xref: /petsc/src/mat/tests/ex125.c (revision 58ad77e8b9ee6fdbdfef97ebcff79a2d98620aab)
1 static char help[] = "Tests MatSolve() and MatMatSolve() (interface to superlu_dist, mumps and mkl_pardiso).\n\
2 Example: mpiexec -n <np> ./ex125 -f <matrix binary file> -nrhs 4 -mat_solver_type <>\n\n";
3 
4 /*
5 -mat_solver_type:
6   superlu
7   superlu_dist
8   mumps
9   mkl_pardiso
10   cusparse
11   petsc
12 */
13 
14 #include <petscmat.h>
15 
16 PetscErrorCode CreateRandom(PetscInt n, PetscInt m, Mat *A)
17 {
18   PetscFunctionBeginUser;
19   PetscCall(MatCreate(PETSC_COMM_WORLD, A));
20   PetscCall(MatSetType(*A, MATAIJ));
21   PetscCall(MatSetFromOptions(*A));
22   PetscCall(MatSetSizes(*A, PETSC_DECIDE, PETSC_DECIDE, n, m));
23   PetscCall(MatSeqAIJSetPreallocation(*A, 5, NULL));
24   PetscCall(MatMPIAIJSetPreallocation(*A, 5, NULL, 5, NULL));
25   PetscCall(MatSetRandom(*A, NULL));
26   PetscCall(MatAssemblyBegin(*A, MAT_FINAL_ASSEMBLY));
27   PetscCall(MatAssemblyEnd(*A, MAT_FINAL_ASSEMBLY));
28   PetscFunctionReturn(PETSC_SUCCESS);
29 }
30 
31 PetscErrorCode CreateIdentity(PetscInt n, Mat *A)
32 {
33   PetscFunctionBeginUser;
34   PetscCall(MatCreate(PETSC_COMM_WORLD, A));
35   PetscCall(MatSetType(*A, MATAIJ));
36   PetscCall(MatSetFromOptions(*A));
37   PetscCall(MatSetSizes(*A, PETSC_DECIDE, PETSC_DECIDE, n, n));
38   PetscCall(MatSetUp(*A));
39   PetscCall(MatAssemblyBegin(*A, MAT_FINAL_ASSEMBLY));
40   PetscCall(MatAssemblyEnd(*A, MAT_FINAL_ASSEMBLY));
41   PetscCall(MatShift(*A, 1.0));
42   PetscFunctionReturn(PETSC_SUCCESS);
43 }
44 
45 int main(int argc, char **args)
46 {
47   Mat           A, Ae, RHS = NULL, RHS1 = NULL, C, F, X;
48   Vec           u, x, b;
49   PetscMPIInt   size;
50   PetscInt      m, n, nfact, nsolve, nrhs, ipack = 5;
51   PetscReal     norm, tol = 10 * PETSC_SQRT_MACHINE_EPSILON;
52   IS            perm = NULL, iperm = NULL;
53   MatFactorInfo info;
54   PetscRandom   rand;
55   PetscBool     flg, symm, testMatSolve = PETSC_TRUE, testMatMatSolve = PETSC_TRUE, testMatMatSolveTranspose = PETSC_TRUE, testMatSolveTranspose = PETSC_TRUE, match = PETSC_FALSE;
56   PetscBool     chol = PETSC_FALSE, view = PETSC_FALSE, matsolvexx = PETSC_FALSE;
57 #if defined(PETSC_HAVE_MUMPS)
58   PetscBool test_mumps_opts = PETSC_FALSE;
59 #endif
60   PetscViewer fd;                       /* viewer */
61   char        file[PETSC_MAX_PATH_LEN]; /* input file name */
62   char        pack[PETSC_MAX_PATH_LEN];
63 
64   PetscFunctionBeginUser;
65   PetscCall(PetscInitialize(&argc, &args, NULL, help));
66   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
67 
68   /* Determine file from which we read the matrix A */
69   PetscCall(PetscOptionsGetString(NULL, NULL, "-f", file, sizeof(file), &flg));
70   if (flg) { /* Load matrix A */
71     PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, file, FILE_MODE_READ, &fd));
72     PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
73     PetscCall(MatSetFromOptions(A));
74     PetscCall(MatLoad(A, fd));
75     PetscCall(PetscViewerDestroy(&fd));
76   } else {
77     n = 13;
78     PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
79     PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
80     PetscCall(MatSetType(A, MATAIJ));
81     PetscCall(MatSetFromOptions(A));
82     PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, n, n));
83     PetscCall(MatSetUp(A));
84     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
85     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
86     PetscCall(MatShift(A, 1.0));
87   }
88 
89   /* if A is symmetric, set its flag -- required by MatGetInertia() */
90   PetscCall(MatIsSymmetric(A, 0.0, &symm));
91   PetscCall(MatSetOption(A, MAT_SYMMETRIC, symm));
92 
93   PetscCall(PetscOptionsGetBool(NULL, NULL, "-cholesky", &chol, NULL));
94 
95   /* test MATNEST support */
96   flg = PETSC_FALSE;
97   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_nest", &flg, NULL));
98   if (flg) {
99     Mat B;
100 
101     flg = PETSC_FALSE;
102     PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_nest_bordered", &flg, NULL));
103     if (!flg) {
104       Mat mats[9] = {NULL, NULL, A, NULL, A, NULL, A, NULL, NULL};
105 
106       /* Create a nested matrix representing
107               | 0 0 A |
108               | 0 A 0 |
109               | A 0 0 |
110       */
111       PetscCall(MatCreateNest(PETSC_COMM_WORLD, 3, NULL, 3, NULL, mats, &B));
112       flg = PETSC_TRUE;
113     } else {
114       Mat mats[4];
115 
116       /* Create a nested matrix representing
117               | Id  R |
118               | R^t A |
119       */
120       PetscCall(MatGetSize(A, NULL, &n));
121       m = n + 12;
122       PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
123       PetscCall(CreateIdentity(m, &mats[0]));
124       PetscCall(CreateRandom(m, n, &mats[1]));
125       mats[3] = A;
126 
127       /* use CreateTranspose/CreateHermitianTranspose or explicit matrix for debugging purposes */
128       flg = PETSC_FALSE;
129       PetscCall(PetscOptionsGetBool(NULL, NULL, "-expl", &flg, NULL));
130 #if PetscDefined(USE_COMPLEX)
131       if (chol) { /* Hermitian transpose not supported by MUMPS Cholesky factor */
132         if (!flg) PetscCall(MatCreateTranspose(mats[1], &mats[2]));
133         else PetscCall(MatTranspose(mats[1], MAT_INITIAL_MATRIX, &mats[2]));
134         flg = PETSC_TRUE;
135       } else {
136         if (!flg) {
137           Mat B;
138 
139           PetscCall(MatDuplicate(mats[1], MAT_COPY_VALUES, &B));
140           PetscCall(MatCreateHermitianTranspose(B, &mats[2]));
141           PetscCall(MatDestroy(&B));
142           if (n == m) {
143             PetscCall(MatScale(mats[2], PetscCMPLX(4.0, -2.0)));
144             PetscCall(MatShift(mats[2], PetscCMPLX(-2.0, 1.0))); // mats[2] = (4 - 2i) B* - (2 - i) I
145             PetscCall(MatCreateHermitianTranspose(mats[2], &B));
146             PetscCall(MatDestroy(mats + 2));
147             PetscCall(MatScale(B, 0.5));
148             PetscCall(MatShift(B, PetscCMPLX(1.0, 0.5)));        // B = 0.5 mats[2]* - (1 - 0.5i) I = (2 + i) B - (1 + 0.5i) I + (1 + 0.5i) I = (2 + i) B
149             PetscCall(MatCreateHermitianTranspose(B, &mats[2])); // mats[2] = B* = (2 - i) B*
150             PetscCall(MatDestroy(&B));
151             PetscCall(MatScale(mats[1], PetscCMPLX(2.0, 1.0))); // mats[1] = (2 + i) B = mats[2]*
152           } else flg = PETSC_TRUE;
153         } else PetscCall(MatHermitianTranspose(mats[1], MAT_INITIAL_MATRIX, &mats[2]));
154       }
155 #else
156       if (!flg) {
157         Mat B;
158 
159         PetscCall(MatDuplicate(mats[1], MAT_COPY_VALUES, &B));
160         PetscCall(MatCreateTranspose(B, &mats[2]));
161         PetscCall(MatDestroy(&B));
162         if (n == m) {
163           PetscCall(MatScale(mats[2], 4.0));
164           PetscCall(MatShift(mats[2], -2.0)); // mats[2] = 4 B' - 2 I
165           PetscCall(MatCreateTranspose(mats[2], &B));
166           PetscCall(MatDestroy(mats + 2));
167           PetscCall(MatScale(B, 0.5));
168           PetscCall(MatShift(B, 1.0));                // B = 0.5 mats[2]' + I = 0.5 (4 B' - 2 I)' + I = 2 B
169           PetscCall(MatCreateTranspose(B, &mats[2])); // mats[2] = B' = 2 B'
170           PetscCall(MatDestroy(&B));
171           PetscCall(MatScale(mats[1], 2.0)); // mats[1] = 2 B = mats[2]'
172         } else flg = PETSC_TRUE;
173       } else PetscCall(MatTranspose(mats[1], MAT_INITIAL_MATRIX, &mats[2]));
174 #endif
175       PetscCall(MatCreateNest(PETSC_COMM_WORLD, 2, NULL, 2, NULL, mats, &B));
176       PetscCall(MatDestroy(&mats[0]));
177       PetscCall(MatDestroy(&mats[1]));
178       PetscCall(MatDestroy(&mats[2]));
179     }
180     PetscCall(MatDestroy(&A));
181     A = B;
182     PetscCall(MatSetOption(A, MAT_SYMMETRIC, symm));
183 
184     /* not all the combinations of MatMat operations are supported by MATNEST. */
185     PetscCall(MatComputeOperator(A, MATAIJ, &Ae));
186   } else {
187     PetscCall(PetscObjectReference((PetscObject)A));
188     Ae  = A;
189     flg = PETSC_TRUE;
190   }
191   PetscCall(MatGetLocalSize(A, &m, &n));
192   PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%" PetscInt_FMT ", %" PetscInt_FMT ")", m, n);
193 
194   PetscCall(MatViewFromOptions(A, NULL, "-A_view"));
195   PetscCall(MatViewFromOptions(Ae, NULL, "-A_view_expl"));
196 
197   /* Create dense matrix C and X; C holds true solution with identical columns */
198   nrhs = 2;
199   PetscCall(PetscOptionsGetInt(NULL, NULL, "-nrhs", &nrhs, NULL));
200   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "ex125: nrhs %" PetscInt_FMT "\n", nrhs));
201   PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
202   PetscCall(MatSetOptionsPrefix(C, "rhs_"));
203   PetscCall(MatSetSizes(C, m, PETSC_DECIDE, PETSC_DECIDE, nrhs));
204   PetscCall(MatSetType(C, MATDENSE));
205   PetscCall(MatSetFromOptions(C));
206   PetscCall(MatSetUp(C));
207 
208   PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_factor", &view, NULL));
209   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_matmatsolve", &testMatMatSolve, NULL));
210   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_matmatsolvetranspose", &testMatMatSolveTranspose, NULL));
211   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_matsolvetranspose", &testMatSolveTranspose, NULL));
212 #if defined(PETSC_HAVE_MUMPS)
213   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_mumps_opts", &test_mumps_opts, NULL));
214 #endif
215 
216   PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rand));
217   PetscCall(PetscRandomSetFromOptions(rand));
218   PetscCall(MatSetRandom(C, rand));
219   PetscCall(MatDuplicate(C, MAT_DO_NOT_COPY_VALUES, &X));
220 
221   /* Create vectors */
222   PetscCall(MatCreateVecs(A, &x, &b));
223   PetscCall(VecDuplicate(x, &u)); /* save the true solution */
224 
225   /* Test Factorization */
226   if (flg) PetscCall(MatGetOrdering(A, MATORDERINGND, &perm, &iperm)); // TODO FIXME: MatConvert_Nest_AIJ() does not support chained MatCreate[Hermitian]Transpose()
227 
228   PetscCall(PetscOptionsGetString(NULL, NULL, "-mat_solver_type", pack, sizeof(pack), NULL));
229 #if defined(PETSC_HAVE_SUPERLU)
230   PetscCall(PetscStrcmp(MATSOLVERSUPERLU, pack, &match));
231   if (match) {
232     PetscCheck(!chol, PETSC_COMM_WORLD, PETSC_ERR_SUP, "SuperLU does not provide Cholesky!");
233     PetscCall(PetscPrintf(PETSC_COMM_WORLD, " SUPERLU LU:\n"));
234     PetscCall(MatGetFactor(A, MATSOLVERSUPERLU, MAT_FACTOR_LU, &F));
235     matsolvexx = PETSC_FALSE; /* Test MatMatSolve(F,RHS,RHS), RHS is a dense matrix, need further work */
236     ipack      = 0;
237     goto skipoptions;
238   }
239 #endif
240 #if defined(PETSC_HAVE_SUPERLU_DIST)
241   PetscCall(PetscStrcmp(MATSOLVERSUPERLU_DIST, pack, &match));
242   if (match) {
243     PetscCheck(!chol, PETSC_COMM_WORLD, PETSC_ERR_SUP, "SuperLU does not provide Cholesky!");
244     PetscCall(PetscPrintf(PETSC_COMM_WORLD, " SUPERLU_DIST LU:\n"));
245     PetscCall(MatGetFactor(A, MATSOLVERSUPERLU_DIST, MAT_FACTOR_LU, &F));
246     matsolvexx = PETSC_TRUE;
247     if (symm) { /* A is symmetric */
248       testMatMatSolveTranspose = PETSC_TRUE;
249       testMatSolveTranspose    = PETSC_TRUE;
250     } else { /* superlu_dist does not support solving A^t x = rhs yet */
251       testMatMatSolveTranspose = PETSC_FALSE;
252       testMatSolveTranspose    = PETSC_FALSE;
253     }
254     ipack = 1;
255     goto skipoptions;
256   }
257 #endif
258 #if defined(PETSC_HAVE_MUMPS)
259   PetscCall(PetscStrcmp(MATSOLVERMUMPS, pack, &match));
260   if (match) {
261     if (chol) {
262       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MUMPS CHOLESKY:\n"));
263       PetscCall(MatGetFactor(A, MATSOLVERMUMPS, MAT_FACTOR_CHOLESKY, &F));
264     } else {
265       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MUMPS LU:\n"));
266       PetscCall(MatGetFactor(A, MATSOLVERMUMPS, MAT_FACTOR_LU, &F));
267     }
268     matsolvexx = PETSC_TRUE;
269     if (test_mumps_opts) {
270       /* test mumps options */
271       PetscInt  icntl;
272       PetscReal cntl;
273 
274       icntl = 2; /* sequential matrix ordering */
275       PetscCall(MatMumpsSetIcntl(F, 7, icntl));
276 
277       cntl = 1.e-6; /* threshold for row pivot detection */
278       PetscCall(MatMumpsSetIcntl(F, 24, 1));
279       PetscCall(MatMumpsSetCntl(F, 3, cntl));
280     }
281     ipack = 2;
282     goto skipoptions;
283   }
284 #endif
285 #if defined(PETSC_HAVE_MKL_PARDISO)
286   PetscCall(PetscStrcmp(MATSOLVERMKL_PARDISO, pack, &match));
287   if (match) {
288     if (chol) {
289       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MKL_PARDISO CHOLESKY:\n"));
290       PetscCall(MatGetFactor(A, MATSOLVERMKL_PARDISO, MAT_FACTOR_CHOLESKY, &F));
291     } else {
292       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MKL_PARDISO LU:\n"));
293       PetscCall(MatGetFactor(A, MATSOLVERMKL_PARDISO, MAT_FACTOR_LU, &F));
294     }
295     ipack = 3;
296     goto skipoptions;
297   }
298 #endif
299 #if defined(PETSC_HAVE_CUDA)
300   PetscCall(PetscStrcmp(MATSOLVERCUSPARSE, pack, &match));
301   if (match) {
302     if (chol) {
303       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " CUSPARSE CHOLESKY:\n"));
304       PetscCall(MatGetFactor(A, MATSOLVERCUSPARSE, MAT_FACTOR_CHOLESKY, &F));
305     } else {
306       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " CUSPARSE LU:\n"));
307       PetscCall(MatGetFactor(A, MATSOLVERCUSPARSE, MAT_FACTOR_LU, &F));
308     }
309     testMatSolveTranspose    = PETSC_FALSE;
310     testMatMatSolveTranspose = PETSC_FALSE;
311     ipack                    = 4;
312     goto skipoptions;
313   }
314 #endif
315   /* PETSc */
316   match = PETSC_TRUE;
317   if (match) {
318     if (chol) {
319       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " PETSC CHOLESKY:\n"));
320       PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &F));
321     } else {
322       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " PETSC LU:\n"));
323       PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_LU, &F));
324     }
325     matsolvexx = PETSC_TRUE;
326     ipack      = 5;
327     goto skipoptions;
328   }
329 
330 skipoptions:
331   PetscCall(MatFactorInfoInitialize(&info));
332   info.fill      = 5.0;
333   info.shifttype = (PetscReal)MAT_SHIFT_NONE;
334   if (chol) {
335     PetscCall(MatCholeskyFactorSymbolic(F, A, perm, &info));
336   } else {
337     PetscCall(MatLUFactorSymbolic(F, A, perm, iperm, &info));
338   }
339 
340   for (nfact = 0; nfact < 2; nfact++) {
341     if (chol) {
342       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %" PetscInt_FMT "-the CHOLESKY numfactorization \n", nfact));
343       PetscCall(MatCholeskyFactorNumeric(F, A, &info));
344     } else {
345       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %" PetscInt_FMT "-the LU numfactorization \n", nfact));
346       PetscCall(MatLUFactorNumeric(F, A, &info));
347     }
348     if (view) {
349       PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_ASCII_INFO));
350       PetscCall(MatView(F, PETSC_VIEWER_STDOUT_WORLD));
351       PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
352       view = PETSC_FALSE;
353     }
354 
355 #if defined(PETSC_HAVE_SUPERLU_DIST)
356     if (ipack == 1) { /* Test MatSuperluDistGetDiagU()
357        -- input: matrix factor F; output: main diagonal of matrix U on all processes */
358       PetscInt     M;
359       PetscScalar *diag;
360   #if !defined(PETSC_USE_COMPLEX)
361       PetscInt nneg, nzero, npos;
362   #endif
363 
364       PetscCall(MatGetSize(F, &M, NULL));
365       PetscCall(PetscMalloc1(M, &diag));
366       PetscCall(MatSuperluDistGetDiagU(F, diag));
367       PetscCall(PetscFree(diag));
368 
369   #if !defined(PETSC_USE_COMPLEX)
370       /* Test MatGetInertia() */
371       if (symm) { /* A is symmetric */
372         PetscCall(MatGetInertia(F, &nneg, &nzero, &npos));
373         PetscCall(PetscViewerASCIIPrintf(PETSC_VIEWER_STDOUT_WORLD, " MatInertia: nneg: %" PetscInt_FMT ", nzero: %" PetscInt_FMT ", npos: %" PetscInt_FMT "\n", nneg, nzero, npos));
374       }
375   #endif
376     }
377 #endif
378 
379 #if defined(PETSC_HAVE_MUMPS)
380     /* mumps interface allows repeated call of MatCholeskyFactorSymbolic(), while the succession calls do nothing */
381     if (ipack == 2) {
382       if (chol) {
383         PetscCall(MatCholeskyFactorSymbolic(F, A, perm, &info));
384         PetscCall(MatCholeskyFactorNumeric(F, A, &info));
385       } else {
386         PetscCall(MatLUFactorSymbolic(F, A, perm, iperm, &info));
387         PetscCall(MatLUFactorNumeric(F, A, &info));
388       }
389     }
390 #endif
391 
392     /* Test MatMatSolve(), A X = B, where B can be dense or sparse */
393     if (testMatMatSolve) {
394       if (!nfact) {
395         PetscCall(MatMatMult(Ae, C, MAT_INITIAL_MATRIX, 2.0, &RHS));
396       } else {
397         PetscCall(MatMatMult(Ae, C, MAT_REUSE_MATRIX, 2.0, &RHS));
398       }
399       for (nsolve = 0; nsolve < 2; nsolve++) {
400         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatMatSolve \n", nsolve));
401         PetscCall(MatMatSolve(F, RHS, X));
402 
403         /* Check the error */
404         PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
405         PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
406         if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "-the MatMatSolve: Norm of error %g, nsolve %" PetscInt_FMT "\n", nsolve, (double)norm, nsolve));
407       }
408 
409       if (matsolvexx) {
410         /* Test MatMatSolve(F,RHS,RHS), RHS is a dense matrix */
411         PetscCall(MatCopy(RHS, X, SAME_NONZERO_PATTERN));
412         PetscCall(MatMatSolve(F, X, X));
413         /* Check the error */
414         PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
415         PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
416         if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "MatMatSolve(F,RHS,RHS): Norm of error %g\n", (double)norm));
417       }
418 
419       if (ipack == 2 && size == 1) {
420         Mat spRHS, spRHST, RHST;
421 
422         PetscCall(MatTranspose(RHS, MAT_INITIAL_MATRIX, &RHST));
423         PetscCall(MatConvert(RHST, MATAIJ, MAT_INITIAL_MATRIX, &spRHST));
424         PetscCall(MatCreateTranspose(spRHST, &spRHS));
425         for (nsolve = 0; nsolve < 2; nsolve++) {
426           PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the sparse MatMatSolve \n", nsolve));
427           PetscCall(MatMatSolve(F, spRHS, X));
428 
429           /* Check the error */
430           PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
431           PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
432           if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "-the sparse MatMatSolve: Norm of error %g, nsolve %" PetscInt_FMT "\n", nsolve, (double)norm, nsolve));
433         }
434         PetscCall(MatDestroy(&spRHST));
435         PetscCall(MatDestroy(&spRHS));
436         PetscCall(MatDestroy(&RHST));
437       }
438     }
439 
440     /* Test testMatMatSolveTranspose(), A^T X = B, where B can be dense or sparse */
441     if (testMatMatSolveTranspose) {
442       if (!nfact) {
443         PetscCall(MatTransposeMatMult(Ae, C, MAT_INITIAL_MATRIX, 2.0, &RHS1));
444       } else {
445         PetscCall(MatTransposeMatMult(Ae, C, MAT_REUSE_MATRIX, 2.0, &RHS1));
446       }
447 
448       for (nsolve = 0; nsolve < 2; nsolve++) {
449         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatMatSolveTranspose\n", nsolve));
450         PetscCall(MatMatSolveTranspose(F, RHS1, X));
451 
452         /* Check the error */
453         PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
454         PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
455         if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "-the MatMatSolveTranspose: Norm of error %g, nsolve %" PetscInt_FMT "\n", nsolve, (double)norm, nsolve));
456       }
457 
458       if (ipack == 2 && size == 1) {
459         Mat spRHS, spRHST, RHST;
460 
461         PetscCall(MatTranspose(RHS1, MAT_INITIAL_MATRIX, &RHST));
462         PetscCall(MatConvert(RHST, MATAIJ, MAT_INITIAL_MATRIX, &spRHST));
463         PetscCall(MatCreateTranspose(spRHST, &spRHS));
464         for (nsolve = 0; nsolve < 2; nsolve++) {
465           PetscCall(MatMatSolveTranspose(F, spRHS, X));
466 
467           /* Check the error */
468           PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
469           PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
470           if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "-the sparse MatMatSolveTranspose: Norm of error %g, nsolve %" PetscInt_FMT "\n", nsolve, (double)norm, nsolve));
471         }
472         PetscCall(MatDestroy(&spRHST));
473         PetscCall(MatDestroy(&spRHS));
474         PetscCall(MatDestroy(&RHST));
475       }
476     }
477 
478     /* Test MatSolve() */
479     if (testMatSolve) {
480       for (nsolve = 0; nsolve < 2; nsolve++) {
481         PetscCall(VecSetRandom(x, rand));
482         PetscCall(VecCopy(x, u));
483         PetscCall(MatMult(Ae, x, b));
484 
485         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatSolve \n", nsolve));
486         PetscCall(MatSolve(F, b, x));
487 
488         /* Check the error */
489         PetscCall(VecAXPY(u, -1.0, x)); /* u <- (-1.0)x + u */
490         PetscCall(VecNorm(u, NORM_2, &norm));
491         if (norm > tol) {
492           PetscReal resi;
493           PetscCall(MatMult(Ae, x, u));   /* u = A*x */
494           PetscCall(VecAXPY(u, -1.0, b)); /* u <- (-1.0)b + u */
495           PetscCall(VecNorm(u, NORM_2, &resi));
496           PetscCall(PetscPrintf(PETSC_COMM_WORLD, "MatSolve: Norm of error %g, resi %g, numfact %" PetscInt_FMT "\n", (double)norm, (double)resi, nfact));
497         }
498       }
499     }
500 
501     /* Test MatSolveTranspose() */
502     if (testMatSolveTranspose) {
503       for (nsolve = 0; nsolve < 2; nsolve++) {
504         PetscCall(VecSetRandom(x, rand));
505         PetscCall(VecCopy(x, u));
506         PetscCall(MatMultTranspose(Ae, x, b));
507 
508         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatSolveTranspose\n", nsolve));
509         PetscCall(MatSolveTranspose(F, b, x));
510 
511         /* Check the error */
512         PetscCall(VecAXPY(u, -1.0, x)); /* u <- (-1.0)x + u */
513         PetscCall(VecNorm(u, NORM_2, &norm));
514         if (norm > tol) {
515           PetscReal resi;
516           PetscCall(MatMultTranspose(Ae, x, u)); /* u = A*x */
517           PetscCall(VecAXPY(u, -1.0, b));        /* u <- (-1.0)b + u */
518           PetscCall(VecNorm(u, NORM_2, &resi));
519           PetscCall(PetscPrintf(PETSC_COMM_WORLD, "MatSolveTranspose: Norm of error %g, resi %g, numfact %" PetscInt_FMT "\n", (double)norm, (double)resi, nfact));
520         }
521       }
522     }
523   }
524 
525   /* Free data structures */
526   PetscCall(MatDestroy(&Ae));
527   PetscCall(MatDestroy(&A));
528   PetscCall(MatDestroy(&C));
529   PetscCall(MatDestroy(&F));
530   PetscCall(MatDestroy(&X));
531   PetscCall(MatDestroy(&RHS));
532   PetscCall(MatDestroy(&RHS1));
533 
534   PetscCall(PetscRandomDestroy(&rand));
535   PetscCall(ISDestroy(&perm));
536   PetscCall(ISDestroy(&iperm));
537   PetscCall(VecDestroy(&x));
538   PetscCall(VecDestroy(&b));
539   PetscCall(VecDestroy(&u));
540   PetscCall(PetscFinalize());
541   return 0;
542 }
543 
544 /*TEST
545 
546    test:
547       requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
548       args: -f ${DATAFILESPATH}/matrices/medium -mat_solver_type petsc
549       output_file: output/ex125.out
550 
551    test:
552       suffix: 2
553       args: -mat_solver_type petsc
554       output_file: output/ex125.out
555 
556    test:
557       suffix: mkl_pardiso
558       requires: mkl_pardiso datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
559       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mkl_pardiso
560 
561    test:
562       suffix: mkl_pardiso_2
563       requires: mkl_pardiso
564       args: -mat_solver_type mkl_pardiso
565       output_file: output/ex125_mkl_pardiso.out
566 
567    test:
568       suffix: mumps
569       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
570       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps
571       output_file: output/ex125_mumps_seq.out
572 
573    test:
574       suffix: mumps_nest
575       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
576       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
577       output_file: output/ex125_mumps_seq.out
578 
579    test:
580       suffix: mumps_2
581       nsize: 3
582       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
583       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps
584       output_file: output/ex125_mumps_par.out
585 
586    test:
587       suffix: mumps_2_nest
588       nsize: 3
589       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
590       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
591       output_file: output/ex125_mumps_par.out
592 
593    test:
594       suffix: mumps_3
595       requires: mumps
596       args: -mat_solver_type mumps
597       output_file: output/ex125_mumps_seq.out
598 
599    test:
600       suffix: mumps_3_nest
601       requires: mumps
602       args: -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
603       output_file: output/ex125_mumps_seq.out
604 
605    test:
606       suffix: mumps_4
607       nsize: 3
608       requires: mumps
609       args: -mat_solver_type mumps
610       output_file: output/ex125_mumps_par.out
611 
612    test:
613       suffix: mumps_4_nest
614       nsize: 3
615       requires: mumps
616       args: -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
617       output_file: output/ex125_mumps_par.out
618 
619    test:
620       suffix: mumps_5
621       nsize: 3
622       requires: mumps
623       args: -mat_solver_type mumps -cholesky
624       output_file: output/ex125_mumps_par_cholesky.out
625 
626    test:
627       suffix: mumps_5_nest
628       nsize: 3
629       requires: mumps
630       args: -mat_solver_type mumps -cholesky -test_nest -test_nest_bordered {{0 1}}
631       output_file: output/ex125_mumps_par_cholesky.out
632 
633    test:
634       suffix: mumps_6
635       nsize: 2
636       requires: mumps
637       args: -mat_solver_type mumps -test_nest -test_nest_bordered -m 13 -n 13
638       output_file: output/ex125_mumps_par.out
639 
640    test:
641       suffix: superlu
642       requires: datafilespath double !complex !defined(PETSC_USE_64BIT_INDICES) superlu
643       args: -f ${DATAFILESPATH}/matrices/medium -mat_solver_type superlu
644       output_file: output/ex125_superlu.out
645 
646    test:
647       suffix: superlu_dist
648       nsize: {{1 3}}
649       requires: datafilespath double !complex !defined(PETSC_USE_64BIT_INDICES) superlu_dist
650       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type superlu_dist -mat_superlu_dist_rowperm NOROWPERM
651       output_file: output/ex125_superlu_dist.out
652 
653    test:
654       suffix: superlu_dist_2
655       nsize: {{1 3}}
656       requires: superlu_dist !complex
657       args: -n 36 -mat_solver_type superlu_dist -mat_superlu_dist_rowperm NOROWPERM
658       output_file: output/ex125_superlu_dist.out
659 
660    test:
661       suffix: superlu_dist_3
662       nsize: {{1 3}}
663       requires: superlu_dist !complex
664       requires: datafilespath double !complex !defined(PETSC_USE_64BIT_INDICES) superlu_dist
665       args: -f ${DATAFILESPATH}/matrices/medium -mat_solver_type superlu_dist -mat_superlu_dist_rowperm NOROWPERM
666       output_file: output/ex125_superlu_dist_nonsymmetric.out
667 
668    test:
669       suffix: superlu_dist_complex
670       nsize: 3
671       requires: datafilespath double superlu_dist complex !defined(PETSC_USE_64BIT_INDICES)
672       args: -f ${DATAFILESPATH}/matrices/farzad_B_rhs -mat_solver_type superlu_dist
673       output_file: output/ex125_superlu_dist_complex.out
674 
675    test:
676       suffix: superlu_dist_complex_2
677       nsize: 3
678       requires: superlu_dist complex
679       args: -mat_solver_type superlu_dist
680       output_file: output/ex125_superlu_dist_complex_2.out
681 
682    test:
683       suffix: cusparse
684       requires: cuda datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
685       #TODO: fix the bug with cholesky
686       #args: -mat_type aijcusparse -f ${DATAFILESPATH}/matrices/small -mat_solver_type cusparse -cholesky {{0 1}separate output}
687       args: -mat_type aijcusparse -f ${DATAFILESPATH}/matrices/small -mat_solver_type cusparse -cholesky {{0}separate output}
688 
689    test:
690       suffix: cusparse_2
691       requires: cuda
692       args: -mat_type aijcusparse -mat_solver_type cusparse -cholesky {{0 1}separate output}
693 
694 TEST*/
695