xref: /petsc/src/mat/tests/ex125.c (revision 9a3a8673b4aea812b2f0c314666d2e7ff14d2577)
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 
CreateRandom(PetscInt n,PetscInt m,Mat * A)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 
CreateIdentity(PetscInt n,Mat * A)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 
main(int argc,char ** args)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, test_inertia;
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   test_inertia = symm;
94   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_inertia", &test_inertia, NULL));
95 
96   PetscCall(PetscOptionsGetBool(NULL, NULL, "-cholesky", &chol, NULL));
97   PetscCall(PetscOptionsGetReal(NULL, NULL, "-tol", &tol, NULL));
98 
99   /* test MATNEST support */
100   flg = PETSC_FALSE;
101   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_nest", &flg, NULL));
102   if (flg) {
103     Mat B;
104 
105     flg = PETSC_FALSE;
106     PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_nest_bordered", &flg, NULL));
107     if (!flg) {
108       Mat mats[9] = {NULL, NULL, A, NULL, A, NULL, A, NULL, NULL};
109 
110       /* Create a nested matrix representing
111               | 0 0 A |
112               | 0 A 0 |
113               | A 0 0 |
114       */
115       PetscCall(MatCreateNest(PETSC_COMM_WORLD, 3, NULL, 3, NULL, mats, &B));
116       flg = PETSC_TRUE;
117     } else {
118       Mat mats[4];
119 
120       /* Create a nested matrix representing
121               | Id  R |
122               | R^t A |
123       */
124       PetscCall(MatGetSize(A, NULL, &n));
125       m = n + 12;
126       PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
127       PetscCall(CreateIdentity(m, &mats[0]));
128       PetscCall(CreateRandom(m, n, &mats[1]));
129       mats[3] = A;
130 
131       /* use CreateTranspose/CreateHermitianTranspose or explicit matrix for debugging purposes */
132       flg = PETSC_FALSE;
133       PetscCall(PetscOptionsGetBool(NULL, NULL, "-expl", &flg, NULL));
134 #if PetscDefined(USE_COMPLEX)
135       if (chol) { /* Hermitian transpose not supported by MUMPS Cholesky factor */
136         if (!flg) PetscCall(MatCreateTranspose(mats[1], &mats[2]));
137         else PetscCall(MatTranspose(mats[1], MAT_INITIAL_MATRIX, &mats[2]));
138         flg = PETSC_TRUE;
139       } else {
140         if (!flg) {
141           Mat B;
142 
143           PetscCall(MatDuplicate(mats[1], MAT_COPY_VALUES, &B));
144           PetscCall(MatCreateHermitianTranspose(B, &mats[2]));
145           PetscCall(MatDestroy(&B));
146           if (n == m) {
147             PetscCall(MatScale(mats[2], PetscCMPLX(4.0, -2.0)));
148             PetscCall(MatShift(mats[2], PetscCMPLX(-2.0, 1.0))); // mats[2] = (4 - 2i) B* - (2 - i) I
149             PetscCall(MatCreateHermitianTranspose(mats[2], &B));
150             PetscCall(MatDestroy(mats + 2));
151             PetscCall(MatScale(B, 0.5));
152             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
153             PetscCall(MatCreateHermitianTranspose(B, &mats[2])); // mats[2] = B* = (2 - i) B*
154             PetscCall(MatDestroy(&B));
155             PetscCall(MatScale(mats[1], PetscCMPLX(2.0, 1.0))); // mats[1] = (2 + i) B = mats[2]*
156           } else flg = PETSC_TRUE;
157         } else PetscCall(MatHermitianTranspose(mats[1], MAT_INITIAL_MATRIX, &mats[2]));
158       }
159 #else
160       if (!flg) {
161         Mat B;
162 
163         PetscCall(MatDuplicate(mats[1], MAT_COPY_VALUES, &B));
164         PetscCall(MatCreateTranspose(B, &mats[2]));
165         PetscCall(MatDestroy(&B));
166         if (n == m) {
167           PetscCall(MatScale(mats[2], 4.0));
168           PetscCall(MatShift(mats[2], -2.0)); // mats[2] = 4 B' - 2 I
169           PetscCall(MatCreateTranspose(mats[2], &B));
170           PetscCall(MatDestroy(mats + 2));
171           PetscCall(MatScale(B, 0.5));
172           PetscCall(MatShift(B, 1.0));                // B = 0.5 mats[2]' + I = 0.5 (4 B' - 2 I)' + I = 2 B
173           PetscCall(MatCreateTranspose(B, &mats[2])); // mats[2] = B' = 2 B'
174           PetscCall(MatDestroy(&B));
175           PetscCall(MatScale(mats[1], 2.0)); // mats[1] = 2 B = mats[2]'
176         } else flg = PETSC_TRUE;
177       } else PetscCall(MatTranspose(mats[1], MAT_INITIAL_MATRIX, &mats[2]));
178 #endif
179       PetscCall(MatCreateNest(PETSC_COMM_WORLD, 2, NULL, 2, NULL, mats, &B));
180       PetscCall(MatDestroy(&mats[0]));
181       PetscCall(MatDestroy(&mats[1]));
182       PetscCall(MatDestroy(&mats[2]));
183     }
184     PetscCall(MatDestroy(&A));
185     A = B;
186     PetscCall(MatSetOption(A, MAT_SYMMETRIC, symm));
187 
188     /* not all the combinations of MatMat operations are supported by MATNEST. */
189     PetscCall(MatComputeOperator(A, MATAIJ, &Ae));
190   } else {
191     PetscCall(PetscObjectReference((PetscObject)A));
192     Ae  = A;
193     flg = PETSC_TRUE;
194   }
195   PetscCall(MatGetLocalSize(A, &m, &n));
196   PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%" PetscInt_FMT ", %" PetscInt_FMT ")", m, n);
197 
198   PetscCall(MatViewFromOptions(A, NULL, "-A_view"));
199   PetscCall(MatViewFromOptions(Ae, NULL, "-A_view_expl"));
200 
201   /* Create dense matrix C and X; C holds true solution with identical columns */
202   nrhs = 2;
203   PetscCall(PetscOptionsGetInt(NULL, NULL, "-nrhs", &nrhs, NULL));
204   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "ex125: nrhs %" PetscInt_FMT "\n", nrhs));
205   PetscCall(MatCreate(PETSC_COMM_WORLD, &C));
206   PetscCall(MatSetOptionsPrefix(C, "rhs_"));
207   PetscCall(MatSetSizes(C, m, PETSC_DECIDE, PETSC_DECIDE, nrhs));
208   PetscCall(MatSetType(C, MATDENSE));
209   PetscCall(MatSetFromOptions(C));
210   PetscCall(MatSetUp(C));
211 
212   PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_factor", &view, NULL));
213   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_matmatsolve", &testMatMatSolve, NULL));
214   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_matmatsolvetranspose", &testMatMatSolveTranspose, NULL));
215   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_matsolvetranspose", &testMatSolveTranspose, NULL));
216 #if defined(PETSC_HAVE_MUMPS)
217   PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_mumps_opts", &test_mumps_opts, NULL));
218 #endif
219 
220   PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rand));
221   PetscCall(PetscRandomSetFromOptions(rand));
222   PetscCall(MatSetRandom(C, rand));
223   PetscCall(MatDuplicate(C, MAT_DO_NOT_COPY_VALUES, &X));
224 
225   /* Create vectors */
226   PetscCall(MatCreateVecs(A, &x, &b));
227   PetscCall(VecDuplicate(x, &u)); /* save the true solution */
228 
229   /* Test Factorization */
230   if (flg) PetscCall(MatGetOrdering(A, MATORDERINGND, &perm, &iperm)); // TODO FIXME: MatConvert_Nest_AIJ() does not support chained MatCreate[Hermitian]Transpose()
231 
232   PetscCall(PetscOptionsGetString(NULL, NULL, "-mat_solver_type", pack, sizeof(pack), NULL));
233 #if defined(PETSC_HAVE_SUPERLU)
234   PetscCall(PetscStrcmp(MATSOLVERSUPERLU, pack, &match));
235   if (match) {
236     PetscCheck(!chol, PETSC_COMM_WORLD, PETSC_ERR_SUP, "SuperLU does not provide Cholesky!");
237     PetscCall(PetscPrintf(PETSC_COMM_WORLD, " SUPERLU LU:\n"));
238     PetscCall(MatGetFactor(A, MATSOLVERSUPERLU, MAT_FACTOR_LU, &F));
239     matsolvexx = PETSC_FALSE; /* Test MatMatSolve(F,RHS,RHS), RHS is a dense matrix, need further work */
240     ipack      = 0;
241     goto skipoptions;
242   }
243 #endif
244 #if defined(PETSC_HAVE_SUPERLU_DIST)
245   PetscCall(PetscStrcmp(MATSOLVERSUPERLU_DIST, pack, &match));
246   if (match) {
247     PetscCheck(!chol, PETSC_COMM_WORLD, PETSC_ERR_SUP, "SuperLU does not provide Cholesky!");
248     PetscCall(PetscPrintf(PETSC_COMM_WORLD, " SUPERLU_DIST LU:\n"));
249     PetscCall(MatGetFactor(A, MATSOLVERSUPERLU_DIST, MAT_FACTOR_LU, &F));
250     matsolvexx = PETSC_TRUE;
251     if (symm) { /* A is symmetric */
252       testMatMatSolveTranspose = PETSC_TRUE;
253       testMatSolveTranspose    = PETSC_TRUE;
254     } else { /* superlu_dist does not support solving A^t x = rhs yet */
255       testMatMatSolveTranspose = PETSC_FALSE;
256       testMatSolveTranspose    = PETSC_FALSE;
257     }
258     ipack = 1;
259     goto skipoptions;
260   }
261 #endif
262 #if defined(PETSC_HAVE_MUMPS)
263   PetscCall(PetscStrcmp(MATSOLVERMUMPS, pack, &match));
264   if (match) {
265     if (chol) {
266       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MUMPS CHOLESKY:\n"));
267       PetscCall(MatGetFactor(A, MATSOLVERMUMPS, MAT_FACTOR_CHOLESKY, &F));
268     } else {
269       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MUMPS LU:\n"));
270       PetscCall(MatGetFactor(A, MATSOLVERMUMPS, MAT_FACTOR_LU, &F));
271     }
272     matsolvexx = PETSC_TRUE;
273     if (test_mumps_opts) {
274       /* test mumps options */
275       PetscInt  icntl;
276       PetscReal cntl;
277 
278       icntl = 2; /* sequential matrix ordering */
279       PetscCall(MatMumpsSetIcntl(F, 7, icntl));
280 
281       cntl = 1.e-6; /* threshold for row pivot detection */
282       PetscCall(MatMumpsSetIcntl(F, 24, 1));
283       PetscCall(MatMumpsSetCntl(F, 3, cntl));
284     }
285     ipack = 2;
286     goto skipoptions;
287   }
288 #endif
289 #if defined(PETSC_HAVE_MKL_PARDISO)
290   PetscCall(PetscStrcmp(MATSOLVERMKL_PARDISO, pack, &match));
291   if (match) {
292     if (chol) {
293       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MKL_PARDISO CHOLESKY:\n"));
294       PetscCall(MatGetFactor(A, MATSOLVERMKL_PARDISO, MAT_FACTOR_CHOLESKY, &F));
295     } else {
296       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " MKL_PARDISO LU:\n"));
297       PetscCall(MatGetFactor(A, MATSOLVERMKL_PARDISO, MAT_FACTOR_LU, &F));
298     }
299     ipack = 3;
300     goto skipoptions;
301   }
302 #endif
303 #if defined(PETSC_HAVE_CUDA)
304   PetscCall(PetscStrcmp(MATSOLVERCUSPARSE, pack, &match));
305   if (match) {
306     if (chol) {
307       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " CUSPARSE CHOLESKY:\n"));
308       PetscCall(MatGetFactor(A, MATSOLVERCUSPARSE, MAT_FACTOR_CHOLESKY, &F));
309     } else {
310       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " CUSPARSE LU:\n"));
311       PetscCall(MatGetFactor(A, MATSOLVERCUSPARSE, MAT_FACTOR_LU, &F));
312     }
313     testMatSolveTranspose    = PETSC_FALSE;
314     testMatMatSolveTranspose = PETSC_FALSE;
315     ipack                    = 4;
316     goto skipoptions;
317   }
318 #endif
319   /* PETSc */
320   match = PETSC_TRUE;
321   if (match) {
322     if (chol) {
323       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " PETSC CHOLESKY:\n"));
324       PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &F));
325     } else {
326       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " PETSC LU:\n"));
327       PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_LU, &F));
328     }
329     matsolvexx = PETSC_TRUE;
330     ipack      = 5;
331     goto skipoptions;
332   }
333 
334 skipoptions:
335   PetscCall(MatFactorInfoInitialize(&info));
336   info.fill      = 5.0;
337   info.shifttype = (PetscReal)MAT_SHIFT_NONE;
338   if (chol) {
339     PetscCall(MatCholeskyFactorSymbolic(F, A, perm, &info));
340   } else {
341     PetscCall(MatLUFactorSymbolic(F, A, perm, iperm, &info));
342   }
343 
344   for (nfact = 0; nfact < 2; nfact++) {
345     if (chol) {
346       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %" PetscInt_FMT "-the CHOLESKY numfactorization \n", nfact));
347       PetscCall(MatCholeskyFactorNumeric(F, A, &info));
348     } else {
349       PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %" PetscInt_FMT "-the LU numfactorization \n", nfact));
350       PetscCall(MatLUFactorNumeric(F, A, &info));
351     }
352     if (view) {
353       PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_ASCII_INFO));
354       PetscCall(MatView(F, PETSC_VIEWER_STDOUT_WORLD));
355       PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
356       view = PETSC_FALSE;
357     }
358 
359 #if defined(PETSC_HAVE_SUPERLU_DIST)
360     if (ipack == 1) { /* Test MatSuperluDistGetDiagU()
361        -- input: matrix factor F; output: main diagonal of matrix U on all processes */
362       PetscInt     M;
363       PetscScalar *diag;
364   #if !defined(PETSC_USE_COMPLEX)
365       PetscInt nneg, nzero, npos;
366   #endif
367 
368       PetscCall(MatGetSize(F, &M, NULL));
369       PetscCall(PetscMalloc1(M, &diag));
370       PetscCall(MatSuperluDistGetDiagU(F, diag));
371       PetscCall(PetscFree(diag));
372 
373   #if !defined(PETSC_USE_COMPLEX)
374       /* Test MatGetInertia() */
375       if (test_inertia) { /* A is symmetric */
376         PetscCall(MatGetInertia(F, &nneg, &nzero, &npos));
377         PetscCall(PetscViewerASCIIPrintf(PETSC_VIEWER_STDOUT_WORLD, " MatInertia: nneg: %" PetscInt_FMT ", nzero: %" PetscInt_FMT ", npos: %" PetscInt_FMT "\n", nneg, nzero, npos));
378       }
379   #endif
380     }
381 #endif
382 
383 #if defined(PETSC_HAVE_MUMPS)
384     /* mumps interface allows repeated call of MatCholeskyFactorSymbolic(), while the succession calls do nothing */
385     if (ipack == 2) {
386       if (chol) {
387         PetscCall(MatCholeskyFactorSymbolic(F, A, perm, &info));
388         PetscCall(MatCholeskyFactorNumeric(F, A, &info));
389       } else {
390         PetscCall(MatLUFactorSymbolic(F, A, perm, iperm, &info));
391         PetscCall(MatLUFactorNumeric(F, A, &info));
392       }
393     }
394 #endif
395 
396     /* Test MatMatSolve(), A X = B, where B can be dense or sparse */
397     if (testMatMatSolve) {
398       if (!nfact) {
399         PetscCall(MatMatMult(Ae, C, MAT_INITIAL_MATRIX, 2.0, &RHS));
400       } else {
401         PetscCall(MatMatMult(Ae, C, MAT_REUSE_MATRIX, 2.0, &RHS));
402       }
403       for (nsolve = 0; nsolve < 2; nsolve++) {
404         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatMatSolve \n", nsolve));
405         PetscCall(MatMatSolve(F, RHS, X));
406 
407         /* Check the error */
408         PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
409         PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
410         if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "-the MatMatSolve: Norm of error %g, nsolve %" PetscInt_FMT "\n", nsolve, (double)norm, nsolve));
411       }
412 
413       if (matsolvexx) {
414         /* Test MatMatSolve(F,RHS,RHS), RHS is a dense matrix */
415         PetscCall(MatCopy(RHS, X, SAME_NONZERO_PATTERN));
416         PetscCall(MatMatSolve(F, X, X));
417         /* Check the error */
418         PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
419         PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
420         if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "MatMatSolve(F,RHS,RHS): Norm of error %g\n", (double)norm));
421       }
422 
423       if (ipack == 2 && size == 1) {
424         Mat spRHS, spRHST, RHST;
425 
426         PetscCall(MatTranspose(RHS, MAT_INITIAL_MATRIX, &RHST));
427         PetscCall(MatConvert(RHST, MATAIJ, MAT_INITIAL_MATRIX, &spRHST));
428         PetscCall(MatCreateTranspose(spRHST, &spRHS));
429         for (nsolve = 0; nsolve < 2; nsolve++) {
430           PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the sparse MatMatSolve \n", nsolve));
431           PetscCall(MatMatSolve(F, spRHS, X));
432 
433           /* Check the error */
434           PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
435           PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
436           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));
437         }
438         PetscCall(MatDestroy(&spRHST));
439         PetscCall(MatDestroy(&spRHS));
440         PetscCall(MatDestroy(&RHST));
441       }
442     }
443 
444     /* Test testMatMatSolveTranspose(), A^T X = B, where B can be dense or sparse */
445     if (testMatMatSolveTranspose) {
446       if (!nfact) {
447         PetscCall(MatTransposeMatMult(Ae, C, MAT_INITIAL_MATRIX, 2.0, &RHS1));
448       } else {
449         PetscCall(MatTransposeMatMult(Ae, C, MAT_REUSE_MATRIX, 2.0, &RHS1));
450       }
451 
452       for (nsolve = 0; nsolve < 2; nsolve++) {
453         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatMatSolveTranspose\n", nsolve));
454         PetscCall(MatMatSolveTranspose(F, RHS1, X));
455 
456         /* Check the error */
457         PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
458         PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
459         if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "-the MatMatSolveTranspose: Norm of error %g, nsolve %" PetscInt_FMT "\n", nsolve, (double)norm, nsolve));
460       }
461 
462       if (ipack == 2 && size == 1) {
463         Mat spRHS, spRHST, RHST;
464 
465         PetscCall(MatTranspose(RHS1, MAT_INITIAL_MATRIX, &RHST));
466         PetscCall(MatConvert(RHST, MATAIJ, MAT_INITIAL_MATRIX, &spRHST));
467         PetscCall(MatCreateTranspose(spRHST, &spRHS));
468         for (nsolve = 0; nsolve < 2; nsolve++) {
469           PetscCall(MatMatSolveTranspose(F, spRHS, X));
470 
471           /* Check the error */
472           PetscCall(MatAXPY(X, -1.0, C, SAME_NONZERO_PATTERN));
473           PetscCall(MatNorm(X, NORM_FROBENIUS, &norm));
474           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));
475         }
476         PetscCall(MatDestroy(&spRHST));
477         PetscCall(MatDestroy(&spRHS));
478         PetscCall(MatDestroy(&RHST));
479       }
480     }
481 
482     /* Test MatSolve() */
483     if (testMatSolve) {
484       for (nsolve = 0; nsolve < 2; nsolve++) {
485         PetscCall(VecSetRandom(x, rand));
486         PetscCall(VecCopy(x, u));
487         PetscCall(MatMult(Ae, x, b));
488 
489         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatSolve \n", nsolve));
490         PetscCall(MatSolve(F, b, x));
491 
492         /* Check the error */
493         PetscCall(VecAXPY(u, -1.0, x)); /* u <- (-1.0)x + u */
494         PetscCall(VecNorm(u, NORM_2, &norm));
495         if (norm > tol) {
496           PetscReal resi;
497           PetscCall(MatMult(Ae, x, u));   /* u = A*x */
498           PetscCall(VecAXPY(u, -1.0, b)); /* u <- (-1.0)b + u */
499           PetscCall(VecNorm(u, NORM_2, &resi));
500           PetscCall(PetscPrintf(PETSC_COMM_WORLD, "MatSolve: Norm of error %g, resi %g, numfact %" PetscInt_FMT "\n", (double)norm, (double)resi, nfact));
501         }
502       }
503     }
504 
505     /* Test MatSolveTranspose() */
506     if (testMatSolveTranspose) {
507       for (nsolve = 0; nsolve < 2; nsolve++) {
508         PetscCall(VecSetRandom(x, rand));
509         PetscCall(VecCopy(x, u));
510         PetscCall(MatMultTranspose(Ae, x, b));
511 
512         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "   %" PetscInt_FMT "-the MatSolveTranspose\n", nsolve));
513         PetscCall(MatSolveTranspose(F, b, x));
514 
515         /* Check the error */
516         PetscCall(VecAXPY(u, -1.0, x)); /* u <- (-1.0)x + u */
517         PetscCall(VecNorm(u, NORM_2, &norm));
518         if (norm > tol) {
519           PetscReal resi;
520           PetscCall(MatMultTranspose(Ae, x, u)); /* u = A*x */
521           PetscCall(VecAXPY(u, -1.0, b));        /* u <- (-1.0)b + u */
522           PetscCall(VecNorm(u, NORM_2, &resi));
523           PetscCall(PetscPrintf(PETSC_COMM_WORLD, "MatSolveTranspose: Norm of error %g, resi %g, numfact %" PetscInt_FMT "\n", (double)norm, (double)resi, nfact));
524         }
525       }
526     }
527   }
528 
529   /* Free data structures */
530   PetscCall(MatDestroy(&Ae));
531   PetscCall(MatDestroy(&A));
532   PetscCall(MatDestroy(&C));
533   PetscCall(MatDestroy(&F));
534   PetscCall(MatDestroy(&X));
535   PetscCall(MatDestroy(&RHS));
536   PetscCall(MatDestroy(&RHS1));
537 
538   PetscCall(PetscRandomDestroy(&rand));
539   PetscCall(ISDestroy(&perm));
540   PetscCall(ISDestroy(&iperm));
541   PetscCall(VecDestroy(&x));
542   PetscCall(VecDestroy(&b));
543   PetscCall(VecDestroy(&u));
544   PetscCall(PetscFinalize());
545   return 0;
546 }
547 
548 /*TEST
549 
550    test:
551       requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
552       args: -f ${DATAFILESPATH}/matrices/medium -mat_solver_type petsc
553       output_file: output/ex125.out
554 
555    test:
556       suffix: 2
557       args: -mat_solver_type petsc
558       output_file: output/ex125.out
559 
560    test:
561       suffix: mkl_pardiso
562       requires: mkl_pardiso datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
563       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mkl_pardiso
564 
565    test:
566       suffix: mkl_pardiso_2
567       requires: mkl_pardiso
568       args: -mat_solver_type mkl_pardiso
569       output_file: output/ex125_mkl_pardiso.out
570 
571    testset:
572       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
573       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps
574       output_file: output/ex125_mumps_seq.out
575 
576       test:
577         requires: defined(PETSC_HAVE_MUMPS_MIXED_PRECISION)
578         suffix: mumps_single
579         args: -pc_precision single -tol 1e-5
580       test:
581         suffix: mumps_double
582         args: -pc_precision double
583 
584    testset:
585       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
586       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
587       output_file: output/ex125_mumps_seq.out
588 
589       test:
590         requires: defined(PETSC_HAVE_MUMPS_MIXED_PRECISION)
591         suffix: mumps_nest_single
592         args: -pc_precision single -tol 1e-4
593       test:
594         suffix: mumps_nest_double
595         args: -pc_precision double
596 
597    testset:
598       nsize: 3
599       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
600       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps
601       output_file: output/ex125_mumps_par.out
602 
603       test:
604         requires: defined(PETSC_HAVE_MUMPS_MIXED_PRECISION)
605         suffix: mumps_2_single
606         args: -pc_precision single -tol 1e-5
607       test:
608         suffix: mumps_2_double
609         args: -pc_precision double
610 
611    test:
612       suffix: mumps_2_nest
613       nsize: 3
614       requires: mumps datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
615       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
616       output_file: output/ex125_mumps_par.out
617 
618    test:
619       suffix: mumps_3
620       requires: mumps
621       args: -mat_solver_type mumps
622       output_file: output/ex125_mumps_seq.out
623 
624    testset:
625       requires: mumps
626       args: -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
627       output_file: output/ex125_mumps_seq.out
628 
629       test:
630         requires: !__float128
631         suffix: mumps_3_nest
632       test:
633         suffix: mumps_3_nest_fp128
634         requires: __float128
635         args: -tol 1e-8
636 
637    test:
638       suffix: mumps_4
639       nsize: 3
640       requires: mumps
641       args: -mat_solver_type mumps
642       output_file: output/ex125_mumps_par.out
643 
644    testset:
645       nsize: 3
646       requires: mumps
647       args: -mat_solver_type mumps -test_nest -test_nest_bordered {{0 1}}
648       output_file: output/ex125_mumps_par.out
649 
650       test:
651         requires: !__float128
652         suffix: mumps_4_nest
653       test:
654         suffix: mumps_4_nest_fp128
655         requires: __float128
656         args: -tol 1e-8
657 
658    test:
659       suffix: mumps_5
660       nsize: 3
661       requires: mumps
662       args: -mat_solver_type mumps -cholesky
663       output_file: output/ex125_mumps_par_cholesky.out
664 
665    testset:
666       nsize: 3
667       requires: mumps
668       args: -mat_solver_type mumps -cholesky -test_nest -test_nest_bordered {{0 1}}
669       output_file: output/ex125_mumps_par_cholesky.out
670 
671       test:
672         requires: !__float128
673         suffix: mumps_5_nest
674       test:
675         suffix: mumps_5_nest_fp128
676         requires: __float128
677         args: -tol 1e-8
678 
679    test:
680       nsize: 2
681       requires: mumps
682       args: -mat_solver_type mumps -test_nest -test_nest_bordered -m 13 -n 13
683       output_file: output/ex125_mumps_par.out
684 
685       test:
686         requires: !__float128
687         suffix: mumps_6
688       test:
689         suffix: mumps_6_fp128
690         requires: __float128
691         args: -tol 1e-8
692 
693    test:
694       suffix: superlu
695       requires: datafilespath double !complex !defined(PETSC_USE_64BIT_INDICES) superlu
696       args: -f ${DATAFILESPATH}/matrices/medium -mat_solver_type superlu
697       output_file: output/ex125_superlu.out
698 
699    test:
700       suffix: superlu_dist
701       nsize: {{1 3}}
702       requires: datafilespath double !complex !defined(PETSC_USE_64BIT_INDICES) superlu_dist
703       args: -f ${DATAFILESPATH}/matrices/small -mat_solver_type superlu_dist -mat_superlu_dist_rowperm NOROWPERM
704       output_file: output/ex125_superlu_dist.out
705 
706    test:
707       suffix: superlu_dist_2
708       nsize: {{1 3}}
709       requires: superlu_dist !complex
710       args: -n 36 -mat_solver_type superlu_dist -mat_superlu_dist_rowperm NOROWPERM
711       output_file: output/ex125_superlu_dist.out
712 
713    test:
714       suffix: superlu_dist_3
715       nsize: {{1 3}}
716       requires: superlu_dist !complex
717       requires: datafilespath double !complex !defined(PETSC_USE_64BIT_INDICES) superlu_dist
718       args: -f ${DATAFILESPATH}/matrices/medium -mat_solver_type superlu_dist -mat_superlu_dist_rowperm NOROWPERM
719       output_file: output/ex125_superlu_dist_nonsymmetric.out
720 
721    test:
722       suffix: superlu_dist_complex
723       nsize: 3
724       requires: datafilespath double superlu_dist complex !defined(PETSC_USE_64BIT_INDICES)
725       args: -f ${DATAFILESPATH}/matrices/farzad_B_rhs -mat_solver_type superlu_dist
726       output_file: output/ex125_superlu_dist_complex.out
727 
728    test:
729       suffix: superlu_dist_complex_2
730       nsize: 3
731       requires: superlu_dist complex
732       args: -mat_solver_type superlu_dist
733       output_file: output/ex125_superlu_dist_complex_2.out
734 
735    test:
736       suffix: cusparse
737       requires: cuda datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
738       #TODO: fix the bug with cholesky
739       #args: -mat_type aijcusparse -f ${DATAFILESPATH}/matrices/small -mat_solver_type cusparse -cholesky {{0 1}separate output}
740       args: -mat_type aijcusparse -f ${DATAFILESPATH}/matrices/small -mat_solver_type cusparse -cholesky {{0}separate output}
741 
742    test:
743       suffix: cusparse_2
744       requires: cuda
745       args: -mat_type aijcusparse -mat_solver_type cusparse -cholesky {{0 1}separate output}
746 
747    testset:
748       nsize: {{1 2}separate output}
749       requires: double !defined(PETSC_USE_64BIT_INDICES) datafilespath !complex
750       args: -f ${DATAFILESPATH}/matrices/mixed_poisson
751       test:
752         requires: superlu_dist TODO # superlu_dist is broken
753         suffix: saddle_point_superlu_dist
754         args: -mat_solver_type superlu_dist -mat_superlu_dist_rowperm {{norowperm largediag_mc64}} -test_inertia 0
755       test:
756         requires: mumps
757         suffix: saddle_point_mumps_lu
758         args: -mat_solver_type mumps -mat_mumps_icntl_14 100
759       test:
760         requires: mumps
761         suffix: saddle_point_mumps_cholesky
762         args: -cholesky -mat_solver_type mumps
763 
764 TEST*/
765