fjac(3,4,k+1) &\n& - tmp1 * njac(3,4,k+1)\nlhs(3,5,cc,k) = tmp2 * fjac(3,5,k+1) &\n& - tmp1 * njac(3,5,k+1)\n\nlhs(4,1,cc,k) = tmp2 * fjac(4,1,k+1) &\n& - tmp1 * njac(4,1,k+1)\nlhs(4,2,cc,k) = tmp2 * fjac(4,2,k+1) &\n& - tmp1 * njac(4,2,k+1)\nlhs(4,3,cc,k) = tmp2 * fjac(4,3,k+1) &\n& - tmp1 * njac(4,3,k+1)\nlhs(4,4,cc,k) = tmp2 * fjac(4,4,k+1) &\n& - tmp1 * njac(4,4,k+1) &\n& - tmp1 * dz4\nlhs(4,5,cc,k) = tmp2 * fjac(4,5,k+1) &\n& - tmp1 * njac(4,5,k+1)\n\nlhs(5,1,cc,k) = tmp2 * fjac(5,1,k+1) &\n& - tmp1 * njac(5,1,k+1)\nlhs(5,2,cc,k) = tmp2 * fjac(5,2,k+1) &\n& - tmp1 * njac(5,2,k+1)\nlhs(5,3,cc,k) = tmp2 * fjac(5,3,k+1) &\n& - tmp1 * njac(5,3,k+1)\nlhs(5,4,cc,k) = tmp2 * fjac(5,4,k+1) &\n& - tmp1 * njac(5,4,k+1)\nlhs(5,5,cc,k) = tmp2 * fjac(5,5,k+1) &\n& - tmp1 * njac(5,5,k+1) &\n& - tmp1 * dz5\n\nenddo\n\n\n\n\nif (timeron) call timer_start(t_solsub)\ncall binvcrhs( lhs(1,1,bb,0), &\n& lhs(1,1,cc,0), &\n& rhs(1,i,j,0) )\n\n\ndo k=1,ksize-1\n\ncall matvec_sub(lhs(1,1,aa,k), &\n& rhs(1,i,j,k-1),rhs(1,i,j,k))\n\ncall matmul_sub(lhs(1,1,aa,k), &\n& lhs(1,1,cc,k-1), &\n& lhs(1,1,bb,k))\n\ncall binvcrhs( lhs(1,1,bb,k), &\n& lhs(1,1,cc,k), &\n& rhs(1,i,j,k) )\n\nenddo\n\n\ncall matvec_sub(lhs(1,1,aa,ksize), &\n& rhs(1,i,j,ksize-1),rhs(1,i,j,ksize))\n\ncall matmul_sub(lhs(1,1,aa,ksize), &\n& lhs(1,1,cc,ksize-1), &\n& lhs(1,1,bb,ksize))\n\ncall binvrhs( lhs(1,1,bb,ksize), &\n& rhs(1,i,j,ksize) )\nif (timeron) call timer_stop(t_solsub)\n\n\n\n\ndo k=ksize-1,0,-1\ndo m=1,BLOCK_SIZE\ndo n=1,BLOCK_SIZE\nrhs(m,i,j,k) = rhs(m,i,j,k) &\n& - lhs(m,n,cc,k)*rhs(n,i,j,k+1)\nenddo\nenddo\nenddo\n\nenddo\nenddo\nif (timeron) call timer_stop(t_zsolve)\n\nreturn\nend

static void cfftz(int is,\nint m,\nint n,\ndcomplex x[][FFTBLOCKPAD],\ndcomplex y[][FFTBLOCKPAD]){\nint i,j,l,mx;\n\n\nmx = (int)(u[0].real);\nif((is != 1 && is != -1) || m < 1 || m > mx){\nprintf("CFFTZ: Either U has not been initialized, or else\n"\n"one of the input parameters is invalid%5d%5d%5d\n", is, m, mx);\nexit(EXIT_FAILURE);\n}\n\n\nfor(l=1; l<=m; l+=2){\nfftz2(is, l, m, n, FFTBLOCK, FFTBLOCKPAD, u, x, y);\nif(l==m){\n\nfor(j=0; j<n; j++){\nfor(i=0; i<FFTBLOCK; i++){\nx[j][i] = y[j][i];\n}\n}\nbreak;\n}\nfftz2(is, l + 1, m, n, FFTBLOCK, FFTBLOCKPAD, u, y, x);\n}\n}

subroutine cfftz (is, m, n, x, y)\n\n\n\nuse ft_data\nimplicit none\n\ninteger is,m,n,i,j,l,mx\ndouble complex x, y\n\ndimension x(fftblockpad,n), y(fftblockpad,n)\n\nmx = u(1)\nif ((is .ne. 1 .and. is .ne. -1) .or. m .lt. 1 .or. m .gt. mx) &\n& then\nwrite (*, 1) is, m, mx\n1 format ('CFFTZ: Either U has not been initialized, or else'/ &\n& 'one of the input parameters is invalid', 3I5)\nstop\nendif\n\ndo l = 1, m, 2\ncall fftz2 (is, l, m, n, fftblock, fftblockpad, u, x, y)\nif (l .eq. m) goto 160\ncall fftz2 (is, l + 1, m, n, fftblock, fftblockpad, u, y, x)\nenddo\n\ngoto 180\n\n160 do j = 1, n\ndo i = 1, fftblock\nx(i,j) = y(i,j)\nenddo\nenddo\n\n180 continue\n\nreturn\nend

void verify(double xcr[],\ndouble xce[],\ndouble xci,\nchar* class_npb,\nboolean* verified){\ndouble xcrref[5], xceref[5], xciref;\ndouble xcrdif[5], xcedif[5], xcidif;\ndouble epsilon, dtref=0.0;\nint m;\n\nepsilon=1.0e-08;\n*class_npb='U';\n*verified=TRUE;\nfor(m=0; m<5; m++){\nxcrref[m]=1.0;\nxceref[m]=1.0;\n}\nxciref=1.0;\nif((nx0==12)&&(ny0==12)&&(nz0==12)&&(itmax==50)){\n*class_npb='S';\ndtref=5.0e-1;\n\nxcrref[0]=1.6196343210976702e-02;\nxcrref[1]=2.1976745164821318e-03;\nxcrref[2]=1.5179927653399185e-03;\nxcrref[3]=1.5029584435994323e-03;\nxcrref[4]=3.4264073155896461e-02;\n\nxceref[0]=6.4223319957960924e-04;\nxceref[1]=8.4144342047347926e-05;\nxceref[2]=5.8588269616485186e-05;\nxceref[3]=5.8474222595157350e-05;\nxceref[4]=1.3103347914111294e-03;\n\nxciref=7.8418928865937083e+00;\n}else if((nx0==33)&&(ny0==33)&&(nz0==33)&&(itmax==300)){\n*class_npb='W'; \ndtref=1.5e-3;\n\nxcrref[0]=0.1236511638192e+02;\nxcrref[1]=0.1317228477799e+01;\nxcrref[2]=0.2550120713095e+01;\nxcrref[3]=0.2326187750252e+01;\nxcrref[4]=0.2826799444189e+02;\n\nxceref[0]=0.4867877144216e+00;\nxceref[1]=0.5064652880982e-01;\nxceref[2]=0.9281818101960e-01;\nxceref[3]=0.8570126542733e-01;\nxceref[4]=0.1084277417792e+01;\n\nxciref=0.1161399311023e+02;\n}else if((nx0==64)&&(ny0==64)&&(nz0==64)&&(itmax==250)){\n*class_npb='A';\ndtref=2.0e+0;\n\nxcrref[0]=7.7902107606689367e+02;\nxcrref[1]=6.3402765259692870e+01;\nxcrref[2]=1.9499249727292479e+02;\nxcrref[3]=1.7845301160418537e+02;\nxcrref[4]=1.8384760349464247e+03;\n\nxceref[0]=2.9964085685471943e+01;\nxceref[1]=2.8194576365003349e+00;\nxceref[2]=7.3473412698774742e+00;\nxceref[3]=6.7139225687777051e+00;\nxceref[4]=7.0715315688392578e+01;\n\nxciref=2.6030925604886277e+01;\n}else if((nx0==102)&&(ny0==102)&&(nz0==102)&&(itmax==250)){\n*class_npb='B';\ndtref=2.0e+0;\n\nxcrref[0]=3.5532672969982736e+03;\nxcrref[1]=2.6214750795310692e+02;\nxcrref[2]=8.8333721850952190e+02;\nxcrref[3]=7.7812774739425265e+02;\nxcrref[4]=7.3087969592545314e+03;\n\nxceref[0]=1.1401176380212709e+02;\nxceref[1]=8.1098963655421574e+00;\nxceref[2]=2.8480597317698308e+01;\nxceref[3]=2.5905394567832939e+01;\nxceref[4]=2.6054907504857413e+02;\n\nxciref=4.7887162703308227e+01;\n}else if((nx0==162)&&(ny0==162)&&(nz0==162)&&(itmax==250)){\n*class_npb='C';\ndtref=2.0e+0;\n\nxcrref[0]=1.03766980323537846e+04;\nxcrref[1]=8.92212458801008552e+02;\nxcrref[2]=2.56238814582660871e+03;\nxcrref[3]=2.19194343857831427e+03;\nxcrref[4]=1.78078057261061185e+04;\n\nxceref[0]=2.15986399716949279e+02;\nxceref[1]=1.55789559239863600e+01;\nxceref[2]=5.41318863077207766e+01;\nxceref[3]=4.82262643154045421e+01;\nxceref[4]=4.55902910043250358e+02;\n\nxciref=6.66404553572181300e+01;\n\nxciref=6.66404553572181300e+01;\n}else if((nx0==408)&&(ny0==408)&&(nz0==408)&&(itmax== 300)){\n*class_npb='D';\ndtref=1.0e+0;\n\nxcrref[0]=0.4868417937025e+05;\nxcrref[1]=0.4696371050071e+04;\nxcrref[2]=0.1218114549776e+05;\nxcrref[3]=0.1033801493461e+05;\nxcrref[4]=0.7142398413817e+05;\n\nxceref[0]=0.3752393004482e+03;\nxceref[1]=0.3084128893659e+02;\nxceref[2]=0.9434276905469e+02;\nxceref[3]=0.8230686681928e+02;\nxceref[4]=0.7002620636210e+03;\n\nxciref=0.8334101392503e+02;\n}else if((nx0==1020)&&(ny0==1020)&&(nz0==1020)&&(itmax==300)){\n*class_npb='E';\ndtref=0.5e+0;\n\nxcrref[0]=0.2099641687874e+06;\nxcrref[1]=0.2130403143165e+05;\nxcrref[2]=0.5319228789371e+05;\nxcrref[3]=0.4509761639833e+05;\nxcrref[4]=0.2932360006590e+06;\n\nxceref[0]=0.4800572578333e+03;\nxceref[1]=0.4221993400184e+02;\nxceref[2]=0.1210851906824e+03;\nxceref[3]=0.1047888986770e+03;\nxceref[4]=0.8363028257389e+03;\n\nxciref=0.9512163272273e+02;\n}else{\n*verified=FALSE;\n}\n\nfor(m=0; m<5; m++){\nxcrdif[m]=fabs((xcr[m]-xcrref[m])/xcrref[m]);\nxcedif[m]=fabs((xce[m]-xceref[m])/xceref[m]);\n}\nxcidif=fabs((xci-xciref)/xciref);\n\nif(*class_npb!='U'){\nprintf("\nVerification being performed for class_npb %c\n",*class_npb);\nprintf(" Accuracy setting for epsilon = %20.13E\n",epsilon);\n*verified=(fabs(dt-dtref)<=epsilon);\nif(!(*verified)){\n*class_npb='U';\nprintf(" DT does not match the reference value of %15.8E\n",dtref);\n}\n}else{\nprintf(" Unknown class_npb\n");\n}\nif(*class_npb!='U'){\nprintf(" Comparison of RMS-norms of residual\n");\n}else{\nprintf(" RMS-norms of residual\n");\n}\nfor(m=0; m<5; m++){\nif(*class_npb=='U'){\nprintf(" %2d %20.13E\n",m+1,xcr[m]);\n}else if(xcrdif[m]<=epsilon){\nprintf(" %2d %20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}else{\n*verified=FALSE;\nprintf(" FAILURE: %2d %20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}\n}\nif(*class_npb!='U'){\nprintf(" Comparison of RMS-norms of solution error\n");\n}else{\nprintf(" RMS-norms of solution error\n");\n}\nfor(m=0; m<5; m++){\nif(*class_npb=='U'){\nprintf(" %2d %20.13E\n",m+1,xce[m]);\n}else if(xcedif[m]<=epsilon){\nprintf(" %2d %20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}else{\n*verified=FALSE;\nprintf(" FAILURE: %2d %20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}\n}\nif(*class_npb!='U'){\nprintf(" Comparison of surface integral\n");\n}else{\nprintf(" Surface integral\n");\n}\nif(*class_npb=='U'){\nprintf(" %20.13E\n",xci);\n}else if(xcidif<=epsilon){\nprintf(" %20.13E%20.13E%20.13E\n",xci,xciref,xcidif);\n}else{\n*verified=FALSE;\nprintf(" FAILURE: %20.13E%20.13E%20.13E\n",xci,xciref,xcidif);\n}\nif(*class_npb=='U'){\nprintf(" No reference values provided\n");\nprintf("No verification performed\n");\n}else if(*verified){\nprintf(" Verification Successful\n");\n}else{\nprintf(" Verification failed\n");\n}\n}

subroutine verify(xcr, xce, xci, class, verified)\n\n\n\nuse, intrinsic :: ieee_arithmetic, only : ieee_is_nan\n\nuse lu_data\n\nimplicit none\n\ndouble precision xcr(5), xce(5), xci\ndouble precision xcrref(5),xceref(5),xciref, &\n& xcrdif(5),xcedif(5),xcidif, &\n& epsilon, dtref\ninteger m\ncharacter class\nlogical verified\n\nepsilon = 1.0d-08\n\nclass = 'U'\nverified = .true.\n\ndo m = 1,5\nxcrref(m) = 1.0\nxceref(m) = 1.0\nend do\nxciref = 1.0\n\nif ( (nx0 .eq. 12 ) .and. &\n& (ny0 .eq. 12 ) .and. &\n& (nz0 .eq. 12 ) .and. &\n& (itmax .eq. 50 )) then\n\nclass = 'S'\ndtref = 5.0d-1\nxcrref(1) = 1.6196343210976702d-02\nxcrref(2) = 2.1976745164821318d-03\nxcrref(3) = 1.5179927653399185d-03\nxcrref(4) = 1.5029584435994323d-03\nxcrref(5) = 3.4264073155896461d-02\n\nxceref(1) = 6.4223319957960924d-04\nxceref(2) = 8.4144342047347926d-05\nxceref(3) = 5.8588269616485186d-05\nxceref(4) = 5.8474222595157350d-05\nxceref(5) = 1.3103347914111294d-03\n\nxciref = 7.8418928865937083d+00\n\n\nelseif ( (nx0 .eq. 33) .and. &\n& (ny0 .eq. 33) .and. &\n& (nz0 .eq. 33) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'W' !SPEC95fp size\ndtref = 1.5d-3\nxcrref(1) = 0.1236511638192d+02\nxcrref(2) = 0.1317228477799d+01\nxcrref(3) = 0.2550120713095d+01\nxcrref(4) = 0.2326187750252d+01\nxcrref(5) = 0.2826799444189d+02\n\n\nxceref(1) = 0.4867877144216d+00\nxceref(2) = 0.5064652880982d-01\nxceref(3) = 0.9281818101960d-01\nxceref(4) = 0.8570126542733d-01\nxceref(5) = 0.1084277417792d+01\n\n\nxciref = 0.1161399311023d+02\n\nelseif ( (nx0 .eq. 64) .and. &\n& (ny0 .eq. 64) .and. &\n& (nz0 .eq. 64) .and. &\n& (itmax .eq. 250) ) then\n\nclass = 'A'\ndtref = 2.0d+0\nxcrref(1) = 7.7902107606689367d+02\nxcrref(2) = 6.3402765259692870d+01\nxcrref(3) = 1.9499249727292479d+02\nxcrref(4) = 1.7845301160418537d+02\nxcrref(5) = 1.8384760349464247d+03\n\nxceref(1) = 2.9964085685471943d+01\nxceref(2) = 2.8194576365003349d+00\nxceref(3) = 7.3473412698774742d+00\nxceref(4) = 6.7139225687777051d+00\nxceref(5) = 7.0715315688392578d+01\n\nxciref = 2.6030925604886277d+01\n\n\nelseif ( (nx0 .eq. 102) .and. &\n& (ny0 .eq. 102) .and. &\n& (nz0 .eq. 102) .and. &\n& (itmax .eq. 250) ) then\n\nclass = 'B'\ndtref = 2.0d+0\n\nxcrref(1) = 3.5532672969982736d+03\nxcrref(2) = 2.6214750795310692d+02\nxcrref(3) = 8.8333721850952190d+02\nxcrref(4) = 7.7812774739425265d+02\nxcrref(5) = 7.3087969592545314d+03\n\nxceref(1) = 1.1401176380212709d+02\nxceref(2) = 8.1098963655421574d+00\nxceref(3) = 2.8480597317698308d+01\nxceref(4) = 2.5905394567832939d+01\nxceref(5) = 2.6054907504857413d+02\n\nxciref = 4.7887162703308227d+01\n\nelseif ( (nx0 .eq. 162) .and. &\n& (ny0 .eq. 162) .and. &\n& (nz0 .eq. 162) .and. &\n& (itmax .eq. 250) ) then\n\nclass = 'C'\ndtref = 2.0d+0\n\nxcrref(1) = 1.03766980323537846d+04\nxcrref(2) = 8.92212458801008552d+02\nxcrref(3) = 2.56238814582660871d+03\nxcrref(4) = 2.19194343857831427d+03\nxcrref(5) = 1.78078057261061185d+04\n\nxceref(1) = 2.15986399716949279d+02\nxceref(2) = 1.55789559239863600d+01\nxceref(3) = 5.41318863077207766d+01\nxceref(4) = 4.82262643154045421d+01\nxceref(5) = 4.55902910043250358d+02\n\nxciref = 6.66404553572181300d+01\n\nxciref = 6.66404553572181300d+01\n\nelseif ( (nx0 .eq. 408) .and. &\n& (ny0 .eq. 408) .and. &\n& (nz0 .eq. 408) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'D'\ndtref = 1.0d+0\n\nxcrref(1) = 0.4868417937025d+05\nxcrref(2) = 0.4696371050071d+04\nxcrref(3) = 0.1218114549776d+05\nxcrref(4) = 0.1033801493461d+05\nxcrref(5) = 0.7142398413817d+05\n\nxceref(1) = 0.3752393004482d+03\nxceref(2) = 0.3084128893659d+02\nxceref(3) = 0.9434276905469d+02\nxceref(4) = 0.8230686681928d+02\nxceref(5) = 0.7002620636210d+03\n\nxciref = 0.8334101392503d+02\n\nelseif ( (nx0 .eq. 1020) .and. &\n& (ny0 .eq. 1020) .and. &\n& (nz0 .eq. 1020) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'E'\ndtref = 0.5d+0\n\nxcrref(1) = 0.2099641687874d+06\nxcrref(2) = 0.2130403143165d+05\nxcrref(3) = 0.5319228789371d+05\nxcrref(4) = 0.4509761639833d+05\nxcrref(5) = 0.2932360006590d+06\n\nxceref(1) = 0.4800572578333d+03\nxceref(2) = 0.4221993400184d+02\nxceref(3) = 0.1210851906824d+03\nxceref(4) = 0.1047888986770d+03\nxceref(5) = 0.8363028257389d+03\n\nxciref = 0.9512163272273d+02\n\nelseif ( (nx0 .eq. 2560) .and. &\n& (ny0 .eq. 2560) .and. &\n& (nz0 .eq. 2560) .and. &\n& (itmax .eq. 300) ) then\n\nclass = 'F'\ndtref = 0.2d+0\n\nxcrref(1) = 0.8505125358152d+06\nxcrref(2) = 0.8774655318044d+05\nxcrref(3) = 0.2167258198851d+06\nxcrref(4) = 0.1838245257371d+06\nxcrref(5) = 0.1175556512415d+07\n\nxceref(1) = 0.5293914132486d+03\nxceref(2) = 0.4784861621068d+02\nxceref(3) = 0.1337701281659d+03\nxceref(4) = 0.1154215049655d+03\nxceref(5) = 0.8956266851467d+03\n\nxciref = 0.1002509436546d+03\n\nelse\nverified = .FALSE.\nendif\n\n\ndo m = 1, 5\n\nxcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))\nxcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))\n\nenddo\nxcidif = dabs((xci - xciref)/xciref)\n\n\n\nif (class .ne. 'U') then\nwrite(*, 1990) class\n1990 format(/, ' Verification being performed for class ', a)\nwrite (*,2000) epsilon\n2000 format(' Accuracy setting for epsilon = ', E20.13)\nverified = (dabs(dt-dtref) .le. epsilon)\nif (.not.verified) then\nclass = 'U'\nwrite (*,1000) dtref\n1000 format(' DT does not match the reference value of ', &\n& E15.8)\nendif\nelse\nwrite(*, 1995)\n1995 format(' Unknown class')\nendif\n\n\nif (class .ne. 'U') then\nwrite (*, 2001)\nelse\nwrite (*, 2005)\nendif\n\n2001 format(' Comparison of RMS-norms of residual')\n2005 format(' RMS-norms of residual')\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(*, 2015) m, xcr(m)\nelse if ((.not.ieee_is_nan(xcrdif(m))) .and. &\n& xcrdif(m) .le. epsilon) then\nwrite (*,2011) m,xcr(m),xcrref(m),xcrdif(m)\nelse\nverified = .false.\nwrite (*,2010) m,xcr(m),xcrref(m),xcrdif(m)\nendif\nenddo\n\nif (class .ne. 'U') then\nwrite (*,2002)\nelse\nwrite (*,2006)\nendif\n2002 format(' Comparison of RMS-norms of solution error')\n2006 format(' RMS-norms of solution error')\n\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(*, 2015) m, xce(m)\nelse if ((.not.ieee_is_nan(xcedif(m))) .and. &\n& xcedif(m) .le. epsilon) then\nwrite (*,2011) m,xce(m),xceref(m),xcedif(m)\nelse\nverified = .false.\nwrite (*,2010) m,xce(m),xceref(m),xcedif(m)\nendif\nenddo\n\n2010 format(' FAILURE: ', i2, 2x, E20.13, E20.13, E20.13)\n2011 format(' ', i2, 2x, E20.13, E20.13, E20.13)\n2015 format(' ', i2, 2x, E20.13)\n\nif (class .ne. 'U') then\nwrite (*,2025)\nelse\nwrite (*,2026)\nendif\n2025 format(' Comparison of surface integral')\n2026 format(' Surface integral')\n\n\nif (class .eq. 'U') then\nwrite(*, 2030) xci\nelse if ((.not.ieee_is_nan(xcidif)) .and. &\n& xcidif .le. epsilon) then\nwrite(*, 2032) xci, xciref, xcidif\nelse\nverified = .false.\nwrite(*, 2031) xci, xciref, xcidif\nendif\n\n2030 format(' ', 4x, E20.13)\n2031 format(' FAILURE: ', 4x, E20.13, E20.13, E20.13)\n2032 format(' ', 4x, E20.13, E20.13, E20.13)\n\n\n\nif (class .eq. 'U') then\nwrite(*, 2022)\nwrite(*, 2023)\n2022 format(' No reference values provided')\n2023 format(' No verification performed')\nelse if (verified) then\nwrite(*, 2020)\n2020 format(' Verification Successful')\nelse\nwrite(*, 2021)\n2021 format(' Verification failed')\nendif\n\nreturn\n\n\nend

static void ipow46(double a,\nint exponent,\ndouble* result){\ndouble q, r;\nint n, n2;\n\n\n*result = 1;\nif(exponent==0){return;}\nq = a;\nr = 1;\nn = exponent;\n\nwhile(n > 1){\nn2 = n/2;\nif(n2*2==n){\nrandlc(&q, q);\nn = n2;\n}else{\nrandlc(&r, q);\nn = n-1;\n}\n}\nrandlc(&r, q);\n*result = r;\n}\n\nstatic void print_timers(){\nint i;\ndouble t, t_m;\nchar* tstrings[T_MAX+1];\ntstrings[1] = (char*)" total ";\ntstrings[2] = (char*)" setup ";\ntstrings[3] = (char*)" fft ";\ntstrings[4] = (char*)" evolve ";\ntstrings[5] = (char*)" checksum ";\ntstrings[6] = (char*)" fftx ";\ntstrings[7] = (char*)" ffty ";\ntstrings[8] = (char*)" fftz ";\n\nt_m = timer_read(T_TOTAL);\nif(t_m <= 0.0){t_m = 1.00;}\nfor(i = 1; i <= T_MAX; i++){\nt = timer_read(i);\nprintf(" timer %2d(%16s) :%9.4f (%6.2f%%)\n",\ni, tstrings[i], t, t*100.0/t_m);\n}\n}\n\nstatic void setup(){\nFILE* fp;\ndebug = FALSE;\n\nif((fp = fopen("timer.flag", "r")) != NULL){\ntimers_enabled = TRUE;\nfclose(fp);\n}else{\ntimers_enabled = FALSE;\n}\n\nniter = NITER_DEFAULT;\n\nprintf("\n\nNAS Parallel Benchmarks 4.1 Parallel C++ version with OpenMP - FT Benchmark\n\n");\nprintf(" Size : %4dx%4dx%4d\n", NX, NY, NZ);\nprintf(" Iterations :%7d\n", niter);\nprintf("\n");\n\ndims[0] = NX;\ndims[1] = NY;\ndims[2] = NZ;\n\n\n\n\n\n\n}

subroutine ipow46(a, exponent, result)\n\n\n\nimplicit none\ndouble precision a, result, dummy, q, r\ninteger exponent, n, n2\nexternal randlc\ndouble precision randlc\nresult = 1\nif (exponent .eq. 0) return\nq = a\nr = 1\nn = exponent\n\n\ndo while (n .gt. 1)\nn2 = n/2\nif (n2 * 2 .eq. n) then\ndummy = randlc(q, q)\nn = n2\nelse\ndummy = randlc(r, q)\nn = n-1\nendif\nend do\ndummy = randlc(r, q)\nresult = r\nreturn\nend

void jacld(int k){\n\nint i, j;\ndouble r43;\ndouble c1345;\ndouble c34;\ndouble tmp1, tmp2, tmp3;\nr43=(4.0/3.0);\nc1345=C1*C3*C4*C5;\nc34=C3*C4;\n\n#pragma omp for nowait schedule(static)\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\n\ntmp1=rho_i[k][j][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nd[j][i][0][0]=1.0+dt*2.0*(tx1*dx1+ty1*dy1+tz1*dz1);\nd[j][i][1][0]=0.0;\nd[j][i][2][0]=0.0;\nd[j][i][3][0]=0.0;\nd[j][i][4][0]=0.0;\nd[j][i][0][1]=-dt*2.0\n*(tx1*r43+ty1+tz1)*c34*tmp2*u[k][j][i][1];\nd[j][i][1][1]=1.0\n+dt*2.0*c34*tmp1*(tx1*r43+ty1+tz1)\n+dt*2.0*(tx1*dx2+ty1*dy2+tz1*dz2);\nd[j][i][2][1]=0.0;\nd[j][i][3][1]=0.0;\nd[j][i][4][1]=0.0;\nd[j][i][0][2]=-dt*2.0\n*(tx1+ty1*r43+tz1)*c34*tmp2*u[k][j][i][2];\nd[j][i][1][2]=0.0;\nd[j][i][2][2]=1.0\n+dt*2.0*c34*tmp1*(tx1+ty1*r43+tz1)\n+dt*2.0*(tx1*dx3+ty1*dy3+tz1*dz3);\nd[j][i][3][2]=0.0;\nd[j][i][4][2]=0.0;\nd[j][i][0][3]=-dt*2.0\n*(tx1+ty1+tz1*r43)*c34*tmp2*u[k][j][i][3];\nd[j][i][1][3]=0.0;\nd[j][i][2][3]=0.0;\nd[j][i][3][3]=1.0\n+dt*2.0*c34*tmp1*(tx1+ty1+tz1*r43)\n+dt*2.0*(tx1*dx4+ty1*dy4+tz1*dz4);\nd[j][i][4][3]=0.0;\nd[j][i][0][4]=-dt*2.0\n*(((tx1*(r43*c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(c34-c1345))*(u[k][j][i][1]*u[k][j][i][1])\n+(tx1*(c34-c1345)\n+ty1*(r43*c34-c1345)\n+tz1*(c34-c1345))*(u[k][j][i][2]*u[k][j][i][2])\n+(tx1*(c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(r43*c34-c1345))*(u[k][j][i][3]*u[k][j][i][3])\n)*tmp3\n+(tx1+ty1+tz1)*c1345*tmp2*u[k][j][i][4]);\nd[j][i][1][4]=dt*2.0*tmp2*u[k][j][i][1]\n*(tx1*(r43*c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(c34-c1345));\nd[j][i][2][4]=dt*2.0*tmp2*u[k][j][i][2]\n*(tx1*(c34-c1345)\n+ty1*(r43*c34-c1345)\n+tz1*(c34-c1345));\nd[j][i][3][4]=dt*2.0*tmp2*u[k][j][i][3]\n*(tx1*(c34-c1345)\n+ty1*(c34-c1345)\n+tz1*(r43*c34-c1345));\nd[j][i][4][4]=1.0\n+dt*2.0*(tx1+ty1+tz1)*c1345*tmp1\n+dt*2.0*(tx1*dx5+ty1*dy5+tz1*dz5);\n\ntmp1=rho_i[k-1][j][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\na[j][i][0][0]=-dt*tz1*dz1;\na[j][i][1][0]=0.0;\na[j][i][2][0]=0.0;\na[j][i][3][0]=-dt*tz2;\na[j][i][4][0]=0.0;\na[j][i][0][1]=-dt*tz2\n*(-(u[k-1][j][i][1]*u[k-1][j][i][3])*tmp2)\n-dt*tz1*(-c34*tmp2*u[k-1][j][i][1]);\na[j][i][1][1]=-dt*tz2*(u[k-1][j][i][3]*tmp1)\n-dt*tz1*c34*tmp1\n-dt*tz1*dz2;\na[j][i][2][1]=0.0;\na[j][i][3][1]=-dt*tz2*(u[k-1][j][i][1]*tmp1);\na[j][i][4][1]=0.0;\na[j][i][0][2]=-dt*tz2\n*(-(u[k-1][j][i][2]*u[k-1][j][i][3])*tmp2)\n-dt*tz1*(-c34*tmp2*u[k-1][j][i][2]);\na[j][i][1][2]=0.0;\na[j][i][2][2]=-dt*tz2*(u[k-1][j][i][3]*tmp1)\n-dt*tz1*(c34*tmp1)\n-dt*tz1*dz3;\na[j][i][3][2]=-dt*tz2*(u[k-1][j][i][2]*tmp1);\na[j][i][4][2]=0.0;\na[j][i][0][3]=-dt*tz2\n*(-(u[k-1][j][i][3]*tmp1)*(u[k-1][j][i][3]*tmp1)\n+C2*qs[k-1][j][i]*tmp1)\n-dt*tz1*(-r43*c34*tmp2*u[k-1][j][i][3]);\na[j][i][1][3]=-dt*tz2\n*(-C2*(u[k-1][j][i][1]*tmp1));\na[j][i][2][3]=-dt*tz2\n*(-C2*(u[k-1][j][i][2]*tmp1));\na[j][i][3][3]=-dt*tz2*(2.0-C2)\n*(u[k-1][j][i][3]*tmp1)\n-dt*tz1*(r43*c34*tmp1)\n-dt*tz1*dz4;\na[j][i][4][3]=-dt*tz2*C2;\na[j][i][0][4]=-dt*tz2\n*((C2*2.0*qs[k-1][j][i]-C1*u[k-1][j][i][4])\n*u[k-1][j][i][3]*tmp2)\n-dt*tz1\n*(-(c34-c1345)*tmp3*(u[k-1][j][i][1]*u[k-1][j][i][1])\n-(c34-c1345)*tmp3*(u[k-1][j][i][2]*u[k-1][j][i][2])\n-(r43*c34-c1345)*tmp3*(u[k-1][j][i][3]*u[k-1][j][i][3])\n-c1345*tmp2*u[k-1][j][i][4]);\na[j][i][1][4]=-dt*tz2\n*(-C2*(u[k-1][j][i][1]*u[k-1][j][i][3])*tmp2)\n-dt*tz1*(c34-c1345)*tmp2*u[k-1][j][i][1];\na[j][i][2][4]=-dt*tz2\n*(-C2*(u[k-1][j][i][2]*u[k-1][j][i][3])*tmp2)\n-dt*tz1*(c34-c1345)*tmp2*u[k-1][j][i][2];\na[j][i][3][4]=-dt*tz2\n*(C1*(u[k-1][j][i][4]*tmp1)\n-C2*(qs[k-1][j][i]*tmp1\n+u[k-1][j][i][3]*u[k-1][j][i][3]*tmp2))\n-dt*tz1*(r43*c34-c1345)*tmp2*u[k-1][j][i][3];\na[j][i][4][4]=-dt*tz2\n*(C1*(u[k-1][j][i][3]*tmp1))\n-dt*tz1*c1345*tmp1\n-dt*tz1*dz5;\n\ntmp1=rho_i[k][j-1][i];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nb[j][i][0][0]=-dt*ty1*dy1;\nb[j][i][1][0]=0.0;\nb[j][i][2][0]=-dt*ty2;\nb[j][i][3][0]=0.0;\nb[j][i][4][0]=0.0;\nb[j][i][0][1]=-dt*ty2\n*(-(u[k][j-1][i][1]*u[k][j-1][i][2])*tmp2)\n-dt*ty1*(-c34*tmp2*u[k][j-1][i][1]);\nb[j][i][1][1]=-dt*ty2*(u[k][j-1][i][2]*tmp1)\n-dt*ty1*(c34*tmp1)\n-dt*ty1*dy2;\nb[j][i][2][1]=-dt*ty2*(u[k][j-1][i][1]*tmp1);\nb[j][i][3][1]=0.0;\nb[j][i][4][1]=0.0;\nb[j][i][0][2]=-dt*ty2\n*(-(u[k][j-1][i][2]*tmp1)*(u[k][j-1][i][2]*tmp1)\n+C2*(qs[k][j-1][i]*tmp1))\n-dt*ty1*(-r43*c34*tmp2*u[k][j-1][i][2]);\nb[j][i][1][2]=-dt*ty2\n*(-C2*(u[k][j-1][i][1]*tmp1));\nb[j][i][2][2]=-dt*ty2*((2.0-C2)*(u[k][j-1][i][2]*tmp1))\n-dt*ty1*(r43*c34*tmp1)\n-dt*ty1*dy3;\nb[j][i][3][2]=-dt*ty2*(-C2*(u[k][j-1][i][3]*tmp1));\nb[j][i][4][2]=-dt*ty2*C2;\nb[j][i][0][3]=-dt*ty2\n*(-(u[k][j-1][i][2]*u[k][j-1][i][3])*tmp2)\n-dt*ty1*(-c34*tmp2*u[k][j-1][i][3]);\nb[j][i][1][3]=0.0;\nb[j][i][2][3]=-dt*ty2*(u[k][j-1][i][3]*tmp1);\nb[j][i][3][3]=-dt*ty2*(u[k][j-1][i][2]*tmp1)\n-dt*ty1*(c34*tmp1)\n-dt*ty1*dy4;\nb[j][i][4][3]=0.0;\nb[j][i][0][4]=-dt*ty2\n*((C2*2.0*qs[k][j-1][i]-C1*u[k][j-1][i][4])\n*(u[k][j-1][i][2]*tmp2))\n-dt*ty1\n*(-(c34-c1345)*tmp3*(u[k][j-1][i][1]*u[k][j-1][i][1])\n-(r43*c34-c1345)*tmp3*(u[k][j-1][i][2]*u[k][j-1][i][2])\n-(c34-c1345)*tmp3*(u[k][j-1][i][3]*u[k][j-1][i][3])\n-c1345*tmp2*u[k][j-1][i][4]);\nb[j][i][1][4]=-dt*ty2\n*(-C2*(u[k][j-1][i][1]*u[k][j-1][i][2])*tmp2)\n-dt*ty1*(c34-c1345)*tmp2*u[k][j-1][i][1];\nb[j][i][2][4]=-dt*ty2\n*(C1*(u[k][j-1][i][4]*tmp1)\n-C2*(qs[k][j-1][i]*tmp1\n+u[k][j-1][i][2]*u[k][j-1][i][2]*tmp2))\n-dt*ty1*(r43*c34-c1345)*tmp2*u[k][j-1][i][2];\nb[j][i][3][4]=-dt*ty2\n*(-C2*(u[k][j-1][i][2]*u[k][j-1][i][3])*tmp2)\n-dt*ty1*(c34-c1345)*tmp2*u[k][j-1][i][3];\nb[j][i][4][4]=-dt*ty2\n*(C1*(u[k][j-1][i][2]*tmp1))\n-dt*ty1*c1345*tmp1\n-dt*ty1*dy5;\n\ntmp1=rho_i[k][j][i-1];\ntmp2=tmp1*tmp1;\ntmp3=tmp1*tmp2;\nc[j][i][0][0]=-dt*tx1*dx1;\nc[j][i][1][0]=-dt*tx2;\nc[j][i][2][0]=0.0;\nc[j][i][3][0]=0.0;\nc[j][i][4][0]=0.0;\nc[j][i][0][1]=-dt*tx2\n*(-(u[k][j][i-1][1]*tmp1)*(u[k][j][i-1][1]*tmp1)\n+C2*qs[k][j][i-1]*tmp1)\n-dt*tx1*(-r43*c34*tmp2*u[k][j][i-1][1]);\nc[j][i][1][1]=-dt*tx2\n*((2.0-C2)*(u[k][j][i-1][1]*tmp1))\n-dt*tx1*(r43*c34*tmp1)\n-dt*tx1*dx2;\nc[j][i][2][1]=-dt*tx2\n*(-C2*(u[k][j][i-1][2]*tmp1));\nc[j][i][3][1]=-dt*tx2\n*(-C2*(u[k][j][i-1][3]*tmp1));\nc[j][i][4][1]=-dt*tx2*C2;\nc[j][i][0][2]=-dt*tx2\n*(-(u[k][j][i-1][1]*u[k][j][i-1][2])*tmp2)\n-dt*tx1*(-c34*tmp2*u[k][j][i-1][2]);\nc[j][i][1][2]=-dt*tx2*(u[k][j][i-1][2]*tmp1);\nc[j][i][2][2]=-dt*tx2*(u[k][j][i-1][1]*tmp1)\n-dt*tx1*(c34*tmp1)\n-dt*tx1*dx3;\nc[j][i][3][2]=0.0;\nc[j][i][4][2]=0.0;\nc[j][i][0][3]=-dt*tx2\n*(-(u[k][j][i-1][1]*u[k][j][i-1][3])*tmp2)\n-dt*tx1*(-c34*tmp2*u[k][j][i-1][3]);\nc[j][i][1][3]=-dt*tx2*(u[k][j][i-1][3]*tmp1);\nc[j][i][2][3]=0.0;\nc[j][i][3][3]=-dt*tx2*(u[k][j][i-1][1]*tmp1)\n-dt*tx1*(c34*tmp1)-dt*tx1*dx4;\nc[j][i][4][3]=0.0;\nc[j][i][0][4]=-dt*tx2\n*((C2*2.0*qs[k][j][i-1]-C1*u[k][j][i-1][4])\n*u[k][j][i-1][1]*tmp2)\n-dt*tx1\n*(-(r43*c34-c1345)*tmp3*(u[k][j][i-1][1]*u[k][j][i-1][1])\n-(c34-c1345)*tmp3*(u[k][j][i-1][2]*u[k][j][i-1][2])\n-(c34-c1345)*tmp3*(u[k][j][i-1][3]*u[k][j][i-1][3])\n-c1345*tmp2*u[k][j][i-1][4]);\nc[j][i][1][4]=-dt*tx2\n*(C1*(u[k][j][i-1][4]*tmp1)\n-C2*(u[k][j][i-1][1]*u[k][j][i-1][1]*tmp2\n+qs[k][j][i-1]*tmp1))\n-dt*tx1*(r43*c34-c1345)*tmp2*u[k][j][i-1][1];\nc[j][i][2][4]=-dt*tx2\n*(-C2*(u[k][j][i-1][2]*u[k][j][i-1][1])*tmp2)\n-dt*tx1*(c34-c1345)*tmp2*u[k][j][i-1][2];\nc[j][i][3][4]=-dt*tx2\n*(-C2*(u[k][j][i-1][3]*u[k][j][i-1][1])*tmp2)\n-dt*tx1*(c34-c1345)*tmp2*u[k][j][i-1][3];\nc[j][i][4][4]=-dt*tx2\n*(C1*(u[k][j][i-1][1]*tmp1))\n-dt*tx1*c1345*tmp1\n-dt*tx1*dx5;\n}\n}\n}

subroutine jacld(j, k)\n\n\n\n\nuse lu_data\nimplicit none\n\ninteger j, k\n\ninteger i\ndouble precision r43\ndouble precision c1345\ndouble precision c34\ndouble precision tmp1, tmp2, tmp3\n\n\n\nr43 = ( 4.0d+00 / 3.0d+00 )\nc1345 = c1 * c3 * c4 * c5\nc34 = c3 * c4\n\ndo i = ist, iend\n\ntmp1 = rho_i(i,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nd(1,1,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 * dx1 &\n& + ty1 * dy1 &\n& + tz1 * dz1 )\nd(1,2,i) = 0.0d+00\nd(1,3,i) = 0.0d+00\nd(1,4,i) = 0.0d+00\nd(1,5,i) = 0.0d+00\n\nd(2,1,i) = -dt * 2.0d+00 &\n& * ( tx1 * r43 + ty1 + tz1 ) &\n& * c34 * tmp2 * u(2,i,j,k)\nd(2,2,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 * r43 + ty1 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx2 &\n& + ty1 * dy2 &\n& + tz1 * dz2 )\nd(2,3,i) = 0.0d+00\nd(2,4,i) = 0.0d+00\nd(2,5,i) = 0.0d+00\n\nd(3,1,i) = -dt * 2.0d+00 &\n& * ( tx1 + ty1 * r43 + tz1 ) &\n& * c34 * tmp2 * u(3,i,j,k)\nd(3,2,i) = 0.0d+00\nd(3,3,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 * r43 + tz1 ) &\n& + dt * 2.0d+00 * ( tx1 * dx3 &\n& + ty1 * dy3 &\n& + tz1 * dz3 )\nd(3,4,i) = 0.0d+00\nd(3,5,i) = 0.0d+00\n\nd(4,1,i) = -dt * 2.0d+00 &\n& * ( tx1 + ty1 + tz1 * r43 ) &\n& * c34 * tmp2 * u(4,i,j,k)\nd(4,2,i) = 0.0d+00\nd(4,3,i) = 0.0d+00\nd(4,4,i) = 1.0d+00 &\n& + dt * 2.0d+00 * c34 * tmp1 &\n& * ( tx1 + ty1 + tz1 * r43 ) &\n& + dt * 2.0d+00 * ( tx1 * dx4 &\n& + ty1 * dy4 &\n& + tz1 * dz4 )\nd(4,5,i) = 0.0d+00\n\nd(5,1,i) = -dt * 2.0d+00 &\n& * ( ( ( tx1 * ( r43*c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * ( u(2,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43*c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) ) * ( u(3,i,j,k) ** 2 ) &\n& + ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43*c34 - c1345 ) ) * ( u(4,i,j,k) ** 2 ) &\n& ) * tmp3 &\n& + ( tx1 + ty1 + tz1 ) * c1345 * tmp2 * u(5,i,j,k) )\n\nd(5,2,i) = dt * 2.0d+00 * tmp2 * u(2,i,j,k) &\n& * ( tx1 * ( r43*c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( c34 - c1345 ) )\nd(5,3,i) = dt * 2.0d+00 * tmp2 * u(3,i,j,k) &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( r43*c34 -c1345 ) &\n& + tz1 * ( c34 - c1345 ) )\nd(5,4,i) = dt * 2.0d+00 * tmp2 * u(4,i,j,k) &\n& * ( tx1 * ( c34 - c1345 ) &\n& + ty1 * ( c34 - c1345 ) &\n& + tz1 * ( r43*c34 - c1345 ) )\nd(5,5,i) = 1.0d+00 &\n& + dt * 2.0d+00 * ( tx1 + ty1 + tz1 ) * c1345 * tmp1 &\n& + dt * 2.0d+00 * ( tx1 * dx5 &\n& + ty1 * dy5 &\n& + tz1 * dz5 )\n\ntmp1 = rho_i(i,j,k-1)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\na(1,1,i) = - dt * tz1 * dz1\na(1,2,i) = 0.0d+00\na(1,3,i) = 0.0d+00\na(1,4,i) = - dt * tz2\na(1,5,i) = 0.0d+00\n\na(2,1,i) = - dt * tz2 &\n& * ( - ( u(2,i,j,k-1)*u(4,i,j,k-1) ) * tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(2,i,j,k-1) )\na(2,2,i) = - dt * tz2 * ( u(4,i,j,k-1) * tmp1 ) &\n& - dt * tz1 * c34 * tmp1 &\n& - dt * tz1 * dz2\na(2,3,i) = 0.0d+00\na(2,4,i) = - dt * tz2 * ( u(2,i,j,k-1) * tmp1 )\na(2,5,i) = 0.0d+00\n\na(3,1,i) = - dt * tz2 &\n& * ( - ( u(3,i,j,k-1)*u(4,i,j,k-1) ) * tmp2 ) &\n& - dt * tz1 * ( - c34 * tmp2 * u(3,i,j,k-1) )\na(3,2,i) = 0.0d+00\na(3,3,i) = - dt * tz2 * ( u(4,i,j,k-1) * tmp1 ) &\n& - dt * tz1 * ( c34 * tmp1 ) &\n& - dt * tz1 * dz3\na(3,4,i) = - dt * tz2 * ( u(3,i,j,k-1) * tmp1 )\na(3,5,i) = 0.0d+00\n\na(4,1,i) = - dt * tz2 &\n& * ( - ( u(4,i,j,k-1) * tmp1 ) ** 2 &\n& + c2 * qs(i,j,k-1) * tmp1 ) &\n& - dt * tz1 * ( - r43 * c34 * tmp2 * u(4,i,j,k-1) )\na(4,2,i) = - dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k-1) * tmp1 ) )\na(4,3,i) = - dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k-1) * tmp1 ) )\na(4,4,i) = - dt * tz2 * ( 2.0d+00 - c2 ) &\n& * ( u(4,i,j,k-1) * tmp1 ) &\n& - dt * tz1 * ( r43 * c34 * tmp1 ) &\n& - dt * tz1 * dz4\na(4,5,i) = - dt * tz2 * c2\n\na(5,1,i) = - dt * tz2 &\n& * ( ( c2 * 2.0d0 * qs(i,j,k-1) &\n& - c1 * u(5,i,j,k-1) ) &\n& * u(4,i,j,k-1) * tmp2 ) &\n& - dt * tz1 &\n& * ( - ( c34 - c1345 ) * tmp3 * (u(2,i,j,k-1)**2) &\n& - ( c34 - c1345 ) * tmp3 * (u(3,i,j,k-1)**2) &\n& - ( r43*c34 - c1345 )* tmp3 * (u(4,i,j,k-1)**2) &\n& - c1345 * tmp2 * u(5,i,j,k-1) )\na(5,2,i) = - dt * tz2 &\n& * ( - c2 * ( u(2,i,j,k-1)*u(4,i,j,k-1) ) * tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(2,i,j,k-1)\na(5,3,i) = - dt * tz2 &\n& * ( - c2 * ( u(3,i,j,k-1)*u(4,i,j,k-1) ) * tmp2 ) &\n& - dt * tz1 * ( c34 - c1345 ) * tmp2 * u(3,i,j,k-1)\na(5,4,i) = - dt * tz2 &\n& * ( c1 * ( u(5,i,j,k-1) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j,k-1) * tmp1 &\n& + u(4,i,j,k-1)*u(4,i,j,k-1) * tmp2 ) ) &\n& - dt * tz1 * ( r43*c34 - c1345 ) * tmp2 * u(4,i,j,k-1)\na(5,5,i) = - dt * tz2 &\n& * ( c1 * ( u(4,i,j,k-1) * tmp1 ) ) &\n& - dt * tz1 * c1345 * tmp1 &\n& - dt * tz1 * dz5\n\ntmp1 = rho_i(i,j-1,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nb(1,1,i) = - dt * ty1 * dy1\nb(1,2,i) = 0.0d+00\nb(1,3,i) = - dt * ty2\nb(1,4,i) = 0.0d+00\nb(1,5,i) = 0.0d+00\n\nb(2,1,i) = - dt * ty2 &\n& * ( - ( u(2,i,j-1,k)*u(3,i,j-1,k) ) * tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(2,i,j-1,k) )\nb(2,2,i) = - dt * ty2 * ( u(3,i,j-1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy2\nb(2,3,i) = - dt * ty2 * ( u(2,i,j-1,k) * tmp1 )\nb(2,4,i) = 0.0d+00\nb(2,5,i) = 0.0d+00\n\nb(3,1,i) = - dt * ty2 &\n& * ( - ( u(3,i,j-1,k) * tmp1 ) ** 2 &\n& + c2 * ( qs(i,j-1,k) * tmp1 ) ) &\n& - dt * ty1 * ( - r43 * c34 * tmp2 * u(3,i,j-1,k) )\nb(3,2,i) = - dt * ty2 &\n& * ( - c2 * ( u(2,i,j-1,k) * tmp1 ) )\nb(3,3,i) = - dt * ty2 * ( ( 2.0d+00 - c2 ) &\n& * ( u(3,i,j-1,k) * tmp1 ) ) &\n& - dt * ty1 * ( r43 * c34 * tmp1 ) &\n& - dt * ty1 * dy3\nb(3,4,i) = - dt * ty2 &\n& * ( - c2 * ( u(4,i,j-1,k) * tmp1 ) )\nb(3,5,i) = - dt * ty2 * c2\n\nb(4,1,i) = - dt * ty2 &\n& * ( - ( u(3,i,j-1,k)*u(4,i,j-1,k) ) * tmp2 ) &\n& - dt * ty1 * ( - c34 * tmp2 * u(4,i,j-1,k) )\nb(4,2,i) = 0.0d+00\nb(4,3,i) = - dt * ty2 * ( u(4,i,j-1,k) * tmp1 )\nb(4,4,i) = - dt * ty2 * ( u(3,i,j-1,k) * tmp1 ) &\n& - dt * ty1 * ( c34 * tmp1 ) &\n& - dt * ty1 * dy4\nb(4,5,i) = 0.0d+00\n\nb(5,1,i) = - dt * ty2 &\n& * ( ( c2 * 2.0d0 * qs(i,j-1,k) &\n& - c1 * u(5,i,j-1,k) ) &\n& * ( u(3,i,j-1,k) * tmp2 ) ) &\n& - dt * ty1 &\n& * ( - ( c34 - c1345 )*tmp3*(u(2,i,j-1,k)**2) &\n& - ( r43*c34 - c1345 )*tmp3*(u(3,i,j-1,k)**2) &\n& - ( c34 - c1345 )*tmp3*(u(4,i,j-1,k)**2) &\n& - c1345*tmp2*u(5,i,j-1,k) )\nb(5,2,i) = - dt * ty2 &\n& * ( - c2 * ( u(2,i,j-1,k)*u(3,i,j-1,k) ) * tmp2 ) &\n& - dt * ty1 &\n& * ( c34 - c1345 ) * tmp2 * u(2,i,j-1,k)\nb(5,3,i) = - dt * ty2 &\n& * ( c1 * ( u(5,i,j-1,k) * tmp1 ) &\n& - c2 &\n& * ( qs(i,j-1,k) * tmp1 &\n& + u(3,i,j-1,k)*u(3,i,j-1,k) * tmp2 ) ) &\n& - dt * ty1 &\n& * ( r43*c34 - c1345 ) * tmp2 * u(3,i,j-1,k)\nb(5,4,i) = - dt * ty2 &\n& * ( - c2 * ( u(3,i,j-1,k)*u(4,i,j-1,k) ) * tmp2 ) &\n& - dt * ty1 * ( c34 - c1345 ) * tmp2 * u(4,i,j-1,k)\nb(5,5,i) = - dt * ty2 &\n& * ( c1 * ( u(3,i,j-1,k) * tmp1 ) ) &\n& - dt * ty1 * c1345 * tmp1 &\n& - dt * ty1 * dy5\n\ntmp1 = rho_i(i-1,j,k)\ntmp2 = tmp1 * tmp1\ntmp3 = tmp1 * tmp2\n\nc(1,1,i) = - dt * tx1 * dx1\nc(1,2,i) = - dt * tx2\nc(1,3,i) = 0.0d+00\nc(1,4,i) = 0.0d+00\nc(1,5,i) = 0.0d+00\n\nc(2,1,i) = - dt * tx2 &\n& * ( - ( u(2,i-1,j,k) * tmp1 ) ** 2 &\n& + c2 * qs(i-1,j,k) * tmp1 ) &\n& - dt * tx1 * ( - r43 * c34 * tmp2 * u(2,i-1,j,k) )\nc(2,2,i) = - dt * tx2 &\n& * ( ( 2.0d+00 - c2 ) * ( u(2,i-1,j,k) * tmp1 ) ) &\n& - dt * tx1 * ( r43 * c34 * tmp1 ) &\n& - dt * tx1 * dx2\nc(2,3,i) = - dt * tx2 &\n& * ( - c2 * ( u(3,i-1,j,k) * tmp1 ) )\nc(2,4,i) = - dt * tx2 &\n& * ( - c2 * ( u(4,i-1,j,k) * tmp1 ) )\nc(2,5,i) = - dt * tx2 * c2\n\nc(3,1,i) = - dt * tx2 &\n& * ( - ( u(2,i-1,j,k) * u(3,i-1,j,k) ) * tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(3,i-1,j,k) )\nc(3,2,i) = - dt * tx2 * ( u(3,i-1,j,k) * tmp1 )\nc(3,3,i) = - dt * tx2 * ( u(2,i-1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx3\nc(3,4,i) = 0.0d+00\nc(3,5,i) = 0.0d+00\n\nc(4,1,i) = - dt * tx2 &\n& * ( - ( u(2,i-1,j,k)*u(4,i-1,j,k) ) * tmp2 ) &\n& - dt * tx1 * ( - c34 * tmp2 * u(4,i-1,j,k) )\nc(4,2,i) = - dt * tx2 * ( u(4,i-1,j,k) * tmp1 )\nc(4,3,i) = 0.0d+00\nc(4,4,i) = - dt * tx2 * ( u(2,i-1,j,k) * tmp1 ) &\n& - dt * tx1 * ( c34 * tmp1 ) &\n& - dt * tx1 * dx4\nc(4,5,i) = 0.0d+00\n\nc(5,1,i) = - dt * tx2 &\n& * ( ( c2 * 2.0d0 * qs(i-1,j,k) &\n& - c1 * u(5,i-1,j,k) ) &\n& * u(2,i-1,j,k) * tmp2 ) &\n& - dt * tx1 &\n& * ( - ( r43*c34 - c1345 ) * tmp3 * ( u(2,i-1,j,k)**2 ) &\n& - ( c34 - c1345 ) * tmp3 * ( u(3,i-1,j,k)**2 ) &\n& - ( c34 - c1345 ) * tmp3 * ( u(4,i-1,j,k)**2 ) &\n& - c1345 * tmp2 * u(5,i-1,j,k) )\nc(5,2,i) = - dt * tx2 &\n& * ( c1 * ( u(5,i-1,j,k) * tmp1 ) &\n& - c2 &\n& * ( u(2,i-1,j,k)*u(2,i-1,j,k) * tmp2 &\n& + qs(i-1,j,k) * tmp1 ) ) &\n& - dt * tx1 &\n& * ( r43*c34 - c1345 ) * tmp2 * u(2,i-1,j,k)\nc(5,3,i) = - dt * tx2 &\n& * ( - c2 * ( u(3,i-1,j,k)*u(2,i-1,j,k) ) * tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(3,i-1,j,k)\nc(5,4,i) = - dt * tx2 &\n& * ( - c2 * ( u(4,i-1,j,k)*u(2,i-1,j,k) ) * tmp2 ) &\n& - dt * tx1 &\n& * ( c34 - c1345 ) * tmp2 * u(4,i-1,j,k)\nc(5,5,i) = - dt * tx2 &\n& * ( c1 * ( u(2,i-1,j,k) * tmp1 ) ) &\n& - dt * tx1 * c1345 * tmp1 &\n& - dt * tx1 * dx5\n\nend do\n\n\nreturn\nend

void adi(){\ncompute_rhs();\ntxinvr();\nx_solve();\ny_solve();\nz_solve();\nadd();\n}

subroutine adi\n\n\ncall compute_rhs\n\ncall txinvr\n\ncall x_solve\n\ncall y_solve\n\ncall z_solve\n\ncall add\n\nreturn\nend

static void sprnvc(int n, int nz, int nn1, double v[], int iv[]){\nint nzv, ii, i;\ndouble vecelt, vecloc;\n\nnzv = 0;\n\nwhile(nzv < nz){\nvecelt = randlc(&tran, amult);\n\n\nvecloc = randlc(&tran, amult);\ni = icnvrt(vecloc, nn1) + 1;\nif(i>n){continue;}\n\n\nboolean was_gen = FALSE;\nfor(ii = 0; ii < nzv; ii++){\nif(iv[ii] == i){\nwas_gen = TRUE;\nbreak;\n}\n}\nif(was_gen){continue;}\nv[nzv] = vecelt;\niv[nzv] = i;\nnzv = nzv + 1;\n}\n}

subroutine sprnvc( n, nz, nn1, v, iv )\n\nuse cg_data, only : amult, tran\n\nimplicit none\n\ndouble precision v(*)\ninteger n, nz, nn1, iv(*)\n\n\n\ninteger nzv, ii, i, icnvrt\n\nexternal randlc, icnvrt\ndouble precision randlc, vecelt, vecloc\n\n\nnzv = 0\n\n100 continue\nif (nzv .ge. nz) goto 110\n\nvecelt = randlc( tran, amult )\n\nvecloc = randlc(tran, amult)\ni = icnvrt(vecloc, nn1) + 1\nif (i .gt. n) goto 100\n\ndo ii = 1, nzv\nif (iv(ii) .eq. i) goto 100\nenddo\nnzv = nzv + 1\nv(nzv) = vecelt\niv(nzv) = i\ngoto 100\n110 continue\n\nreturn\nend

void ssor(int niter){\n\nint i, j, k, m, n;\nint istep;\ndouble tmp, tv[ISIZ2*(ISIZ1/2*2+1)*5];\ndouble delunm[5];\n\ntmp=1.0/(omega*(2.0-omega));\n\n\n#pragma omp parallel for private(i,j,n,m)\nfor(j=0; j<ISIZ2; j++){\nfor(i=0; i<ISIZ1; i++){\nfor(n=0; n<5; n++){\nfor(m=0; m<5; m++){\na[j][i][n][m]=0.0;\nb[j][i][n][m]=0.0;\nc[j][i][n][m]=0.0;\nd[j][i][n][m]=0.0;\n}\n}\n}\n}\nfor(i=1;i<=T_LAST;i++){timer_clear(i);}\n\n\n#pragma omp parallel\n{\n\nrhs();\n\n\nl2norm( nx0,\nny0,\nnz0,\nist,\niend,\njst,\njend,\nrsd,\nrsdnm);\n} \n\n\nfor(i=1;i<=T_LAST;i++){timer_clear(i);}\ntimer_start(1);\n\n#pragma omp parallel private(istep,i,j,k,m)\n{\n\nfor(istep=1; istep<=niter; istep++){\nif((istep%20)==0||istep==itmax||istep==1){\n#pragma omp master\nif(niter>1){printf(" Time step %4d\n",istep);}\n}\n\nif(timeron){\n#pragma omp master\ntimer_start(T_RHS);\n}\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nrsd[k][j][i][m]=dt*rsd[k][j][i][m];\n}\n}\n}\n}\nif(timeron){\n#pragma omp master\ntimer_stop(T_RHS);\n}\n\nfor(k=1; k<nz-1; k++){\n\nif(timeron){\n#pragma omp master\ntimer_start(T_JACLD);\n}\njacld(k);\nif(timeron){\n#pragma omp master\ntimer_stop(T_JACLD);\n}\n\n\nif(timeron){\n#pragma omp master\ntimer_start(T_BLTS);\n}\n\nblts( nx,\nny,\nnz,\nk,\nomega,\nrsd,\na,\nb,\nc,\nd,\nist,\niend,\njst,\njend,\nnx0,\nny0);\n\nif(timeron){\n#pragma omp master\ntimer_stop(T_BLTS);\n}\n}\n\n#pragma omp barrier\n\nfor(k=nz-2; k>0; k--){\n\nif(timeron){\n#pragma omp master\ntimer_start(T_JACU);\n}\njacu(k);\nif(timeron){\n#pragma omp master\ntimer_stop(T_JACU);\n}\n\nif(timeron){\n#pragma omp master\ntimer_start(T_BUTS);\n}\n\nbuts( nx,\nny,\nnz,\nk,\nomega,\nrsd,\ntv,\nd,\na,\nb,\nc,\nist,\niend,\njst,\njend,\nnx0,\nny0);\n\nif(timeron){\n#pragma omp master\ntimer_stop(T_BUTS);\n}\n}\n\n#pragma omp barrier\n\n\nif(timeron){\n#pragma omp master\ntimer_start(T_ADD);\n}\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nu[k][j][i][m]=u[k][j][i][m]+tmp*rsd[k][j][i][m];\n}\n}\n}\n}\nif(timeron){\n#pragma omp master\ntimer_stop(T_ADD);\n}\n\n\nif((istep%inorm)==0){\nif(timeron){\n#pragma omp master\ntimer_start(T_L2NORM);\n}\nl2norm( nx0,\nny0,\nnz0,\nist,\niend,\njst,\njend,\nrsd,\ndelunm);\nif(timeron){\n#pragma omp master\ntimer_stop(T_L2NORM);\n}\n}\n\nrhs();\n\n\nif(((istep%inorm)==0)||( istep == itmax)){\nif(timeron){\n#pragma omp master\ntimer_start(T_L2NORM);\n}\nl2norm( nx0,\nny0,\nnz0,\nist,\niend,\njst,\njend,\nrsd,\nrsdnm);\nif(timeron){\n#pragma omp master\ntimer_stop(T_L2NORM);\n}\n}\n\nif((rsdnm[0]<tolrsd[0])&&\n(rsdnm[1]<tolrsd[1])&&\n(rsdnm[2]<tolrsd[2])&&\n(rsdnm[3]<tolrsd[3])&&\n(rsdnm[4]<tolrsd[4])){\n#pragma omp master\nprintf("\nconvergence was achieved after %4d pseudo-time steps\n",istep);\nbreak;\n}\n}\n} \n\ntimer_stop(1);\nmaxtime=timer_read(1);\n}

subroutine ssor(niter)\n\n\n\nuse lu_data\nimplicit none\n\ninteger niter\n\ninteger i, j, k, m, n\ninteger istep\ndouble precision tmp, tmp2\ndouble precision delunm(5)\n\nexternal timer_read\ndouble precision timer_read\n\n\ntmp = 1.0d+00 / ( omega * ( 2.0d+00 - omega ) )\n\ndo i = 1, t_last\ncall timer_clear(i)\nend do\n\ncall rhs\n\ncall l2norm( isiz1, isiz2, isiz3, nx0, ny0, nz0, &\n& ist, iend, jst, jend, &\n& rsd, rsdnm )\n\n\ndo i = 1, t_last\ncall timer_clear(i)\nend do\ncall timer_start(1)\n\ndo istep = 1, niter\n\nif (mod ( istep, 20) .eq. 0 .or. &\n& istep .eq. itmax .or. &\n& istep .eq. 1) then\nif (niter .gt. 1) write( *, 200) istep\n200 format(' Time step ', i4)\nendif\n\nif (timeron) call timer_start(t_rhs)\ntmp2 = dt\ndo k = 2, nz - 1\ndo j = jst, jend\ndo i = ist, iend\ndo m = 1, 5\nrsd(m,i,j,k) = tmp2 * rsd(m,i,j,k)\nend do\nend do\nend do\nend do\nif (timeron) call timer_stop(t_rhs)\n\nif (timeron) call timer_start(t_blts)\ndo k = 2, nz -1\ndo j = jst, jend\n\ncall jacld(j, k)\n\ncall blts( isiz1, isiz2, isiz3, &\n& nx, ny, nz, &\n& omega, &\n& rsd, &\n& a, b, c, d, &\n& ist, iend, j, k )\n\nend do\nend do\nif (timeron) call timer_stop(t_blts)\n\nif (timeron) call timer_start(t_buts)\ndo k = nz - 1, 2, -1\ndo j = jend, jst, -1\n\ncall jacu(j, k)\n\ncall buts( isiz1, isiz2, isiz3, &\n& nx, ny, nz, &\n& omega, &\n& rsd, &\n& d, a, b, c, &\n& ist, iend, j, k )\n\nend do\nend do\nif (timeron) call timer_stop(t_buts)\n\n\nif (timeron) call timer_start(t_add)\ntmp2 = tmp\ndo k = 2, nz-1\ndo j = jst, jend\ndo i = ist, iend\ndo m = 1, 5\nu( m, i, j, k ) = u( m, i, j, k ) &\n& + tmp2 * rsd( m, i, j, k )\nend do\nend do\nend do\nend do\nif (timeron) call timer_stop(t_add)\n\nif ( mod ( istep, inorm ) .eq. 0 ) then\nif (timeron) call timer_start(t_l2norm)\ncall l2norm( isiz1, isiz2, isiz3, nx0, ny0, nz0, &\n& ist, iend, jst, jend, &\n& rsd, delunm )\nif (timeron) call timer_stop(t_l2norm)\nend if\n\ncall rhs\n\nif ( ( mod ( istep, inorm ) .eq. 0 ) .or. &\n& ( istep .eq. itmax ) ) then\nif (timeron) call timer_start(t_l2norm)\ncall l2norm( isiz1, isiz2, isiz3, nx0, ny0, nz0, &\n& ist, iend, jst, jend, &\n& rsd, rsdnm )\nif (timeron) call timer_stop(t_l2norm)\nend if\n\nif ( ( rsdnm(1) .lt. tolrsd(1) ) .and. &\n& ( rsdnm(2) .lt. tolrsd(2) ) .and. &\n& ( rsdnm(3) .lt. tolrsd(3) ) .and. &\n& ( rsdnm(4) .lt. tolrsd(4) ) .and. &\n& ( rsdnm(5) .lt. tolrsd(5) ) ) then\nwrite (*,1004) istep\ngo to 900\nend if\n\nend do\n900 continue\n\ncall timer_stop(1)\nmaxtime= timer_read(1)\n\n\n\nreturn\n\n1001 format (1x/5x,'pseudo-time SSOR iteration no.=',i4/)\n1004 format (1x/1x,'convergence was achieved after ',i4, &\n& ' pseudo-time steps' )\n1006 format (1x/1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for first pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for second pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for third pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for fourth pde = ',1pe12.5/, &\n& 1x,'RMS-norm of SSOR-iteration correction ', &\n& 'for fifth pde = ',1pe12.5)\n1007 format (1x/1x,'RMS-norm of steady-state residual for ', &\n& 'first pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'second pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'third pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'fourth pde = ',1pe12.5/, &\n& 1x,'RMS-norm of steady-state residual for ', &\n& 'fifth pde = ',1pe12.5)\n\nend

static void comm3(void* pointer_u, int n1, int n2, int n3, int kk){\n#ifdef __clang__\nusing custom_cast = double (*)[n2][n1];\ncustom_cast u = reinterpret_cast<custom_cast>(pointer_u);\n#else\ndouble (*u)[n2][n1] = (double (*)[n2][n1])pointer_u;\n#endif\n\nint i1, i2, i3;\nif(timeron){\n#pragma omp master\ntimer_start(T_COMM3);\n}\n#pragma omp for\nfor(i3 = 1; i3 < n3-1; i3++){\n\nfor(i2 = 1; i2 < n2-1; i2++){\nu[i3][i2][0] = u[i3][i2][n1-2];\nu[i3][i2][n1-1] = u[i3][i2][1];\n}\n\nfor(i1 = 0; i1 < n1; i1++){\nu[i3][0][i1] = u[i3][n2-2][i1];\nu[i3][n2-1][i1] = u[i3][1][i1];\n}\n}\n\n#pragma omp for\nfor(i2 = 0; i2 < n2; i2++){\nfor(i1 = 0; i1 < n1; i1++){\nu[0][i2][i1] = u[n3-2][i2][i1];\nu[n3-1][i2][i1] = u[1][i2][i1];\n}\n}\n\nif(timeron){\n#pragma omp master\ntimer_stop(T_COMM3);\n}\n}

subroutine comm3(u,n1,n2,n3,kk)\n\n\n\nuse mg_data\nimplicit none\n\ninteger n1, n2, n3, kk\ndouble precision u(n1,n2,n3)\ninteger i1, i2, i3\n\nif (timeron) call timer_start(T_comm3)\ndo i3=2,n3-1\ndo i2=2,n2-1\nu( 1,i2,i3) = u(n1-1,i2,i3)\nu(n1,i2,i3) = u( 2,i2,i3)\nenddo\n\ndo i1=1,n1\nu(i1, 1,i3) = u(i1,n2-1,i3)\nu(i1,n2,i3) = u(i1, 2,i3)\nenddo\nenddo\n\ndo i2=1,n2\ndo i1=1,n1\nu(i1,i2, 1) = u(i1,i2,n3-1)\nu(i1,i2,n3) = u(i1,i2, 2)\nenddo\nenddo\nif (timeron) call timer_stop(T_comm3)\n\nreturn\nend

void exact_solution(double xi, double eta, double zeta, double dtemp[]){\nint m;\nfor(m=0; m<5; m++){\ndtemp[m]=ce[0][m]+xi*\n(ce[1][m]+xi*\n(ce[4][m]+xi*\n(ce[7][m]+xi*\nce[10][m])))+eta*\n(ce[2][m]+eta*\n(ce[5][m]+eta*\n(ce[8][m]+eta*\nce[11][m])))+zeta*\n(ce[3][m]+zeta*\n(ce[6][m]+zeta*\n(ce[9][m]+zeta*\nce[12][m])));\n}\n}

subroutine exact_solution(xi,eta,zeta,dtemp)\n\n\n\nuse sp_data\nimplicit none\n\ndouble precision xi, eta, zeta\ndouble precision dtemp(5)\ninteger m\n\ndo m = 1, 5\ndtemp(m) = ce(m,1) + &\n& xi*(ce(m,2) + xi*(ce(m,5) + xi*(ce(m,8) + xi*ce(m,11)))) + &\n& eta*(ce(m,3) + eta*(ce(m,6) + eta*(ce(m,9) + eta*ce(m,12))))+ &\n& zeta*(ce(m,4) + zeta*(ce(m,7) + zeta*(ce(m,10) + &\n& zeta*ce(m,13))))\nend do\n\nreturn\nend

static void compute_initial_conditions(void* pointer_u0,\nint d1,\nint d2,\nint d3){\ndcomplex (*u0)[NY][NX] = (dcomplex(*)[NY][NX])pointer_u0;\n\nint k, j;\ndouble x0, start, an, starts[NZ];\nstart = SEED;\n\n\nipow46(A, 0, &an);\nrandlc(&start, an);\nipow46(A, 2*NX*NY, &an);\n\nstarts[0] = start;\nfor(int k=1; k<dims[2]; k++){\nrandlc(&start, an);\nstarts[k] = start;\n}\n\n\n#pragma omp parallel for private(k,j,x0)\nfor(k=0; k<dims[2]; k++){\nx0 = starts[k];\nfor(j=0; j<dims[1]; j++){\nvranlc(2*NX, &x0, A, (double*)&u0[k][j][0]);\n}\n}\n}

subroutine compute_initial_conditions(u0, d1, d2, d3)\n\n\n\nuse ft_data\nimplicit none\n\ninteger d1, d2, d3\ndouble complex u0(d1+1, d2, d3)\ninteger k, j\ndouble precision x0, start, an, dummy, starts(nz)\n\n\nstart = seed\ncall ipow46(a, 0, an)\ndummy = randlc(start, an)\ncall ipow46(a, 2*nx*ny, an)\n\nstarts(1) = start\ndo k = 2, dims(3)\ndummy = randlc(start, an)\nstarts(k) = start\nend do\n\ndo k = 1, dims(3)\nx0 = starts(k)\ndo j = 1, dims(2)\ncall vranlc(2*nx, x0, a, u0(1, j, k))\nend do\nend do\n\nreturn\nend

void setiv(){\n\nint i, j, k, m;\ndouble xi, eta, zeta;\ndouble pxi, peta, pzeta;\ndouble ue_1jk[5], ue_nx0jk[5], ue_i1k[5];\ndouble ue_iny0k[5], ue_ij1[5], ue_ijnz[5];\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nzeta=((double)k)/(nz-1);\nfor(j=1; j<ny-1; j++){\neta=((double)j)/(ny0-1);\nfor(i=1; i<nx-1; i++){\nxi=((double)i)/(nx0-1);\nexact(0, j, k, ue_1jk);\nexact(nx0-1, j, k, ue_nx0jk);\nexact(i, 0, k, ue_i1k);\nexact(i, ny0-1, k, ue_iny0k);\nexact(i, j, 0, ue_ij1);\nexact(i, j, nz-1, ue_ijnz);\nfor(m=0; m<5; m++){\npxi=(1.0-xi)*ue_1jk[m]\n+xi*ue_nx0jk[m];\npeta=(1.0-eta)*ue_i1k[m]\n+eta*ue_iny0k[m];\npzeta=(1.0-zeta)*ue_ij1[m]\n+zeta*ue_ijnz[m];\nu[k][j][i][m]=pxi+peta+pzeta\n-pxi*peta-peta*pzeta-pzeta*pxi\n+pxi*peta*pzeta;\n}\n}\n}\n}\n}

subroutine setiv\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision xi, eta, zeta\ndouble precision pxi, peta, pzeta\ndouble precision ue_1jk(5),ue_nx0jk(5),ue_i1k(5), &\n& ue_iny0k(5),ue_ij1(5),ue_ijnz(5)\n\n\ndo k = 2, nz - 1\ndo j = 2, ny - 1\nzeta = ( dble (k-1) ) / (nz-1)\neta = ( dble (j-1) ) / (ny0-1)\ndo i = 2, nx - 1\nxi = ( dble (i-1) ) / (nx0-1)\ncall exact (1,j,k,ue_1jk)\ncall exact (nx0,j,k,ue_nx0jk)\ncall exact (i,1,k,ue_i1k)\ncall exact (i,ny0,k,ue_iny0k)\ncall exact (i,j,1,ue_ij1)\ncall exact (i,j,nz,ue_ijnz)\ndo m = 1, 5\npxi = ( 1.0d+00 - xi ) * ue_1jk(m) &\n& + xi * ue_nx0jk(m)\npeta = ( 1.0d+00 - eta ) * ue_i1k(m) &\n& + eta * ue_iny0k(m)\npzeta = ( 1.0d+00 - zeta ) * ue_ij1(m) &\n& + zeta * ue_ijnz(m)\n\nu( m, i, j, k ) = pxi + peta + pzeta &\n& - pxi * peta - peta * pzeta - pzeta * pxi &\n& + pxi * peta * pzeta\n\nend do\nend do\nend do\nend do\n\nreturn\nend

void verify(int no_time_steps, char* class_npb, boolean* verified){\ndouble xcrref[5], xceref[5], xcrdif[5], xcedif[5], epsilon, xce[5], xcr[5], dtref;\nint m;\n\nepsilon=1.0e-08;\n\nerror_norm(xce);\ncompute_rhs();\nrhs_norm(xcr);\nfor(m=0;m<5;m++){xcr[m]=xcr[m]/dt;}\n*class_npb='U';\n*verified=TRUE;\nfor(m=0;m<5;m++){xcrref[m]=1.0;xceref[m]=1.0;}\n\nif((grid_points[0]==12)&&(grid_points[1]==12)&&(grid_points[2]==12)&&(no_time_steps==100)){\n*class_npb='S';\ndtref=1.5e-2;\n\nxcrref[0]=2.7470315451339479e-02;\nxcrref[1]=1.0360746705285417e-02;\nxcrref[2]=1.6235745065095532e-02;\nxcrref[3]=1.5840557224455615e-02;\nxcrref[4]=3.4849040609362460e-02;\n\nxceref[0]=2.7289258557377227e-05;\nxceref[1]=1.0364446640837285e-05;\nxceref[2]=1.6154798287166471e-05;\nxceref[3]=1.5750704994480102e-05;\nxceref[4]=3.4177666183390531e-05;\n\n}else if((grid_points[0]==36)&&(grid_points[1]==36)&&(grid_points[2]==36)&&(no_time_steps==400)){\n*class_npb='W';\ndtref=1.5e-3;\n\nxcrref[0]=0.1893253733584e-02;\nxcrref[1]=0.1717075447775e-03;\nxcrref[2]=0.2778153350936e-03;\nxcrref[3]=0.2887475409984e-03;\nxcrref[4]=0.3143611161242e-02;\n\nxceref[0]=0.7542088599534e-04;\nxceref[1]=0.6512852253086e-05;\nxceref[2]=0.1049092285688e-04;\nxceref[3]=0.1128838671535e-04;\nxceref[4]=0.1212845639773e-03;\n\n}else if((grid_points[0]==64)&&(grid_points[1]==64)&&(grid_points[2]==64)&&(no_time_steps==400)){\n*class_npb='A';\ndtref=1.5e-3;\n\nxcrref[0]=2.4799822399300195;\nxcrref[1]=1.1276337964368832;\nxcrref[2]=1.5028977888770491;\nxcrref[3]=1.4217816211695179;\nxcrref[4]=2.1292113035138280;\n\nxceref[0]=1.0900140297820550e-04;\nxceref[1]=3.7343951769282091e-05;\nxceref[2]=5.0092785406541633e-05;\nxceref[3]=4.7671093939528255e-05;\nxceref[4]=1.3621613399213001e-04;\n\n}else if((grid_points[0]==102)&&(grid_points[1]==102)&&(grid_points[2]==102)&&(no_time_steps==400)){\n*class_npb='B';\ndtref=1.0e-3;\n\nxcrref[0]=0.6903293579998e+02;\nxcrref[1]=0.3095134488084e+02;\nxcrref[2]=0.4103336647017e+02;\nxcrref[3]=0.3864769009604e+02;\nxcrref[4]=0.5643482272596e+02;\n\nxceref[0]=0.9810006190188e-02;\nxceref[1]=0.1022827905670e-02;\nxceref[2]=0.1720597911692e-02;\nxceref[3]=0.1694479428231e-02;\nxceref[4]=0.1847456263981e-01;\n\n}else if((grid_points[0]==162)&&(grid_points[1]==162)&&(grid_points[2]==162)&&(no_time_steps==400)){\n*class_npb='C';\ndtref=0.67e-3;\n\nxcrref[0]=0.5881691581829e+03;\nxcrref[1]=0.2454417603569e+03;\nxcrref[2]=0.3293829191851e+03;\nxcrref[3]=0.3081924971891e+03;\nxcrref[4]=0.4597223799176e+03;\n\nxceref[0]=0.2598120500183e+00;\nxceref[1]=0.2590888922315e-01;\nxceref[2]=0.5132886416320e-01;\nxceref[3]=0.4806073419454e-01;\nxceref[4]=0.5483377491301e+00;\n\n}else if((grid_points[0]==408)&&(grid_points[1]==408)&&(grid_points[2]==408)&&(no_time_steps==500)){\n*class_npb='D';\ndtref=0.30e-3;\n\nxcrref[0]=0.1044696216887e+05;\nxcrref[1]=0.3204427762578e+04;\nxcrref[2]=0.4648680733032e+04;\nxcrref[3]=0.4238923283697e+04;\nxcrref[4]=0.7588412036136e+04;\n\nxceref[0]=0.5089471423669e+01;\nxceref[1]=0.5323514855894e+00;\nxceref[2]=0.1187051008971e+01;\nxceref[3]=0.1083734951938e+01;\nxceref[4]=0.1164108338568e+02;\n\n}else if((grid_points[0]==1020)&&(grid_points[1]==1020)&&(grid_points[2]==1020)&&(no_time_steps==500)){\n*class_npb='E';\ndtref=0.10e-3;\n\nxcrref[0]=0.6255387422609e+05;\nxcrref[1]=0.1495317020012e+05;\nxcrref[2]=0.2347595750586e+05;\nxcrref[3]=0.2091099783534e+05;\nxcrref[4]=0.4770412841218e+05;\n\nxceref[0]=0.6742735164909e+02;\nxceref[1]=0.5390656036938e+01;\nxceref[2]=0.1680647196477e+02;\nxceref[3]=0.1536963126457e+02;\nxceref[4]=0.1575330146156e+03;\n}else{\n*verified=FALSE;\n}\n\nfor(m=0; m<5; m++){\nxcrdif[m]=fabs((xcr[m]-xcrref[m])/xcrref[m]);\nxcedif[m]=fabs((xce[m]-xceref[m])/xceref[m]);\n}\n\nif(*class_npb!='U'){\nprintf(" Verification being performed for class %c\n",*class_npb);\nprintf(" accuracy setting for epsilon = %20.13E\n",epsilon);\n*verified=(fabs(dt-dtref)<=epsilon);\nif(!(*verified)){\n*class_npb='U';\nprintf(" DT does not match the reference value of %15.8E\n",dtref);\n}\n}else{\nprintf(" Unknown class\n");\n}\nif(*class_npb!='U'){\nprintf(" Comparison of RMS-norms of residual\n");\n}else{\nprintf(" RMS-norms of residual\n");\n}\nfor(m=0;m<5;m++){\nif(*class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xcr[m]);\n}else if(xcrdif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}else {\n*verified=FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xcr[m],xcrref[m],xcrdif[m]);\n}\n}\nif(*class_npb!='U'){\nprintf(" Comparison of RMS-norms of solution error\n");\n}else{\nprintf(" RMS-norms of solution error\n");\n}\nfor(m=0;m<5;m++){\nif(*class_npb=='U'){\nprintf(" %2d%20.13E\n",m+1,xce[m]);\n}else if(xcedif[m]<=epsilon){\nprintf(" %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}else{\n*verified = FALSE;\nprintf(" FAILURE: %2d%20.13E%20.13E%20.13E\n",m+1,xce[m],xceref[m],xcedif[m]);\n}\n}\nif(*class_npb=='U'){\nprintf(" No reference values provided\n");\nprintf(" No verification performed\n");\n}else if(*verified){\nprintf(" Verification Successful\n");\n}else{\nprintf(" Verification failed\n");\n}\n}

subroutine verify(no_time_steps, class, verified)\n\n\n\nuse, intrinsic :: ieee_arithmetic, only : ieee_is_nan\n\nuse sp_data\n\nimplicit none\n\ndouble precision xcrref(5),xceref(5),xcrdif(5),xcedif(5), &\n& epsilon, xce(5), xcr(5), dtref\ninteger m, no_time_steps\ncharacter class\nlogical verified\n\nepsilon = 1.0d-08\n\n\ncall error_norm(xce)\ncall compute_rhs\n\ncall rhs_norm(xcr)\n\ndo m = 1, 5\nxcr(m) = xcr(m) / dt\nenddo\n\nclass = 'U'\nverified = .true.\n\ndo m = 1,5\nxcrref(m) = 1.0\nxceref(m) = 1.0\nend do\n\nif ( (grid_points(1) .eq. 12 ) .and. &\n& (grid_points(2) .eq. 12 ) .and. &\n& (grid_points(3) .eq. 12 ) .and. &\n& (no_time_steps .eq. 100 )) then\n\nclass = 'S'\ndtref = 1.5d-2\n\nxcrref(1) = 2.7470315451339479d-02\nxcrref(2) = 1.0360746705285417d-02\nxcrref(3) = 1.6235745065095532d-02\nxcrref(4) = 1.5840557224455615d-02\nxcrref(5) = 3.4849040609362460d-02\n\nxceref(1) = 2.7289258557377227d-05\nxceref(2) = 1.0364446640837285d-05\nxceref(3) = 1.6154798287166471d-05\nxceref(4) = 1.5750704994480102d-05\nxceref(5) = 3.4177666183390531d-05\n\n\nelseif ( (grid_points(1) .eq. 36) .and. &\n& (grid_points(2) .eq. 36) .and. &\n& (grid_points(3) .eq. 36) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'W'\ndtref = 1.5d-3\n\nxcrref(1) = 0.1893253733584d-02\nxcrref(2) = 0.1717075447775d-03\nxcrref(3) = 0.2778153350936d-03\nxcrref(4) = 0.2887475409984d-03\nxcrref(5) = 0.3143611161242d-02\n\nxceref(1) = 0.7542088599534d-04\nxceref(2) = 0.6512852253086d-05\nxceref(3) = 0.1049092285688d-04\nxceref(4) = 0.1128838671535d-04\nxceref(5) = 0.1212845639773d-03\n\nelseif ( (grid_points(1) .eq. 64) .and. &\n& (grid_points(2) .eq. 64) .and. &\n& (grid_points(3) .eq. 64) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'A'\ndtref = 1.5d-3\n\nxcrref(1) = 2.4799822399300195d0\nxcrref(2) = 1.1276337964368832d0\nxcrref(3) = 1.5028977888770491d0\nxcrref(4) = 1.4217816211695179d0\nxcrref(5) = 2.1292113035138280d0\n\nxceref(1) = 1.0900140297820550d-04\nxceref(2) = 3.7343951769282091d-05\nxceref(3) = 5.0092785406541633d-05\nxceref(4) = 4.7671093939528255d-05\nxceref(5) = 1.3621613399213001d-04\n\nelseif ( (grid_points(1) .eq. 102) .and. &\n& (grid_points(2) .eq. 102) .and. &\n& (grid_points(3) .eq. 102) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'B'\ndtref = 1.0d-3\n\nxcrref(1) = 0.6903293579998d+02\nxcrref(2) = 0.3095134488084d+02\nxcrref(3) = 0.4103336647017d+02\nxcrref(4) = 0.3864769009604d+02\nxcrref(5) = 0.5643482272596d+02\n\nxceref(1) = 0.9810006190188d-02\nxceref(2) = 0.1022827905670d-02\nxceref(3) = 0.1720597911692d-02\nxceref(4) = 0.1694479428231d-02\nxceref(5) = 0.1847456263981d-01\n\nelseif ( (grid_points(1) .eq. 162) .and. &\n& (grid_points(2) .eq. 162) .and. &\n& (grid_points(3) .eq. 162) .and. &\n& (no_time_steps .eq. 400) ) then\n\nclass = 'C'\ndtref = 0.67d-3\n\nxcrref(1) = 0.5881691581829d+03\nxcrref(2) = 0.2454417603569d+03\nxcrref(3) = 0.3293829191851d+03\nxcrref(4) = 0.3081924971891d+03\nxcrref(5) = 0.4597223799176d+03\n\nxceref(1) = 0.2598120500183d+00\nxceref(2) = 0.2590888922315d-01\nxceref(3) = 0.5132886416320d-01\nxceref(4) = 0.4806073419454d-01\nxceref(5) = 0.5483377491301d+00\n\nelseif ( (grid_points(1) .eq. 408) .and. &\n& (grid_points(2) .eq. 408) .and. &\n& (grid_points(3) .eq. 408) .and. &\n& (no_time_steps .eq. 500) ) then\n\nclass = 'D'\ndtref = 0.30d-3\n\nxcrref(1) = 0.1044696216887d+05\nxcrref(2) = 0.3204427762578d+04\nxcrref(3) = 0.4648680733032d+04\nxcrref(4) = 0.4238923283697d+04\nxcrref(5) = 0.7588412036136d+04\n\nxceref(1) = 0.5089471423669d+01\nxceref(2) = 0.5323514855894d+00\nxceref(3) = 0.1187051008971d+01\nxceref(4) = 0.1083734951938d+01\nxceref(5) = 0.1164108338568d+02\n\nelseif ( (grid_points(1) .eq. 1020) .and. &\n& (grid_points(2) .eq. 1020) .and. &\n& (grid_points(3) .eq. 1020) .and. &\n& (no_time_steps .eq. 500) ) then\n\nclass = 'E'\ndtref = 0.10d-3\n\nxcrref(1) = 0.6255387422609d+05\nxcrref(2) = 0.1495317020012d+05\nxcrref(3) = 0.2347595750586d+05\nxcrref(4) = 0.2091099783534d+05\nxcrref(5) = 0.4770412841218d+05\n\nxceref(1) = 0.6742735164909d+02\nxceref(2) = 0.5390656036938d+01\nxceref(3) = 0.1680647196477d+02\nxceref(4) = 0.1536963126457d+02\nxceref(5) = 0.1575330146156d+03\n\nelseif ( (grid_points(1) .eq. 2560) .and. &\n& (grid_points(2) .eq. 2560) .and. &\n& (grid_points(3) .eq. 2560) .and. &\n& (no_time_steps .eq. 500) ) then\n\nclass = 'F'\ndtref = 0.15d-4\n\nxcrref(1) = 0.9281628449462d+05\nxcrref(2) = 0.2230152287675d+05\nxcrref(3) = 0.3493102358632d+05\nxcrref(4) = 0.3114096186689d+05\nxcrref(5) = 0.7424426448298d+05\n\nxceref(1) = 0.2683717702444d+03\nxceref(2) = 0.2030647554028d+02\nxceref(3) = 0.6734864248234d+02\nxceref(4) = 0.5947451301640d+02\nxceref(5) = 0.5417636652565d+03\n\n\nelse\nverified = .false.\nendif\n\n\ndo m = 1, 5\n\nxcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))\nxcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))\n\nenddo\n\n\nif (class .ne. 'U') then\nwrite(*, 1990) class\n1990 format(' Verification being performed for class ', a)\nwrite (*,2000) epsilon\n2000 format(' accuracy setting for epsilon = ', E20.13)\nverified = (dabs(dt-dtref) .le. epsilon)\nif (.not.verified) then\nclass = 'U'\nwrite (*,1000) dtref\n1000 format(' DT does not match the reference value of ', &\n& E15.8)\nendif\nelse\nwrite(*, 1995)\n1995 format(' Unknown class')\nendif\n\n\nif (class .ne. 'U') then\nwrite (*, 2001)\nelse\nwrite (*, 2005)\nendif\n\n2001 format(' Comparison of RMS-norms of residual')\n2005 format(' RMS-norms of residual')\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(*, 2015) m, xcr(m)\nelse if ((.not.ieee_is_nan(xcrdif(m))) .and. &\n& xcrdif(m) .le. epsilon) then\nwrite (*,2011) m,xcr(m),xcrref(m),xcrdif(m)\nelse\nverified = .false.\nwrite (*,2010) m,xcr(m),xcrref(m),xcrdif(m)\nendif\nenddo\n\nif (class .ne. 'U') then\nwrite (*,2002)\nelse\nwrite (*,2006)\nendif\n2002 format(' Comparison of RMS-norms of solution error')\n2006 format(' RMS-norms of solution error')\n\ndo m = 1, 5\nif (class .eq. 'U') then\nwrite(*, 2015) m, xce(m)\nelse if ((.not.ieee_is_nan(xcedif(m))) .and. &\n& xcedif(m) .le. epsilon) then\nwrite (*,2011) m,xce(m),xceref(m),xcedif(m)\nelse\nverified = .false.\nwrite (*,2010) m,xce(m),xceref(m),xcedif(m)\nendif\nenddo\n\n2010 format(' FAILURE: ', i2, E20.13, E20.13, E20.13)\n2011 format(' ', i2, E20.13, E20.13, E20.13)\n2015 format(' ', i2, E20.13)\n\nif (class .eq. 'U') then\nwrite(*, 2022)\nwrite(*, 2023)\n2022 format(' No reference values provided')\n2023 format(' No verification performed')\nelse if (verified) then\nwrite(*, 2020)\n2020 format(' Verification Successful')\nelse\nwrite(*, 2021)\n2021 format(' Verification failed')\nendif\n\nreturn\n\n\nend

void add(){\nint i, j, k, m;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_ADD);}\n#pragma omp for\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++){\nu[k][j][i][m]=u[k][j][i][m]+rhs[k][j][i][m];\n}\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_ADD);}\n}

subroutine add\n\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m\n\nif (timeron) call timer_start(t_add)\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nu(m,i,j,k) = u(m,i,j,k) + rhs(m,i,j,k)\nenddo\nenddo\nenddo\nenddo\nif (timeron) call timer_stop(t_add)\n\nreturn\nend

void z_solve(){\nint i, j, k, k1, k2, m;\ndouble ru1, fac1, fac2;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_ZSOLVE);}\n#pragma omp for\nfor(j=1; j<=ny2; j++){\ndouble cv[PROBLEM_SIZE], rhos[PROBLEM_SIZE];\ndouble lhs[IMAXP+1][IMAXP+1][5];\ndouble lhsp[IMAXP+1][IMAXP+1][5];\ndouble lhsm[IMAXP+1][IMAXP+1][5];\n\nfor(i=1; i<=nx2; i++){\nfor(m=0; m<5; m++){\nlhs[0][i][m]=0.0;\nlhsp[0][i][m]=0.0;\nlhsm[0][i][m]=0.0;\nlhs[nz2+1][i][m]=0.0;\nlhsp[nz2+1][i][m]=0.0;\nlhsm[nz2+1][i][m]=0.0;\n}\nlhs[0][i][2]=1.0;\nlhsp[0][i][2]=1.0;\nlhsm[0][i][2]=1.0;\nlhs[nz2+1][i][2]=1.0;\nlhsp[nz2+1][i][2]=1.0;\nlhsm[nz2+1][i][2]=1.0;\n}\n\n\nfor(i=1; i<=nx2; i++){\nfor(k=0; k<=nz2+1; k++){\nru1=c3c4*rho_i[k][j][i];\ncv[k]=ws[k][j][i];\nrhos[k]=max(max(dz4+con43*ru1, dz5+c1c5*ru1), max(dzmax+ru1, dz1));\n}\nfor(k=1; k<=nz2; k++){\nlhs[k][i][0]=0.0;\nlhs[k][i][1]=-dttz2*cv[k-1]-dttz1*rhos[k-1];\nlhs[k][i][2]=1.0+c2dttz1*rhos[k];\nlhs[k][i][3]=dttz2*cv[k+1]-dttz1*rhos[k+1];\nlhs[k][i][4]=0.0;\n}\n}\n\nfor(i=1; i<=nx2; i++){\nk=1;\nlhs[k][i][2]=lhs[k][i][2]+comz5;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nlhs[k][i][4]=lhs[k][i][4]+comz1;\nk=2;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz6;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nlhs[k][i][4]=lhs[k][i][4]+comz1;\n}\nfor(k=3; k<=nz2-2; k++){\nfor(i=1; i<=nx2; i++){\nlhs[k][i][0]=lhs[k][i][0]+comz1;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz6;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nlhs[k][i][4]=lhs[k][i][4]+comz1;\n}\n}\nfor(i=1; i<=nx2; i++){\nk=nz2-1;\nlhs[k][i][0]=lhs[k][i][0]+comz1;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz6;\nlhs[k][i][3]=lhs[k][i][3]-comz4;\nk=nz2;\nlhs[k][i][0]=lhs[k][i][0]+comz1;\nlhs[k][i][1]=lhs[k][i][1]-comz4;\nlhs[k][i][2]=lhs[k][i][2]+comz5;\n}\n\nfor(k=1; k<=nz2; k++){\nfor(i=1; i<=nx2; i++){\nlhsp[k][i][0]=lhs[k][i][0];\nlhsp[k][i][1]=lhs[k][i][1]-dttz2*speed[k-1][j][i];\nlhsp[k][i][2]=lhs[k][i][2];\nlhsp[k][i][3]=lhs[k][i][3]+dttz2*speed[k+1][j][i];\nlhsp[k][i][4]=lhs[k][i][4];\nlhsm[k][i][0]=lhs[k][i][0];\nlhsm[k][i][1]=lhs[k][i][1]+dttz2*speed[k-1][j][i];\nlhsm[k][i][2]=lhs[k][i][2];\nlhsm[k][i][3]=lhs[k][i][3]-dttz2*speed[k+1][j][i];\nlhsm[k][i][4]=lhs[k][i][4];\n}\n}\n\nfor(k=0; k<=grid_points[2]-3; k++){\nk1=k+1;\nk2=k+2;\nfor(i=1; i<=nx2; i++){\nfac1=1.0/lhs[k][i][2];\nlhs[k][i][3]=fac1*lhs[k][i][3];\nlhs[k][i][4]=fac1*lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\n}\nlhs[k1][i][2]=lhs[k1][i][2]-lhs[k1][i][1]*lhs[k][i][3];\nlhs[k1][i][3]=lhs[k1][i][3]-lhs[k1][i][1]*lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhs[k1][i][1]*rhs[k][j][i][m];\n}\nlhs[k2][i][1]=lhs[k2][i][1]-lhs[k2][i][0]*lhs[k][i][3];\nlhs[k2][i][2]=lhs[k2][i][2]-lhs[k2][i][0]*lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k2][j][i][m]=rhs[k2][j][i][m]-lhs[k2][i][0]*rhs[k][j][i][m];\n}\n}\n}\n\nk=grid_points[2]-2;\nk1=grid_points[2]-1;\nfor(i=1; i<=nx2; i++){\nfac1=1.0/lhs[k][i][2];\nlhs[k][i][3]=fac1*lhs[k][i][3];\nlhs[k][i][4]=fac1*lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\n}\nlhs[k1][i][2]=lhs[k1][i][2]-lhs[k1][i][1]*lhs[k][i][3];\nlhs[k1][i][3]=lhs[k1][i][3]-lhs[k1][i][1]*lhs[k][i][4];\nfor(m=0; m<3; m++){\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhs[k1][i][1]*rhs[k][j][i][m];\n}\n\nfac2=1.0/lhs[k1][i][2];\nfor(m=0; m<3; m++){\nrhs[k1][j][i][m]=fac2*rhs[k1][j][i][m];\n}\n}\n\nfor(k=0; k<=grid_points[2]-3; k++){\nk1=k+1;\nk2=k+2;\nfor(i=1; i<=nx2; i++){\nm=3;\nfac1=1.0/lhsp[k][i][2];\nlhsp[k][i][3]=fac1*lhsp[k][i][3];\nlhsp[k][i][4]=fac1*lhsp[k][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsp[k1][i][2]=lhsp[k1][i][2]-lhsp[k1][i][1]*lhsp[k][i][3];\nlhsp[k1][i][3]=lhsp[k1][i][3]-lhsp[k1][i][1]*lhsp[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsp[k1][i][1]*rhs[k][j][i][m];\nlhsp[k2][i][1]=lhsp[k2][i][1]-lhsp[k2][i][0]*lhsp[k][i][3];\nlhsp[k2][i][2]=lhsp[k2][i][2]-lhsp[k2][i][0]*lhsp[k][i][4];\nrhs[k2][j][i][m]=rhs[k2][j][i][m]-lhsp[k2][i][0]*rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[k][i][2];\nlhsm[k][i][3]=fac1*lhsm[k][i][3];\nlhsm[k][i][4]=fac1*lhsm[k][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsm[k1][i][2]=lhsm[k1][i][2]-lhsm[k1][i][1]*lhsm[k][i][3];\nlhsm[k1][i][3]=lhsm[k1][i][3]-lhsm[k1][i][1]*lhsm[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsm[k1][i][1]*rhs[k][j][i][m];\nlhsm[k2][i][1]=lhsm[k2][i][1]-lhsm[k2][i][0]*lhsm[k][i][3];\nlhsm[k2][i][2]=lhsm[k2][i][2]-lhsm[k2][i][0]*lhsm[k][i][4];\nrhs[k2][j][i][m]=rhs[k2][j][i][m]-lhsm[k2][i][0]*rhs[k][j][i][m];\n}\n}\n\nk=grid_points[2]-2;\nk1=grid_points[2]-1;\nfor(i=1; i<=nx2; i++){\nm=3;\nfac1=1.0/lhsp[k][i][2];\nlhsp[k][i][3]=fac1*lhsp[k][i][3];\nlhsp[k][i][4]=fac1*lhsp[k][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsp[k1][i][2]=lhsp[k1][i][2]-lhsp[k1][i][1]*lhsp[k][i][3];\nlhsp[k1][i][3]=lhsp[k1][i][3]-lhsp[k1][i][1]*lhsp[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsp[k1][i][1]*rhs[k][j][i][m];\nm=4;\nfac1=1.0/lhsm[k][i][2];\nlhsm[k][i][3]=fac1*lhsm[k][i][3];\nlhsm[k][i][4]=fac1*lhsm[k][i][4];\nrhs[k][j][i][m]=fac1*rhs[k][j][i][m];\nlhsm[k1][i][2]=lhsm[k1][i][2]-lhsm[k1][i][1]*lhsm[k][i][3];\nlhsm[k1][i][3]=lhsm[k1][i][3]-lhsm[k1][i][1]*lhsm[k][i][4];\nrhs[k1][j][i][m]=rhs[k1][j][i][m]-lhsm[k1][i][1]*rhs[k][j][i][m];\n\nrhs[k1][j][i][3]=rhs[k1][j][i][3]/lhsp[k1][i][2];\nrhs[k1][j][i][4]=rhs[k1][j][i][4]/lhsm[k1][i][2];\n}\n\nk=grid_points[2]-2;\nk1=grid_points[2]-1;\nfor(i=1; i<=nx2; i++){\nfor(m=0; m<3; m++){\nrhs[k][j][i][m]=rhs[k][j][i][m]-lhs[k][i][3]*rhs[k1][j][i][m];\n}\nrhs[k][j][i][3]=rhs[k][j][i][3]-lhsp[k][i][3]*rhs[k1][j][i][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-lhsm[k][i][3]*rhs[k1][j][i][4];\n}\n\nfor(k=grid_points[2]-3; k>=0; k--){\nk1=k+1;\nk2=k+2;\nfor(i=1; i<=nx2; i++){\nfor (m = 0; m < 3; m++) {\nrhs[k][j][i][m]=rhs[k][j][i][m]-\nlhs[k][i][3]*rhs[k1][j][i][m]-\nlhs[k][i][4]*rhs[k2][j][i][m];\n}\n\nrhs[k][j][i][3]=rhs[k][j][i][3]-\nlhsp[k][i][3]*rhs[k1][j][i][3]-\nlhsp[k][i][4]*rhs[k2][j][i][3];\nrhs[k][j][i][4]=rhs[k][j][i][4]-\nlhsm[k][i][3]*rhs[k1][j][i][4]-\nlhsm[k][i][4]*rhs[k2][j][i][4];\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_ZSOLVE);}\ntzetar();\n}

subroutine z_solve\n\n\n\nuse sp_data\nuse work_lhs\n\nimplicit none\n\ninteger i, j, k, k1, k2, m\ndouble precision ru1, fac1, fac2\n\n\n\n\nif (timeron) call timer_start(t_zsolve)\ndo j = 1, ny2\ndo i = 1, nx2\n\ncall lhsinit(nz2+1, lhs, lhsp, lhsm)\n\n\n\ndo k = 0, nz2 + 1\nru1 = c3c4*rho_i(i,j,k)\ncv(k) = ws(i,j,k)\nrhov(k) = dmax1(dz4 + con43 * ru1, &\n& dz5 + c1c5 * ru1, &\n& dzmax + ru1, &\n& dz1)\nend do\n\ndo k = 1, nz2\nlhs(1,k) = 0.0d0\nlhs(2,k) = -dttz2 * cv(k-1) - dttz1 * rhov(k-1)\nlhs(3,k) = 1.0 + c2dttz1 * rhov(k)\nlhs(4,k) = dttz2 * cv(k+1) - dttz1 * rhov(k+1)\nlhs(5,k) = 0.0d0\nend do\n\n\nk = 1\nlhs(3,k) = lhs(3,k) + comz5\nlhs(4,k) = lhs(4,k) - comz4\nlhs(5,k) = lhs(5,k) + comz1\n\nk = 2\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz6\nlhs(4,k) = lhs(4,k) - comz4\nlhs(5,k) = lhs(5,k) + comz1\n\ndo k = 3, nz2-2\nlhs(1,k) = lhs(1,k) + comz1\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz6\nlhs(4,k) = lhs(4,k) - comz4\nlhs(5,k) = lhs(5,k) + comz1\nend do\n\nk = nz2-1\nlhs(1,k) = lhs(1,k) + comz1\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz6\nlhs(4,k) = lhs(4,k) - comz4\n\nk = nz2\nlhs(1,k) = lhs(1,k) + comz1\nlhs(2,k) = lhs(2,k) - comz4\nlhs(3,k) = lhs(3,k) + comz5\n\n\ndo k = 1, nz2\nlhsp(1,k) = lhs(1,k)\nlhsp(2,k) = lhs(2,k) - &\n& dttz2 * speed(i,j,k-1)\nlhsp(3,k) = lhs(3,k)\nlhsp(4,k) = lhs(4,k) + &\n& dttz2 * speed(i,j,k+1)\nlhsp(5,k) = lhs(5,k)\nlhsm(1,k) = lhs(1,k)\nlhsm(2,k) = lhs(2,k) + &\n& dttz2 * speed(i,j,k-1)\nlhsm(3,k) = lhs(3,k)\nlhsm(4,k) = lhs(4,k) - &\n& dttz2 * speed(i,j,k+1)\nlhsm(5,k) = lhs(5,k)\nend do\n\n\n\ndo k = 0, grid_points(3)-3\nk1 = k + 1\nk2 = k + 2\nfac1 = 1.d0/lhs(3,k)\nlhs(4,k) = fac1*lhs(4,k)\nlhs(5,k) = fac1*lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nend do\nlhs(3,k1) = lhs(3,k1) - &\n& lhs(2,k1)*lhs(4,k)\nlhs(4,k1) = lhs(4,k1) - &\n& lhs(2,k1)*lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhs(2,k1)*rhs(m,i,j,k)\nend do\nlhs(2,k2) = lhs(2,k2) - &\n& lhs(1,k2)*lhs(4,k)\nlhs(3,k2) = lhs(3,k2) - &\n& lhs(1,k2)*lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k2) = rhs(m,i,j,k2) - &\n& lhs(1,k2)*rhs(m,i,j,k)\nend do\nend do\n\nk = grid_points(3)-2\nk1 = grid_points(3)-1\nfac1 = 1.d0/lhs(3,k)\nlhs(4,k) = fac1*lhs(4,k)\nlhs(5,k) = fac1*lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nend do\nlhs(3,k1) = lhs(3,k1) - &\n& lhs(2,k1)*lhs(4,k)\nlhs(4,k1) = lhs(4,k1) - &\n& lhs(2,k1)*lhs(5,k)\ndo m = 1, 3\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhs(2,k1)*rhs(m,i,j,k)\nend do\nfac2 = 1.d0/lhs(3,k1)\ndo m = 1, 3\nrhs(m,i,j,k1) = fac2*rhs(m,i,j,k1)\nend do\n\ndo k = 0, grid_points(3)-3\nk1 = k + 1\nk2 = k + 2\nm = 4\nfac1 = 1.d0/lhsp(3,k)\nlhsp(4,k) = fac1*lhsp(4,k)\nlhsp(5,k) = fac1*lhsp(5,k)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsp(3,k1) = lhsp(3,k1) - &\n& lhsp(2,k1)*lhsp(4,k)\nlhsp(4,k1) = lhsp(4,k1) - &\n& lhsp(2,k1)*lhsp(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsp(2,k1)*rhs(m,i,j,k)\nlhsp(2,k2) = lhsp(2,k2) - &\n& lhsp(1,k2)*lhsp(4,k)\nlhsp(3,k2) = lhsp(3,k2) - &\n& lhsp(1,k2)*lhsp(5,k)\nrhs(m,i,j,k2) = rhs(m,i,j,k2) - &\n& lhsp(1,k2)*rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,k)\nlhsm(4,k) = fac1*lhsm(4,k)\nlhsm(5,k) = fac1*lhsm(5,k)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsm(3,k1) = lhsm(3,k1) - &\n& lhsm(2,k1)*lhsm(4,k)\nlhsm(4,k1) = lhsm(4,k1) - &\n& lhsm(2,k1)*lhsm(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsm(2,k1)*rhs(m,i,j,k)\nlhsm(2,k2) = lhsm(2,k2) - &\n& lhsm(1,k2)*lhsm(4,k)\nlhsm(3,k2) = lhsm(3,k2) - &\n& lhsm(1,k2)*lhsm(5,k)\nrhs(m,i,j,k2) = rhs(m,i,j,k2) - &\n& lhsm(1,k2)*rhs(m,i,j,k)\nend do\n\nk = grid_points(3)-2\nk1 = grid_points(3)-1\nm = 4\nfac1 = 1.d0/lhsp(3,k)\nlhsp(4,k) = fac1*lhsp(4,k)\nlhsp(5,k) = fac1*lhsp(5,k)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsp(3,k1) = lhsp(3,k1) - &\n& lhsp(2,k1)*lhsp(4,k)\nlhsp(4,k1) = lhsp(4,k1) - &\n& lhsp(2,k1)*lhsp(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsp(2,k1)*rhs(m,i,j,k)\nm = 5\nfac1 = 1.d0/lhsm(3,k)\nlhsm(4,k) = fac1*lhsm(4,k)\nlhsm(5,k) = fac1*lhsm(5,k)\nrhs(m,i,j,k) = fac1*rhs(m,i,j,k)\nlhsm(3,k1) = lhsm(3,k1) - &\n& lhsm(2,k1)*lhsm(4,k)\nlhsm(4,k1) = lhsm(4,k1) - &\n& lhsm(2,k1)*lhsm(5,k)\nrhs(m,i,j,k1) = rhs(m,i,j,k1) - &\n& lhsm(2,k1)*rhs(m,i,j,k)\nrhs(4,i,j,k1) = rhs(4,i,j,k1)/lhsp(3,k1)\nrhs(5,i,j,k1) = rhs(5,i,j,k1)/lhsm(3,k1)\n\n\n\nk = grid_points(3)-2\nk1 = grid_points(3)-1\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,k)*rhs(m,i,j,k1)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,k)*rhs(4,i,j,k1)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,k)*rhs(5,i,j,k1)\n\n\ndo k = grid_points(3)-3, 0, -1\nk1 = k + 1\nk2 = k + 2\ndo m = 1, 3\nrhs(m,i,j,k) = rhs(m,i,j,k) - &\n& lhs(4,k)*rhs(m,i,j,k1) - &\n& lhs(5,k)*rhs(m,i,j,k2)\nend do\n\nrhs(4,i,j,k) = rhs(4,i,j,k) - &\n& lhsp(4,k)*rhs(4,i,j,k1) - &\n& lhsp(5,k)*rhs(4,i,j,k2)\nrhs(5,i,j,k) = rhs(5,i,j,k) - &\n& lhsm(4,k)*rhs(5,i,j,k1) - &\n& lhsm(5,k)*rhs(5,i,j,k2)\nend do\n\nend do\nend do\nif (timeron) call timer_stop(t_zsolve)\n\ncall tzetar\n\nreturn\nend

void erhs(){\n\nint i, j, k, m;\ndouble xi, eta, zeta;\ndouble q;\ndouble u21, u31, u41;\ndouble tmp;\ndouble u21i, u31i, u41i, u51i;\ndouble u21j, u31j, u41j, u51j;\ndouble u21k, u31k, u41k, u51k;\ndouble u21im1, u31im1, u41im1, u51im1;\ndouble u21jm1, u31jm1, u41jm1, u51jm1;\ndouble u21km1, u31km1, u41km1, u51km1;\ndouble flux[ISIZ1][5];\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nfor(j=0; j<ny; j++){\nfor(i=0; i<nx; i++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=0.0;\n}\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nzeta=((double)k)/(nz-1);\nfor(j=0; j<ny; j++){\neta=((double)j)/(ny0-1 );\nfor(i=0; i<nx; i++){\nxi=((double)i)/(nx0-1);\nfor(m=0; m<5; m++){\nrsd[k][j][i][m]=ce[0][m]+\n(ce[1][m]+\n(ce[4][m]+\n(ce[7][m]+\nce[10][m]*xi)*xi)*xi)*xi+\n(ce[2][m]+\n(ce[5][m]+\n(ce[8][m]+\nce[11][m]*eta)*eta)*eta)*eta+\n(ce[3][m]+\n(ce[6][m]+\n(ce[9][m]+\nce[12][m]*zeta)*zeta)*zeta)*zeta;\n}\n}\n}\n}\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(j=jst; j<jend; j++){\nfor(i=0; i<nx; i++){\nflux[i][0]=rsd[k][j][i][1];\nu21=rsd[k][j][i][1]/rsd[k][j][i][0];\nq=0.50*(rsd[k][j][i][1]*rsd[k][j][i][1]\n+rsd[k][j][i][2]*rsd[k][j][i][2]\n+rsd[k][j][i][3]*rsd[k][j][i][3])\n/rsd[k][j][i][0];\nflux[i][1]=rsd[k][j][i][1]*u21+C2*(rsd[k][j][i][4]-q);\nflux[i][2]=rsd[k][j][i][2]*u21;\nflux[i][3]=rsd[k][j][i][3]*u21;\nflux[i][4]=(C1*rsd[k][j][i][4]-C2*q)*u21;\n}\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-tx2*(flux[i+1][m]-flux[i-1][m]);\n}\n}\nfor(i=ist; i<nx; i++){\ntmp=1.0/rsd[k][j][i][0];\nu21i=tmp*rsd[k][j][i][1];\nu31i=tmp*rsd[k][j][i][2];\nu41i=tmp*rsd[k][j][i][3];\nu51i=tmp*rsd[k][j][i][4];\ntmp=1.0/rsd[k][j][i-1][0];\nu21im1=tmp*rsd[k][j][i-1][1];\nu31im1=tmp*rsd[k][j][i-1][2];\nu41im1=tmp*rsd[k][j][i-1][3];\nu51im1=tmp*rsd[k][j][i-1][4];\nflux[i][1]=(4.0/3.0)*tx3*(u21i-u21im1);\nflux[i][2]=tx3*(u31i-u31im1);\nflux[i][3]=tx3*(u41i-u41im1);\nflux[i][4]=0.50*(1.0-C1*C5)\n*tx3*((u21i*u21i+u31i*u31i+u41i*u41i)\n-(u21im1*u21im1+u31im1*u31im1+u41im1*u41im1))\n+(1.0/6.0)\n*tx3*(u21i*u21i-u21im1*u21im1)\n+C1*C5*tx3*(u51i-u51im1);\n}\nfor(i=ist; i<iend; i++){\nfrct[k][j][i][0]=frct[k][j][i][0]\n+dx1*tx1*(rsd[k][j][i-1][0]\n-2.0*rsd[k][j][i][0]\n+rsd[k][j][i+1][0]);\nfrct[k][j][i][1]=frct[k][j][i][1]\n+tx3*C3*C4*(flux[i+1][1]-flux[i][1])\n+dx2*tx1*(rsd[k][j][i-1][1]\n-2.0*rsd[k][j][i][1]\n+rsd[k][j][i+1][1]);\nfrct[k][j][i][2]=frct[k][j][i][2]\n+tx3*C3*C4*(flux[i+1][2]-flux[i][2])\n+dx3*tx1*(rsd[k][j][i-1][2]\n-2.0*rsd[k][j][i][2]\n+rsd[k][j][i+1][2]);\nfrct[k][j][i][3]=frct[k][j][i][3]\n+tx3*C3*C4*(flux[i+1][3]-flux[i][3])\n+dx4*tx1*(rsd[k][j][i-1][3]\n-2.0*rsd[k][j][i][3]\n+rsd[k][j][i+1][3]);\nfrct[k][j][i][4]=frct[k][j][i][4]\n+tx3*C3*C4*(flux[i+1][4]-flux[i][4])\n+dx5*tx1*(rsd[k][j][i-1][4]\n-2.0*rsd[k][j][i][4]\n+rsd[k][j][i+1][4]);\n}\n\nfor(m=0; m<5; m++){\nfrct[k][j][1][m]=frct[k][j][1][m]\n-dssp*(+5.0*rsd[k][j][1][m]\n-4.0*rsd[k][j][2][m]\n+rsd[k][j][3][m]);\nfrct[k][j][2][m]=frct[k][j][2][m]\n-dssp*(-4.0*rsd[k][j][1][m]\n+6.0*rsd[k][j][2][m]\n-4.0*rsd[k][j][3][m]\n+rsd[k][j][4][m]);\n}\nfor(i=3; i<nx-3; i++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-dssp*(rsd[k][j][i-2][m]\n-4.0*rsd[k][j][i-1][m]\n+6.0*rsd[k][j][i][m]\n-4.0*rsd[k][j][i+1][m]\n+rsd[k][j][i+2][m] );\n}\n}\nfor(m=0; m<5; m++){\nfrct[k][j][nx-3][m]=frct[k][j][nx-3][m]\n-dssp*(rsd[k][j][nx-5][m]\n-4.0*rsd[k][j][nx-4][m]\n+6.0*rsd[k][j][nx-3][m]\n-4.0*rsd[k][j][nx-2][m] );\nfrct[k][j][nx-2][m]=frct[k][j][nx-2][m]\n-dssp*(rsd[k][j][nx-4][m]\n-4.0*rsd[k][j][nx-3][m]\n+5.0*rsd[k][j][nx-2][m] );\n}\n}\n}\n\n#pragma omp for\nfor(k=1; k<nz-1; k++){\nfor(i=ist; i<iend; i++){\nfor(j=0; j<ny; j++){\nflux[j][0]=rsd[k][j][i][2];\nu31=rsd[k][j][i][2]/rsd[k][j][i][0];\nq=0.50*(rsd[k][j][i][1]*rsd[k][j][i][1]\n+rsd[k][j][i][2]*rsd[k][j][i][2]\n+rsd[k][j][i][3]*rsd[k][j][i][3])\n/rsd[k][j][i][0];\nflux[j][1]=rsd[k][j][i][1]*u31;\nflux[j][2]=rsd[k][j][i][2]*u31+C2*(rsd[k][j][i][4]-q);\nflux[j][3]=rsd[k][j][i][3]*u31;\nflux[j][4]=(C1*rsd[k][j][i][4]-C2*q)*u31;\n}\nfor(j=jst; j<jend;j++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-ty2*(flux[j+1][m]-flux[j-1][m]);\n}\n}\nfor(j=jst; j<ny; j++){\ntmp=1.0/rsd[k][j][i][0];\nu21j=tmp*rsd[k][j][i][1];\nu31j=tmp*rsd[k][j][i][2];\nu41j=tmp*rsd[k][j][i][3];\nu51j=tmp*rsd[k][j][i][4];\ntmp=1.0/rsd[k][j-1][i][0];\nu21jm1=tmp*rsd[k][j-1][i][1];\nu31jm1=tmp*rsd[k][j-1][i][2];\nu41jm1=tmp*rsd[k][j-1][i][3];\nu51jm1=tmp*rsd[k][j-1][i][4];\nflux[j][1]=ty3*(u21j-u21jm1);\nflux[j][2]=(4.0/3.0)*ty3*(u31j-u31jm1);\nflux[j][3]=ty3*(u41j-u41jm1);\nflux[j][4]=0.50*(1.0-C1*C5)\n*ty3*((u21j*u21j+u31j*u31j+u41j*u41j)\n-(u21jm1*u21jm1+u31jm1*u31jm1+u41jm1*u41jm1))\n+(1.0/6.0)\n*ty3*(u31j*u31j-u31jm1*u31jm1)\n+C1*C5*ty3*(u51j-u51jm1);\n}\nfor(j=jst; j<jend; j++){\nfrct[k][j][i][0]=frct[k][j][i][0]\n+dy1*ty1*(rsd[k][j-1][i][0]\n-2.0*rsd[k][j][i][0]\n+rsd[k][j+1][i][0]);\nfrct[k][j][i][1]=frct[k][j][i][1]\n+ty3*C3*C4*(flux[j+1][1]-flux[j][1])\n+dy2*ty1*(rsd[k][j-1][i][1]\n-2.0*rsd[k][j][i][1]\n+rsd[k][j+1][i][1]);\nfrct[k][j][i][2]=frct[k][j][i][2]\n+ty3*C3*C4*(flux[j+1][2]-flux[j][2])\n+dy3*ty1*(rsd[k][j-1][i][2]\n-2.0*rsd[k][j][i][2]\n+rsd[k][j+1][i][2]);\nfrct[k][j][i][3]=frct[k][j][i][3]\n+ty3*C3*C4*(flux[j+1][3]-flux[j][3])\n+dy4*ty1*(rsd[k][j-1][i][3]\n-2.0*rsd[k][j][i][3]\n+rsd[k][j+1][i][3]);\nfrct[k][j][i][4]=frct[k][j][i][4]\n+ty3*C3*C4*(flux[j+1][4]-flux[j][4])\n+dy5*ty1*(rsd[k][j-1][i][4]\n-2.0*rsd[k][j][i][4]\n+rsd[k][j+1][i][4] );\n}\n\nfor(m=0; m<5; m++){\nfrct[k][1][i][m]=frct[k][1][i][m]\n-dssp*(+5.0*rsd[k][1][i][m]\n-4.0*rsd[k][2][i][m]\n+rsd[k][3][i][m]);\nfrct[k][2][i][m]=frct[k][2][i][m]\n-dssp*(-4.0*rsd[k][1][i][m]\n+6.0*rsd[k][2][i][m]\n-4.0*rsd[k][3][i][m]\n+rsd[k][4][i][m]);\n}\nfor(j=3; j<ny-3; j++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-dssp*(rsd[k][j-2][i][m]\n-4.0*rsd[k][j-1][i][m]\n+6.0*rsd[k][j][i][m]\n-4.0*rsd[k][j+1][i][m]\n+rsd[k][j+2][i][m]);\n}\n}\nfor(m=0; m<5; m++){\nfrct[k][ny-3][i][m]=frct[k][ny-3][i][m]\n-dssp*(rsd[k][ny-5][i][m]\n-4.0*rsd[k][ny-4][i][m]\n+6.0*rsd[k][ny-3][i][m]\n-4.0*rsd[k][ny-2][i][m]);\nfrct[k][ny-2][i][m]=frct[k][ny-2][i][m]\n-dssp*(rsd[k][ny-4][i][m]\n-4.0*rsd[k][ny-3][i][m]\n+5.0*rsd[k][ny-2][i][m]);\n}\n}\n}\n\n#pragma omp for\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(k=0; k<nz; k++){\nflux[k][0]=rsd[k][j][i][3];\nu41=rsd[k][j][i][3]/rsd[k][j][i][0];\nq=0.50*(rsd[k][j][i][1]*rsd[k][j][i][1]\n+rsd[k][j][i][2]*rsd[k][j][i][2]\n+rsd[k][j][i][3]*rsd[k][j][i][3])\n/rsd[k][j][i][0];\nflux[k][1]=rsd[k][j][i][1]*u41;\nflux[k][2]=rsd[k][j][i][2]*u41;\nflux[k][3]=rsd[k][j][i][3]*u41+C2*(rsd[k][j][i][4]-q);\nflux[k][4]=(C1*rsd[k][j][i][4]-C2*q)*u41;\n}\nfor(k=1; k<nz-1; k++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-tz2*(flux[k+1][m]-flux[k-1][m]);\n}\n}\nfor(k=1; k<nz; k++){\ntmp=1.0/rsd[k][j][i][0];\nu21k=tmp*rsd[k][j][i][1];\nu31k=tmp*rsd[k][j][i][2];\nu41k=tmp*rsd[k][j][i][3];\nu51k=tmp*rsd[k][j][i][4];\ntmp=1.0/rsd[k-1][j][i][0];\nu21km1=tmp*rsd[k-1][j][i][1];\nu31km1=tmp*rsd[k-1][j][i][2];\nu41km1=tmp*rsd[k-1][j][i][3];\nu51km1=tmp*rsd[k-1][j][i][4];\nflux[k][1]=tz3*(u21k-u21km1);\nflux[k][2]=tz3*(u31k-u31km1);\nflux[k][3]=(4.0/3.0)*tz3*(u41k-u41km1);\nflux[k][4]=0.50*(1.0-C1*C5)\n*tz3*((u21k*u21k+u31k*u31k+u41k*u41k)\n-(u21km1*u21km1+u31km1*u31km1+u41km1*u41km1))\n+(1.0/6.0)\n*tz3*(u41k*u41k-u41km1*u41km1)\n+C1*C5*tz3*(u51k-u51km1);\n}\nfor(k=1; k<nz-1; k++){\nfrct[k][j][i][0]=frct[k][j][i][0]\n+dz1*tz1*(rsd[k+1][j][i][0]\n-2.0*rsd[k][j][i][0]\n+rsd[k-1][j][i][0]);\nfrct[k][j][i][1]=frct[k][j][i][1]\n+tz3*C3*C4*(flux[k+1][1]-flux[k][1])\n+dz2*tz1*(rsd[k+1][j][i][1]\n-2.0*rsd[k][j][i][1]\n+rsd[k-1][j][i][1]);\nfrct[k][j][i][2]=frct[k][j][i][2]\n+tz3*C3*C4*(flux[k+1][2]-flux[k][2])\n+dz3*tz1*(rsd[k+1][j][i][2]\n-2.0*rsd[k][j][i][2]\n+rsd[k-1][j][i][2]);\nfrct[k][j][i][3]=frct[k][j][i][3]\n+tz3*C3*C4*(flux[k+1][3]-flux[k][3])\n+dz4*tz1*(rsd[k+1][j][i][3]\n-2.0*rsd[k][j][i][3]\n+rsd[k-1][j][i][3]);\nfrct[k][j][i][4]=frct[k][j][i][4]\n+tz3*C3*C4*(flux[k+1][4]-flux[k][4])\n+dz5*tz1*(rsd[k+1][j][i][4]\n-2.0*rsd[k][j][i][4]\n+rsd[k-1][j][i][4]);\n}\n\nfor(m=0; m<5; m++){\nfrct[1][j][i][m]=frct[1][j][i][m]\n-dssp*(+5.0*rsd[1][j][i][m]\n-4.0*rsd[2][j][i][m]\n+rsd[3][j][i][m]);\nfrct[2][j][i][m]=frct[2][j][i][m]\n-dssp*(-4.0*rsd[1][j][i][m]\n+6.0*rsd[2][j][i][m]\n-4.0*rsd[3][j][i][m]\n+rsd[4][j][i][m]);\n}\nfor(k=3; k<nz-3; k++){\nfor(m=0; m<5; m++){\nfrct[k][j][i][m]=frct[k][j][i][m]\n-dssp*(rsd[k-2][j][i][m]\n-4.0*rsd[k-1][j][i][m]\n+6.0*rsd[k][j][i][m]\n-4.0*rsd[k+1][j][i][m]\n+rsd[k+2][j][i][m]);\n}\n}\nfor(m=0; m<5; m++){\nfrct[nz-3][j][i][m]=frct[nz-3][j][i][m]\n-dssp*(rsd[nz-5][j][i][m]\n-4.0*rsd[nz-4][j][i][m]\n+6.0*rsd[nz-3][j][i][m]\n-4.0*rsd[nz-2][j][i][m]);\nfrct[nz-2][j][i][m]=frct[nz-2][j][i][m]\n-dssp*(rsd[nz-4][j][i][m]\n-4.0*rsd[nz-3][j][i][m]\n+5.0*rsd[nz-2][j][i][m]);\n}\n}\n}\n}

subroutine erhs\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision xi, eta, zeta\ndouble precision q\ndouble precision u21, u31, u41\ndouble precision tmp\ndouble precision u21i, u31i, u41i, u51i\ndouble precision u21j, u31j, u41j, u51j\ndouble precision u21k, u31k, u41k, u51k\ndouble precision u21im1, u31im1, u41im1, u51im1\ndouble precision u21jm1, u31jm1, u41jm1, u51jm1\ndouble precision u21km1, u31km1, u41km1, u51km1\n\n\ndo k = 1, nz\ndo j = 1, ny\ndo i = 1, nx\ndo m = 1, 5\nfrct( m, i, j, k ) = 0.0d+00\nend do\nend do\nend do\nend do\n\ndo k = 1, nz\ndo j = 1, ny\nzeta = ( dble(k-1) ) / ( nz - 1 )\neta = ( dble(j-1) ) / ( ny0 - 1 )\ndo i = 1, nx\nxi = ( dble(i-1) ) / ( nx0 - 1 )\ndo m = 1, 5\nrsd(m,i,j,k) = ce(m,1) &\n& + (ce(m,2) &\n& + (ce(m,5) &\n& + (ce(m,8) &\n& + ce(m,11) * xi) * xi) * xi) * xi &\n& + (ce(m,3) &\n& + (ce(m,6) &\n& + (ce(m,9) &\n& + ce(m,12) * eta) * eta) * eta) * eta &\n& + (ce(m,4) &\n& + (ce(m,7) &\n& + (ce(m,10) &\n& + ce(m,13) * zeta) * zeta) * zeta) * zeta\nend do\nend do\nend do\nend do\n\n\ndo k = 2, nz - 1\ndo j = jst, jend\ndo i = 1, nx\nflux(1,i) = rsd(2,i,j,k)\nu21 = rsd(2,i,j,k) / rsd(1,i,j,k)\nq = 0.50d+00 * ( rsd(2,i,j,k) * rsd(2,i,j,k) &\n& + rsd(3,i,j,k) * rsd(3,i,j,k) &\n& + rsd(4,i,j,k) * rsd(4,i,j,k) ) &\n& / rsd(1,i,j,k)\nflux(2,i) = rsd(2,i,j,k) * u21 + c2 * &\n& ( rsd(5,i,j,k) - q )\nflux(3,i) = rsd(3,i,j,k) * u21\nflux(4,i) = rsd(4,i,j,k) * u21\nflux(5,i) = ( c1 * rsd(5,i,j,k) - c2 * q ) * u21\nend do\n\ndo i = ist, iend\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - tx2 * ( flux(m,i+1) - flux(m,i-1) )\nend do\nend do\ndo i = ist, nx\ntmp = 1.0d+00 / rsd(1,i,j,k)\n\nu21i = tmp * rsd(2,i,j,k)\nu31i = tmp * rsd(3,i,j,k)\nu41i = tmp * rsd(4,i,j,k)\nu51i = tmp * rsd(5,i,j,k)\n\ntmp = 1.0d+00 / rsd(1,i-1,j,k)\n\nu21im1 = tmp * rsd(2,i-1,j,k)\nu31im1 = tmp * rsd(3,i-1,j,k)\nu41im1 = tmp * rsd(4,i-1,j,k)\nu51im1 = tmp * rsd(5,i-1,j,k)\n\nflux(2,i) = (4.0d+00/3.0d+00) * tx3 * &\n& ( u21i - u21im1 )\nflux(3,i) = tx3 * ( u31i - u31im1 )\nflux(4,i) = tx3 * ( u41i - u41im1 )\nflux(5,i) = 0.50d+00 * ( 1.0d+00 - c1*c5 ) &\n& * tx3 * ( ( u21i **2 + u31i **2 + u41i **2 ) &\n& - ( u21im1**2 + u31im1**2 + u41im1**2 ) ) &\n& + (1.0d+00/6.0d+00) &\n& * tx3 * ( u21i**2 - u21im1**2 ) &\n& + c1 * c5 * tx3 * ( u51i - u51im1 )\nend do\n\ndo i = ist, iend\nfrct(1,i,j,k) = frct(1,i,j,k) &\n& + dx1 * tx1 * ( rsd(1,i-1,j,k) &\n& - 2.0d+00 * rsd(1,i,j,k) &\n& + rsd(1,i+1,j,k) )\nfrct(2,i,j,k) = frct(2,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(2,i+1) - flux(2,i) ) &\n& + dx2 * tx1 * ( rsd(2,i-1,j,k) &\n& - 2.0d+00 * rsd(2,i,j,k) &\n& + rsd(2,i+1,j,k) )\nfrct(3,i,j,k) = frct(3,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(3,i+1) - flux(3,i) ) &\n& + dx3 * tx1 * ( rsd(3,i-1,j,k) &\n& - 2.0d+00 * rsd(3,i,j,k) &\n& + rsd(3,i+1,j,k) )\nfrct(4,i,j,k) = frct(4,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(4,i+1) - flux(4,i) ) &\n& + dx4 * tx1 * ( rsd(4,i-1,j,k) &\n& - 2.0d+00 * rsd(4,i,j,k) &\n& + rsd(4,i+1,j,k) )\nfrct(5,i,j,k) = frct(5,i,j,k) &\n& + tx3 * c3 * c4 * ( flux(5,i+1) - flux(5,i) ) &\n& + dx5 * tx1 * ( rsd(5,i-1,j,k) &\n& - 2.0d+00 * rsd(5,i,j,k) &\n& + rsd(5,i+1,j,k) )\nend do\n\ndo m = 1, 5\nfrct(m,2,j,k) = frct(m,2,j,k) &\n& - dssp * ( + 5.0d+00 * rsd(m,2,j,k) &\n& - 4.0d+00 * rsd(m,3,j,k) &\n& + rsd(m,4,j,k) )\nfrct(m,3,j,k) = frct(m,3,j,k) &\n& - dssp * ( - 4.0d+00 * rsd(m,2,j,k) &\n& + 6.0d+00 * rsd(m,3,j,k) &\n& - 4.0d+00 * rsd(m,4,j,k) &\n& + rsd(m,5,j,k) )\nend do\n\ndo i = 4, nx - 3\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - dssp * ( rsd(m,i-2,j,k) &\n& - 4.0d+00 * rsd(m,i-1,j,k) &\n& + 6.0d+00 * rsd(m,i,j,k) &\n& - 4.0d+00 * rsd(m,i+1,j,k) &\n& + rsd(m,i+2,j,k) )\nend do\nend do\n\ndo m = 1, 5\nfrct(m,nx-2,j,k) = frct(m,nx-2,j,k) &\n& - dssp * ( rsd(m,nx-4,j,k) &\n& - 4.0d+00 * rsd(m,nx-3,j,k) &\n& + 6.0d+00 * rsd(m,nx-2,j,k) &\n& - 4.0d+00 * rsd(m,nx-1,j,k) )\nfrct(m,nx-1,j,k) = frct(m,nx-1,j,k) &\n& - dssp * ( rsd(m,nx-3,j,k) &\n& - 4.0d+00 * rsd(m,nx-2,j,k) &\n& + 5.0d+00 * rsd(m,nx-1,j,k) )\nend do\n\nend do\nend do\n\n\ndo k = 2, nz - 1\ndo i = ist, iend\ndo j = 1, ny\nflux(1,j) = rsd(3,i,j,k)\nu31 = rsd(3,i,j,k) / rsd(1,i,j,k)\nq = 0.50d+00 * ( rsd(2,i,j,k) * rsd(2,i,j,k) &\n& + rsd(3,i,j,k) * rsd(3,i,j,k) &\n& + rsd(4,i,j,k) * rsd(4,i,j,k) ) &\n& / rsd(1,i,j,k)\nflux(2,j) = rsd(2,i,j,k) * u31\nflux(3,j) = rsd(3,i,j,k) * u31 + c2 * &\n& ( rsd(5,i,j,k) - q )\nflux(4,j) = rsd(4,i,j,k) * u31\nflux(5,j) = ( c1 * rsd(5,i,j,k) - c2 * q ) * u31\nend do\n\ndo j = jst, jend\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - ty2 * ( flux(m,j+1) - flux(m,j-1) )\nend do\nend do\n\ndo j = jst, ny\ntmp = 1.0d+00 / rsd(1,i,j,k)\n\nu21j = tmp * rsd(2,i,j,k)\nu31j = tmp * rsd(3,i,j,k)\nu41j = tmp * rsd(4,i,j,k)\nu51j = tmp * rsd(5,i,j,k)\n\ntmp = 1.0d+00 / rsd(1,i,j-1,k)\n\nu21jm1 = tmp * rsd(2,i,j-1,k)\nu31jm1 = tmp * rsd(3,i,j-1,k)\nu41jm1 = tmp * rsd(4,i,j-1,k)\nu51jm1 = tmp * rsd(5,i,j-1,k)\n\nflux(2,j) = ty3 * ( u21j - u21jm1 )\nflux(3,j) = (4.0d+00/3.0d+00) * ty3 * &\n& ( u31j - u31jm1 )\nflux(4,j) = ty3 * ( u41j - u41jm1 )\nflux(5,j) = 0.50d+00 * ( 1.0d+00 - c1*c5 ) &\n& * ty3 * ( ( u21j **2 + u31j **2 + u41j **2 ) &\n& - ( u21jm1**2 + u31jm1**2 + u41jm1**2 ) ) &\n& + (1.0d+00/6.0d+00) &\n& * ty3 * ( u31j**2 - u31jm1**2 ) &\n& + c1 * c5 * ty3 * ( u51j - u51jm1 )\nend do\n\ndo j = jst, jend\nfrct(1,i,j,k) = frct(1,i,j,k) &\n& + dy1 * ty1 * ( rsd(1,i,j-1,k) &\n& - 2.0d+00 * rsd(1,i,j,k) &\n& + rsd(1,i,j+1,k) )\nfrct(2,i,j,k) = frct(2,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(2,j+1) - flux(2,j) ) &\n& + dy2 * ty1 * ( rsd(2,i,j-1,k) &\n& - 2.0d+00 * rsd(2,i,j,k) &\n& + rsd(2,i,j+1,k) )\nfrct(3,i,j,k) = frct(3,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(3,j+1) - flux(3,j) ) &\n& + dy3 * ty1 * ( rsd(3,i,j-1,k) &\n& - 2.0d+00 * rsd(3,i,j,k) &\n& + rsd(3,i,j+1,k) )\nfrct(4,i,j,k) = frct(4,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(4,j+1) - flux(4,j) ) &\n& + dy4 * ty1 * ( rsd(4,i,j-1,k) &\n& - 2.0d+00 * rsd(4,i,j,k) &\n& + rsd(4,i,j+1,k) )\nfrct(5,i,j,k) = frct(5,i,j,k) &\n& + ty3 * c3 * c4 * ( flux(5,j+1) - flux(5,j) ) &\n& + dy5 * ty1 * ( rsd(5,i,j-1,k) &\n& - 2.0d+00 * rsd(5,i,j,k) &\n& + rsd(5,i,j+1,k) )\nend do\n\ndo m = 1, 5\nfrct(m,i,2,k) = frct(m,i,2,k) &\n& - dssp * ( + 5.0d+00 * rsd(m,i,2,k) &\n& - 4.0d+00 * rsd(m,i,3,k) &\n& + rsd(m,i,4,k) )\nfrct(m,i,3,k) = frct(m,i,3,k) &\n& - dssp * ( - 4.0d+00 * rsd(m,i,2,k) &\n& + 6.0d+00 * rsd(m,i,3,k) &\n& - 4.0d+00 * rsd(m,i,4,k) &\n& + rsd(m,i,5,k) )\nend do\n\ndo j = 4, ny - 3\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - dssp * ( rsd(m,i,j-2,k) &\n& - 4.0d+00 * rsd(m,i,j-1,k) &\n& + 6.0d+00 * rsd(m,i,j,k) &\n& - 4.0d+00 * rsd(m,i,j+1,k) &\n& + rsd(m,i,j+2,k) )\nend do\nend do\n\ndo m = 1, 5\nfrct(m,i,ny-2,k) = frct(m,i,ny-2,k) &\n& - dssp * ( rsd(m,i,ny-4,k) &\n& - 4.0d+00 * rsd(m,i,ny-3,k) &\n& + 6.0d+00 * rsd(m,i,ny-2,k) &\n& - 4.0d+00 * rsd(m,i,ny-1,k) )\nfrct(m,i,ny-1,k) = frct(m,i,ny-1,k) &\n& - dssp * ( rsd(m,i,ny-3,k) &\n& - 4.0d+00 * rsd(m,i,ny-2,k) &\n& + 5.0d+00 * rsd(m,i,ny-1,k) )\nend do\n\nend do\nend do\n\ndo j = jst, jend\ndo i = ist, iend\ndo k = 1, nz\nflux(1,k) = rsd(4,i,j,k)\nu41 = rsd(4,i,j,k) / rsd(1,i,j,k)\nq = 0.50d+00 * ( rsd(2,i,j,k) * rsd(2,i,j,k) &\n& + rsd(3,i,j,k) * rsd(3,i,j,k) &\n& + rsd(4,i,j,k) * rsd(4,i,j,k) ) &\n& / rsd(1,i,j,k)\nflux(2,k) = rsd(2,i,j,k) * u41\nflux(3,k) = rsd(3,i,j,k) * u41\nflux(4,k) = rsd(4,i,j,k) * u41 + c2 * &\n& ( rsd(5,i,j,k) - q )\nflux(5,k) = ( c1 * rsd(5,i,j,k) - c2 * q ) * u41\nend do\n\ndo k = 2, nz - 1\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - tz2 * ( flux(m,k+1) - flux(m,k-1) )\nend do\nend do\n\ndo k = 2, nz\ntmp = 1.0d+00 / rsd(1,i,j,k)\n\nu21k = tmp * rsd(2,i,j,k)\nu31k = tmp * rsd(3,i,j,k)\nu41k = tmp * rsd(4,i,j,k)\nu51k = tmp * rsd(5,i,j,k)\n\ntmp = 1.0d+00 / rsd(1,i,j,k-1)\n\nu21km1 = tmp * rsd(2,i,j,k-1)\nu31km1 = tmp * rsd(3,i,j,k-1)\nu41km1 = tmp * rsd(4,i,j,k-1)\nu51km1 = tmp * rsd(5,i,j,k-1)\n\nflux(2,k) = tz3 * ( u21k - u21km1 )\nflux(3,k) = tz3 * ( u31k - u31km1 )\nflux(4,k) = (4.0d+00/3.0d+00) * tz3 * ( u41k &\n& - u41km1 )\nflux(5,k) = 0.50d+00 * ( 1.0d+00 - c1*c5 ) &\n& * tz3 * ( ( u21k **2 + u31k **2 + u41k **2 ) &\n& - ( u21km1**2 + u31km1**2 + u41km1**2 ) ) &\n& + (1.0d+00/6.0d+00) &\n& * tz3 * ( u41k**2 - u41km1**2 ) &\n& + c1 * c5 * tz3 * ( u51k - u51km1 )\nend do\n\ndo k = 2, nz - 1\nfrct(1,i,j,k) = frct(1,i,j,k) &\n& + dz1 * tz1 * ( rsd(1,i,j,k+1) &\n& - 2.0d+00 * rsd(1,i,j,k) &\n& + rsd(1,i,j,k-1) )\nfrct(2,i,j,k) = frct(2,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(2,k+1) - flux(2,k) ) &\n& + dz2 * tz1 * ( rsd(2,i,j,k+1) &\n& - 2.0d+00 * rsd(2,i,j,k) &\n& + rsd(2,i,j,k-1) )\nfrct(3,i,j,k) = frct(3,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(3,k+1) - flux(3,k) ) &\n& + dz3 * tz1 * ( rsd(3,i,j,k+1) &\n& - 2.0d+00 * rsd(3,i,j,k) &\n& + rsd(3,i,j,k-1) )\nfrct(4,i,j,k) = frct(4,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(4,k+1) - flux(4,k) ) &\n& + dz4 * tz1 * ( rsd(4,i,j,k+1) &\n& - 2.0d+00 * rsd(4,i,j,k) &\n& + rsd(4,i,j,k-1) )\nfrct(5,i,j,k) = frct(5,i,j,k) &\n& + tz3 * c3 * c4 * ( flux(5,k+1) - flux(5,k) ) &\n& + dz5 * tz1 * ( rsd(5,i,j,k+1) &\n& - 2.0d+00 * rsd(5,i,j,k) &\n& + rsd(5,i,j,k-1) )\nend do\n\ndo m = 1, 5\nfrct(m,i,j,2) = frct(m,i,j,2) &\n& - dssp * ( + 5.0d+00 * rsd(m,i,j,2) &\n& - 4.0d+00 * rsd(m,i,j,3) &\n& + rsd(m,i,j,4) )\nfrct(m,i,j,3) = frct(m,i,j,3) &\n& - dssp * (- 4.0d+00 * rsd(m,i,j,2) &\n& + 6.0d+00 * rsd(m,i,j,3) &\n& - 4.0d+00 * rsd(m,i,j,4) &\n& + rsd(m,i,j,5) )\nend do\n\ndo k = 4, nz - 3\ndo m = 1, 5\nfrct(m,i,j,k) = frct(m,i,j,k) &\n& - dssp * ( rsd(m,i,j,k-2) &\n& - 4.0d+00 * rsd(m,i,j,k-1) &\n& + 6.0d+00 * rsd(m,i,j,k) &\n& - 4.0d+00 * rsd(m,i,j,k+1) &\n& + rsd(m,i,j,k+2) )\nend do\nend do\n\ndo m = 1, 5\nfrct(m,i,j,nz-2) = frct(m,i,j,nz-2) &\n& - dssp * ( rsd(m,i,j,nz-4) &\n& - 4.0d+00 * rsd(m,i,j,nz-3) &\n& + 6.0d+00 * rsd(m,i,j,nz-2) &\n& - 4.0d+00 * rsd(m,i,j,nz-1) )\nfrct(m,i,j,nz-1) = frct(m,i,j,nz-1) &\n& - dssp * ( rsd(m,i,j,nz-3) &\n& - 4.0d+00 * rsd(m,i,j,nz-2) &\n& + 5.0d+00 * rsd(m,i,j,nz-1) )\nend do\nend do\nend do\n\nreturn\nend

void txinvr(){\nint i, j, k;\ndouble t1, t2, t3, ac, ru1, uu, vv, ww, r1, r2, r3, r4, r5, ac2inv;\nint thread_id = omp_get_thread_num();\n\nif(timeron && thread_id==0){timer_start(T_TXINVR);}\n#pragma omp for\nfor(k=1; k<=nz2; k++){\nfor(j=1; j<=ny2; j++){\nfor(i=1; i<=nx2; i++){\nru1=rho_i[k][j][i];\nuu=us[k][j][i];\nvv=vs[k][j][i];\nww=ws[k][j][i];\nac=speed[k][j][i];\nac2inv=ac*ac;\nr1=rhs[k][j][i][0];\nr2=rhs[k][j][i][1];\nr3=rhs[k][j][i][2];\nr4=rhs[k][j][i][3];\nr5=rhs[k][j][i][4];\nt1=c2/ac2inv*(qs[k][j][i]*r1-uu*r2-vv*r3-ww*r4+r5);\nt2=bt*ru1*(uu*r1-r2);\nt3=(bt*ru1*ac)*t1;\nrhs[k][j][i][0]=r1-t1;\nrhs[k][j][i][1]=-ru1*(ww*r1-r4);\nrhs[k][j][i][2]=ru1*(vv*r1-r3);\nrhs[k][j][i][3]=-t2+t3;\nrhs[k][j][i][4]=t2+t3;\n}\n}\n}\nif(timeron && thread_id==0){timer_stop(T_TXINVR);}\n}

subroutine txinvr\n\n\n\nuse sp_data\nimplicit none\n\ninteger i, j, k\ndouble precision t1, t2, t3, ac, ru1, uu, vv, ww, r1, r2, r3, &\n& r4, r5, ac2inv\n\n\nif (timeron) call timer_start(t_txinvr)\ndo k = 1, nz2\ndo j = 1, ny2\ndo i = 1, nx2\n\nru1 = rho_i(i,j,k)\nuu = us(i,j,k)\nvv = vs(i,j,k)\nww = ws(i,j,k)\nac = speed(i,j,k)\nac2inv = ac*ac\n\nr1 = rhs(1,i,j,k)\nr2 = rhs(2,i,j,k)\nr3 = rhs(3,i,j,k)\nr4 = rhs(4,i,j,k)\nr5 = rhs(5,i,j,k)\n\nt1 = c2 / ac2inv * ( qs(i,j,k)*r1 - uu*r2 - &\n& vv*r3 - ww*r4 + r5 )\nt2 = bt * ru1 * ( uu * r1 - r2 )\nt3 = ( bt * ru1 * ac ) * t1\n\nrhs(1,i,j,k) = r1 - t1\nrhs(2,i,j,k) = - ru1 * ( ww*r1 - r4 )\nrhs(3,i,j,k) = ru1 * ( vv*r1 - r3 )\nrhs(4,i,j,k) = - t2 + t3\nrhs(5,i,j,k) = t2 + t3\n\nend do\nend do\nend do\nif (timeron) call timer_stop(t_txinvr)\n\nreturn\nend

void blts(int nx,\nint ny,\nint nz,\nint k,\ndouble omega,\ndouble v[][ISIZ2/2*2+1][ISIZ1/2*2+1][5],\ndouble ldz[][ISIZ1/2*2+1][5][5],\ndouble ldy[][ISIZ1/2*2+1][5][5],\ndouble ldx[][ISIZ1/2*2+1][5][5],\ndouble d[][ISIZ1/2*2+1][5][5],\nint ist,\nint iend,\nint jst,\nint jend,\nint nx0,\nint ny0){\n\nint i, j, m;\ndouble tmp, tmp1;\ndouble tmat[5][5], tv[5];\n\n#pragma omp for nowait schedule(static)\nfor(j=jst; j<jend; j++){\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\nv[k][j][i][m]= v[k][j][i][m]\n-omega*(ldz[j][i][0][m]*v[k-1][j][i][0]\n+ldz[j][i][1][m]*v[k-1][j][i][1]\n+ldz[j][i][2][m]*v[k-1][j][i][2]\n+ldz[j][i][3][m]*v[k-1][j][i][3]\n+ldz[j][i][4][m]*v[k-1][j][i][4]);\n}\n}\n}\n\n#pragma omp for nowait schedule(static)\nfor(j=jst; j<jend; j++){\n\nif (j != jst) {\nwhile (flag[j-1] == 0){\n#pragma omp flush\n;\n}\n}\nif (j != jend-1) {\nwhile (flag[j] == 1){\n#pragma omp flush\n;\n}\n}\n\nfor(i=ist; i<iend; i++){\nfor(m=0; m<5; m++){\ntv[m]=v[k][j][i][m]\n-omega*(ldy[j][i][0][m]*v[k][j-1][i][0]\n+ldx[j][i][0][m]*v[k][j][i-1][0]\n+ldy[j][i][1][m]*v[k][j-1][i][1]\n+ldx[j][i][1][m]*v[k][j][i-1][1]\n+ldy[j][i][2][m]*v[k][j-1][i][2]\n+ldx[j][i][2][m]*v[k][j][i-1][2]\n+ldy[j][i][3][m]*v[k][j-1][i][3]\n+ldx[j][i][3][m]*v[k][j][i-1][3]\n+ldy[j][i][4][m]*v[k][j-1][i][4]\n+ldx[j][i][4][m]*v[k][j][i-1][4]);\n}\n\nfor(m=0; m<5; m++){\ntmat[0][m]=d[j][i][0][m];\ntmat[1][m]=d[j][i][1][m];\ntmat[2][m]=d[j][i][2][m];\ntmat[3][m]=d[j][i][3][m];\ntmat[4][m]=d[j][i][4][m];\n}\n\ntmp1=1.0/tmat[0][0];\ntmp=tmp1*tmat[0][1];\ntmat[1][1]=tmat[1][1]-tmp*tmat[1][0];\ntmat[2][1]=tmat[2][1]-tmp*tmat[2][0];\ntmat[3][1]=tmat[3][1]-tmp*tmat[3][0];\ntmat[4][1]=tmat[4][1]-tmp*tmat[4][0];\ntv[1]=tv[1]-tv[0]*tmp;\n\ntmp=tmp1*tmat[0][2];\ntmat[1][2]=tmat[1][2]-tmp*tmat[1][0];\ntmat[2][2]=tmat[2][2]-tmp*tmat[2][0];\ntmat[3][2]=tmat[3][2]-tmp*tmat[3][0];\ntmat[4][2]=tmat[4][2]-tmp*tmat[4][0];\ntv[2]=tv[2]-tv[0]*tmp;\n\ntmp=tmp1*tmat[0][3];\ntmat[1][3]=tmat[1][3]-tmp*tmat[1][0];\ntmat[2][3]=tmat[2][3]-tmp*tmat[2][0];\ntmat[3][3]=tmat[3][3]-tmp*tmat[3][0];\ntmat[4][3]=tmat[4][3]-tmp*tmat[4][0];\ntv[3]=tv[3]-tv[0]*tmp;\n\ntmp=tmp1*tmat[0][4];\ntmat[1][4]=tmat[1][4]-tmp*tmat[1][0];\ntmat[2][4]=tmat[2][4]-tmp*tmat[2][0];\ntmat[3][4]=tmat[3][4]-tmp*tmat[3][0];\ntmat[4][4]=tmat[4][4]-tmp*tmat[4][0];\ntv[4]=tv[4]-tv[0]*tmp;\n\ntmp1=1.0/tmat[1][1];\ntmp=tmp1*tmat[1][2];\ntmat[2][2]=tmat[2][2]-tmp*tmat[2][1];\ntmat[3][2]=tmat[3][2]-tmp*tmat[3][1];\ntmat[4][2]=tmat[4][2]-tmp*tmat[4][1];\ntv[2]=tv[2]-tv[1]*tmp;\n\ntmp=tmp1*tmat[1][3];\ntmat[2][3]=tmat[2][3]-tmp*tmat[2][1];\ntmat[3][3]=tmat[3][3]-tmp*tmat[3][1];\ntmat[4][3]=tmat[4][3]-tmp*tmat[4][1];\ntv[3]=tv[3]-tv[1]*tmp;\n\ntmp=tmp1*tmat[1][4];\ntmat[2][4]=tmat[2][4]-tmp*tmat[2][1];\ntmat[3][4]=tmat[3][4]-tmp*tmat[3][1];\ntmat[4][4]=tmat[4][4]-tmp*tmat[4][1];\ntv[4]=tv[4]-tv[1]*tmp;\n\ntmp1=1.0/tmat[2][2];\ntmp=tmp1*tmat[2][3];\ntmat[3][3]=tmat[3][3]-tmp*tmat[3][2];\ntmat[4][3]=tmat[4][3]-tmp*tmat[4][2];\ntv[3]=tv[3]-tv[2]*tmp;\n\ntmp=tmp1*tmat[2][4];\ntmat[3][4]=tmat[3][4]-tmp*tmat[3][2];\ntmat[4][4]=tmat[4][4]-tmp*tmat[4][2];\ntv[4]=tv[4]-tv[2]*tmp;\n\ntmp1=1.0/tmat[3][3];\ntmp=tmp1*tmat[3][4];\ntmat[4][4]=tmat[4][4]-tmp*tmat[4][3];\ntv[4]=tv[4]-tv[3]*tmp;\n\nv[k][j][i][4]=tv[4]/tmat[4][4];\ntv[3]=tv[3]\n-tmat[4][3]*v[k][j][i][4];\nv[k][j][i][3]=tv[3]/tmat[3][3];\ntv[2]=tv[2]\n-tmat[3][2]*v[k][j][i][3]\n-tmat[4][2]*v[k][j][i][4];\nv[k][j][i][2]=tv[2]/tmat[2][2];\ntv[1]=tv[1]\n-tmat[2][1]*v[k][j][i][2]\n-tmat[3][1]*v[k][j][i][3]\n-tmat[4][1]*v[k][j][i][4];\nv[k][j][i][1]=tv[1]/tmat[1][1];\ntv[0]=tv[0]\n-tmat[1][0]*v[k][j][i][1]\n-tmat[2][0]*v[k][j][i][2]\n-tmat[3][0]*v[k][j][i][3]\n-tmat[4][0]*v[k][j][i][4];\nv[k][j][i][0]=tv[0]/tmat[0][0];\n}\n\nif (j != jend-1) flag[j] = 1;\nif (j != jst) flag[j-1] = 0;\n}\n}

subroutine blts ( ldmx, ldmy, ldmz, &\n& nx, ny, nz, &\n& omega, &\n& v, &\n& ldz, ldy, ldx, d, &\n& ist, iend, j, k )\n\n\n\nimplicit none\n\ninteger ldmx, ldmy, ldmz\ninteger nx, ny, nz\ndouble precision omega\ndouble precision v( 5, ldmx/2*2+1, ldmy/2*2+1, ldmz), &\n& ldz( 5, 5, ldmx ), &\n& ldy( 5, 5, ldmx ), &\n& ldx( 5, 5, ldmx ), &\n& d ( 5, 5, ldmx )\ninteger ist, iend, j, k\n\ninteger i, m\ndouble precision tmp, tmp1\ndouble precision tmat(5,5), tv(5)\n\n\ndo i = ist, iend\ndo m = 1, 5\n\ntv( m ) = v( m, i, j, k ) &\n& - omega * ( ldz( m, 1, i ) * v( 1, i, j, k-1 ) &\n& + ldz( m, 2, i ) * v( 2, i, j, k-1 ) &\n& + ldz( m, 3, i ) * v( 3, i, j, k-1 ) &\n& + ldz( m, 4, i ) * v( 4, i, j, k-1 ) &\n& + ldz( m, 5, i ) * v( 5, i, j, k-1 ) )\n\ntv( m ) = tv( m ) &\n& - omega * ( ldy( m, 1, i ) * v( 1, i, j-1, k ) &\n& + ldx( m, 1, i ) * v( 1, i-1, j, k ) &\n& + ldy( m, 2, i ) * v( 2, i, j-1, k ) &\n& + ldx( m, 2, i ) * v( 2, i-1, j, k ) &\n& + ldy( m, 3, i ) * v( 3, i, j-1, k ) &\n& + ldx( m, 3, i ) * v( 3, i-1, j, k ) &\n& + ldy( m, 4, i ) * v( 4, i, j-1, k ) &\n& + ldx( m, 4, i ) * v( 4, i-1, j, k ) &\n& + ldy( m, 5, i ) * v( 5, i, j-1, k ) &\n& + ldx( m, 5, i ) * v( 5, i-1, j, k ) )\n\nend do\n\ndo m = 1, 5\ntmat( m, 1 ) = d( m, 1, i )\ntmat( m, 2 ) = d( m, 2, i )\ntmat( m, 3 ) = d( m, 3, i )\ntmat( m, 4 ) = d( m, 4, i )\ntmat( m, 5 ) = d( m, 5, i )\nend do\n\ntmp1 = 1.0d+00 / tmat( 1, 1 )\ntmp = tmp1 * tmat( 2, 1 )\ntmat( 2, 2 ) = tmat( 2, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 2, 3 ) = tmat( 2, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 2, 4 ) = tmat( 2, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 2, 5 ) = tmat( 2, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 2 ) = tv( 2 ) &\n& - tv( 1 ) * tmp\n\ntmp = tmp1 * tmat( 3, 1 )\ntmat( 3, 2 ) = tmat( 3, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 3, 3 ) = tmat( 3, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 3, 4 ) = tmat( 3, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 3, 5 ) = tmat( 3, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 3 ) = tv( 3 ) &\n& - tv( 1 ) * tmp\n\ntmp = tmp1 * tmat( 4, 1 )\ntmat( 4, 2 ) = tmat( 4, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 4, 3 ) = tmat( 4, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 4, 4 ) = tmat( 4, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 4, 5 ) = tmat( 4, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 4 ) = tv( 4 ) &\n& - tv( 1 ) * tmp\n\ntmp = tmp1 * tmat( 5, 1 )\ntmat( 5, 2 ) = tmat( 5, 2 ) &\n& - tmp * tmat( 1, 2 )\ntmat( 5, 3 ) = tmat( 5, 3 ) &\n& - tmp * tmat( 1, 3 )\ntmat( 5, 4 ) = tmat( 5, 4 ) &\n& - tmp * tmat( 1, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 1, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 1 ) * tmp\n\n\n\ntmp1 = 1.0d+00 / tmat( 2, 2 )\ntmp = tmp1 * tmat( 3, 2 )\ntmat( 3, 3 ) = tmat( 3, 3 ) &\n& - tmp * tmat( 2, 3 )\ntmat( 3, 4 ) = tmat( 3, 4 ) &\n& - tmp * tmat( 2, 4 )\ntmat( 3, 5 ) = tmat( 3, 5 ) &\n& - tmp * tmat( 2, 5 )\ntv( 3 ) = tv( 3 ) &\n& - tv( 2 ) * tmp\n\ntmp = tmp1 * tmat( 4, 2 )\ntmat( 4, 3 ) = tmat( 4, 3 ) &\n& - tmp * tmat( 2, 3 )\ntmat( 4, 4 ) = tmat( 4, 4 ) &\n& - tmp * tmat( 2, 4 )\ntmat( 4, 5 ) = tmat( 4, 5 ) &\n& - tmp * tmat( 2, 5 )\ntv( 4 ) = tv( 4 ) &\n& - tv( 2 ) * tmp\n\ntmp = tmp1 * tmat( 5, 2 )\ntmat( 5, 3 ) = tmat( 5, 3 ) &\n& - tmp * tmat( 2, 3 )\ntmat( 5, 4 ) = tmat( 5, 4 ) &\n& - tmp * tmat( 2, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 2, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 2 ) * tmp\n\n\n\ntmp1 = 1.0d+00 / tmat( 3, 3 )\ntmp = tmp1 * tmat( 4, 3 )\ntmat( 4, 4 ) = tmat( 4, 4 ) &\n& - tmp * tmat( 3, 4 )\ntmat( 4, 5 ) = tmat( 4, 5 ) &\n& - tmp * tmat( 3, 5 )\ntv( 4 ) = tv( 4 ) &\n& - tv( 3 ) * tmp\n\ntmp = tmp1 * tmat( 5, 3 )\ntmat( 5, 4 ) = tmat( 5, 4 ) &\n& - tmp * tmat( 3, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 3, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 3 ) * tmp\n\n\n\ntmp1 = 1.0d+00 / tmat( 4, 4 )\ntmp = tmp1 * tmat( 5, 4 )\ntmat( 5, 5 ) = tmat( 5, 5 ) &\n& - tmp * tmat( 4, 5 )\ntv( 5 ) = tv( 5 ) &\n& - tv( 4 ) * tmp\n\nv( 5, i, j, k ) = tv( 5 ) &\n& / tmat( 5, 5 )\n\ntv( 4 ) = tv( 4 ) &\n& - tmat( 4, 5 ) * v( 5, i, j, k )\nv( 4, i, j, k ) = tv( 4 ) &\n& / tmat( 4, 4 )\n\ntv( 3 ) = tv( 3 ) &\n& - tmat( 3, 4 ) * v( 4, i, j, k ) &\n& - tmat( 3, 5 ) * v( 5, i, j, k )\nv( 3, i, j, k ) = tv( 3 ) &\n& / tmat( 3, 3 )\n\ntv( 2 ) = tv( 2 ) &\n& - tmat( 2, 3 ) * v( 3, i, j, k ) &\n& - tmat( 2, 4 ) * v( 4, i, j, k ) &\n& - tmat( 2, 5 ) * v( 5, i, j, k )\nv( 2, i, j, k ) = tv( 2 ) &\n& / tmat( 2, 2 )\n\ntv( 1 ) = tv( 1 ) &\n& - tmat( 1, 2 ) * v( 2, i, j, k ) &\n& - tmat( 1, 3 ) * v( 3, i, j, k ) &\n& - tmat( 1, 4 ) * v( 4, i, j, k ) &\n& - tmat( 1, 5 ) * v( 5, i, j, k )\nv( 1, i, j, k ) = tv( 1 ) &\n& / tmat( 1, 1 )\n\n\nenddo\n\n\nreturn\nend

static void cffts2(int is,\nint d1,\nint d2,\nint d3,\nvoid* pointer_x,\nvoid* pointer_xout,\ndcomplex y1[][FFTBLOCKPAD],\ndcomplex y2[][FFTBLOCKPAD]){\ndcomplex (*x)[NY][NX] = (dcomplex(*)[NY][NX])pointer_x;\ndcomplex (*xout)[NY][NX] = (dcomplex(*)[NY][NX])pointer_xout;\n\nint logd2;\nint i, j, k, ii;\n\nlogd2 = ilog2(d2);\n\nif(timers_enabled){\n#pragma omp master\ntimer_start(T_FFTY);\n}\n\n#pragma omp for\nfor(k=0; k<d3; k++){\nfor(ii=0; ii<=d1-FFTBLOCK; ii+=FFTBLOCK){\nfor(j=0; j<d2; j++){\nfor(i=0; i<FFTBLOCK; i++){\ny1[j][i] = x[k][j][i+ii];\n}\n}\ncfftz(is, logd2, d2, y1, y2);\nfor(j=0; j<d2; j++){\nfor(i=0; i<FFTBLOCK; i++){\nxout[k][j][i+ii] = y1[j][i];\n}\n}\n}\n}\n\nif(timers_enabled){\n#pragma omp master\ntimer_stop(T_FFTY);\n}\n}

subroutine cffts2(is, d1, d2, d3, x, xout, y1, y2)\n\n\nuse ft_data\nimplicit none\n\ninteger is, d1, d2, d3, logd2\ndouble complex x(d1+1,d2,d3)\ndouble complex xout(d1+1,d2,d3)\ndouble complex y1(fftblockpad, d2), y2(fftblockpad, d2)\ninteger i, j, k, ii, in\n\nlogd2 = ilog2(d2)\n\nif (timers_enabled) call timer_start(T_ffty)\ndo k = 1, d3\ndo in = 0, d1/fftblock - 1\nii = in*fftblock\ndo j = 1, d2\ndo i = 1, fftblock\ny1(i,j) = x(i+ii,j,k)\nenddo\nenddo\n\ncall cfftz (is, logd2, d2, y1, y2)\n\ndo j = 1, d2\ndo i = 1, fftblock\nxout(i+ii,j,k) = y1(i,j)\nenddo\nenddo\nenddo\nenddo\nif (timers_enabled) call timer_stop(T_ffty)\n\nreturn\nend

void setbv(){\n\nint i, j, k, m;\ndouble temp1[5], temp2[5];\n\n#pragma omp for\nfor(j=0; j<ny; j++){\nfor(i=0; i<nx; i++){\nexact(i, j, 0, temp1);\nexact(i, j, nz-1, temp2);\nfor(m=0; m<5; m++){\nu[0][j][i][m]=temp1[m];\nu[nz-1][j][i][m]=temp2[m];\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nfor(i=0; i<nx; i++){\nexact(i, 0, k, temp1);\nexact(i, ny-1, k, temp2);\nfor(m=0; m<5; m++){\nu[k][0][i][m]=temp1[m];\nu[k][ny-1][i][m]=temp2[m];\n}\n}\n}\n\n#pragma omp for\nfor(k=0; k<nz; k++){\nfor(j=0; j<ny; j++){\nexact(0, j, k, temp1);\nexact(nx-1, j, k, temp2);\nfor(m=0; m<5; m++){\nu[k][j][0][m]=temp1[m];\nu[k][j][nx-1][m]=temp2[m];\n}\n}\n}\n}

subroutine setbv\n\n\n\nuse lu_data\nimplicit none\n\ninteger i, j, k, m\ndouble precision temp1(5), temp2(5)\n\ndo j = 1, ny\ndo i = 1, nx\ncall exact( i, j, 1, temp1 )\ncall exact( i, j, nz, temp2 )\ndo m = 1, 5\nu( m, i, j, 1 ) = temp1(m)\nu( m, i, j, nz ) = temp2(m)\nend do\nend do\nend do\n\ndo k = 1, nz\ndo i = 1, nx\ncall exact( i, 1, k, temp1 )\ncall exact( i, ny, k, temp2 )\ndo m = 1, 5\nu( m, i, 1, k ) = temp1(m)\nu( m, i, ny, k ) = temp2(m)\nend do\nend do\nend do\n\ndo k = 1, nz\ndo j = 1, ny\ncall exact( 1, j, k, temp1 )\ncall exact( nx, j, k, temp2 )\ndo m = 1, 5\nu( m, 1, j, k ) = temp1(m)\nu( m, nx, j, k ) = temp2(m)\nend do\nend do\nend do\n\nreturn\nend

void adi(){\ncompute_rhs();\nx_solve();\ny_solve();\nz_solve();\nadd();\n}

subroutine adi\n\n\ncall compute_rhs\n\ncall x_solve\n\ncall y_solve\n\ncall z_solve\n\ncall add\n\nreturn\nend

void exact_rhs(){\ndouble dtemp[5], xi, eta, zeta, dtpp;\nint m, i, j, k, ip1, im1, jp1, jm1, km1, kp1;\n\nfor(k=0; k<=grid_points[2]-1; k++){\nfor(j=0; j<= grid_points[1]-1; j++){\nfor(i=0; i<=grid_points[0]-1; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=0.0;\n}\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)k*dnzm1;\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)j*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)i*dnxm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][i]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][i]=dtpp*dtemp[m];\n}\ncuf[i]=buf[1][i]*buf[1][i];\nbuf[0][i]=cuf[i]+buf[2][i]*buf[2][i]+buf[3][i]*buf[3][i];\nq[i]=0.5*(buf[1][i]*ue[1][i]+buf[2][i]*ue[2][i]+\nbuf[3][i]*ue[3][i]);\n}\nfor(i=1; i<=grid_points[0]-2; i++){\nim1=i-1;\nip1=i+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntx2*(ue[1][ip1]-ue[1][im1])+\ndx1tx1*(ue[0][ip1]-2.0*ue[0][i]+ue[0][im1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tx2*(\n(ue[1][ip1]*buf[1][ip1]+c2*(ue[4][ip1]-q[ip1]))-\n(ue[1][im1]*buf[1][im1]+c2*(ue[4][im1]-q[im1])))+\nxxcon1*(buf[1][ip1]-2.0*buf[1][i]+buf[1][im1])+\ndx2tx1*(ue[1][ip1]-2.0*ue[1][i]+ue[1][im1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tx2*(\nue[2][ip1]*buf[1][ip1]-ue[2][im1]*buf[1][im1])+\nxxcon2*(buf[2][ip1]-2.0*buf[2][i]+buf[2][im1])+\ndx3tx1*(ue[2][ip1]-2.0*ue[2][i]+ue[2][im1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tx2*(\nue[3][ip1]*buf[1][ip1]-ue[3][im1]*buf[1][im1])+\nxxcon2*(buf[3][ip1]-2.0*buf[3][i]+buf[3][im1])+\ndx4tx1*(ue[3][ip1]-2.0*ue[3][i]+ue[3][im1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tx2*(\nbuf[1][ip1]*(c1*ue[4][ip1]-c2*q[ip1])-\nbuf[1][im1]*(c1*ue[4][im1]-c2*q[im1]))+\n0.5*xxcon3*(buf[0][ip1]-2.0*buf[0][i]+buf[0][im1])+\nxxcon4*(cuf[ip1]-2.0*cuf[i]+cuf[im1])+\nxxcon5*(buf[4][ip1]-2.0*buf[4][i]+buf[4][im1])+\ndx5tx1*(ue[4][ip1]-2.0*ue[4][i]+ue[4][im1]);\n}\n\nfor(m=0; m<5; m++){\ni=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(5.0*ue[m][i]-4.0*ue[m][i+1]+ue[m][i+2]);\ni=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(-4.0*ue[m][i-1]+6.0*ue[m][i]-\n4.0*ue[m][i+1]+ue[m][i+2]);\n}\nfor(m=0; m<5; m++){\nfor(i=3; i<=grid_points[0]-4; i++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][i-2]-4.0*ue[m][i-1]+\n6.0*ue[m][i]-4.0*ue[m][i+1]+ue[m][i+2]);\n}\n}\nfor(m=0; m<5; m++){\ni=grid_points[0]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][i-2]-4.0*ue[m][i-1]+\n6.0*ue[m][i]-4.0*ue[m][i+1]);\ni=grid_points[0]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][i-2]-4.0*ue[m][i-1]+5.0*ue[m][i]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nzeta=(double)k*dnzm1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)i*dnxm1;\nfor(j=0;j<=grid_points[1]-1;j++){\neta=(double)j*dnym1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][j]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][j]=dtpp*dtemp[m];\n}\ncuf[j]=buf[2][j]*buf[2][j];\nbuf[0][j]=cuf[j]+buf[1][j]*buf[1][j]+buf[3][j]*buf[3][j];\nq[j]=0.5*(buf[1][j]*ue[1][j]+buf[2][j]*ue[2][j]+\nbuf[3][j]*ue[3][j]);\n}\nfor(j=1; j<=grid_points[1]-2; j++){\njm1=j-1;\njp1=j+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\nty2*(ue[2][jp1]-ue[2][jm1])+\ndy1ty1*(ue[0][jp1]-2.0*ue[0][j]+ue[0][jm1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-ty2*(\nue[1][jp1]*buf[2][jp1]-ue[1][jm1]*buf[2][jm1])+\nyycon2*(buf[1][jp1]-2.0*buf[1][j]+buf[1][jm1])+\ndy2ty1*(ue[1][jp1]-2.0*ue[1][j]+ue[1][jm1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-ty2*(\n(ue[2][jp1]*buf[2][jp1]+c2*(ue[4][jp1]-q[jp1]))-\n(ue[2][jm1]*buf[2][jm1]+c2*(ue[4][jm1]-q[jm1])))+\nyycon1*(buf[2][jp1]-2.0*buf[2][j]+buf[2][jm1])+\ndy3ty1*(ue[2][jp1]-2.0*ue[2][j]+ue[2][jm1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-ty2*(\nue[3][jp1]*buf[2][jp1]-ue[3][jm1]*buf[2][jm1])+\nyycon2*(buf[3][jp1]-2.0*buf[3][j]+buf[3][jm1])+\ndy4ty1*(ue[3][jp1]-2.0*ue[3][j]+ue[3][jm1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-ty2*(\nbuf[2][jp1]*(c1*ue[4][jp1]-c2*q[jp1])-\nbuf[2][jm1]*(c1*ue[4][jm1]-c2*q[jm1]))+\n0.5*yycon3*(buf[0][jp1]-2.0*buf[0][j]+\nbuf[0][jm1])+\nyycon4*(cuf[jp1]-2.0*cuf[j]+cuf[jm1])+\nyycon5*(buf[4][jp1]-2.0*buf[4][j]+buf[4][jm1])+\ndy5ty1*(ue[4][jp1]-2.0*ue[4][j]+ue[4][jm1]);\n}\n\nfor(m=0; m<5; m++){\nj=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(5.0*ue[m][j]-4.0*ue[m][j+1]+ue[m][j+2]);\nj=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(-4.0*ue[m][j-1]+6.0*ue[m][j]-\n4.0*ue[m][j+1]+ue[m][j+2]);\n}\nfor(m=0; m<5; m++){\nfor(j=3; j<=grid_points[1]-4; j++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][j-2]-4.0*ue[m][j-1]+\n6.0*ue[m][j]-4.0*ue[m][j+1]+ue[m][j+2]);\n}\n}\nfor(m=0; m<5; m++){\nj=grid_points[1]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][j-2]-4.0*ue[m][j-1]+\n6.0*ue[m][j]-4.0*ue[m][j+1]);\nj=grid_points[1]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][j-2]-4.0*ue[m][j-1]+5.0*ue[m][j]);\n}\n}\n}\n\nfor(j=1; j<=grid_points[1]-2; j++){\neta=(double)j*dnym1;\nfor(i=1; i<=grid_points[0]-2; i++){\nxi=(double)i*dnxm1;\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)k*dnzm1;\nexact_solution(xi, eta, zeta, dtemp);\nfor(m=0; m<5; m++){\nue[m][k]=dtemp[m];\n}\ndtpp=1.0/dtemp[0];\nfor(m=1; m<5; m++){\nbuf[m][k]=dtpp*dtemp[m];\n}\ncuf[k]=buf[3][k]*buf[3][k];\nbuf[0][k]=cuf[k]+buf[1][k]*buf[1][k]+buf[2][k]*buf[2][k];\nq[k]=0.5*(buf[1][k]*ue[1][k]+buf[2][k]*ue[2][k]+\nbuf[3][k]*ue[3][k]);\n}\nfor(k=1; k<=grid_points[2]-2; k++){\nkm1=k-1;\nkp1=k+1;\nforcing[k][j][i][0]=forcing[k][j][i][0]-\ntz2*(ue[3][kp1]-ue[3][km1])+\ndz1tz1*(ue[0][kp1]-2.0*ue[0][k]+ue[0][km1]);\nforcing[k][j][i][1]=forcing[k][j][i][1]-tz2*(\nue[1][kp1]*buf[3][kp1]-ue[1][km1]*buf[3][km1])+\nzzcon2*(buf[1][kp1]-2.0*buf[1][k]+buf[1][km1])+\ndz2tz1*(ue[1][kp1]-2.0*ue[1][k]+ue[1][km1]);\nforcing[k][j][i][2]=forcing[k][j][i][2]-tz2*(\nue[2][kp1]*buf[3][kp1]-ue[2][km1]*buf[3][km1])+\nzzcon2*(buf[2][kp1]-2.0*buf[2][k]+buf[2][km1])+\ndz3tz1*(ue[2][kp1]-2.0*ue[2][k]+ue[2][km1]);\nforcing[k][j][i][3]=forcing[k][j][i][3]-tz2*(\n(ue[3][kp1]*buf[3][kp1]+c2*(ue[4][kp1]-q[kp1]))-\n(ue[3][km1]*buf[3][km1]+c2*(ue[4][km1]-q[km1])))+\nzzcon1*(buf[3][kp1]-2.0*buf[3][k]+buf[3][km1])+\ndz4tz1*(ue[3][kp1]-2.0*ue[3][k]+ue[3][km1]);\nforcing[k][j][i][4]=forcing[k][j][i][4]-tz2*(\nbuf[3][kp1]*(c1*ue[4][kp1]-c2*q[kp1])-\nbuf[3][km1]*(c1*ue[4][km1]-c2*q[km1]))+\n0.5*zzcon3*(buf[0][kp1]-2.0*buf[0][k]+buf[0][km1])+\nzzcon4*(cuf[kp1]-2.0*cuf[k]+cuf[km1])+\nzzcon5*(buf[4][kp1]-2.0*buf[4][k]+buf[4][km1])+\ndz5tz1*(ue[4][kp1]-2.0*ue[4][k]+ue[4][km1]);\n}\n\nfor(m=0; m<5; m++){\nk=1;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(5.0*ue[m][k]-4.0*ue[m][k+1]+ue[m][k+2]);\nk=2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(-4.0*ue[m][k-1]+6.0*ue[m][k]-\n4.0*ue[m][k+1]+ue[m][k+2]);\n}\nfor(m=0; m<5; m++){\nfor(k=3; k<=grid_points[2]-4; k++){\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][k-2]-4.0*ue[m][k-1]+\n6.0*ue[m][k]-4.0*ue[m][k+1]+ue[m][k+2]);\n}\n}\nfor(m=0; m<5; m++){\nk=grid_points[2]-3;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][k-2]-4.0*ue[m][k-1]+\n6.0*ue[m][k]-4.0*ue[m][k+1]);\nk=grid_points[2]-2;\nforcing[k][j][i][m]=forcing[k][j][i][m]-dssp*\n(ue[m][k-2]-4.0*ue[m][k-1]+5.0*ue[m][k]);\n}\n}\n}\n\nfor(k=1; k<=grid_points[2]-2; k++){\nfor(j=1; j<=grid_points[1]-2; j++){\nfor(i=1; i<=grid_points[0]-2; i++){\nfor(m=0; m<5; m++){\nforcing[k][j][i][m]=-1.0*forcing[k][j][i][m];\n}\n}\n}\n}\n}

subroutine exact_rhs\n\n\n\nuse sp_data\nimplicit none\n\ndouble precision dtemp(5), xi, eta, zeta, dtpp\ninteger m, i, j, k, ip1, im1, jp1, &\n& jm1, km1, kp1\n\ndo k= 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\ndo i = 0, grid_points(1)-1\ndo m = 1, 5\nforcing(m,i,j,k) = 0.0d0\nend do\nend do\nend do\nend do\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\n\ndo i=0, grid_points(1)-1\nxi = dble(i) * dnxm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(i,m) = dtemp(m)\nend do\n\ndtpp = 1.0d0 / dtemp(1)\n\ndo m = 2, 5\nbuf(i,m) = dtpp * dtemp(m)\nend do\n\ncuf(i) = buf(i,2) * buf(i,2)\nbuf(i,1) = cuf(i) + buf(i,3) * buf(i,3) + &\n& buf(i,4) * buf(i,4)\nq(i) = 0.5d0*(buf(i,2)*ue(i,2) + buf(i,3)*ue(i,3) + &\n& buf(i,4)*ue(i,4))\n\nend do\n\ndo i = 1, grid_points(1)-2\nim1 = i-1\nip1 = i+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tx2*( ue(ip1,2)-ue(im1,2) )+ &\n& dx1tx1*(ue(ip1,1)-2.0d0*ue(i,1)+ue(im1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tx2 * ( &\n& (ue(ip1,2)*buf(ip1,2)+c2*(ue(ip1,5)-q(ip1)))- &\n& (ue(im1,2)*buf(im1,2)+c2*(ue(im1,5)-q(im1))))+ &\n& xxcon1*(buf(ip1,2)-2.0d0*buf(i,2)+buf(im1,2))+ &\n& dx2tx1*( ue(ip1,2)-2.0d0* ue(i,2)+ue(im1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tx2 * ( &\n& ue(ip1,3)*buf(ip1,2)-ue(im1,3)*buf(im1,2))+ &\n& xxcon2*(buf(ip1,3)-2.0d0*buf(i,3)+buf(im1,3))+ &\n& dx3tx1*( ue(ip1,3)-2.0d0*ue(i,3) +ue(im1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tx2*( &\n& ue(ip1,4)*buf(ip1,2)-ue(im1,4)*buf(im1,2))+ &\n& xxcon2*(buf(ip1,4)-2.0d0*buf(i,4)+buf(im1,4))+ &\n& dx4tx1*( ue(ip1,4)-2.0d0* ue(i,4)+ ue(im1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tx2*( &\n& buf(ip1,2)*(c1*ue(ip1,5)-c2*q(ip1))- &\n& buf(im1,2)*(c1*ue(im1,5)-c2*q(im1)))+ &\n& 0.5d0*xxcon3*(buf(ip1,1)-2.0d0*buf(i,1)+ &\n& buf(im1,1))+ &\n& xxcon4*(cuf(ip1)-2.0d0*cuf(i)+cuf(im1))+ &\n& xxcon5*(buf(ip1,5)-2.0d0*buf(i,5)+buf(im1,5))+ &\n& dx5tx1*( ue(ip1,5)-2.0d0* ue(i,5)+ ue(im1,5))\nend do\n\ndo m = 1, 5\ni = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0*ue(i,m) - 4.0d0*ue(i+1,m) +ue(i+2,m))\ni = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0*ue(i-1,m) + 6.0d0*ue(i,m) - &\n& 4.0d0*ue(i+1,m) + ue(i+2,m))\nend do\n\ndo m = 1, 5\ndo i = 3, grid_points(1)-4\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp* &\n& (ue(i-2,m) - 4.0d0*ue(i-1,m) + &\n& 6.0d0*ue(i,m) - 4.0d0*ue(i+1,m) + ue(i+2,m))\nend do\nend do\n\ndo m = 1, 5\ni = grid_points(1)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(i-2,m) - 4.0d0*ue(i-1,m) + &\n& 6.0d0*ue(i,m) - 4.0d0*ue(i+1,m))\ni = grid_points(1)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(i-2,m) - 4.0d0*ue(i-1,m) + 5.0d0*ue(i,m))\nend do\n\nend do\nend do\n\ndo k = 1, grid_points(3)-2\ndo i=1, grid_points(1)-2\nzeta = dble(k) * dnzm1\nxi = dble(i) * dnxm1\n\ndo j=0, grid_points(2)-1\neta = dble(j) * dnym1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(j,m) = dtemp(m)\nend do\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(j,m) = dtpp * dtemp(m)\nend do\n\ncuf(j) = buf(j,3) * buf(j,3)\nbuf(j,1) = cuf(j) + buf(j,2) * buf(j,2) + &\n& buf(j,4) * buf(j,4)\nq(j) = 0.5d0*(buf(j,2)*ue(j,2) + buf(j,3)*ue(j,3) + &\n& buf(j,4)*ue(j,4))\nend do\n\ndo j = 1, grid_points(2)-2\njm1 = j-1\njp1 = j+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& ty2*( ue(jp1,3)-ue(jm1,3) )+ &\n& dy1ty1*(ue(jp1,1)-2.0d0*ue(j,1)+ue(jm1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - ty2*( &\n& ue(jp1,2)*buf(jp1,3)-ue(jm1,2)*buf(jm1,3))+ &\n& yycon2*(buf(jp1,2)-2.0d0*buf(j,2)+buf(jm1,2))+ &\n& dy2ty1*( ue(jp1,2)-2.0* ue(j,2)+ ue(jm1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - ty2*( &\n& (ue(jp1,3)*buf(jp1,3)+c2*(ue(jp1,5)-q(jp1)))- &\n& (ue(jm1,3)*buf(jm1,3)+c2*(ue(jm1,5)-q(jm1))))+ &\n& yycon1*(buf(jp1,3)-2.0d0*buf(j,3)+buf(jm1,3))+ &\n& dy3ty1*( ue(jp1,3)-2.0d0*ue(j,3) +ue(jm1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - ty2*( &\n& ue(jp1,4)*buf(jp1,3)-ue(jm1,4)*buf(jm1,3))+ &\n& yycon2*(buf(jp1,4)-2.0d0*buf(j,4)+buf(jm1,4))+ &\n& dy4ty1*( ue(jp1,4)-2.0d0*ue(j,4)+ ue(jm1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - ty2*( &\n& buf(jp1,3)*(c1*ue(jp1,5)-c2*q(jp1))- &\n& buf(jm1,3)*(c1*ue(jm1,5)-c2*q(jm1)))+ &\n& 0.5d0*yycon3*(buf(jp1,1)-2.0d0*buf(j,1)+ &\n& buf(jm1,1))+ &\n& yycon4*(cuf(jp1)-2.0d0*cuf(j)+cuf(jm1))+ &\n& yycon5*(buf(jp1,5)-2.0d0*buf(j,5)+buf(jm1,5))+ &\n& dy5ty1*(ue(jp1,5)-2.0d0*ue(j,5)+ue(jm1,5))\nend do\n\ndo m = 1, 5\nj = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0*ue(j,m) - 4.0d0*ue(j+1,m) +ue(j+2,m))\nj = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0*ue(j-1,m) + 6.0d0*ue(j,m) - &\n& 4.0d0*ue(j+1,m) + ue(j+2,m))\nend do\n\ndo m = 1, 5\ndo j = 3, grid_points(2)-4\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp* &\n& (ue(j-2,m) - 4.0d0*ue(j-1,m) + &\n& 6.0d0*ue(j,m) - 4.0d0*ue(j+1,m) + ue(j+2,m))\nend do\nend do\n\ndo m = 1, 5\nj = grid_points(2)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(j-2,m) - 4.0d0*ue(j-1,m) + &\n& 6.0d0*ue(j,m) - 4.0d0*ue(j+1,m))\nj = grid_points(2)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(j-2,m) - 4.0d0*ue(j-1,m) + 5.0d0*ue(j,m))\n\nend do\n\nend do\nend do\n\ndo j=1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\neta = dble(j) * dnym1\nxi = dble(i) * dnxm1\n\ndo k=0, grid_points(3)-1\nzeta = dble(k) * dnzm1\n\ncall exact_solution(xi, eta, zeta, dtemp)\ndo m = 1, 5\nue(k,m) = dtemp(m)\nend do\n\ndtpp = 1.0d0/dtemp(1)\n\ndo m = 2, 5\nbuf(k,m) = dtpp * dtemp(m)\nend do\n\ncuf(k) = buf(k,4) * buf(k,4)\nbuf(k,1) = cuf(k) + buf(k,2) * buf(k,2) + &\n& buf(k,3) * buf(k,3)\nq(k) = 0.5d0*(buf(k,2)*ue(k,2) + buf(k,3)*ue(k,3) + &\n& buf(k,4)*ue(k,4))\nend do\n\ndo k=1, grid_points(3)-2\nkm1 = k-1\nkp1 = k+1\n\nforcing(1,i,j,k) = forcing(1,i,j,k) - &\n& tz2*( ue(kp1,4)-ue(km1,4) )+ &\n& dz1tz1*(ue(kp1,1)-2.0d0*ue(k,1)+ue(km1,1))\n\nforcing(2,i,j,k) = forcing(2,i,j,k) - tz2 * ( &\n& ue(kp1,2)*buf(kp1,4)-ue(km1,2)*buf(km1,4))+ &\n& zzcon2*(buf(kp1,2)-2.0d0*buf(k,2)+buf(km1,2))+ &\n& dz2tz1*( ue(kp1,2)-2.0d0* ue(k,2)+ ue(km1,2))\n\nforcing(3,i,j,k) = forcing(3,i,j,k) - tz2 * ( &\n& ue(kp1,3)*buf(kp1,4)-ue(km1,3)*buf(km1,4))+ &\n& zzcon2*(buf(kp1,3)-2.0d0*buf(k,3)+buf(km1,3))+ &\n& dz3tz1*(ue(kp1,3)-2.0d0*ue(k,3)+ue(km1,3))\n\nforcing(4,i,j,k) = forcing(4,i,j,k) - tz2 * ( &\n& (ue(kp1,4)*buf(kp1,4)+c2*(ue(kp1,5)-q(kp1)))- &\n& (ue(km1,4)*buf(km1,4)+c2*(ue(km1,5)-q(km1))))+ &\n& zzcon1*(buf(kp1,4)-2.0d0*buf(k,4)+buf(km1,4))+ &\n& dz4tz1*( ue(kp1,4)-2.0d0*ue(k,4) +ue(km1,4))\n\nforcing(5,i,j,k) = forcing(5,i,j,k) - tz2 * ( &\n& buf(kp1,4)*(c1*ue(kp1,5)-c2*q(kp1))- &\n& buf(km1,4)*(c1*ue(km1,5)-c2*q(km1)))+ &\n& 0.5d0*zzcon3*(buf(kp1,1)-2.0d0*buf(k,1) &\n& +buf(km1,1))+ &\n& zzcon4*(cuf(kp1)-2.0d0*cuf(k)+cuf(km1))+ &\n& zzcon5*(buf(kp1,5)-2.0d0*buf(k,5)+buf(km1,5))+ &\n& dz5tz1*( ue(kp1,5)-2.0d0*ue(k,5)+ ue(km1,5))\nend do\n\ndo m = 1, 5\nk = 1\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (5.0d0*ue(k,m) - 4.0d0*ue(k+1,m) +ue(k+2,m))\nk = 2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (-4.0d0*ue(k-1,m) + 6.0d0*ue(k,m) - &\n& 4.0d0*ue(k+1,m) + ue(k+2,m))\nend do\n\ndo m = 1, 5\ndo k = 3, grid_points(3)-4\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp* &\n& (ue(k-2,m) - 4.0d0*ue(k-1,m) + &\n& 6.0d0*ue(k,m) - 4.0d0*ue(k+1,m) + ue(k+2,m))\nend do\nend do\n\ndo m = 1, 5\nk = grid_points(3)-3\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(k-2,m) - 4.0d0*ue(k-1,m) + &\n& 6.0d0*ue(k,m) - 4.0d0*ue(k+1,m))\nk = grid_points(3)-2\nforcing(m,i,j,k) = forcing(m,i,j,k) - dssp * &\n& (ue(k-2,m) - 4.0d0*ue(k-1,m) + 5.0d0*ue(k,m))\nend do\n\nend do\nend do\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nforcing(m,i,j,k) = -1.d0 * forcing(m,i,j,k)\nend do\nend do\nend do\nend do\n\nreturn\nend

static void vecset(int n, double v[], int iv[], int* nzv, int i, double val){\nint k;\nboolean set;\n\nset = FALSE;\nfor(k = 0; k < *nzv; k++){\nif(iv[k] == i){\nv[k] = val;\nset = TRUE;\n}\n}\nif(set == FALSE){\nv[*nzv] = val;\niv[*nzv] = i;\n*nzv = *nzv + 1;\n}\n}

subroutine vecset(n, v, iv, nzv, i, val)\n\nimplicit none\n\ninteger n, iv(*), nzv, i, k\ndouble precision v(*), val\n\n\nlogical set\n\nset = .false.\ndo k = 1, nzv\nif (iv(k) .eq. i) then\nv(k) = val\nset = .true.\nendif\nenddo\nif (.not. set) then\nnzv = nzv + 1\nv(nzv) = val\niv(nzv) = i\nendif\nreturn\nend

void error_norm(double rms[5]){\nint i, j, k, m, d;\ndouble xi, eta, zeta, u_exact[5], add;\nfor(m=0;m<5;m++){rms[m]=0.0;}\nfor(k=0; k<=grid_points[2]-1; k++){\nzeta=(double)(k)*dnzm1;\nfor(j=0; j<=grid_points[1]-1; j++){\neta=(double)(j)*dnym1;\nfor(i=0; i<=grid_points[0]-1; i++){\nxi=(double)(i)*dnxm1;\nexact_solution(xi, eta, zeta, u_exact);\nfor(m=0; m<5; m++){\nadd=u[k][j][i][m]-u_exact[m];\nrms[m]=rms[m]+add*add;\n}\n}\n}\n}\nfor(m=0; m<5; m++){\nfor(d=0; d<3; d++){\nrms[m]=rms[m]/(double)(grid_points[d]-2);\n}\nrms[m]=sqrt(rms[m]);\n}\n}

subroutine error_norm(rms)\n\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, m, d\ndouble precision xi, eta, zeta, u_exact(5), rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 0, grid_points(3)-1\ndo j = 0, grid_points(2)-1\nzeta = dble(k) * dnzm1\neta = dble(j) * dnym1\ndo i = 0, grid_points(1)-1\nxi = dble(i) * dnxm1\ncall exact_solution(xi, eta, zeta, u_exact)\n\ndo m = 1, 5\nadd = u(m,i,j,k)-u_exact(m)\nrms(m) = rms(m) + add*add\nenddo\nenddo\nenddo\nenddo\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nenddo\nrms(m) = dsqrt(rms(m))\nenddo\n\nreturn\nend\n\n\n\nsubroutine rhs_norm(rms)\n\n\nuse bt_data\nimplicit none\n\ninteger i, j, k, d, m\ndouble precision rms(5), add\n\ndo m = 1, 5\nrms(m) = 0.0d0\nenddo\n\ndo k = 1, grid_points(3)-2\ndo j = 1, grid_points(2)-2\ndo i = 1, grid_points(1)-2\ndo m = 1, 5\nadd = rhs(m,i,j,k)\nrms(m) = rms(m) + add*add\nenddo\nenddo\nenddo\nenddo\n\ndo m = 1, 5\ndo d = 1, 3\nrms(m) = rms(m) / dble(grid_points(d)-2)\nenddo\nrms(m) = dsqrt(rms(m))\nenddo\n\nreturn\nend

static void bubble(double ten[][MM], int j1[][MM], int j2[][MM], int j3[][MM], int m, int ind){\ndouble temp;\nint i, j_temp;\n\nif(ind == 1){\nfor(i = 0; i < m-1; i++){\nif(ten[ind][i] > ten[ind][i+1]){\ntemp = ten[ind][i+1];\nten[ind][i+1] = ten[ind][i];\nten[ind][i] = temp;\n\nj_temp = j1[ind][i+1];\nj1[ind][i+1] = j1[ind][i];\nj1[ind][i] = j_temp;\n\nj_temp = j2[ind][i+1];\nj2[ind][i+1] = j2[ind][i];\nj2[ind][i] = j_temp;\n\nj_temp = j3[ind][i+1];\nj3[ind][i+1] = j3[ind][i];\nj3[ind][i] = j_temp;\n}else{\nreturn;\n}\n}\n}else{\nfor(i = 0; i < m-1; i++){\nif(ten[ind][i] < ten[ind][i+1]){\ntemp = ten[ind][i+1];\nten[ind][i+1] = ten[ind][i];\nten[ind][i] = temp;\n\nj_temp = j1[ind][i+1];\nj1[ind][i+1] = j1[ind][i];\nj1[ind][i] = j_temp;\n\nj_temp = j2[ind][i+1];\nj2[ind][i+1] = j2[ind][i];\nj2[ind][i] = j_temp;\n\nj_temp = j3[ind][i+1];\nj3[ind][i+1] = j3[ind][i];\nj3[ind][i] = j_temp;\n}else{\nreturn;\n}\n}\n}\n}

subroutine bubble( ten, j1, j2, j3, m, ind )\n\n\nimplicit none\n\n\ninteger m, ind, j1( m, 0:1 ), j2( m, 0:1 ), j3( m, 0:1 )\ndouble precision ten( m, 0:1 )\ndouble precision temp\ninteger i, j_temp\n\nif( ind .eq. 1 )then\n\ndo i=1,m-1\nif( ten(i,ind) .gt. ten(i+1,ind) )then\n\ntemp = ten( i+1, ind )\nten( i+1, ind ) = ten( i, ind )\nten( i, ind ) = temp\n\nj_temp = j1( i+1, ind )\nj1( i+1, ind ) = j1( i, ind )\nj1( i, ind ) = j_temp\n\nj_temp = j2( i+1, ind )\nj2( i+1, ind ) = j2( i, ind )\nj2( i, ind ) = j_temp\n\nj_temp = j3( i+1, ind )\nj3( i+1, ind ) = j3( i, ind )\nj3( i, ind ) = j_temp\n\nelse\nreturn\nendif\nenddo\n\nelse\n\ndo i=1,m-1\nif( ten(i,ind) .lt. ten(i+1,ind) )then\n\ntemp = ten( i+1, ind )\nten( i+1, ind ) = ten( i, ind )\nten( i, ind ) = temp\n\nj_temp = j1( i+1, ind )\nj1( i+1, ind ) = j1( i, ind )\nj1( i, ind ) = j_temp\n\nj_temp = j2( i+1, ind )\nj2( i+1, ind ) = j2( i, ind )\nj2( i, ind ) = j_temp\n\nj_temp = j3( i+1, ind )\nj3( i+1, ind ) = j3( i, ind )\nj3( i, ind ) = j_temp\n\nelse\nreturn\nendif\nenddo\n\nendif\n\nreturn\nend