xref: /petsc/src/mat/impls/shell/shell.c (revision 5d8720fa41fb4169420198de95a3fb9ffc339d07)
1 /*
2    This provides a simple shell for Fortran (and C programmers) to
3   create a very simple matrix class for use with KSP without coding
4   much of anything.
5 */
6 
7 #include <../src/mat/impls/shell/shell.h> /*I "petscmat.h" I*/
8 
9 /*
10      Store and scale values on zeroed rows
11      xx = [x_1, 0], 0 on zeroed columns
12 */
13 static PetscErrorCode MatShellPreZeroRight(Mat A, Vec x, Vec *xx)
14 {
15   Mat_Shell *shell = (Mat_Shell *)A->data;
16 
17   PetscFunctionBegin;
18   *xx = x;
19   if (shell->zrows) {
20     PetscCall(VecSet(shell->zvals_w, 0.0));
21     PetscCall(VecScatterBegin(shell->zvals_sct_c, x, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
22     PetscCall(VecScatterEnd(shell->zvals_sct_c, x, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
23     PetscCall(VecPointwiseMult(shell->zvals_w, shell->zvals_w, shell->zvals));
24   }
25   if (shell->zcols) {
26     if (!shell->right_work) PetscCall(MatCreateVecs(A, &shell->right_work, NULL));
27     PetscCall(VecCopy(x, shell->right_work));
28     PetscCall(VecISSet(shell->right_work, shell->zcols, 0.0));
29     *xx = shell->right_work;
30   }
31   PetscFunctionReturn(PETSC_SUCCESS);
32 }
33 
34 /* Insert properly diagonally scaled values stored in MatShellPreZeroRight */
35 static PetscErrorCode MatShellPostZeroLeft(Mat A, Vec x)
36 {
37   Mat_Shell *shell = (Mat_Shell *)A->data;
38 
39   PetscFunctionBegin;
40   if (shell->zrows) {
41     PetscCall(VecScatterBegin(shell->zvals_sct_r, shell->zvals_w, x, INSERT_VALUES, SCATTER_REVERSE));
42     PetscCall(VecScatterEnd(shell->zvals_sct_r, shell->zvals_w, x, INSERT_VALUES, SCATTER_REVERSE));
43   }
44   PetscFunctionReturn(PETSC_SUCCESS);
45 }
46 
47 /*
48      Store and scale values on zeroed rows
49      xx = [x_1, 0], 0 on zeroed rows
50 */
51 static PetscErrorCode MatShellPreZeroLeft(Mat A, Vec x, Vec *xx)
52 {
53   Mat_Shell *shell = (Mat_Shell *)A->data;
54 
55   PetscFunctionBegin;
56   *xx = NULL;
57   if (!shell->zrows) {
58     *xx = x;
59   } else {
60     if (!shell->left_work) PetscCall(MatCreateVecs(A, NULL, &shell->left_work));
61     PetscCall(VecCopy(x, shell->left_work));
62     PetscCall(VecSet(shell->zvals_w, 0.0));
63     PetscCall(VecScatterBegin(shell->zvals_sct_r, shell->zvals_w, shell->left_work, INSERT_VALUES, SCATTER_REVERSE));
64     PetscCall(VecScatterEnd(shell->zvals_sct_r, shell->zvals_w, shell->left_work, INSERT_VALUES, SCATTER_REVERSE));
65     PetscCall(VecScatterBegin(shell->zvals_sct_r, x, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
66     PetscCall(VecScatterEnd(shell->zvals_sct_r, x, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
67     PetscCall(VecPointwiseMult(shell->zvals_w, shell->zvals_w, shell->zvals));
68     *xx = shell->left_work;
69   }
70   PetscFunctionReturn(PETSC_SUCCESS);
71 }
72 
73 /* Zero zero-columns contributions, sum contributions from properly scaled values stored in MatShellPreZeroLeft */
74 static PetscErrorCode MatShellPostZeroRight(Mat A, Vec x)
75 {
76   Mat_Shell *shell = (Mat_Shell *)A->data;
77 
78   PetscFunctionBegin;
79   if (shell->zcols) PetscCall(VecISSet(x, shell->zcols, 0.0));
80   if (shell->zrows) {
81     PetscCall(VecScatterBegin(shell->zvals_sct_c, shell->zvals_w, x, ADD_VALUES, SCATTER_REVERSE));
82     PetscCall(VecScatterEnd(shell->zvals_sct_c, shell->zvals_w, x, ADD_VALUES, SCATTER_REVERSE));
83   }
84   PetscFunctionReturn(PETSC_SUCCESS);
85 }
86 
87 /*
88       xx = diag(left)*x
89 */
90 static PetscErrorCode MatShellPreScaleLeft(Mat A, Vec x, Vec *xx, PetscBool conjugate)
91 {
92   Mat_Shell *shell = (Mat_Shell *)A->data;
93 
94   PetscFunctionBegin;
95   *xx = NULL;
96   if (!shell->left) {
97     *xx = x;
98   } else {
99     if (!shell->left_work) PetscCall(VecDuplicate(shell->left, &shell->left_work));
100     if (conjugate) { /* get arrays because there is no VecPointwiseMultConj() */
101       PetscInt           i, m;
102       const PetscScalar *d, *xarray;
103       PetscScalar       *w;
104       PetscCall(VecGetLocalSize(x, &m));
105       PetscCall(VecGetArrayRead(shell->left, &d));
106       PetscCall(VecGetArrayRead(x, &xarray));
107       PetscCall(VecGetArrayWrite(shell->left_work, &w));
108       for (i = 0; i < m; i++) w[i] = PetscConj(d[i]) * xarray[i];
109       PetscCall(VecRestoreArrayRead(shell->dshift, &d));
110       PetscCall(VecRestoreArrayRead(x, &xarray));
111       PetscCall(VecRestoreArrayWrite(shell->left_work, &w));
112     } else PetscCall(VecPointwiseMult(shell->left_work, x, shell->left));
113     *xx = shell->left_work;
114   }
115   PetscFunctionReturn(PETSC_SUCCESS);
116 }
117 
118 /*
119      xx = diag(right)*x
120 */
121 static PetscErrorCode MatShellPreScaleRight(Mat A, Vec x, Vec *xx)
122 {
123   Mat_Shell *shell = (Mat_Shell *)A->data;
124 
125   PetscFunctionBegin;
126   *xx = NULL;
127   if (!shell->right) {
128     *xx = x;
129   } else {
130     if (!shell->right_work) PetscCall(VecDuplicate(shell->right, &shell->right_work));
131     PetscCall(VecPointwiseMult(shell->right_work, x, shell->right));
132     *xx = shell->right_work;
133   }
134   PetscFunctionReturn(PETSC_SUCCESS);
135 }
136 
137 /*
138     x = diag(left)*x
139 */
140 static PetscErrorCode MatShellPostScaleLeft(Mat A, Vec x)
141 {
142   Mat_Shell *shell = (Mat_Shell *)A->data;
143 
144   PetscFunctionBegin;
145   if (shell->left) PetscCall(VecPointwiseMult(x, x, shell->left));
146   PetscFunctionReturn(PETSC_SUCCESS);
147 }
148 
149 /*
150     x = diag(right)*x
151 */
152 static PetscErrorCode MatShellPostScaleRight(Mat A, Vec x, PetscBool conjugate)
153 {
154   Mat_Shell *shell = (Mat_Shell *)A->data;
155 
156   PetscFunctionBegin;
157   if (shell->right) {
158     if (conjugate) { /* get arrays because there is no VecPointwiseMultConj() */
159       PetscInt           i, m;
160       const PetscScalar *d;
161       PetscScalar       *xarray;
162       PetscCall(VecGetLocalSize(x, &m));
163       PetscCall(VecGetArrayRead(shell->right, &d));
164       PetscCall(VecGetArray(x, &xarray));
165       for (i = 0; i < m; i++) xarray[i] = PetscConj(d[i]) * xarray[i];
166       PetscCall(VecRestoreArrayRead(shell->dshift, &d));
167       PetscCall(VecRestoreArray(x, &xarray));
168     } else PetscCall(VecPointwiseMult(x, x, shell->right));
169   }
170   PetscFunctionReturn(PETSC_SUCCESS);
171 }
172 
173 /*
174          Y = vscale*Y + diag(dshift)*X + vshift*X
175 
176          On input Y already contains A*x
177 
178          If conjugate=PETSC_TRUE then vscale, dshift, and vshift are conjugated
179 */
180 static PetscErrorCode MatShellShiftAndScale(Mat A, Vec X, Vec Y, PetscBool conjugate)
181 {
182   Mat_Shell  *shell  = (Mat_Shell *)A->data;
183   PetscScalar vscale = conjugate ? PetscConj(shell->vscale) : shell->vscale;
184   PetscScalar vshift = conjugate ? PetscConj(shell->vshift) : shell->vshift;
185 
186   PetscFunctionBegin;
187   if (shell->dshift) { /* get arrays because there is no VecPointwiseMultAdd() */
188     PetscInt           i, m;
189     const PetscScalar *x, *d;
190     PetscScalar       *y;
191     PetscCall(VecGetLocalSize(X, &m));
192     PetscCall(VecGetArrayRead(shell->dshift, &d));
193     PetscCall(VecGetArrayRead(X, &x));
194     PetscCall(VecGetArray(Y, &y));
195     if (conjugate)
196       for (i = 0; i < m; i++) y[i] = vscale * y[i] + PetscConj(d[i]) * x[i];
197     else
198       for (i = 0; i < m; i++) y[i] = vscale * y[i] + d[i] * x[i];
199     PetscCall(VecRestoreArrayRead(shell->dshift, &d));
200     PetscCall(VecRestoreArrayRead(X, &x));
201     PetscCall(VecRestoreArray(Y, &y));
202   } else {
203     PetscCall(VecScale(Y, vscale));
204   }
205   if (vshift != 0.0) PetscCall(VecAXPY(Y, vshift, X)); /* if test is for non-square matrices */
206   PetscFunctionReturn(PETSC_SUCCESS);
207 }
208 
209 static PetscErrorCode MatShellGetContext_Shell(Mat mat, void *ctx)
210 {
211   Mat_Shell *shell = (Mat_Shell *)mat->data;
212 
213   PetscFunctionBegin;
214   if (shell->ctxcontainer) PetscCall(PetscContainerGetPointer(shell->ctxcontainer, (void **)ctx));
215   else *(void **)ctx = NULL;
216   PetscFunctionReturn(PETSC_SUCCESS);
217 }
218 
219 /*@
220   MatShellGetContext - Returns the user-provided context associated with a `MATSHELL` shell matrix.
221 
222   Not Collective
223 
224   Input Parameter:
225 . mat - the matrix, should have been created with `MatCreateShell()`
226 
227   Output Parameter:
228 . ctx - the user provided context
229 
230   Level: advanced
231 
232   Fortran Notes:
233   You must write a Fortran interface definition for this
234   function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.
235 
236 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellSetOperation()`, `MatShellSetContext()`
237 @*/
238 PetscErrorCode MatShellGetContext(Mat mat, void *ctx)
239 {
240   PetscFunctionBegin;
241   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
242   PetscAssertPointer(ctx, 2);
243   PetscUseMethod(mat, "MatShellGetContext_C", (Mat, void *), (mat, ctx));
244   PetscFunctionReturn(PETSC_SUCCESS);
245 }
246 
247 static PetscErrorCode MatZeroRowsColumns_Local_Shell(Mat mat, PetscInt nr, PetscInt rows[], PetscInt nc, PetscInt cols[], PetscScalar diag, PetscBool rc)
248 {
249   Mat_Shell      *shell = (Mat_Shell *)mat->data;
250   Vec             x = NULL, b = NULL;
251   IS              is1, is2;
252   const PetscInt *ridxs;
253   PetscInt       *idxs, *gidxs;
254   PetscInt        cum, rst, cst, i;
255 
256   PetscFunctionBegin;
257   if (!shell->zvals) PetscCall(MatCreateVecs(mat, NULL, &shell->zvals));
258   if (!shell->zvals_w) PetscCall(VecDuplicate(shell->zvals, &shell->zvals_w));
259   PetscCall(MatGetOwnershipRange(mat, &rst, NULL));
260   PetscCall(MatGetOwnershipRangeColumn(mat, &cst, NULL));
261 
262   /* Expand/create index set of zeroed rows */
263   PetscCall(PetscMalloc1(nr, &idxs));
264   for (i = 0; i < nr; i++) idxs[i] = rows[i] + rst;
265   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), nr, idxs, PETSC_OWN_POINTER, &is1));
266   PetscCall(ISSort(is1));
267   PetscCall(VecISSet(shell->zvals, is1, diag));
268   if (shell->zrows) {
269     PetscCall(ISSum(shell->zrows, is1, &is2));
270     PetscCall(ISDestroy(&shell->zrows));
271     PetscCall(ISDestroy(&is1));
272     shell->zrows = is2;
273   } else shell->zrows = is1;
274 
275   /* Create scatters for diagonal values communications */
276   PetscCall(VecScatterDestroy(&shell->zvals_sct_c));
277   PetscCall(VecScatterDestroy(&shell->zvals_sct_r));
278 
279   /* row scatter: from/to left vector */
280   PetscCall(MatCreateVecs(mat, &x, &b));
281   PetscCall(VecScatterCreate(b, shell->zrows, shell->zvals_w, shell->zrows, &shell->zvals_sct_r));
282 
283   /* col scatter: from right vector to left vector */
284   PetscCall(ISGetIndices(shell->zrows, &ridxs));
285   PetscCall(ISGetLocalSize(shell->zrows, &nr));
286   PetscCall(PetscMalloc1(nr, &gidxs));
287   for (i = 0, cum = 0; i < nr; i++) {
288     if (ridxs[i] >= mat->cmap->N) continue;
289     gidxs[cum] = ridxs[i];
290     cum++;
291   }
292   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), cum, gidxs, PETSC_OWN_POINTER, &is1));
293   PetscCall(VecScatterCreate(x, is1, shell->zvals_w, is1, &shell->zvals_sct_c));
294   PetscCall(ISDestroy(&is1));
295   PetscCall(VecDestroy(&x));
296   PetscCall(VecDestroy(&b));
297 
298   /* Expand/create index set of zeroed columns */
299   if (rc) {
300     PetscCall(PetscMalloc1(nc, &idxs));
301     for (i = 0; i < nc; i++) idxs[i] = cols[i] + cst;
302     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), nc, idxs, PETSC_OWN_POINTER, &is1));
303     PetscCall(ISSort(is1));
304     if (shell->zcols) {
305       PetscCall(ISSum(shell->zcols, is1, &is2));
306       PetscCall(ISDestroy(&shell->zcols));
307       PetscCall(ISDestroy(&is1));
308       shell->zcols = is2;
309     } else shell->zcols = is1;
310   }
311   PetscFunctionReturn(PETSC_SUCCESS);
312 }
313 
314 static PetscErrorCode MatZeroRows_Shell(Mat mat, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
315 {
316   Mat_Shell *shell = (Mat_Shell *)mat->data;
317   PetscInt   nr, *lrows;
318 
319   PetscFunctionBegin;
320   if (x && b) {
321     Vec          xt;
322     PetscScalar *vals;
323     PetscInt    *gcols, i, st, nl, nc;
324 
325     PetscCall(PetscMalloc1(n, &gcols));
326     for (i = 0, nc = 0; i < n; i++)
327       if (rows[i] < mat->cmap->N) gcols[nc++] = rows[i];
328 
329     PetscCall(MatCreateVecs(mat, &xt, NULL));
330     PetscCall(VecCopy(x, xt));
331     PetscCall(PetscCalloc1(nc, &vals));
332     PetscCall(VecSetValues(xt, nc, gcols, vals, INSERT_VALUES)); /* xt = [x1, 0] */
333     PetscCall(PetscFree(vals));
334     PetscCall(VecAssemblyBegin(xt));
335     PetscCall(VecAssemblyEnd(xt));
336     PetscCall(VecAYPX(xt, -1.0, x)); /* xt = [0, x2] */
337 
338     PetscCall(VecGetOwnershipRange(xt, &st, NULL));
339     PetscCall(VecGetLocalSize(xt, &nl));
340     PetscCall(VecGetArray(xt, &vals));
341     for (i = 0; i < nl; i++) {
342       PetscInt g = i + st;
343       if (g > mat->rmap->N) continue;
344       if (PetscAbsScalar(vals[i]) == 0.0) continue;
345       PetscCall(VecSetValue(b, g, diag * vals[i], INSERT_VALUES));
346     }
347     PetscCall(VecRestoreArray(xt, &vals));
348     PetscCall(VecAssemblyBegin(b));
349     PetscCall(VecAssemblyEnd(b)); /* b  = [b1, x2 * diag] */
350     PetscCall(VecDestroy(&xt));
351     PetscCall(PetscFree(gcols));
352   }
353   PetscCall(PetscLayoutMapLocal(mat->rmap, n, rows, &nr, &lrows, NULL));
354   PetscCall(MatZeroRowsColumns_Local_Shell(mat, nr, lrows, 0, NULL, diag, PETSC_FALSE));
355   if (shell->axpy) PetscCall(MatZeroRows(shell->axpy, n, rows, 0.0, NULL, NULL));
356   PetscCall(PetscFree(lrows));
357   PetscFunctionReturn(PETSC_SUCCESS);
358 }
359 
360 static PetscErrorCode MatZeroRowsColumns_Shell(Mat mat, PetscInt n, const PetscInt rowscols[], PetscScalar diag, Vec x, Vec b)
361 {
362   Mat_Shell *shell = (Mat_Shell *)mat->data;
363   PetscInt  *lrows, *lcols;
364   PetscInt   nr, nc;
365   PetscBool  congruent;
366 
367   PetscFunctionBegin;
368   if (x && b) {
369     Vec          xt, bt;
370     PetscScalar *vals;
371     PetscInt    *grows, *gcols, i, st, nl;
372 
373     PetscCall(PetscMalloc2(n, &grows, n, &gcols));
374     for (i = 0, nr = 0; i < n; i++)
375       if (rowscols[i] < mat->rmap->N) grows[nr++] = rowscols[i];
376     for (i = 0, nc = 0; i < n; i++)
377       if (rowscols[i] < mat->cmap->N) gcols[nc++] = rowscols[i];
378     PetscCall(PetscCalloc1(n, &vals));
379 
380     PetscCall(MatCreateVecs(mat, &xt, &bt));
381     PetscCall(VecCopy(x, xt));
382     PetscCall(VecSetValues(xt, nc, gcols, vals, INSERT_VALUES)); /* xt = [x1, 0] */
383     PetscCall(VecAssemblyBegin(xt));
384     PetscCall(VecAssemblyEnd(xt));
385     PetscCall(VecAXPY(xt, -1.0, x));                             /* xt = [0, -x2] */
386     PetscCall(MatMult(mat, xt, bt));                             /* bt = [-A12*x2,-A22*x2] */
387     PetscCall(VecSetValues(bt, nr, grows, vals, INSERT_VALUES)); /* bt = [-A12*x2,0] */
388     PetscCall(VecAssemblyBegin(bt));
389     PetscCall(VecAssemblyEnd(bt));
390     PetscCall(VecAXPY(b, 1.0, bt));                              /* b  = [b1 - A12*x2, b2] */
391     PetscCall(VecSetValues(bt, nr, grows, vals, INSERT_VALUES)); /* b  = [b1 - A12*x2, 0] */
392     PetscCall(VecAssemblyBegin(bt));
393     PetscCall(VecAssemblyEnd(bt));
394     PetscCall(PetscFree(vals));
395 
396     PetscCall(VecGetOwnershipRange(xt, &st, NULL));
397     PetscCall(VecGetLocalSize(xt, &nl));
398     PetscCall(VecGetArray(xt, &vals));
399     for (i = 0; i < nl; i++) {
400       PetscInt g = i + st;
401       if (g > mat->rmap->N) continue;
402       if (PetscAbsScalar(vals[i]) == 0.0) continue;
403       PetscCall(VecSetValue(b, g, -diag * vals[i], INSERT_VALUES));
404     }
405     PetscCall(VecRestoreArray(xt, &vals));
406     PetscCall(VecAssemblyBegin(b));
407     PetscCall(VecAssemblyEnd(b)); /* b  = [b1 - A12*x2, x2 * diag] */
408     PetscCall(VecDestroy(&xt));
409     PetscCall(VecDestroy(&bt));
410     PetscCall(PetscFree2(grows, gcols));
411   }
412   PetscCall(PetscLayoutMapLocal(mat->rmap, n, rowscols, &nr, &lrows, NULL));
413   PetscCall(MatHasCongruentLayouts(mat, &congruent));
414   if (congruent) {
415     nc    = nr;
416     lcols = lrows;
417   } else { /* MatZeroRowsColumns implicitly assumes the rowscols indices are for a square matrix, here we handle a more general case */
418     PetscInt i, nt, *t;
419 
420     PetscCall(PetscMalloc1(n, &t));
421     for (i = 0, nt = 0; i < n; i++)
422       if (rowscols[i] < mat->cmap->N) t[nt++] = rowscols[i];
423     PetscCall(PetscLayoutMapLocal(mat->cmap, nt, t, &nc, &lcols, NULL));
424     PetscCall(PetscFree(t));
425   }
426   PetscCall(MatZeroRowsColumns_Local_Shell(mat, nr, lrows, nc, lcols, diag, PETSC_TRUE));
427   if (!congruent) PetscCall(PetscFree(lcols));
428   PetscCall(PetscFree(lrows));
429   if (shell->axpy) PetscCall(MatZeroRowsColumns(shell->axpy, n, rowscols, 0.0, NULL, NULL));
430   PetscFunctionReturn(PETSC_SUCCESS);
431 }
432 
433 static PetscErrorCode MatDestroy_Shell(Mat mat)
434 {
435   Mat_Shell              *shell = (Mat_Shell *)mat->data;
436   MatShellMatFunctionList matmat;
437 
438   PetscFunctionBegin;
439   if (shell->ops->destroy) PetscCall((*shell->ops->destroy)(mat));
440   PetscCall(PetscMemzero(shell->ops, sizeof(struct _MatShellOps)));
441   PetscCall(VecDestroy(&shell->left));
442   PetscCall(VecDestroy(&shell->right));
443   PetscCall(VecDestroy(&shell->dshift));
444   PetscCall(VecDestroy(&shell->left_work));
445   PetscCall(VecDestroy(&shell->right_work));
446   PetscCall(VecDestroy(&shell->left_add_work));
447   PetscCall(VecDestroy(&shell->right_add_work));
448   PetscCall(VecDestroy(&shell->axpy_left));
449   PetscCall(VecDestroy(&shell->axpy_right));
450   PetscCall(MatDestroy(&shell->axpy));
451   PetscCall(VecDestroy(&shell->zvals_w));
452   PetscCall(VecDestroy(&shell->zvals));
453   PetscCall(VecScatterDestroy(&shell->zvals_sct_c));
454   PetscCall(VecScatterDestroy(&shell->zvals_sct_r));
455   PetscCall(ISDestroy(&shell->zrows));
456   PetscCall(ISDestroy(&shell->zcols));
457 
458   matmat = shell->matmat;
459   while (matmat) {
460     MatShellMatFunctionList next = matmat->next;
461 
462     PetscCall(PetscObjectComposeFunction((PetscObject)mat, matmat->composedname, NULL));
463     PetscCall(PetscFree(matmat->composedname));
464     PetscCall(PetscFree(matmat->resultname));
465     PetscCall(PetscFree(matmat));
466     matmat = next;
467   }
468   PetscCall(MatShellSetContext(mat, NULL));
469   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellGetContext_C", NULL));
470   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetContext_C", NULL));
471   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetContextDestroy_C", NULL));
472   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetVecType_C", NULL));
473   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetManageScalingShifts_C", NULL));
474   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellGetScalingShifts_C", NULL));
475   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetOperation_C", NULL));
476   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellGetOperation_C", NULL));
477   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetMatProductOperation_C", NULL));
478   PetscCall(PetscFree(mat->data));
479   PetscFunctionReturn(PETSC_SUCCESS);
480 }
481 
482 typedef struct {
483   PetscErrorCode (*numeric)(Mat, Mat, Mat, void *);
484   PetscErrorCode (*destroy)(void *);
485   void *userdata;
486   Mat   B;
487   Mat   Bt;
488   Mat   axpy;
489 } MatMatDataShell;
490 
491 static PetscErrorCode DestroyMatMatDataShell(void *data)
492 {
493   MatMatDataShell *mmdata = (MatMatDataShell *)data;
494 
495   PetscFunctionBegin;
496   if (mmdata->destroy) PetscCall((*mmdata->destroy)(mmdata->userdata));
497   PetscCall(MatDestroy(&mmdata->B));
498   PetscCall(MatDestroy(&mmdata->Bt));
499   PetscCall(MatDestroy(&mmdata->axpy));
500   PetscCall(PetscFree(mmdata));
501   PetscFunctionReturn(PETSC_SUCCESS);
502 }
503 
504 static PetscErrorCode MatProductNumeric_Shell_X(Mat D)
505 {
506   Mat_Product     *product;
507   Mat              A, B;
508   MatMatDataShell *mdata;
509   PetscScalar      zero = 0.0;
510 
511   PetscFunctionBegin;
512   MatCheckProduct(D, 1);
513   product = D->product;
514   PetscCheck(product->data, PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "Product data empty");
515   A     = product->A;
516   B     = product->B;
517   mdata = (MatMatDataShell *)product->data;
518   if (mdata->numeric) {
519     Mat_Shell *shell                = (Mat_Shell *)A->data;
520     PetscErrorCode (*stashsym)(Mat) = D->ops->productsymbolic;
521     PetscErrorCode (*stashnum)(Mat) = D->ops->productnumeric;
522     PetscBool useBmdata = PETSC_FALSE, newB = PETSC_TRUE;
523 
524     if (shell->managescalingshifts) {
525       PetscCheck(!shell->zcols && !shell->zrows, PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProduct not supported with zeroed rows/columns");
526       if (shell->right || shell->left) {
527         useBmdata = PETSC_TRUE;
528         if (!mdata->B) {
529           PetscCall(MatDuplicate(B, MAT_SHARE_NONZERO_PATTERN, &mdata->B));
530         } else {
531           newB = PETSC_FALSE;
532         }
533         PetscCall(MatCopy(B, mdata->B, SAME_NONZERO_PATTERN));
534       }
535       switch (product->type) {
536       case MATPRODUCT_AB: /* s L A R B + v L R B + L D R B */
537         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, shell->right, NULL));
538         break;
539       case MATPRODUCT_AtB: /* s R A^t L B + v R L B + R D L B */
540         if (shell->left) PetscCall(MatDiagonalScale(mdata->B, shell->left, NULL));
541         break;
542       case MATPRODUCT_ABt: /* s L A R B^t + v L R B^t + L D R B^t */
543         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, NULL, shell->right));
544         break;
545       case MATPRODUCT_RARt: /* s B L A R B^t + v B L R B^t + B L D R B^t */
546         if (shell->right && shell->left) {
547           PetscBool flg;
548 
549           PetscCall(VecEqual(shell->right, shell->left, &flg));
550           PetscCheck(flg, PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProductSymbolic type %s not supported for %s and %s matrices because left scaling != from right scaling", MatProductTypes[product->type], ((PetscObject)A)->type_name,
551                      ((PetscObject)B)->type_name);
552         }
553         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, NULL, shell->right));
554         break;
555       case MATPRODUCT_PtAP: /* s B^t L A R B + v B^t L R B + B^t L D R B */
556         if (shell->right && shell->left) {
557           PetscBool flg;
558 
559           PetscCall(VecEqual(shell->right, shell->left, &flg));
560           PetscCheck(flg, PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProductSymbolic type %s not supported for %s and %s matrices because left scaling != from right scaling", MatProductTypes[product->type], ((PetscObject)A)->type_name,
561                      ((PetscObject)B)->type_name);
562         }
563         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, shell->right, NULL));
564         break;
565       default:
566         SETERRQ(PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProductSymbolic type %s not supported for %s and %s matrices", MatProductTypes[product->type], ((PetscObject)A)->type_name, ((PetscObject)B)->type_name);
567       }
568     }
569     /* allow the user to call MatMat operations on D */
570     D->product              = NULL;
571     D->ops->productsymbolic = NULL;
572     D->ops->productnumeric  = NULL;
573 
574     PetscCall((*mdata->numeric)(A, useBmdata ? mdata->B : B, D, mdata->userdata));
575 
576     /* clear any leftover user data and restore D pointers */
577     PetscCall(MatProductClear(D));
578     D->ops->productsymbolic = stashsym;
579     D->ops->productnumeric  = stashnum;
580     D->product              = product;
581 
582     if (shell->managescalingshifts) {
583       PetscCall(MatScale(D, shell->vscale));
584       switch (product->type) {
585       case MATPRODUCT_AB:  /* s L A R B + v L R B + L D R B */
586       case MATPRODUCT_ABt: /* s L A R B^t + v L R B^t + L D R B^t */
587         if (shell->left) {
588           PetscCall(MatDiagonalScale(D, shell->left, NULL));
589           if (shell->dshift || shell->vshift != zero) {
590             if (!shell->left_work) PetscCall(MatCreateVecs(A, NULL, &shell->left_work));
591             if (shell->dshift) {
592               PetscCall(VecCopy(shell->dshift, shell->left_work));
593               PetscCall(VecShift(shell->left_work, shell->vshift));
594               PetscCall(VecPointwiseMult(shell->left_work, shell->left_work, shell->left));
595             } else {
596               PetscCall(VecSet(shell->left_work, shell->vshift));
597             }
598             if (product->type == MATPRODUCT_ABt) {
599               MatReuse     reuse = mdata->Bt ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;
600               MatStructure str   = mdata->Bt ? SUBSET_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN;
601 
602               PetscCall(MatTranspose(mdata->B, reuse, &mdata->Bt));
603               PetscCall(MatDiagonalScale(mdata->Bt, shell->left_work, NULL));
604               PetscCall(MatAXPY(D, 1.0, mdata->Bt, str));
605             } else {
606               MatStructure str = newB ? DIFFERENT_NONZERO_PATTERN : SUBSET_NONZERO_PATTERN;
607 
608               PetscCall(MatDiagonalScale(mdata->B, shell->left_work, NULL));
609               PetscCall(MatAXPY(D, 1.0, mdata->B, str));
610             }
611           }
612         }
613         break;
614       case MATPRODUCT_AtB: /* s R A^t L B + v R L B + R D L B */
615         if (shell->right) {
616           PetscCall(MatDiagonalScale(D, shell->right, NULL));
617           if (shell->dshift || shell->vshift != zero) {
618             MatStructure str = newB ? DIFFERENT_NONZERO_PATTERN : SUBSET_NONZERO_PATTERN;
619 
620             if (!shell->right_work) PetscCall(MatCreateVecs(A, &shell->right_work, NULL));
621             if (shell->dshift) {
622               PetscCall(VecCopy(shell->dshift, shell->right_work));
623               PetscCall(VecShift(shell->right_work, shell->vshift));
624               PetscCall(VecPointwiseMult(shell->right_work, shell->right_work, shell->right));
625             } else {
626               PetscCall(VecSet(shell->right_work, shell->vshift));
627             }
628             PetscCall(MatDiagonalScale(mdata->B, shell->right_work, NULL));
629             PetscCall(MatAXPY(D, 1.0, mdata->B, str));
630           }
631         }
632         break;
633       case MATPRODUCT_PtAP: /* s B^t L A R B + v B^t L R B + B^t L D R B */
634       case MATPRODUCT_RARt: /* s B L A R B^t + v B L R B^t + B L D R B^t */
635         PetscCheck(!shell->dshift && shell->vshift == zero, PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProductSymbolic type %s not supported for %s and %s matrices with diagonal shift", MatProductTypes[product->type], ((PetscObject)A)->type_name,
636                    ((PetscObject)B)->type_name);
637         break;
638       default:
639         SETERRQ(PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProductSymbolic type %s not supported for %s and %s matrices", MatProductTypes[product->type], ((PetscObject)A)->type_name, ((PetscObject)B)->type_name);
640       }
641       if (shell->axpy && shell->axpy_vscale != zero) {
642         Mat              X;
643         PetscObjectState axpy_state;
644         MatStructure     str = DIFFERENT_NONZERO_PATTERN; /* not sure it is safe to ever use SUBSET_NONZERO_PATTERN */
645 
646         PetscCall(MatShellGetContext(shell->axpy, &X));
647         PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
648         PetscCheck(shell->axpy_state == axpy_state, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Invalid AXPY state: cannot modify the X matrix passed to MatAXPY(Y,a,X,...)");
649         if (!mdata->axpy) {
650           str = DIFFERENT_NONZERO_PATTERN;
651           PetscCall(MatProductCreate(shell->axpy, B, NULL, &mdata->axpy));
652           PetscCall(MatProductSetType(mdata->axpy, product->type));
653           PetscCall(MatProductSetFromOptions(mdata->axpy));
654           PetscCall(MatProductSymbolic(mdata->axpy));
655         } else { /* May be that shell->axpy has changed */
656           PetscBool flg;
657 
658           PetscCall(MatProductReplaceMats(shell->axpy, B, NULL, mdata->axpy));
659           PetscCall(MatHasOperation(mdata->axpy, MATOP_PRODUCTSYMBOLIC, &flg));
660           if (!flg) {
661             str = DIFFERENT_NONZERO_PATTERN;
662             PetscCall(MatProductSetFromOptions(mdata->axpy));
663             PetscCall(MatProductSymbolic(mdata->axpy));
664           }
665         }
666         PetscCall(MatProductNumeric(mdata->axpy));
667         PetscCall(MatAXPY(D, shell->axpy_vscale, mdata->axpy, str));
668       }
669     }
670   } else SETERRQ(PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "Missing numeric operation");
671   PetscFunctionReturn(PETSC_SUCCESS);
672 }
673 
674 static PetscErrorCode MatProductSymbolic_Shell_X(Mat D)
675 {
676   Mat_Product            *product;
677   Mat                     A, B;
678   MatShellMatFunctionList matmat;
679   Mat_Shell              *shell;
680   PetscBool               flg = PETSC_FALSE;
681   char                    composedname[256];
682   MatMatDataShell        *mdata;
683 
684   PetscFunctionBegin;
685   MatCheckProduct(D, 1);
686   product = D->product;
687   PetscCheck(!product->data, PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "Product data not empty");
688   A      = product->A;
689   B      = product->B;
690   shell  = (Mat_Shell *)A->data;
691   matmat = shell->matmat;
692   PetscCall(PetscSNPrintf(composedname, sizeof(composedname), "MatProductSetFromOptions_%s_%s_C", ((PetscObject)A)->type_name, ((PetscObject)B)->type_name));
693   while (matmat) {
694     PetscCall(PetscStrcmp(composedname, matmat->composedname, &flg));
695     flg = (PetscBool)(flg && (matmat->ptype == product->type));
696     if (flg) break;
697     matmat = matmat->next;
698   }
699   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Composedname \"%s\" for product type %s not found", composedname, MatProductTypes[product->type]);
700   switch (product->type) {
701   case MATPRODUCT_AB:
702     PetscCall(MatSetSizes(D, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
703     break;
704   case MATPRODUCT_AtB:
705     PetscCall(MatSetSizes(D, A->cmap->n, B->cmap->n, A->cmap->N, B->cmap->N));
706     break;
707   case MATPRODUCT_ABt:
708     PetscCall(MatSetSizes(D, A->rmap->n, B->rmap->n, A->rmap->N, B->rmap->N));
709     break;
710   case MATPRODUCT_RARt:
711     PetscCall(MatSetSizes(D, B->rmap->n, B->rmap->n, B->rmap->N, B->rmap->N));
712     break;
713   case MATPRODUCT_PtAP:
714     PetscCall(MatSetSizes(D, B->cmap->n, B->cmap->n, B->cmap->N, B->cmap->N));
715     break;
716   default:
717     SETERRQ(PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProductSymbolic type %s not supported for %s and %s matrices", MatProductTypes[product->type], ((PetscObject)A)->type_name, ((PetscObject)B)->type_name);
718   }
719   /* respect users who passed in a matrix for which resultname is the base type */
720   if (matmat->resultname) {
721     PetscCall(PetscObjectBaseTypeCompare((PetscObject)D, matmat->resultname, &flg));
722     if (!flg) PetscCall(MatSetType(D, matmat->resultname));
723   }
724   /* If matrix type was not set or different, we need to reset this pointers */
725   D->ops->productsymbolic = MatProductSymbolic_Shell_X;
726   D->ops->productnumeric  = MatProductNumeric_Shell_X;
727   /* attach product data */
728   PetscCall(PetscNew(&mdata));
729   mdata->numeric = matmat->numeric;
730   mdata->destroy = matmat->destroy;
731   if (matmat->symbolic) {
732     PetscCall((*matmat->symbolic)(A, B, D, &mdata->userdata));
733   } else { /* call general setup if symbolic operation not provided */
734     PetscCall(MatSetUp(D));
735   }
736   PetscCheck(D->product, PetscObjectComm((PetscObject)D), PETSC_ERR_COR, "Product disappeared after user symbolic phase");
737   PetscCheck(!D->product->data, PetscObjectComm((PetscObject)D), PETSC_ERR_COR, "Product data not empty after user symbolic phase");
738   D->product->data    = mdata;
739   D->product->destroy = DestroyMatMatDataShell;
740   /* Be sure to reset these pointers if the user did something unexpected */
741   D->ops->productsymbolic = MatProductSymbolic_Shell_X;
742   D->ops->productnumeric  = MatProductNumeric_Shell_X;
743   PetscFunctionReturn(PETSC_SUCCESS);
744 }
745 
746 static PetscErrorCode MatProductSetFromOptions_Shell_X(Mat D)
747 {
748   Mat_Product            *product;
749   Mat                     A, B;
750   MatShellMatFunctionList matmat;
751   Mat_Shell              *shell;
752   PetscBool               flg;
753   char                    composedname[256];
754 
755   PetscFunctionBegin;
756   MatCheckProduct(D, 1);
757   product = D->product;
758   A       = product->A;
759   B       = product->B;
760   PetscCall(MatIsShell(A, &flg));
761   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);
762   shell  = (Mat_Shell *)A->data;
763   matmat = shell->matmat;
764   PetscCall(PetscSNPrintf(composedname, sizeof(composedname), "MatProductSetFromOptions_%s_%s_C", ((PetscObject)A)->type_name, ((PetscObject)B)->type_name));
765   while (matmat) {
766     PetscCall(PetscStrcmp(composedname, matmat->composedname, &flg));
767     flg = (PetscBool)(flg && (matmat->ptype == product->type));
768     if (flg) break;
769     matmat = matmat->next;
770   }
771   if (flg) {
772     D->ops->productsymbolic = MatProductSymbolic_Shell_X;
773   } else PetscCall(PetscInfo(D, "  symbolic product %s not registered for product type %s\n", composedname, MatProductTypes[product->type]));
774   PetscFunctionReturn(PETSC_SUCCESS);
775 }
776 
777 static PetscErrorCode MatShellSetMatProductOperation_Private(Mat A, MatProductType ptype, PetscErrorCode (*symbolic)(Mat, Mat, Mat, void **), PetscErrorCode (*numeric)(Mat, Mat, Mat, void *), PetscErrorCode (*destroy)(void *), char *composedname, const char *resultname)
778 {
779   PetscBool               flg;
780   Mat_Shell              *shell;
781   MatShellMatFunctionList matmat;
782 
783   PetscFunctionBegin;
784   PetscCheck(numeric, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing numeric routine");
785   PetscCheck(composedname, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing composed name");
786 
787   /* add product callback */
788   shell  = (Mat_Shell *)A->data;
789   matmat = shell->matmat;
790   if (!matmat) {
791     PetscCall(PetscNew(&shell->matmat));
792     matmat = shell->matmat;
793   } else {
794     MatShellMatFunctionList entry = matmat;
795     while (entry) {
796       PetscCall(PetscStrcmp(composedname, entry->composedname, &flg));
797       flg    = (PetscBool)(flg && (entry->ptype == ptype));
798       matmat = entry;
799       if (flg) goto set;
800       entry = entry->next;
801     }
802     PetscCall(PetscNew(&matmat->next));
803     matmat = matmat->next;
804   }
805 
806 set:
807   matmat->symbolic = symbolic;
808   matmat->numeric  = numeric;
809   matmat->destroy  = destroy;
810   matmat->ptype    = ptype;
811   PetscCall(PetscFree(matmat->composedname));
812   PetscCall(PetscFree(matmat->resultname));
813   PetscCall(PetscStrallocpy(composedname, &matmat->composedname));
814   PetscCall(PetscStrallocpy(resultname, &matmat->resultname));
815   PetscCall(PetscInfo(A, "Composing %s for product type %s with result %s\n", matmat->composedname, MatProductTypes[matmat->ptype], matmat->resultname ? matmat->resultname : "not specified"));
816   PetscCall(PetscObjectComposeFunction((PetscObject)A, matmat->composedname, MatProductSetFromOptions_Shell_X));
817   PetscFunctionReturn(PETSC_SUCCESS);
818 }
819 
820 /*@C
821   MatShellSetMatProductOperation - Allows user to set a matrix matrix operation for a `MATSHELL` shell matrix.
822 
823   Logically Collective; No Fortran Support
824 
825   Input Parameters:
826 + A        - the `MATSHELL` shell matrix
827 . ptype    - the product type
828 . symbolic - the function for the symbolic phase (can be `NULL`)
829 . numeric  - the function for the numerical phase
830 . destroy  - the function for the destruction of the needed data generated during the symbolic phase (can be `NULL`)
831 . Btype    - the matrix type for the matrix to be multiplied against
832 - Ctype    - the matrix type for the result (can be `NULL`)
833 
834   Level: advanced
835 
836   Example Usage:
837 .vb
838   extern PetscErrorCode usersymbolic(Mat, Mat, Mat, void**);
839   extern PetscErrorCode usernumeric(Mat, Mat, Mat, void*);
840   extern PetscErrorCode userdestroy(void*);
841 
842   MatCreateShell(comm, m, n, M, N, ctx, &A);
843   MatShellSetMatProductOperation(
844     A, MATPRODUCT_AB, usersymbolic, usernumeric, userdestroy,MATSEQAIJ, MATDENSE
845   );
846   // create B of type SEQAIJ etc..
847   MatProductCreate(A, B, PETSC_NULLPTR, &C);
848   MatProductSetType(C, MATPRODUCT_AB);
849   MatProductSetFromOptions(C);
850   MatProductSymbolic(C); // actually runs the user defined symbolic operation
851   MatProductNumeric(C); // actually runs the user defined numeric operation
852   // use C = A * B
853 .ve
854 
855   Notes:
856   `MATPRODUCT_ABC` is not supported yet.
857 
858   If the symbolic phase is not specified, `MatSetUp()` is called on the result matrix that must have its type set if Ctype is `NULL`.
859 
860   Any additional data needed by the matrix product needs to be returned during the symbolic phase and destroyed with the destroy callback.
861   PETSc will take care of calling the user-defined callbacks.
862   It is allowed to specify the same callbacks for different Btype matrix types.
863   The couple (Btype,ptype) uniquely identifies the operation, the last specified callbacks takes precedence.
864 
865 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatSetOperation()`, `MatProductType`, `MatType`, `MatSetUp()`
866 @*/
867 PetscErrorCode MatShellSetMatProductOperation(Mat A, MatProductType ptype, PetscErrorCode (*symbolic)(Mat, Mat, Mat, void **), PetscErrorCode (*numeric)(Mat, Mat, Mat, void *), PetscErrorCode (*destroy)(void *), MatType Btype, MatType Ctype)
868 {
869   PetscFunctionBegin;
870   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
871   PetscValidLogicalCollectiveEnum(A, ptype, 2);
872   PetscCheck(ptype != MATPRODUCT_ABC, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for product type %s", MatProductTypes[ptype]);
873   PetscCheck(numeric, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "Missing numeric routine, argument 4");
874   PetscAssertPointer(Btype, 6);
875   if (Ctype) PetscAssertPointer(Ctype, 7);
876   PetscTryMethod(A, "MatShellSetMatProductOperation_C", (Mat, MatProductType, PetscErrorCode (*)(Mat, Mat, Mat, void **), PetscErrorCode (*)(Mat, Mat, Mat, void *), PetscErrorCode (*)(void *), MatType, MatType), (A, ptype, symbolic, numeric, destroy, Btype, Ctype));
877   PetscFunctionReturn(PETSC_SUCCESS);
878 }
879 
880 static PetscErrorCode MatShellSetMatProductOperation_Shell(Mat A, MatProductType ptype, PetscErrorCode (*symbolic)(Mat, Mat, Mat, void **), PetscErrorCode (*numeric)(Mat, Mat, Mat, void *), PetscErrorCode (*destroy)(void *), MatType Btype, MatType Ctype)
881 {
882   PetscBool   flg;
883   char        composedname[256];
884   MatRootName Bnames = MatRootNameList, Cnames = MatRootNameList;
885   PetscMPIInt size;
886 
887   PetscFunctionBegin;
888   PetscValidType(A, 1);
889   while (Bnames) { /* user passed in the root name */
890     PetscCall(PetscStrcmp(Btype, Bnames->rname, &flg));
891     if (flg) break;
892     Bnames = Bnames->next;
893   }
894   while (Cnames) { /* user passed in the root name */
895     PetscCall(PetscStrcmp(Ctype, Cnames->rname, &flg));
896     if (flg) break;
897     Cnames = Cnames->next;
898   }
899   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
900   Btype = Bnames ? (size > 1 ? Bnames->mname : Bnames->sname) : Btype;
901   Ctype = Cnames ? (size > 1 ? Cnames->mname : Cnames->sname) : Ctype;
902   PetscCall(PetscSNPrintf(composedname, sizeof(composedname), "MatProductSetFromOptions_%s_%s_C", ((PetscObject)A)->type_name, Btype));
903   PetscCall(MatShellSetMatProductOperation_Private(A, ptype, symbolic, numeric, destroy, composedname, Ctype));
904   PetscFunctionReturn(PETSC_SUCCESS);
905 }
906 
907 static PetscErrorCode MatCopy_Shell(Mat A, Mat B, MatStructure str)
908 {
909   Mat_Shell              *shellA = (Mat_Shell *)A->data, *shellB = (Mat_Shell *)B->data;
910   PetscBool               matflg;
911   MatShellMatFunctionList matmatA;
912 
913   PetscFunctionBegin;
914   PetscCall(MatIsShell(B, &matflg));
915   PetscCheck(matflg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Matrix %s not derived from MATSHELL", ((PetscObject)B)->type_name);
916 
917   B->ops[0]      = A->ops[0];
918   shellB->ops[0] = shellA->ops[0];
919 
920   if (shellA->ops->copy) PetscCall((*shellA->ops->copy)(A, B, str));
921   shellB->vscale = shellA->vscale;
922   shellB->vshift = shellA->vshift;
923   if (shellA->dshift) {
924     if (!shellB->dshift) PetscCall(VecDuplicate(shellA->dshift, &shellB->dshift));
925     PetscCall(VecCopy(shellA->dshift, shellB->dshift));
926   } else {
927     PetscCall(VecDestroy(&shellB->dshift));
928   }
929   if (shellA->left) {
930     if (!shellB->left) PetscCall(VecDuplicate(shellA->left, &shellB->left));
931     PetscCall(VecCopy(shellA->left, shellB->left));
932   } else {
933     PetscCall(VecDestroy(&shellB->left));
934   }
935   if (shellA->right) {
936     if (!shellB->right) PetscCall(VecDuplicate(shellA->right, &shellB->right));
937     PetscCall(VecCopy(shellA->right, shellB->right));
938   } else {
939     PetscCall(VecDestroy(&shellB->right));
940   }
941   PetscCall(MatDestroy(&shellB->axpy));
942   shellB->axpy_vscale = 0.0;
943   shellB->axpy_state  = 0;
944   if (shellA->axpy) {
945     PetscCall(PetscObjectReference((PetscObject)shellA->axpy));
946     shellB->axpy        = shellA->axpy;
947     shellB->axpy_vscale = shellA->axpy_vscale;
948     shellB->axpy_state  = shellA->axpy_state;
949   }
950   if (shellA->zrows) {
951     PetscCall(ISDuplicate(shellA->zrows, &shellB->zrows));
952     if (shellA->zcols) PetscCall(ISDuplicate(shellA->zcols, &shellB->zcols));
953     PetscCall(VecDuplicate(shellA->zvals, &shellB->zvals));
954     PetscCall(VecCopy(shellA->zvals, shellB->zvals));
955     PetscCall(VecDuplicate(shellA->zvals_w, &shellB->zvals_w));
956     PetscCall(PetscObjectReference((PetscObject)shellA->zvals_sct_r));
957     PetscCall(PetscObjectReference((PetscObject)shellA->zvals_sct_c));
958     shellB->zvals_sct_r = shellA->zvals_sct_r;
959     shellB->zvals_sct_c = shellA->zvals_sct_c;
960   }
961 
962   matmatA = shellA->matmat;
963   if (matmatA) {
964     while (matmatA->next) {
965       PetscCall(MatShellSetMatProductOperation_Private(B, matmatA->ptype, matmatA->symbolic, matmatA->numeric, matmatA->destroy, matmatA->composedname, matmatA->resultname));
966       matmatA = matmatA->next;
967     }
968   }
969   PetscFunctionReturn(PETSC_SUCCESS);
970 }
971 
972 static PetscErrorCode MatDuplicate_Shell(Mat mat, MatDuplicateOption op, Mat *M)
973 {
974   PetscFunctionBegin;
975   PetscCall(MatCreateShell(PetscObjectComm((PetscObject)mat), mat->rmap->n, mat->cmap->n, mat->rmap->N, mat->cmap->N, NULL, M));
976   ((Mat_Shell *)(*M)->data)->ctxcontainer = ((Mat_Shell *)mat->data)->ctxcontainer;
977   PetscCall(PetscObjectCompose((PetscObject)*M, "MatShell ctx", (PetscObject)((Mat_Shell *)(*M)->data)->ctxcontainer));
978   PetscCall(PetscObjectChangeTypeName((PetscObject)*M, ((PetscObject)mat)->type_name));
979   if (op == MAT_COPY_VALUES) PetscCall(MatCopy(mat, *M, SAME_NONZERO_PATTERN));
980   PetscCall(PetscObjectCopyFortranFunctionPointers((PetscObject)mat, (PetscObject)*M));
981   PetscFunctionReturn(PETSC_SUCCESS);
982 }
983 
984 static PetscErrorCode MatMult_Shell(Mat A, Vec x, Vec y)
985 {
986   Mat_Shell       *shell = (Mat_Shell *)A->data;
987   Vec              xx;
988   PetscObjectState instate, outstate;
989 
990   PetscFunctionBegin;
991   PetscCall(MatShellPreZeroRight(A, x, &xx));
992   PetscCall(MatShellPreScaleRight(A, xx, &xx));
993   PetscCall(PetscObjectStateGet((PetscObject)y, &instate));
994   PetscCall((*shell->ops->mult)(A, xx, y));
995   PetscCall(PetscObjectStateGet((PetscObject)y, &outstate));
996   if (instate == outstate) {
997     /* increase the state of the output vector since the user did not update its state themself as should have been done */
998     PetscCall(PetscObjectStateIncrease((PetscObject)y));
999   }
1000   PetscCall(MatShellShiftAndScale(A, xx, y, PETSC_FALSE));
1001   PetscCall(MatShellPostScaleLeft(A, y));
1002   PetscCall(MatShellPostZeroLeft(A, y));
1003 
1004   if (shell->axpy) {
1005     Mat              X;
1006     PetscObjectState axpy_state;
1007 
1008     PetscCall(MatShellGetContext(shell->axpy, &X));
1009     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1010     PetscCheck(shell->axpy_state == axpy_state, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Invalid AXPY state: cannot modify the X matrix passed to MatAXPY(Y,a,X,...)");
1011 
1012     PetscCall(MatCreateVecs(shell->axpy, shell->axpy_right ? NULL : &shell->axpy_right, shell->axpy_left ? NULL : &shell->axpy_left));
1013     PetscCall(VecCopy(x, shell->axpy_right));
1014     PetscCall(MatMult(shell->axpy, shell->axpy_right, shell->axpy_left));
1015     PetscCall(VecAXPY(y, shell->axpy_vscale, shell->axpy_left));
1016   }
1017   PetscFunctionReturn(PETSC_SUCCESS);
1018 }
1019 
1020 static PetscErrorCode MatMultAdd_Shell(Mat A, Vec x, Vec y, Vec z)
1021 {
1022   Mat_Shell *shell = (Mat_Shell *)A->data;
1023 
1024   PetscFunctionBegin;
1025   if (y == z) {
1026     if (!shell->right_add_work) PetscCall(VecDuplicate(z, &shell->right_add_work));
1027     PetscCall(MatMult(A, x, shell->right_add_work));
1028     PetscCall(VecAXPY(z, 1.0, shell->right_add_work));
1029   } else {
1030     PetscCall(MatMult(A, x, z));
1031     PetscCall(VecAXPY(z, 1.0, y));
1032   }
1033   PetscFunctionReturn(PETSC_SUCCESS);
1034 }
1035 
1036 static PetscErrorCode MatMultTranspose_Shell(Mat A, Vec x, Vec y)
1037 {
1038   Mat_Shell       *shell = (Mat_Shell *)A->data;
1039   Vec              xx;
1040   PetscObjectState instate, outstate;
1041 
1042   PetscFunctionBegin;
1043   PetscCall(MatShellPreZeroLeft(A, x, &xx));
1044   PetscCall(MatShellPreScaleLeft(A, xx, &xx, PETSC_FALSE));
1045   PetscCall(PetscObjectStateGet((PetscObject)y, &instate));
1046   PetscCall((*shell->ops->multtranspose)(A, xx, y));
1047   PetscCall(PetscObjectStateGet((PetscObject)y, &outstate));
1048   if (instate == outstate) {
1049     /* increase the state of the output vector since the user did not update its state themself as should have been done */
1050     PetscCall(PetscObjectStateIncrease((PetscObject)y));
1051   }
1052   PetscCall(MatShellShiftAndScale(A, xx, y, PETSC_FALSE));
1053   PetscCall(MatShellPostScaleRight(A, y, PETSC_FALSE));
1054   PetscCall(MatShellPostZeroRight(A, y));
1055 
1056   if (shell->axpy) {
1057     Mat              X;
1058     PetscObjectState axpy_state;
1059 
1060     PetscCall(MatShellGetContext(shell->axpy, &X));
1061     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1062     PetscCheck(shell->axpy_state == axpy_state, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Invalid AXPY state: cannot modify the X matrix passed to MatAXPY(Y,a,X,...)");
1063     PetscCall(MatCreateVecs(shell->axpy, shell->axpy_right ? NULL : &shell->axpy_right, shell->axpy_left ? NULL : &shell->axpy_left));
1064     PetscCall(VecCopy(x, shell->axpy_left));
1065     PetscCall(MatMultTranspose(shell->axpy, shell->axpy_left, shell->axpy_right));
1066     PetscCall(VecAXPY(y, shell->axpy_vscale, shell->axpy_right));
1067   }
1068   PetscFunctionReturn(PETSC_SUCCESS);
1069 }
1070 
1071 static PetscErrorCode MatMultHermitianTranspose_Shell(Mat A, Vec x, Vec y)
1072 {
1073   Mat_Shell       *shell = (Mat_Shell *)A->data;
1074   Vec              xx;
1075   PetscObjectState instate, outstate;
1076 
1077   PetscFunctionBegin;
1078   PetscCall(MatShellPreZeroLeft(A, x, &xx));
1079   PetscCall(MatShellPreScaleLeft(A, xx, &xx, PETSC_TRUE));
1080   PetscCall(PetscObjectStateGet((PetscObject)y, &instate));
1081   PetscCall((*shell->ops->multhermitiantranspose)(A, xx, y));
1082   PetscCall(PetscObjectStateGet((PetscObject)y, &outstate));
1083   if (instate == outstate) {
1084     /* increase the state of the output vector since the user did not update its state themself as should have been done */
1085     PetscCall(PetscObjectStateIncrease((PetscObject)y));
1086   }
1087   PetscCall(MatShellShiftAndScale(A, xx, y, PETSC_TRUE));
1088   PetscCall(MatShellPostScaleRight(A, y, PETSC_TRUE));
1089   PetscCall(MatShellPostZeroRight(A, y));
1090 
1091   if (shell->axpy) {
1092     Mat              X;
1093     PetscObjectState axpy_state;
1094 
1095     PetscCall(MatShellGetContext(shell->axpy, &X));
1096     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1097     PetscCheck(shell->axpy_state == axpy_state, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Invalid AXPY state: cannot modify the X matrix passed to MatAXPY(Y,a,X,...)");
1098     PetscCall(MatCreateVecs(shell->axpy, shell->axpy_right ? NULL : &shell->axpy_right, shell->axpy_left ? NULL : &shell->axpy_left));
1099     PetscCall(VecCopy(x, shell->axpy_left));
1100     PetscCall(MatMultHermitianTranspose(shell->axpy, shell->axpy_left, shell->axpy_right));
1101     PetscCall(VecAXPY(y, PetscConj(shell->axpy_vscale), shell->axpy_right));
1102   }
1103   PetscFunctionReturn(PETSC_SUCCESS);
1104 }
1105 
1106 static PetscErrorCode MatMultTransposeAdd_Shell(Mat A, Vec x, Vec y, Vec z)
1107 {
1108   Mat_Shell *shell = (Mat_Shell *)A->data;
1109 
1110   PetscFunctionBegin;
1111   if (y == z) {
1112     if (!shell->left_add_work) PetscCall(VecDuplicate(z, &shell->left_add_work));
1113     PetscCall(MatMultTranspose(A, x, shell->left_add_work));
1114     PetscCall(VecAXPY(z, 1.0, shell->left_add_work));
1115   } else {
1116     PetscCall(MatMultTranspose(A, x, z));
1117     PetscCall(VecAXPY(z, 1.0, y));
1118   }
1119   PetscFunctionReturn(PETSC_SUCCESS);
1120 }
1121 
1122 static PetscErrorCode MatMultHermitianTransposeAdd_Shell(Mat A, Vec x, Vec y, Vec z)
1123 {
1124   Mat_Shell *shell = (Mat_Shell *)A->data;
1125 
1126   PetscFunctionBegin;
1127   if (y == z) {
1128     if (!shell->left_add_work) PetscCall(VecDuplicate(z, &shell->left_add_work));
1129     PetscCall(MatMultHermitianTranspose(A, x, shell->left_add_work));
1130     PetscCall(VecAXPY(z, 1.0, shell->left_add_work));
1131   } else {
1132     PetscCall(MatMultHermitianTranspose(A, x, z));
1133     PetscCall(VecAXPY(z, 1.0, y));
1134   }
1135   PetscFunctionReturn(PETSC_SUCCESS);
1136 }
1137 
1138 /*
1139           diag(left)(vscale*A + diag(dshift) + vshift I)diag(right)
1140 */
1141 static PetscErrorCode MatGetDiagonal_Shell(Mat A, Vec v)
1142 {
1143   Mat_Shell *shell = (Mat_Shell *)A->data;
1144 
1145   PetscFunctionBegin;
1146   if (shell->ops->getdiagonal) {
1147     PetscCall((*shell->ops->getdiagonal)(A, v));
1148   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Must provide shell matrix with routine to return diagonal using\nMatShellSetOperation(S,MATOP_GET_DIAGONAL,...)");
1149   PetscCall(VecScale(v, shell->vscale));
1150   if (shell->dshift) PetscCall(VecAXPY(v, 1.0, shell->dshift));
1151   PetscCall(VecShift(v, shell->vshift));
1152   if (shell->left) PetscCall(VecPointwiseMult(v, v, shell->left));
1153   if (shell->right) PetscCall(VecPointwiseMult(v, v, shell->right));
1154   if (shell->zrows) {
1155     PetscCall(VecScatterBegin(shell->zvals_sct_r, shell->zvals, v, INSERT_VALUES, SCATTER_REVERSE));
1156     PetscCall(VecScatterEnd(shell->zvals_sct_r, shell->zvals, v, INSERT_VALUES, SCATTER_REVERSE));
1157   }
1158   if (shell->axpy) {
1159     Mat              X;
1160     PetscObjectState axpy_state;
1161 
1162     PetscCall(MatShellGetContext(shell->axpy, &X));
1163     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1164     PetscCheck(shell->axpy_state == axpy_state, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Invalid AXPY state: cannot modify the X matrix passed to MatAXPY(Y,a,X,...)");
1165     PetscCall(MatCreateVecs(shell->axpy, NULL, shell->axpy_left ? NULL : &shell->axpy_left));
1166     PetscCall(MatGetDiagonal(shell->axpy, shell->axpy_left));
1167     PetscCall(VecAXPY(v, shell->axpy_vscale, shell->axpy_left));
1168   }
1169   PetscFunctionReturn(PETSC_SUCCESS);
1170 }
1171 
1172 static PetscErrorCode MatGetDiagonalBlock_Shell(Mat A, Mat *b)
1173 {
1174   Mat_Shell *shell = (Mat_Shell *)A->data;
1175   Vec        left = NULL, right = NULL;
1176 
1177   PetscFunctionBegin;
1178   PetscCheck(!shell->zrows && !shell->zcols, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot call MatGetDiagonalBlock() if MatZeroRows() or MatZeroRowsColumns() has been called on the input Mat"); // TODO FIXME
1179   PetscCheck(!shell->axpy, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot call MatGetDiagonalBlock() if MatAXPY() has been called on the input Mat");                                               // TODO FIXME
1180   PetscCheck(!shell->dshift, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot call MatGetDiagonalBlock() if MatDiagonalSet() has been called on the input Mat");                                      // TODO FIXME
1181   if (shell->ops->getdiagonalblock) {
1182     PetscCall((*shell->ops->getdiagonalblock)(A, b));
1183   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Must provide shell matrix with routine to return diagonal block using\nMatShellSetOperation(S,MATOP_GET_DIAGONAL_BLOCK,...)");
1184   PetscCall(MatScale(*b, shell->vscale));
1185   PetscCall(MatShift(*b, shell->vshift));
1186   if (shell->left) {
1187     PetscCall(VecCreateLocalVector(shell->left, &left));
1188     PetscCall(VecGetLocalVectorRead(shell->left, left));
1189   }
1190   if (shell->right) {
1191     PetscCall(VecCreateLocalVector(shell->right, &right));
1192     PetscCall(VecGetLocalVectorRead(shell->right, right));
1193   }
1194   PetscCall(MatDiagonalScale(*b, left, right));
1195   if (shell->left) {
1196     PetscCall(VecRestoreLocalVectorRead(shell->left, left));
1197     PetscCall(VecDestroy(&left));
1198   }
1199   if (shell->right) {
1200     PetscCall(VecRestoreLocalVectorRead(shell->right, right));
1201     PetscCall(VecDestroy(&right));
1202   }
1203   PetscFunctionReturn(PETSC_SUCCESS);
1204 }
1205 
1206 static PetscErrorCode MatShift_Shell(Mat Y, PetscScalar a)
1207 {
1208   Mat_Shell *shell = (Mat_Shell *)Y->data;
1209   PetscBool  flg;
1210 
1211   PetscFunctionBegin;
1212   PetscCall(MatHasCongruentLayouts(Y, &flg));
1213   PetscCheck(flg, PetscObjectComm((PetscObject)Y), PETSC_ERR_SUP, "Cannot shift shell matrix if it is not congruent");
1214   if (shell->left || shell->right) {
1215     if (!shell->dshift) {
1216       PetscCall(VecDuplicate(shell->left ? shell->left : shell->right, &shell->dshift));
1217       PetscCall(VecSet(shell->dshift, a));
1218     } else {
1219       if (shell->left) PetscCall(VecPointwiseMult(shell->dshift, shell->dshift, shell->left));
1220       if (shell->right) PetscCall(VecPointwiseMult(shell->dshift, shell->dshift, shell->right));
1221       PetscCall(VecShift(shell->dshift, a));
1222     }
1223     if (shell->left) PetscCall(VecPointwiseDivide(shell->dshift, shell->dshift, shell->left));
1224     if (shell->right) PetscCall(VecPointwiseDivide(shell->dshift, shell->dshift, shell->right));
1225   } else shell->vshift += a;
1226   if (shell->zrows) PetscCall(VecShift(shell->zvals, a));
1227   PetscFunctionReturn(PETSC_SUCCESS);
1228 }
1229 
1230 static PetscErrorCode MatDiagonalSet_Shell_Private(Mat A, Vec D, PetscScalar s)
1231 {
1232   Mat_Shell *shell = (Mat_Shell *)A->data;
1233 
1234   PetscFunctionBegin;
1235   if (!shell->dshift) PetscCall(VecDuplicate(D, &shell->dshift));
1236   if (shell->left || shell->right) {
1237     if (!shell->right_work) PetscCall(VecDuplicate(shell->left ? shell->left : shell->right, &shell->right_work));
1238     if (shell->left && shell->right) {
1239       PetscCall(VecPointwiseDivide(shell->right_work, D, shell->left));
1240       PetscCall(VecPointwiseDivide(shell->right_work, shell->right_work, shell->right));
1241     } else if (shell->left) {
1242       PetscCall(VecPointwiseDivide(shell->right_work, D, shell->left));
1243     } else {
1244       PetscCall(VecPointwiseDivide(shell->right_work, D, shell->right));
1245     }
1246     PetscCall(VecAXPY(shell->dshift, s, shell->right_work));
1247   } else {
1248     PetscCall(VecAXPY(shell->dshift, s, D));
1249   }
1250   PetscFunctionReturn(PETSC_SUCCESS);
1251 }
1252 
1253 static PetscErrorCode MatDiagonalSet_Shell(Mat A, Vec D, InsertMode ins)
1254 {
1255   Mat_Shell *shell = (Mat_Shell *)A->data;
1256   Vec        d;
1257   PetscBool  flg;
1258 
1259   PetscFunctionBegin;
1260   PetscCall(MatHasCongruentLayouts(A, &flg));
1261   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot diagonal set or shift shell matrix if it is not congruent");
1262   if (ins == INSERT_VALUES) {
1263     PetscCall(VecDuplicate(D, &d));
1264     PetscCall(MatGetDiagonal(A, d));
1265     PetscCall(MatDiagonalSet_Shell_Private(A, d, -1.));
1266     PetscCall(MatDiagonalSet_Shell_Private(A, D, 1.));
1267     PetscCall(VecDestroy(&d));
1268     if (shell->zrows) PetscCall(VecCopy(D, shell->zvals));
1269   } else {
1270     PetscCall(MatDiagonalSet_Shell_Private(A, D, 1.));
1271     if (shell->zrows) PetscCall(VecAXPY(shell->zvals, 1.0, D));
1272   }
1273   PetscFunctionReturn(PETSC_SUCCESS);
1274 }
1275 
1276 static PetscErrorCode MatScale_Shell(Mat Y, PetscScalar a)
1277 {
1278   Mat_Shell *shell = (Mat_Shell *)Y->data;
1279 
1280   PetscFunctionBegin;
1281   shell->vscale *= a;
1282   shell->vshift *= a;
1283   if (shell->dshift) PetscCall(VecScale(shell->dshift, a));
1284   shell->axpy_vscale *= a;
1285   if (shell->zrows) PetscCall(VecScale(shell->zvals, a));
1286   PetscFunctionReturn(PETSC_SUCCESS);
1287 }
1288 
1289 static PetscErrorCode MatDiagonalScale_Shell(Mat Y, Vec left, Vec right)
1290 {
1291   Mat_Shell *shell = (Mat_Shell *)Y->data;
1292 
1293   PetscFunctionBegin;
1294   if (left) {
1295     if (!shell->left) {
1296       PetscCall(VecDuplicate(left, &shell->left));
1297       PetscCall(VecCopy(left, shell->left));
1298     } else {
1299       PetscCall(VecPointwiseMult(shell->left, shell->left, left));
1300     }
1301     if (shell->zrows) PetscCall(VecPointwiseMult(shell->zvals, shell->zvals, left));
1302   }
1303   if (right) {
1304     if (!shell->right) {
1305       PetscCall(VecDuplicate(right, &shell->right));
1306       PetscCall(VecCopy(right, shell->right));
1307     } else {
1308       PetscCall(VecPointwiseMult(shell->right, shell->right, right));
1309     }
1310     if (shell->zrows) {
1311       if (!shell->left_work) PetscCall(MatCreateVecs(Y, NULL, &shell->left_work));
1312       PetscCall(VecSet(shell->zvals_w, 1.0));
1313       PetscCall(VecScatterBegin(shell->zvals_sct_c, right, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
1314       PetscCall(VecScatterEnd(shell->zvals_sct_c, right, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
1315       PetscCall(VecPointwiseMult(shell->zvals, shell->zvals, shell->zvals_w));
1316     }
1317   }
1318   if (shell->axpy) PetscCall(MatDiagonalScale(shell->axpy, left, right));
1319   PetscFunctionReturn(PETSC_SUCCESS);
1320 }
1321 
1322 PETSC_INTERN PetscErrorCode MatAssemblyEnd_Shell(Mat Y, MatAssemblyType t)
1323 {
1324   Mat_Shell *shell = (Mat_Shell *)Y->data;
1325 
1326   PetscFunctionBegin;
1327   if (t == MAT_FINAL_ASSEMBLY) {
1328     shell->vshift      = 0.0;
1329     shell->vscale      = 1.0;
1330     shell->axpy_vscale = 0.0;
1331     shell->axpy_state  = 0;
1332     PetscCall(VecDestroy(&shell->dshift));
1333     PetscCall(VecDestroy(&shell->left));
1334     PetscCall(VecDestroy(&shell->right));
1335     PetscCall(MatDestroy(&shell->axpy));
1336     PetscCall(VecDestroy(&shell->axpy_left));
1337     PetscCall(VecDestroy(&shell->axpy_right));
1338     PetscCall(VecScatterDestroy(&shell->zvals_sct_c));
1339     PetscCall(VecScatterDestroy(&shell->zvals_sct_r));
1340     PetscCall(ISDestroy(&shell->zrows));
1341     PetscCall(ISDestroy(&shell->zcols));
1342   }
1343   PetscFunctionReturn(PETSC_SUCCESS);
1344 }
1345 
1346 static PetscErrorCode MatMissingDiagonal_Shell(Mat A, PetscBool *missing, PetscInt *d)
1347 {
1348   PetscFunctionBegin;
1349   *missing = PETSC_FALSE;
1350   PetscFunctionReturn(PETSC_SUCCESS);
1351 }
1352 
1353 static PetscErrorCode MatAXPY_Shell(Mat Y, PetscScalar a, Mat X, MatStructure str)
1354 {
1355   Mat_Shell *shell = (Mat_Shell *)Y->data;
1356 
1357   PetscFunctionBegin;
1358   if (X == Y) {
1359     PetscCall(MatScale(Y, 1.0 + a));
1360     PetscFunctionReturn(PETSC_SUCCESS);
1361   }
1362   if (!shell->axpy) {
1363     PetscCall(MatConvertFrom_Shell(X, MATSHELL, MAT_INITIAL_MATRIX, &shell->axpy));
1364     shell->axpy_vscale = a;
1365     PetscCall(PetscObjectStateGet((PetscObject)X, &shell->axpy_state));
1366   } else {
1367     PetscCall(MatAXPY(shell->axpy, a / shell->axpy_vscale, X, str));
1368   }
1369   PetscFunctionReturn(PETSC_SUCCESS);
1370 }
1371 
1372 static struct _MatOps MatOps_Values = {NULL,
1373                                        NULL,
1374                                        NULL,
1375                                        NULL,
1376                                        /* 4*/ MatMultAdd_Shell,
1377                                        NULL,
1378                                        MatMultTransposeAdd_Shell,
1379                                        NULL,
1380                                        NULL,
1381                                        NULL,
1382                                        /*10*/ NULL,
1383                                        NULL,
1384                                        NULL,
1385                                        NULL,
1386                                        NULL,
1387                                        /*15*/ NULL,
1388                                        NULL,
1389                                        NULL,
1390                                        MatDiagonalScale_Shell,
1391                                        NULL,
1392                                        /*20*/ NULL,
1393                                        MatAssemblyEnd_Shell,
1394                                        NULL,
1395                                        NULL,
1396                                        /*24*/ MatZeroRows_Shell,
1397                                        NULL,
1398                                        NULL,
1399                                        NULL,
1400                                        NULL,
1401                                        /*29*/ NULL,
1402                                        NULL,
1403                                        NULL,
1404                                        /*32*/ NULL,
1405                                        NULL,
1406                                        /*34*/ MatDuplicate_Shell,
1407                                        NULL,
1408                                        NULL,
1409                                        NULL,
1410                                        NULL,
1411                                        /*39*/ MatAXPY_Shell,
1412                                        NULL,
1413                                        NULL,
1414                                        NULL,
1415                                        MatCopy_Shell,
1416                                        /*44*/ NULL,
1417                                        MatScale_Shell,
1418                                        MatShift_Shell,
1419                                        MatDiagonalSet_Shell,
1420                                        MatZeroRowsColumns_Shell,
1421                                        /*49*/ NULL,
1422                                        NULL,
1423                                        NULL,
1424                                        NULL,
1425                                        NULL,
1426                                        /*54*/ NULL,
1427                                        NULL,
1428                                        NULL,
1429                                        NULL,
1430                                        NULL,
1431                                        /*59*/ NULL,
1432                                        MatDestroy_Shell,
1433                                        NULL,
1434                                        MatConvertFrom_Shell,
1435                                        NULL,
1436                                        /*64*/ NULL,
1437                                        NULL,
1438                                        NULL,
1439                                        NULL,
1440                                        NULL,
1441                                        /*69*/ NULL,
1442                                        NULL,
1443                                        MatConvert_Shell,
1444                                        NULL,
1445                                        NULL,
1446                                        /*74*/ NULL,
1447                                        NULL,
1448                                        NULL,
1449                                        NULL,
1450                                        NULL,
1451                                        /*79*/ NULL,
1452                                        NULL,
1453                                        NULL,
1454                                        NULL,
1455                                        NULL,
1456                                        /*84*/ NULL,
1457                                        NULL,
1458                                        NULL,
1459                                        NULL,
1460                                        NULL,
1461                                        /*89*/ NULL,
1462                                        NULL,
1463                                        NULL,
1464                                        NULL,
1465                                        NULL,
1466                                        /*94*/ NULL,
1467                                        NULL,
1468                                        NULL,
1469                                        NULL,
1470                                        NULL,
1471                                        /*99*/ NULL,
1472                                        NULL,
1473                                        NULL,
1474                                        NULL,
1475                                        NULL,
1476                                        /*104*/ NULL,
1477                                        NULL,
1478                                        NULL,
1479                                        NULL,
1480                                        NULL,
1481                                        /*109*/ NULL,
1482                                        NULL,
1483                                        NULL,
1484                                        NULL,
1485                                        MatMissingDiagonal_Shell,
1486                                        /*114*/ NULL,
1487                                        NULL,
1488                                        NULL,
1489                                        NULL,
1490                                        NULL,
1491                                        /*119*/ NULL,
1492                                        NULL,
1493                                        NULL,
1494                                        MatMultHermitianTransposeAdd_Shell,
1495                                        NULL,
1496                                        /*124*/ NULL,
1497                                        NULL,
1498                                        NULL,
1499                                        NULL,
1500                                        NULL,
1501                                        /*129*/ NULL,
1502                                        NULL,
1503                                        NULL,
1504                                        NULL,
1505                                        NULL,
1506                                        /*134*/ NULL,
1507                                        NULL,
1508                                        NULL,
1509                                        NULL,
1510                                        NULL,
1511                                        /*139*/ NULL,
1512                                        NULL,
1513                                        NULL,
1514                                        NULL,
1515                                        NULL,
1516                                        /*144*/ NULL,
1517                                        NULL,
1518                                        NULL,
1519                                        NULL,
1520                                        NULL,
1521                                        NULL,
1522                                        /*150*/ NULL,
1523                                        NULL,
1524                                        NULL,
1525                                        NULL,
1526                                        NULL,
1527                                        NULL};
1528 
1529 static PetscErrorCode MatShellSetContext_Shell(Mat mat, void *ctx)
1530 {
1531   Mat_Shell *shell = (Mat_Shell *)mat->data;
1532 
1533   PetscFunctionBegin;
1534   if (ctx) {
1535     PetscContainer ctxcontainer;
1536     PetscCall(PetscContainerCreate(PetscObjectComm((PetscObject)mat), &ctxcontainer));
1537     PetscCall(PetscContainerSetPointer(ctxcontainer, ctx));
1538     PetscCall(PetscObjectCompose((PetscObject)mat, "MatShell ctx", (PetscObject)ctxcontainer));
1539     shell->ctxcontainer = ctxcontainer;
1540     PetscCall(PetscContainerDestroy(&ctxcontainer));
1541   } else {
1542     PetscCall(PetscObjectCompose((PetscObject)mat, "MatShell ctx", NULL));
1543     shell->ctxcontainer = NULL;
1544   }
1545   PetscFunctionReturn(PETSC_SUCCESS);
1546 }
1547 
1548 static PetscErrorCode MatShellSetContextDestroy_Shell(Mat mat, PetscErrorCode (*f)(void *))
1549 {
1550   Mat_Shell *shell = (Mat_Shell *)mat->data;
1551 
1552   PetscFunctionBegin;
1553   if (shell->ctxcontainer) PetscCall(PetscContainerSetUserDestroy(shell->ctxcontainer, f));
1554   PetscFunctionReturn(PETSC_SUCCESS);
1555 }
1556 
1557 PetscErrorCode MatShellSetContext_Immutable(Mat mat, void *ctx)
1558 {
1559   PetscFunctionBegin;
1560   SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot call MatShellSetContext() for a %s, it is used internally by the structure", ((PetscObject)mat)->type_name);
1561   PetscFunctionReturn(PETSC_SUCCESS);
1562 }
1563 
1564 PetscErrorCode MatShellSetContextDestroy_Immutable(Mat mat, PetscErrorCode (*f)(void *))
1565 {
1566   PetscFunctionBegin;
1567   SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot call MatShellSetContextDestroy() for a %s, it is used internally by the structure", ((PetscObject)mat)->type_name);
1568   PetscFunctionReturn(PETSC_SUCCESS);
1569 }
1570 
1571 PetscErrorCode MatShellSetManageScalingShifts_Immutable(Mat mat)
1572 {
1573   PetscFunctionBegin;
1574   SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot call MatShellSetManageScalingShifts() for a %s, it is used internally by the structure", ((PetscObject)mat)->type_name);
1575   PetscFunctionReturn(PETSC_SUCCESS);
1576 }
1577 
1578 static PetscErrorCode MatShellSetVecType_Shell(Mat mat, VecType vtype)
1579 {
1580   PetscFunctionBegin;
1581   PetscCall(PetscFree(mat->defaultvectype));
1582   PetscCall(PetscStrallocpy(vtype, (char **)&mat->defaultvectype));
1583   PetscFunctionReturn(PETSC_SUCCESS);
1584 }
1585 
1586 static PetscErrorCode MatShellSetManageScalingShifts_Shell(Mat A)
1587 {
1588   Mat_Shell *shell = (Mat_Shell *)A->data;
1589 
1590   PetscFunctionBegin;
1591   shell->managescalingshifts = PETSC_FALSE;
1592   A->ops->diagonalset        = NULL;
1593   A->ops->diagonalscale      = NULL;
1594   A->ops->scale              = NULL;
1595   A->ops->shift              = NULL;
1596   A->ops->axpy               = NULL;
1597   PetscFunctionReturn(PETSC_SUCCESS);
1598 }
1599 
1600 static PetscErrorCode MatShellGetScalingShifts_Shell(Mat A, PetscScalar *vshift, PetscScalar *vscale, Vec *dshift, Vec *left, Vec *right, Mat *axpy, IS *zrows, IS *zcols)
1601 {
1602   Mat_Shell *shell = (Mat_Shell *)A->data;
1603 
1604   PetscFunctionBegin;
1605   PetscCheck(shell->managescalingshifts, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot get scaling and shifts if MatShellSetManageScalingShifts() has been called");
1606   if (vshift == MAT_SHELL_NOT_ALLOWED) PetscCheck(shell->vshift == 0.0, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: vshift != 0.0, set via MatShift()");
1607   else if (vshift) *vshift = shell->vshift;
1608   if (vscale == MAT_SHELL_NOT_ALLOWED) PetscCheck(shell->vscale == 1.0, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: vscale != 1.0, set via MatScale()");
1609   else if (vscale) *vscale = shell->vscale;
1610   if (dshift == MAT_SHELL_NOT_ALLOWED) PetscCheck(!shell->dshift, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: dshift, set via MatDiagonalSet()");
1611   else if (dshift) *dshift = shell->dshift;
1612   if (left == MAT_SHELL_NOT_ALLOWED) PetscCheck(!shell->left, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: left, set via MatDiagonalScale()");
1613   else if (left) *left = shell->left;
1614   if (right == MAT_SHELL_NOT_ALLOWED) PetscCheck(!shell->right, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: right, set via MatDiagonalScale()");
1615   else if (right) *right = shell->right;
1616   if (axpy == MAT_SHELL_NOT_ALLOWED) PetscCheck(!shell->axpy, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: axpy, set via MatAXPY()");
1617   else if (axpy) *axpy = shell->axpy;
1618   if (zrows == MAT_SHELL_NOT_ALLOWED) PetscCheck(!shell->zrows, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: zrows, set via MatZeroRows()");
1619   else if (zrows) *zrows = shell->zrows;
1620   if (zcols == MAT_SHELL_NOT_ALLOWED) PetscCheck(!shell->zcols, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Non-trivial member in parent MatShell: zcols, set via MatZeroRowsColumns()");
1621   else if (zcols) *zcols = shell->zcols;
1622   PetscFunctionReturn(PETSC_SUCCESS);
1623 }
1624 
1625 static PetscErrorCode MatShellSetOperation_Shell(Mat mat, MatOperation op, void (*f)(void))
1626 {
1627   Mat_Shell *shell = (Mat_Shell *)mat->data;
1628 
1629   PetscFunctionBegin;
1630   switch (op) {
1631   case MATOP_DESTROY:
1632     shell->ops->destroy = (PetscErrorCode (*)(Mat))f;
1633     break;
1634   case MATOP_VIEW:
1635     if (!mat->ops->viewnative) mat->ops->viewnative = mat->ops->view;
1636     mat->ops->view = (PetscErrorCode (*)(Mat, PetscViewer))f;
1637     break;
1638   case MATOP_COPY:
1639     shell->ops->copy = (PetscErrorCode (*)(Mat, Mat, MatStructure))f;
1640     break;
1641   case MATOP_DIAGONAL_SET:
1642   case MATOP_DIAGONAL_SCALE:
1643   case MATOP_SHIFT:
1644   case MATOP_SCALE:
1645   case MATOP_AXPY:
1646   case MATOP_ZERO_ROWS:
1647   case MATOP_ZERO_ROWS_COLUMNS:
1648     PetscCheck(!shell->managescalingshifts, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MATSHELL is managing scalings and shifts, see MatShellSetManageScalingShifts()");
1649     (((void (**)(void))mat->ops)[op]) = f;
1650     break;
1651   case MATOP_GET_DIAGONAL:
1652     if (shell->managescalingshifts) {
1653       shell->ops->getdiagonal = (PetscErrorCode (*)(Mat, Vec))f;
1654       mat->ops->getdiagonal   = MatGetDiagonal_Shell;
1655     } else {
1656       shell->ops->getdiagonal = NULL;
1657       mat->ops->getdiagonal   = (PetscErrorCode (*)(Mat, Vec))f;
1658     }
1659     break;
1660   case MATOP_GET_DIAGONAL_BLOCK:
1661     if (shell->managescalingshifts) {
1662       shell->ops->getdiagonalblock = (PetscErrorCode (*)(Mat, Mat *))f;
1663       mat->ops->getdiagonalblock   = MatGetDiagonalBlock_Shell;
1664     } else {
1665       shell->ops->getdiagonalblock = NULL;
1666       mat->ops->getdiagonalblock   = (PetscErrorCode (*)(Mat, Mat *))f;
1667     }
1668     break;
1669   case MATOP_MULT:
1670     if (shell->managescalingshifts) {
1671       shell->ops->mult = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1672       mat->ops->mult   = MatMult_Shell;
1673     } else {
1674       shell->ops->mult = NULL;
1675       mat->ops->mult   = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1676     }
1677     break;
1678   case MATOP_MULT_TRANSPOSE:
1679     if (shell->managescalingshifts) {
1680       shell->ops->multtranspose = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1681       mat->ops->multtranspose   = MatMultTranspose_Shell;
1682     } else {
1683       shell->ops->multtranspose = NULL;
1684       mat->ops->multtranspose   = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1685     }
1686     break;
1687   case MATOP_MULT_HERMITIAN_TRANSPOSE:
1688     if (shell->managescalingshifts) {
1689       shell->ops->multhermitiantranspose = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1690       mat->ops->multhermitiantranspose   = MatMultHermitianTranspose_Shell;
1691     } else {
1692       shell->ops->multhermitiantranspose = NULL;
1693       mat->ops->multhermitiantranspose   = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1694     }
1695     break;
1696   default:
1697     (((void (**)(void))mat->ops)[op]) = f;
1698     break;
1699   }
1700   PetscFunctionReturn(PETSC_SUCCESS);
1701 }
1702 
1703 static PetscErrorCode MatShellGetOperation_Shell(Mat mat, MatOperation op, void (**f)(void))
1704 {
1705   Mat_Shell *shell = (Mat_Shell *)mat->data;
1706 
1707   PetscFunctionBegin;
1708   switch (op) {
1709   case MATOP_DESTROY:
1710     *f = (void (*)(void))shell->ops->destroy;
1711     break;
1712   case MATOP_VIEW:
1713     *f = (void (*)(void))mat->ops->view;
1714     break;
1715   case MATOP_COPY:
1716     *f = (void (*)(void))shell->ops->copy;
1717     break;
1718   case MATOP_DIAGONAL_SET:
1719   case MATOP_DIAGONAL_SCALE:
1720   case MATOP_SHIFT:
1721   case MATOP_SCALE:
1722   case MATOP_AXPY:
1723   case MATOP_ZERO_ROWS:
1724   case MATOP_ZERO_ROWS_COLUMNS:
1725     *f = (((void (**)(void))mat->ops)[op]);
1726     break;
1727   case MATOP_GET_DIAGONAL:
1728     if (shell->ops->getdiagonal) *f = (void (*)(void))shell->ops->getdiagonal;
1729     else *f = (((void (**)(void))mat->ops)[op]);
1730     break;
1731   case MATOP_GET_DIAGONAL_BLOCK:
1732     if (shell->ops->getdiagonalblock) *f = (void (*)(void))shell->ops->getdiagonalblock;
1733     else *f = (((void (**)(void))mat->ops)[op]);
1734     break;
1735   case MATOP_MULT:
1736     if (shell->ops->mult) *f = (void (*)(void))shell->ops->mult;
1737     else *f = (((void (**)(void))mat->ops)[op]);
1738     break;
1739   case MATOP_MULT_TRANSPOSE:
1740     if (shell->ops->multtranspose) *f = (void (*)(void))shell->ops->multtranspose;
1741     else *f = (((void (**)(void))mat->ops)[op]);
1742     break;
1743   case MATOP_MULT_HERMITIAN_TRANSPOSE:
1744     if (shell->ops->multhermitiantranspose) *f = (void (*)(void))shell->ops->multhermitiantranspose;
1745     else *f = (((void (**)(void))mat->ops)[op]);
1746     break;
1747   default:
1748     *f = (((void (**)(void))mat->ops)[op]);
1749   }
1750   PetscFunctionReturn(PETSC_SUCCESS);
1751 }
1752 
1753 /*MC
1754   MATSHELL - MATSHELL = "shell" - A matrix type to be used to define your own matrix type with its own data structure -- perhaps matrix-free.
1755 
1756   Level: advanced
1757 
1758   Notes:
1759   See `MatCreateShell()` for details on the usage of `MATSHELL`
1760 
1761   `PCSHELL` can be used in conjunction with `MATSHELL` to provide a custom preconditioner appropriate for your `MATSHELL`. Since
1762   many standard preconditioners such as `PCILU` depend on having an explicit representation of the matrix entries they cannot be used
1763   directly with `MATSHELL`.
1764 
1765 .seealso: [](ch_matrices), `Mat`, `MatCreateShell()`, `PCSHELL`
1766 M*/
1767 
1768 PETSC_EXTERN PetscErrorCode MatCreate_Shell(Mat A)
1769 {
1770   Mat_Shell *b;
1771 
1772   PetscFunctionBegin;
1773   PetscCall(PetscNew(&b));
1774   A->data   = (void *)b;
1775   A->ops[0] = MatOps_Values;
1776 
1777   b->ctxcontainer        = NULL;
1778   b->vshift              = 0.0;
1779   b->vscale              = 1.0;
1780   b->managescalingshifts = PETSC_TRUE;
1781   A->assembled           = PETSC_TRUE;
1782   A->preallocated        = PETSC_FALSE;
1783 
1784   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetContext_C", MatShellGetContext_Shell));
1785   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", MatShellSetContext_Shell));
1786   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContextDestroy_C", MatShellSetContextDestroy_Shell));
1787   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetVecType_C", MatShellSetVecType_Shell));
1788   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetManageScalingShifts_C", MatShellSetManageScalingShifts_Shell));
1789   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetScalingShifts_C", MatShellGetScalingShifts_Shell));
1790   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetOperation_C", MatShellSetOperation_Shell));
1791   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetOperation_C", MatShellGetOperation_Shell));
1792   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetMatProductOperation_C", MatShellSetMatProductOperation_Shell));
1793   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATSHELL));
1794   PetscFunctionReturn(PETSC_SUCCESS);
1795 }
1796 
1797 /*@C
1798   MatCreateShell - Creates a new matrix of `MatType` `MATSHELL` for use with a user-defined
1799   private matrix data storage format.
1800 
1801   Collective
1802 
1803   Input Parameters:
1804 + comm - MPI communicator
1805 . m    - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
1806 . n    - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
1807 . M    - number of global rows (may be `PETSC_DETERMINE` to have calculated if `m` is given)
1808 . N    - number of global columns (may be `PETSC_DETERMINE` to have calculated if `n` is given)
1809 - ctx  - pointer to data needed by the shell matrix routines
1810 
1811   Output Parameter:
1812 . A - the matrix
1813 
1814   Level: advanced
1815 
1816   Example Usage:
1817 .vb
1818   extern PetscErrorCode mult(Mat, Vec, Vec);
1819 
1820   MatCreateShell(comm, m, n, M, N, ctx, &mat);
1821   MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))mult);
1822   MatShellSetContext(mat,ctx);
1823   // Use matrix for operations that have been set
1824   MatDestroy(mat);
1825 .ve
1826 
1827   Notes:
1828   The shell matrix type is intended to provide a simple way for users to write a custom matrix specifically for their application.
1829 
1830   `MatCreateShell()` is used in conjunction with `MatShellSetContext()` and `MatShellSetOperation()`.
1831 
1832   PETSc requires that matrices and vectors being used for certain
1833   operations are partitioned accordingly.  For example, when
1834   creating a shell matrix, `A`, that supports parallel matrix-vector
1835   products using `MatMult`(A,x,y) the user should set the number
1836   of local matrix rows to be the number of local elements of the
1837   corresponding result vector, y. Note that this is information is
1838   required for use of the matrix interface routines, even though
1839   the shell matrix may not actually be physically partitioned.
1840   For example,
1841 
1842 .vb
1843      Vec x, y
1844      extern PetscErrorCode mult(Mat,Vec,Vec);
1845      Mat A
1846 
1847      VecCreateMPI(comm,PETSC_DECIDE,M,&y);
1848      VecCreateMPI(comm,PETSC_DECIDE,N,&x);
1849      VecGetLocalSize(y,&m);
1850      VecGetLocalSize(x,&n);
1851      MatCreateShell(comm,m,n,M,N,ctx,&A);
1852      MatShellSetOperation(mat,MATOP_MULT,(void(*)(void))mult);
1853      MatMult(A,x,y);
1854      MatDestroy(&A);
1855      VecDestroy(&y);
1856      VecDestroy(&x);
1857 .ve
1858 
1859   `MATSHELL` handles `MatShift()`, `MatDiagonalSet()`, `MatDiagonalScale()`, `MatAXPY()`, `MatScale()`, `MatZeroRows()` and `MatZeroRowsColumns()`
1860   internally, so these  operations cannot be overwritten unless `MatShellSetManageScalingShifts()` is called.
1861 
1862   Developer Notes:
1863   For rectangular matrices do all the scalings and shifts make sense?
1864 
1865   Regarding shifting and scaling. The general form is
1866 
1867   diag(left)(vscale*A + diag(dshift) + vshift I)diag(right)
1868 
1869   The order you apply the operations is important. For example if you have a dshift then
1870   apply a MatScale(s) you get s*vscale*A + s*diag(shift). But if you first scale and then shift
1871   you get s*vscale*A + diag(shift)
1872 
1873   A is the user provided function.
1874 
1875   `KSP`/`PC` uses changes in the `Mat`'s "state" to decide if preconditioners need to be rebuilt `PCSetUp()` only calls the setup() for
1876   for the `PC` implementation if the `Mat` state has increased from the previous call. Thus to get changes in a `MATSHELL` to trigger
1877   an update in the preconditioner you must call `MatAssemblyBegin()` and `MatAssemblyEnd()` or `PetscObjectStateIncrease`((`PetscObject`)mat);
1878   each time the `MATSHELL` matrix has changed.
1879 
1880   Matrix-matrix product operations can be specified using `MatShellSetMatProductOperation()`
1881 
1882   Calling `MatAssemblyBegin()`/`MatAssemblyEnd()` on a `MATSHELL` removes any previously supplied shift and scales that were provided
1883   with `MatDiagonalSet()`, `MatShift()`, `MatScale()`, or `MatDiagonalScale()`.
1884 
1885   Fortran Notes:
1886   To use this from Fortran with a `ctx` you must write an interface definition for this
1887   function and for `MatShellGetContext()` that tells Fortran the Fortran derived data type you are passing
1888   in as the `ctx` argument.
1889 
1890 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatShellSetOperation()`, `MatHasOperation()`, `MatShellGetContext()`, `MatShellSetContext()`, `MatShellSetManageScalingShifts()`, `MatShellSetMatProductOperation()`
1891 @*/
1892 PetscErrorCode MatCreateShell(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, void *ctx, Mat *A)
1893 {
1894   PetscFunctionBegin;
1895   PetscCall(MatCreate(comm, A));
1896   PetscCall(MatSetSizes(*A, m, n, M, N));
1897   PetscCall(MatSetType(*A, MATSHELL));
1898   PetscCall(MatShellSetContext(*A, ctx));
1899   PetscCall(MatSetUp(*A));
1900   PetscFunctionReturn(PETSC_SUCCESS);
1901 }
1902 
1903 /*@
1904   MatShellSetContext - sets the context for a `MATSHELL` shell matrix
1905 
1906   Logically Collective
1907 
1908   Input Parameters:
1909 + mat - the `MATSHELL` shell matrix
1910 - ctx - the context
1911 
1912   Level: advanced
1913 
1914   Note:
1915   This provides an easy way, along with `MatCreateShell()` and `MatShellSetOperation()` to provide a custom matrix format
1916   specifically for your application.
1917 
1918   Fortran Notes:
1919   You must write a Fortran interface definition for this
1920   function that tells Fortran the Fortran derived data type that you are passing in as the `ctx` argument.
1921 
1922 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`
1923 @*/
1924 PetscErrorCode MatShellSetContext(Mat mat, void *ctx)
1925 {
1926   PetscFunctionBegin;
1927   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1928   PetscTryMethod(mat, "MatShellSetContext_C", (Mat, void *), (mat, ctx));
1929   PetscFunctionReturn(PETSC_SUCCESS);
1930 }
1931 
1932 /*@C
1933   MatShellSetContextDestroy - sets the destroy function for a `MATSHELL` shell matrix context
1934 
1935   Logically Collective
1936 
1937   Input Parameters:
1938 + mat - the shell matrix
1939 - f   - the context destroy function
1940 
1941   Level: advanced
1942 
1943   Note:
1944   If the `MatShell` is never duplicated, the behavior of this function is equivalent
1945   to `MatShellSetOperation`(`Mat`,`MATOP_DESTROY`,f). However, `MatShellSetContextDestroy()`
1946   ensures proper reference counting for the user provided context data in the case that
1947   the `MATSHELL` is duplicated.
1948 
1949 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellSetContext()`
1950 @*/
1951 PetscErrorCode MatShellSetContextDestroy(Mat mat, PetscErrorCode (*f)(void *))
1952 {
1953   PetscFunctionBegin;
1954   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1955   PetscTryMethod(mat, "MatShellSetContextDestroy_C", (Mat, PetscErrorCode (*)(void *)), (mat, f));
1956   PetscFunctionReturn(PETSC_SUCCESS);
1957 }
1958 
1959 /*@C
1960   MatShellSetVecType - Sets the `VecType` of `Vec` returned by `MatCreateVecs()`
1961 
1962   Logically Collective
1963 
1964   Input Parameters:
1965 + mat   - the `MATSHELL` shell matrix
1966 - vtype - type to use for creating vectors
1967 
1968   Level: advanced
1969 
1970 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateVecs()`
1971 @*/
1972 PetscErrorCode MatShellSetVecType(Mat mat, VecType vtype)
1973 {
1974   PetscFunctionBegin;
1975   PetscTryMethod(mat, "MatShellSetVecType_C", (Mat, VecType), (mat, vtype));
1976   PetscFunctionReturn(PETSC_SUCCESS);
1977 }
1978 
1979 /*@
1980   MatShellSetManageScalingShifts - Allows the user to control the scaling and shift operations of the `MATSHELL`. Must be called immediately
1981   after `MatCreateShell()`
1982 
1983   Logically Collective
1984 
1985   Input Parameter:
1986 . A - the `MATSHELL` shell matrix
1987 
1988   Level: advanced
1989 
1990 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatShellSetOperation()`
1991 @*/
1992 PetscErrorCode MatShellSetManageScalingShifts(Mat A)
1993 {
1994   PetscFunctionBegin;
1995   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
1996   PetscTryMethod(A, "MatShellSetManageScalingShifts_C", (Mat), (A));
1997   PetscFunctionReturn(PETSC_SUCCESS);
1998 }
1999 
2000 /*@C
2001   MatShellGetScalingShifts - Gets members of a `MATSHELL` used internally for scaling and
2002   shifting the `Mat` or calling `MatAXPY()`, `MatZeroRows()`, or `MatZeroRowsColumns()` with it
2003 
2004   Logically Collective
2005 
2006   Input Parameter:
2007 . A - the `MATSHELL` shell matrix
2008 
2009   Output Parameters:
2010 + vshift - `PetscScalar` pointer (can be `NULL`), see `MatShift()`, or `MAT_SHELL_NOT_ALLOWED` if the internal shift should be 0
2011 . vscale - `PetscScalar` pointer (can be `NULL`), see `MatScale()`, or `MAT_SHELL_NOT_ALLOWED` if the internal scaling should be 1
2012 . dshift - `Vec` pointer (can be `NULL`), see `MatDiagonalSet()`, or `MAT_SHELL_NOT_ALLOWED` if the internal shift should be `NULL`
2013 . left   - `Vec` pointer (can be `NULL`), see `MatDiagonalScale()`, or `MAT_SHELL_NOT_ALLOWED` if the internal scaling should be `NULL`
2014 . right  - `Vec` pointer (can be `NULL`), see `MatDiagonalScale()`, or `MAT_SHELL_NOT_ALLOWED` if the internal scaling should be `NULL`
2015 . axpy   - `Mat` pointer (can be `NULL`), or `MAT_SHELL_NOT_ALLOWED` if `MatAXPY()` should have not been called on `A`
2016 . zrows  - `Vec` pointer (can be `NULL`), or `MAT_SHELL_NOT_ALLOWED` if `MatZeroRows()` should have not been called on `A`
2017 - zcols  - `Vec` pointer (can be `NULL`), or `MAT_SHELL_NOT_ALLOWED` if `MatZeroRowsColumns()` should have not been called on `A`
2018 
2019   Level: advanced
2020 
2021   Developer Notes:
2022   This is mostly useful to check for corner-cases in `MatType` deriving from
2023   `MATSHELL`, e.g, `MATCOMPOSITE` or `MATTRANSPOSEVIRTUAL`, since scaling and
2024   shifts often require extra work which is not always implemented.
2025 
2026 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShift()`, `MatScale()`, `MatDiagonalSet()`, `MatDiagonalScale()`, `MatAXPY()`, `MatZeroRows()`, `MatZeroRowsColumns()`, `MatShellSetManageScalingShifts()`
2027 @*/
2028 PetscErrorCode MatShellGetScalingShifts(Mat A, PetscScalar *vshift, PetscScalar *vscale, Vec *dshift, Vec *left, Vec *right, Mat *axpy, IS *zrows, IS *zcols)
2029 {
2030   PetscFunctionBegin;
2031   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2032   PetscTryMethod(A, "MatShellGetScalingShifts_C", (Mat, PetscScalar *, PetscScalar *, Vec *, Vec *, Vec *, Mat *, IS *, IS *), (A, vshift, vscale, dshift, left, right, axpy, zrows, zcols));
2033   PetscFunctionReturn(PETSC_SUCCESS);
2034 }
2035 
2036 /*@C
2037   MatShellTestMult - Compares the multiply routine provided to the `MATSHELL` with differencing on a given function.
2038 
2039   Logically Collective; No Fortran Support
2040 
2041   Input Parameters:
2042 + mat  - the `MATSHELL` shell matrix
2043 . f    - the function
2044 . base - differences are computed around this vector, see `MatMFFDSetBase()`, for Jacobians this is the point at which the Jacobian is being evaluated
2045 - ctx  - an optional context for the function
2046 
2047   Output Parameter:
2048 . flg - `PETSC_TRUE` if the multiply is likely correct
2049 
2050   Options Database Key:
2051 . -mat_shell_test_mult_view - print if any differences are detected between the products and print the difference
2052 
2053   Level: advanced
2054 
2055 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellTestMultTranspose()`
2056 @*/
2057 PetscErrorCode MatShellTestMult(Mat mat, PetscErrorCode (*f)(void *, Vec, Vec), Vec base, void *ctx, PetscBool *flg)
2058 {
2059   PetscInt  m, n;
2060   Mat       mf, Dmf, Dmat, Ddiff;
2061   PetscReal Diffnorm, Dmfnorm;
2062   PetscBool v = PETSC_FALSE, flag = PETSC_TRUE;
2063 
2064   PetscFunctionBegin;
2065   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2066   PetscCall(PetscOptionsHasName(NULL, ((PetscObject)mat)->prefix, "-mat_shell_test_mult_view", &v));
2067   PetscCall(MatGetLocalSize(mat, &m, &n));
2068   PetscCall(MatCreateMFFD(PetscObjectComm((PetscObject)mat), m, n, PETSC_DECIDE, PETSC_DECIDE, &mf));
2069   PetscCall(MatMFFDSetFunction(mf, f, ctx));
2070   PetscCall(MatMFFDSetBase(mf, base, NULL));
2071 
2072   PetscCall(MatComputeOperator(mf, MATAIJ, &Dmf));
2073   PetscCall(MatComputeOperator(mat, MATAIJ, &Dmat));
2074 
2075   PetscCall(MatDuplicate(Dmat, MAT_COPY_VALUES, &Ddiff));
2076   PetscCall(MatAXPY(Ddiff, -1.0, Dmf, DIFFERENT_NONZERO_PATTERN));
2077   PetscCall(MatNorm(Ddiff, NORM_FROBENIUS, &Diffnorm));
2078   PetscCall(MatNorm(Dmf, NORM_FROBENIUS, &Dmfnorm));
2079   if (Diffnorm / Dmfnorm > 10 * PETSC_SQRT_MACHINE_EPSILON) {
2080     flag = PETSC_FALSE;
2081     if (v) {
2082       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL and matrix-free multiple appear to produce different results.\n Norm Ratio %g Difference results followed by finite difference one\n", (double)(Diffnorm / Dmfnorm)));
2083       PetscCall(MatViewFromOptions(Ddiff, (PetscObject)mat, "-mat_shell_test_mult_view"));
2084       PetscCall(MatViewFromOptions(Dmf, (PetscObject)mat, "-mat_shell_test_mult_view"));
2085       PetscCall(MatViewFromOptions(Dmat, (PetscObject)mat, "-mat_shell_test_mult_view"));
2086     }
2087   } else if (v) {
2088     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL and matrix-free multiple appear to produce the same results\n"));
2089   }
2090   if (flg) *flg = flag;
2091   PetscCall(MatDestroy(&Ddiff));
2092   PetscCall(MatDestroy(&mf));
2093   PetscCall(MatDestroy(&Dmf));
2094   PetscCall(MatDestroy(&Dmat));
2095   PetscFunctionReturn(PETSC_SUCCESS);
2096 }
2097 
2098 /*@C
2099   MatShellTestMultTranspose - Compares the multiply transpose routine provided to the `MATSHELL` with differencing on a given function.
2100 
2101   Logically Collective; No Fortran Support
2102 
2103   Input Parameters:
2104 + mat  - the `MATSHELL` shell matrix
2105 . f    - the function
2106 . base - differences are computed around this vector, see `MatMFFDSetBase()`, for Jacobians this is the point at which the Jacobian is being evaluated
2107 - ctx  - an optional context for the function
2108 
2109   Output Parameter:
2110 . flg - `PETSC_TRUE` if the multiply is likely correct
2111 
2112   Options Database Key:
2113 . -mat_shell_test_mult_view - print if any differences are detected between the products and print the difference
2114 
2115   Level: advanced
2116 
2117 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellTestMult()`
2118 @*/
2119 PetscErrorCode MatShellTestMultTranspose(Mat mat, PetscErrorCode (*f)(void *, Vec, Vec), Vec base, void *ctx, PetscBool *flg)
2120 {
2121   Vec       x, y, z;
2122   PetscInt  m, n, M, N;
2123   Mat       mf, Dmf, Dmat, Ddiff;
2124   PetscReal Diffnorm, Dmfnorm;
2125   PetscBool v = PETSC_FALSE, flag = PETSC_TRUE;
2126 
2127   PetscFunctionBegin;
2128   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2129   PetscCall(PetscOptionsHasName(NULL, ((PetscObject)mat)->prefix, "-mat_shell_test_mult_transpose_view", &v));
2130   PetscCall(MatCreateVecs(mat, &x, &y));
2131   PetscCall(VecDuplicate(y, &z));
2132   PetscCall(MatGetLocalSize(mat, &m, &n));
2133   PetscCall(MatGetSize(mat, &M, &N));
2134   PetscCall(MatCreateMFFD(PetscObjectComm((PetscObject)mat), m, n, M, N, &mf));
2135   PetscCall(MatMFFDSetFunction(mf, f, ctx));
2136   PetscCall(MatMFFDSetBase(mf, base, NULL));
2137   PetscCall(MatComputeOperator(mf, MATAIJ, &Dmf));
2138   PetscCall(MatTranspose(Dmf, MAT_INPLACE_MATRIX, &Dmf));
2139   PetscCall(MatComputeOperatorTranspose(mat, MATAIJ, &Dmat));
2140 
2141   PetscCall(MatDuplicate(Dmat, MAT_COPY_VALUES, &Ddiff));
2142   PetscCall(MatAXPY(Ddiff, -1.0, Dmf, DIFFERENT_NONZERO_PATTERN));
2143   PetscCall(MatNorm(Ddiff, NORM_FROBENIUS, &Diffnorm));
2144   PetscCall(MatNorm(Dmf, NORM_FROBENIUS, &Dmfnorm));
2145   if (Diffnorm / Dmfnorm > 10 * PETSC_SQRT_MACHINE_EPSILON) {
2146     flag = PETSC_FALSE;
2147     if (v) {
2148       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL and matrix-free multiple appear to produce different results.\n Norm Ratio %g Difference results followed by finite difference one\n", (double)(Diffnorm / Dmfnorm)));
2149       PetscCall(MatViewFromOptions(Ddiff, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2150       PetscCall(MatViewFromOptions(Dmf, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2151       PetscCall(MatViewFromOptions(Dmat, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2152     }
2153   } else if (v) {
2154     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL transpose and matrix-free multiple appear to produce the same results\n"));
2155   }
2156   if (flg) *flg = flag;
2157   PetscCall(MatDestroy(&mf));
2158   PetscCall(MatDestroy(&Dmat));
2159   PetscCall(MatDestroy(&Ddiff));
2160   PetscCall(MatDestroy(&Dmf));
2161   PetscCall(VecDestroy(&x));
2162   PetscCall(VecDestroy(&y));
2163   PetscCall(VecDestroy(&z));
2164   PetscFunctionReturn(PETSC_SUCCESS);
2165 }
2166 
2167 /*@C
2168   MatShellSetOperation - Allows user to set a matrix operation for a `MATSHELL` shell matrix.
2169 
2170   Logically Collective
2171 
2172   Input Parameters:
2173 + mat - the `MATSHELL` shell matrix
2174 . op  - the name of the operation
2175 - g   - the function that provides the operation.
2176 
2177   Level: advanced
2178 
2179   Example Usage:
2180 .vb
2181   extern PetscErrorCode usermult(Mat, Vec, Vec);
2182 
2183   MatCreateShell(comm, m, n, M, N, ctx, &A);
2184   MatShellSetOperation(A, MATOP_MULT, (void(*)(void))usermult);
2185 .ve
2186 
2187   Notes:
2188   See the file include/petscmat.h for a complete list of matrix
2189   operations, which all have the form MATOP_<OPERATION>, where
2190   <OPERATION> is the name (in all capital letters) of the
2191   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).
2192 
2193   All user-provided functions (except for `MATOP_DESTROY`) should have the same calling
2194   sequence as the usual matrix interface routines, since they
2195   are intended to be accessed via the usual matrix interface
2196   routines, e.g.,
2197 $       MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
2198 
2199   In particular each function MUST return an error code of 0 on success and
2200   nonzero on failure.
2201 
2202   Within each user-defined routine, the user should call
2203   `MatShellGetContext()` to obtain the user-defined context that was
2204   set by `MatCreateShell()`.
2205 
2206   Use `MatSetOperation()` to set an operation for any matrix type. For matrix product operations (i.e. `MatMatXXX()`, `MatTransposeMatXXX()` etc)
2207   use `MatShellSetMatProductOperation()`
2208 
2209   Fortran Notes:
2210   For `MatCreateVecs()` the user code should check if the input left or right matrix is -1 and in that case not
2211   generate a matrix. See src/mat/tests/ex120f.F
2212 
2213 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatSetOperation()`, `MatShellSetManageScalingShifts()`, `MatShellSetMatProductOperation()`
2214 @*/
2215 PetscErrorCode MatShellSetOperation(Mat mat, MatOperation op, void (*g)(void))
2216 {
2217   PetscFunctionBegin;
2218   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2219   PetscTryMethod(mat, "MatShellSetOperation_C", (Mat, MatOperation, void (*)(void)), (mat, op, g));
2220   PetscFunctionReturn(PETSC_SUCCESS);
2221 }
2222 
2223 /*@C
2224   MatShellGetOperation - Gets a matrix function for a `MATSHELL` shell matrix.
2225 
2226   Not Collective
2227 
2228   Input Parameters:
2229 + mat - the `MATSHELL` shell matrix
2230 - op  - the name of the operation
2231 
2232   Output Parameter:
2233 . g - the function that provides the operation.
2234 
2235   Level: advanced
2236 
2237   Notes:
2238   See the file include/petscmat.h for a complete list of matrix
2239   operations, which all have the form MATOP_<OPERATION>, where
2240   <OPERATION> is the name (in all capital letters) of the
2241   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).
2242 
2243   All user-provided functions have the same calling
2244   sequence as the usual matrix interface routines, since they
2245   are intended to be accessed via the usual matrix interface
2246   routines, e.g.,
2247 $       MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
2248 
2249   Within each user-defined routine, the user should call
2250   `MatShellGetContext()` to obtain the user-defined context that was
2251   set by `MatCreateShell()`.
2252 
2253 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellSetOperation()`, `MatShellSetContext()`
2254 @*/
2255 PetscErrorCode MatShellGetOperation(Mat mat, MatOperation op, void (**g)(void))
2256 {
2257   PetscFunctionBegin;
2258   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2259   PetscUseMethod(mat, "MatShellGetOperation_C", (Mat, MatOperation, void (**)(void)), (mat, op, g));
2260   PetscFunctionReturn(PETSC_SUCCESS);
2261 }
2262 
2263 /*@
2264   MatIsShell - Inquires if a matrix is derived from `MATSHELL`
2265 
2266   Input Parameter:
2267 . mat - the matrix
2268 
2269   Output Parameter:
2270 . flg - the Boolean value
2271 
2272   Level: developer
2273 
2274 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MATMFFD`, `MatCreateShell()`, `MATTRANSPOSEVIRTUAL`, `MATSCHURCOMPLEMENT`
2275 @*/
2276 PetscErrorCode MatIsShell(Mat mat, PetscBool *flg)
2277 {
2278   PetscFunctionBegin;
2279   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2280   PetscAssertPointer(flg, 2);
2281   *flg = (PetscBool)(mat->ops->destroy == MatDestroy_Shell);
2282   PetscFunctionReturn(PETSC_SUCCESS);
2283 }
2284