xref: /petsc/src/mat/impls/shell/shell.c (revision b6555650ae2ecd16e003bc8820c90b5d0e396fe0)
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 ctxdestroy(void*);
841 
842   MatCreateShell(comm, m, n, M, N, ctx, &A);
843   MatShellSetMatProductOperation(
844     A, MATPRODUCT_AB, usersymbolic, usernumeric, ctxdestroy,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                                        MatConvert_Shell,
1443                                        NULL,
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*/ MatMissingDiagonal_Shell,
1477                                        NULL,
1478                                        NULL,
1479                                        NULL,
1480                                        NULL,
1481                                        /*109*/ NULL,
1482                                        NULL,
1483                                        NULL,
1484                                        NULL,
1485                                        MatMultHermitianTransposeAdd_Shell,
1486                                        /*114*/ NULL,
1487                                        NULL,
1488                                        NULL,
1489                                        NULL,
1490                                        NULL,
1491                                        /*119*/ NULL,
1492                                        NULL,
1493                                        NULL,
1494                                        NULL,
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 
1517 static PetscErrorCode MatShellSetContext_Shell(Mat mat, void *ctx)
1518 {
1519   Mat_Shell *shell = (Mat_Shell *)mat->data;
1520 
1521   PetscFunctionBegin;
1522   if (ctx) {
1523     PetscContainer ctxcontainer;
1524     PetscCall(PetscContainerCreate(PetscObjectComm((PetscObject)mat), &ctxcontainer));
1525     PetscCall(PetscContainerSetPointer(ctxcontainer, ctx));
1526     PetscCall(PetscObjectCompose((PetscObject)mat, "MatShell ctx", (PetscObject)ctxcontainer));
1527     shell->ctxcontainer = ctxcontainer;
1528     PetscCall(PetscContainerDestroy(&ctxcontainer));
1529   } else {
1530     PetscCall(PetscObjectCompose((PetscObject)mat, "MatShell ctx", NULL));
1531     shell->ctxcontainer = NULL;
1532   }
1533   PetscFunctionReturn(PETSC_SUCCESS);
1534 }
1535 
1536 static PetscErrorCode MatShellSetContextDestroy_Shell(Mat mat, PetscCtxDestroyFn *f)
1537 {
1538   Mat_Shell *shell = (Mat_Shell *)mat->data;
1539 
1540   PetscFunctionBegin;
1541   if (shell->ctxcontainer) PetscCall(PetscContainerSetCtxDestroy(shell->ctxcontainer, f));
1542   PetscFunctionReturn(PETSC_SUCCESS);
1543 }
1544 
1545 PetscErrorCode MatShellSetContext_Immutable(Mat mat, void *ctx)
1546 {
1547   PetscFunctionBegin;
1548   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);
1549   PetscFunctionReturn(PETSC_SUCCESS);
1550 }
1551 
1552 PetscErrorCode MatShellSetContextDestroy_Immutable(Mat mat, PetscCtxDestroyFn *f)
1553 {
1554   PetscFunctionBegin;
1555   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);
1556   PetscFunctionReturn(PETSC_SUCCESS);
1557 }
1558 
1559 PetscErrorCode MatShellSetManageScalingShifts_Immutable(Mat mat)
1560 {
1561   PetscFunctionBegin;
1562   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);
1563   PetscFunctionReturn(PETSC_SUCCESS);
1564 }
1565 
1566 static PetscErrorCode MatShellSetVecType_Shell(Mat mat, VecType vtype)
1567 {
1568   PetscFunctionBegin;
1569   PetscCall(PetscFree(mat->defaultvectype));
1570   PetscCall(PetscStrallocpy(vtype, (char **)&mat->defaultvectype));
1571   PetscFunctionReturn(PETSC_SUCCESS);
1572 }
1573 
1574 static PetscErrorCode MatShellSetManageScalingShifts_Shell(Mat A)
1575 {
1576   Mat_Shell *shell = (Mat_Shell *)A->data;
1577 
1578   PetscFunctionBegin;
1579   shell->managescalingshifts = PETSC_FALSE;
1580   A->ops->diagonalset        = NULL;
1581   A->ops->diagonalscale      = NULL;
1582   A->ops->scale              = NULL;
1583   A->ops->shift              = NULL;
1584   A->ops->axpy               = NULL;
1585   PetscFunctionReturn(PETSC_SUCCESS);
1586 }
1587 
1588 static PetscErrorCode MatShellGetScalingShifts_Shell(Mat A, PetscScalar *vshift, PetscScalar *vscale, Vec *dshift, Vec *left, Vec *right, Mat *axpy, IS *zrows, IS *zcols)
1589 {
1590   Mat_Shell *shell = (Mat_Shell *)A->data;
1591 
1592   PetscFunctionBegin;
1593   PetscCheck(shell->managescalingshifts, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot get scaling and shifts if MatShellSetManageScalingShifts() has been called");
1594   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()");
1595   else if (vshift) *vshift = shell->vshift;
1596   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()");
1597   else if (vscale) *vscale = shell->vscale;
1598   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()");
1599   else if (dshift) *dshift = shell->dshift;
1600   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()");
1601   else if (left) *left = shell->left;
1602   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()");
1603   else if (right) *right = shell->right;
1604   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()");
1605   else if (axpy) *axpy = shell->axpy;
1606   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()");
1607   else if (zrows) *zrows = shell->zrows;
1608   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()");
1609   else if (zcols) *zcols = shell->zcols;
1610   PetscFunctionReturn(PETSC_SUCCESS);
1611 }
1612 
1613 static PetscErrorCode MatShellSetOperation_Shell(Mat mat, MatOperation op, void (*f)(void))
1614 {
1615   Mat_Shell *shell = (Mat_Shell *)mat->data;
1616 
1617   PetscFunctionBegin;
1618   switch (op) {
1619   case MATOP_DESTROY:
1620     shell->ops->destroy = (PetscErrorCode (*)(Mat))f;
1621     break;
1622   case MATOP_VIEW:
1623     if (!mat->ops->viewnative) mat->ops->viewnative = mat->ops->view;
1624     mat->ops->view = (PetscErrorCode (*)(Mat, PetscViewer))f;
1625     break;
1626   case MATOP_COPY:
1627     shell->ops->copy = (PetscErrorCode (*)(Mat, Mat, MatStructure))f;
1628     break;
1629   case MATOP_DIAGONAL_SET:
1630   case MATOP_DIAGONAL_SCALE:
1631   case MATOP_SHIFT:
1632   case MATOP_SCALE:
1633   case MATOP_AXPY:
1634   case MATOP_ZERO_ROWS:
1635   case MATOP_ZERO_ROWS_COLUMNS:
1636     PetscCheck(!shell->managescalingshifts, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MATSHELL is managing scalings and shifts, see MatShellSetManageScalingShifts()");
1637     (((void (**)(void))mat->ops)[op]) = f;
1638     break;
1639   case MATOP_GET_DIAGONAL:
1640     if (shell->managescalingshifts) {
1641       shell->ops->getdiagonal = (PetscErrorCode (*)(Mat, Vec))f;
1642       mat->ops->getdiagonal   = MatGetDiagonal_Shell;
1643     } else {
1644       shell->ops->getdiagonal = NULL;
1645       mat->ops->getdiagonal   = (PetscErrorCode (*)(Mat, Vec))f;
1646     }
1647     break;
1648   case MATOP_GET_DIAGONAL_BLOCK:
1649     if (shell->managescalingshifts) {
1650       shell->ops->getdiagonalblock = (PetscErrorCode (*)(Mat, Mat *))f;
1651       mat->ops->getdiagonalblock   = MatGetDiagonalBlock_Shell;
1652     } else {
1653       shell->ops->getdiagonalblock = NULL;
1654       mat->ops->getdiagonalblock   = (PetscErrorCode (*)(Mat, Mat *))f;
1655     }
1656     break;
1657   case MATOP_MULT:
1658     if (shell->managescalingshifts) {
1659       shell->ops->mult = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1660       mat->ops->mult   = MatMult_Shell;
1661     } else {
1662       shell->ops->mult = NULL;
1663       mat->ops->mult   = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1664     }
1665     break;
1666   case MATOP_MULT_TRANSPOSE:
1667     if (shell->managescalingshifts) {
1668       shell->ops->multtranspose = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1669       mat->ops->multtranspose   = MatMultTranspose_Shell;
1670     } else {
1671       shell->ops->multtranspose = NULL;
1672       mat->ops->multtranspose   = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1673     }
1674     break;
1675   case MATOP_MULT_HERMITIAN_TRANSPOSE:
1676     if (shell->managescalingshifts) {
1677       shell->ops->multhermitiantranspose = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1678       mat->ops->multhermitiantranspose   = MatMultHermitianTranspose_Shell;
1679     } else {
1680       shell->ops->multhermitiantranspose = NULL;
1681       mat->ops->multhermitiantranspose   = (PetscErrorCode (*)(Mat, Vec, Vec))f;
1682     }
1683     break;
1684   default:
1685     (((void (**)(void))mat->ops)[op]) = f;
1686     break;
1687   }
1688   PetscFunctionReturn(PETSC_SUCCESS);
1689 }
1690 
1691 static PetscErrorCode MatShellGetOperation_Shell(Mat mat, MatOperation op, void (**f)(void))
1692 {
1693   Mat_Shell *shell = (Mat_Shell *)mat->data;
1694 
1695   PetscFunctionBegin;
1696   switch (op) {
1697   case MATOP_DESTROY:
1698     *f = (void (*)(void))shell->ops->destroy;
1699     break;
1700   case MATOP_VIEW:
1701     *f = (void (*)(void))mat->ops->view;
1702     break;
1703   case MATOP_COPY:
1704     *f = (void (*)(void))shell->ops->copy;
1705     break;
1706   case MATOP_DIAGONAL_SET:
1707   case MATOP_DIAGONAL_SCALE:
1708   case MATOP_SHIFT:
1709   case MATOP_SCALE:
1710   case MATOP_AXPY:
1711   case MATOP_ZERO_ROWS:
1712   case MATOP_ZERO_ROWS_COLUMNS:
1713     *f = (((void (**)(void))mat->ops)[op]);
1714     break;
1715   case MATOP_GET_DIAGONAL:
1716     if (shell->ops->getdiagonal) *f = (void (*)(void))shell->ops->getdiagonal;
1717     else *f = (((void (**)(void))mat->ops)[op]);
1718     break;
1719   case MATOP_GET_DIAGONAL_BLOCK:
1720     if (shell->ops->getdiagonalblock) *f = (void (*)(void))shell->ops->getdiagonalblock;
1721     else *f = (((void (**)(void))mat->ops)[op]);
1722     break;
1723   case MATOP_MULT:
1724     if (shell->ops->mult) *f = (void (*)(void))shell->ops->mult;
1725     else *f = (((void (**)(void))mat->ops)[op]);
1726     break;
1727   case MATOP_MULT_TRANSPOSE:
1728     if (shell->ops->multtranspose) *f = (void (*)(void))shell->ops->multtranspose;
1729     else *f = (((void (**)(void))mat->ops)[op]);
1730     break;
1731   case MATOP_MULT_HERMITIAN_TRANSPOSE:
1732     if (shell->ops->multhermitiantranspose) *f = (void (*)(void))shell->ops->multhermitiantranspose;
1733     else *f = (((void (**)(void))mat->ops)[op]);
1734     break;
1735   default:
1736     *f = (((void (**)(void))mat->ops)[op]);
1737   }
1738   PetscFunctionReturn(PETSC_SUCCESS);
1739 }
1740 
1741 /*MC
1742   MATSHELL - MATSHELL = "shell" - A matrix type to be used to define your own matrix type with its own data structure -- perhaps matrix-free.
1743 
1744   Level: advanced
1745 
1746   Notes:
1747   See `MatCreateShell()` for details on the usage of `MATSHELL`
1748 
1749   `PCSHELL` can be used in conjunction with `MATSHELL` to provide a custom preconditioner appropriate for your `MATSHELL`. Since
1750   many standard preconditioners such as `PCILU` depend on having an explicit representation of the matrix entries they cannot be used
1751   directly with `MATSHELL`.
1752 
1753 .seealso: [](ch_matrices), `Mat`, `MatCreateShell()`, `PCSHELL`
1754 M*/
1755 
1756 PETSC_EXTERN PetscErrorCode MatCreate_Shell(Mat A)
1757 {
1758   Mat_Shell *b;
1759 
1760   PetscFunctionBegin;
1761   PetscCall(PetscNew(&b));
1762   A->data   = (void *)b;
1763   A->ops[0] = MatOps_Values;
1764 
1765   b->ctxcontainer        = NULL;
1766   b->vshift              = 0.0;
1767   b->vscale              = 1.0;
1768   b->managescalingshifts = PETSC_TRUE;
1769   A->assembled           = PETSC_TRUE;
1770   A->preallocated        = PETSC_FALSE;
1771 
1772   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetContext_C", MatShellGetContext_Shell));
1773   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", MatShellSetContext_Shell));
1774   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContextDestroy_C", MatShellSetContextDestroy_Shell));
1775   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetVecType_C", MatShellSetVecType_Shell));
1776   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetManageScalingShifts_C", MatShellSetManageScalingShifts_Shell));
1777   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetScalingShifts_C", MatShellGetScalingShifts_Shell));
1778   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetOperation_C", MatShellSetOperation_Shell));
1779   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetOperation_C", MatShellGetOperation_Shell));
1780   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetMatProductOperation_C", MatShellSetMatProductOperation_Shell));
1781   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATSHELL));
1782   PetscFunctionReturn(PETSC_SUCCESS);
1783 }
1784 
1785 /*@C
1786   MatCreateShell - Creates a new matrix of `MatType` `MATSHELL` for use with a user-defined
1787   private matrix data storage format.
1788 
1789   Collective
1790 
1791   Input Parameters:
1792 + comm - MPI communicator
1793 . m    - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
1794 . n    - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
1795 . M    - number of global rows (may be `PETSC_DETERMINE` to have calculated if `m` is given)
1796 . N    - number of global columns (may be `PETSC_DETERMINE` to have calculated if `n` is given)
1797 - ctx  - pointer to data needed by the shell matrix routines
1798 
1799   Output Parameter:
1800 . A - the matrix
1801 
1802   Level: advanced
1803 
1804   Example Usage:
1805 .vb
1806   extern PetscErrorCode mult(Mat, Vec, Vec);
1807 
1808   MatCreateShell(comm, m, n, M, N, ctx, &mat);
1809   MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))mult);
1810   MatShellSetContext(mat,ctx);
1811   // Use matrix for operations that have been set
1812   MatDestroy(mat);
1813 .ve
1814 
1815   Notes:
1816   The shell matrix type is intended to provide a simple way for users to write a custom matrix specifically for their application.
1817 
1818   `MatCreateShell()` is used in conjunction with `MatShellSetContext()` and `MatShellSetOperation()`.
1819 
1820   PETSc requires that matrices and vectors being used for certain
1821   operations are partitioned accordingly.  For example, when
1822   creating a shell matrix, `A`, that supports parallel matrix-vector
1823   products using `MatMult`(A,x,y) the user should set the number
1824   of local matrix rows to be the number of local elements of the
1825   corresponding result vector, y. Note that this is information is
1826   required for use of the matrix interface routines, even though
1827   the shell matrix may not actually be physically partitioned.
1828   For example,
1829 
1830 .vb
1831      Vec x, y
1832      extern PetscErrorCode mult(Mat,Vec,Vec);
1833      Mat A
1834 
1835      VecCreateMPI(comm,PETSC_DECIDE,M,&y);
1836      VecCreateMPI(comm,PETSC_DECIDE,N,&x);
1837      VecGetLocalSize(y,&m);
1838      VecGetLocalSize(x,&n);
1839      MatCreateShell(comm,m,n,M,N,ctx,&A);
1840      MatShellSetOperation(mat,MATOP_MULT,(void(*)(void))mult);
1841      MatMult(A,x,y);
1842      MatDestroy(&A);
1843      VecDestroy(&y);
1844      VecDestroy(&x);
1845 .ve
1846 
1847   `MATSHELL` handles `MatShift()`, `MatDiagonalSet()`, `MatDiagonalScale()`, `MatAXPY()`, `MatScale()`, `MatZeroRows()` and `MatZeroRowsColumns()`
1848   internally, so these  operations cannot be overwritten unless `MatShellSetManageScalingShifts()` is called.
1849 
1850   Developer Notes:
1851   For rectangular matrices do all the scalings and shifts make sense?
1852 
1853   Regarding shifting and scaling. The general form is
1854 
1855   diag(left)(vscale*A + diag(dshift) + vshift I)diag(right)
1856 
1857   The order you apply the operations is important. For example if you have a dshift then
1858   apply a MatScale(s) you get s*vscale*A + s*diag(shift). But if you first scale and then shift
1859   you get s*vscale*A + diag(shift)
1860 
1861   A is the user provided function.
1862 
1863   `KSP`/`PC` uses changes in the `Mat`'s "state" to decide if preconditioners need to be rebuilt `PCSetUp()` only calls the setup() for
1864   for the `PC` implementation if the `Mat` state has increased from the previous call. Thus to get changes in a `MATSHELL` to trigger
1865   an update in the preconditioner you must call `MatAssemblyBegin()` and `MatAssemblyEnd()` or `PetscObjectStateIncrease`((`PetscObject`)mat);
1866   each time the `MATSHELL` matrix has changed.
1867 
1868   Matrix-matrix product operations can be specified using `MatShellSetMatProductOperation()`
1869 
1870   Calling `MatAssemblyBegin()`/`MatAssemblyEnd()` on a `MATSHELL` removes any previously supplied shift and scales that were provided
1871   with `MatDiagonalSet()`, `MatShift()`, `MatScale()`, or `MatDiagonalScale()`.
1872 
1873   Fortran Notes:
1874   To use this from Fortran with a `ctx` you must write an interface definition for this
1875   function and for `MatShellGetContext()` that tells Fortran the Fortran derived data type you are passing
1876   in as the `ctx` argument.
1877 
1878 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatShellSetOperation()`, `MatHasOperation()`, `MatShellGetContext()`, `MatShellSetContext()`, `MatShellSetManageScalingShifts()`, `MatShellSetMatProductOperation()`
1879 @*/
1880 PetscErrorCode MatCreateShell(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, void *ctx, Mat *A)
1881 {
1882   PetscFunctionBegin;
1883   PetscCall(MatCreate(comm, A));
1884   PetscCall(MatSetSizes(*A, m, n, M, N));
1885   PetscCall(MatSetType(*A, MATSHELL));
1886   PetscCall(MatShellSetContext(*A, ctx));
1887   PetscCall(MatSetUp(*A));
1888   PetscFunctionReturn(PETSC_SUCCESS);
1889 }
1890 
1891 /*@
1892   MatShellSetContext - sets the context for a `MATSHELL` shell matrix
1893 
1894   Logically Collective
1895 
1896   Input Parameters:
1897 + mat - the `MATSHELL` shell matrix
1898 - ctx - the context
1899 
1900   Level: advanced
1901 
1902   Note:
1903   This provides an easy way, along with `MatCreateShell()` and `MatShellSetOperation()` to provide a custom matrix format
1904   specifically for your application.
1905 
1906   Fortran Notes:
1907   You must write a Fortran interface definition for this
1908   function that tells Fortran the Fortran derived data type that you are passing in as the `ctx` argument.
1909 
1910 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`
1911 @*/
1912 PetscErrorCode MatShellSetContext(Mat mat, void *ctx)
1913 {
1914   PetscFunctionBegin;
1915   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1916   PetscTryMethod(mat, "MatShellSetContext_C", (Mat, void *), (mat, ctx));
1917   PetscFunctionReturn(PETSC_SUCCESS);
1918 }
1919 
1920 /*@C
1921   MatShellSetContextDestroy - sets the destroy function for a `MATSHELL` shell matrix context
1922 
1923   Logically Collective
1924 
1925   Input Parameters:
1926 + mat - the shell matrix
1927 - f   - the context destroy function, see `PetscCtxDestroyFn` for calling sequence
1928 
1929   Level: advanced
1930 
1931   Note:
1932   If the `MatShell` is never duplicated, the behavior of this function is equivalent
1933   to `MatShellSetOperation`(`Mat`,`MATOP_DESTROY`,f). However, `MatShellSetContextDestroy()`
1934   ensures proper reference counting for the user provided context data in the case that
1935   the `MATSHELL` is duplicated.
1936 
1937 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellSetContext()`,
1938           `PetscCtxDestroyFn`
1939 @*/
1940 PetscErrorCode MatShellSetContextDestroy(Mat mat, PetscCtxDestroyFn *f)
1941 {
1942   PetscFunctionBegin;
1943   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1944   PetscTryMethod(mat, "MatShellSetContextDestroy_C", (Mat, PetscCtxDestroyFn *), (mat, f));
1945   PetscFunctionReturn(PETSC_SUCCESS);
1946 }
1947 
1948 /*@C
1949   MatShellSetVecType - Sets the `VecType` of `Vec` returned by `MatCreateVecs()`
1950 
1951   Logically Collective
1952 
1953   Input Parameters:
1954 + mat   - the `MATSHELL` shell matrix
1955 - vtype - type to use for creating vectors
1956 
1957   Level: advanced
1958 
1959 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateVecs()`
1960 @*/
1961 PetscErrorCode MatShellSetVecType(Mat mat, VecType vtype)
1962 {
1963   PetscFunctionBegin;
1964   PetscTryMethod(mat, "MatShellSetVecType_C", (Mat, VecType), (mat, vtype));
1965   PetscFunctionReturn(PETSC_SUCCESS);
1966 }
1967 
1968 /*@
1969   MatShellSetManageScalingShifts - Allows the user to control the scaling and shift operations of the `MATSHELL`. Must be called immediately
1970   after `MatCreateShell()`
1971 
1972   Logically Collective
1973 
1974   Input Parameter:
1975 . A - the `MATSHELL` shell matrix
1976 
1977   Level: advanced
1978 
1979 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatShellSetOperation()`
1980 @*/
1981 PetscErrorCode MatShellSetManageScalingShifts(Mat A)
1982 {
1983   PetscFunctionBegin;
1984   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
1985   PetscTryMethod(A, "MatShellSetManageScalingShifts_C", (Mat), (A));
1986   PetscFunctionReturn(PETSC_SUCCESS);
1987 }
1988 
1989 /*@C
1990   MatShellGetScalingShifts - Gets members of a `MATSHELL` used internally for scaling and
1991   shifting the `Mat` or calling `MatAXPY()`, `MatZeroRows()`, or `MatZeroRowsColumns()` with it
1992 
1993   Logically Collective
1994 
1995   Input Parameter:
1996 . A - the `MATSHELL` shell matrix
1997 
1998   Output Parameters:
1999 + vshift - `PetscScalar` pointer (can be `NULL`), see `MatShift()`, or `MAT_SHELL_NOT_ALLOWED` if the internal shift should be 0
2000 . vscale - `PetscScalar` pointer (can be `NULL`), see `MatScale()`, or `MAT_SHELL_NOT_ALLOWED` if the internal scaling should be 1
2001 . dshift - `Vec` pointer (can be `NULL`), see `MatDiagonalSet()`, or `MAT_SHELL_NOT_ALLOWED` if the internal shift should be `NULL`
2002 . left   - `Vec` pointer (can be `NULL`), see `MatDiagonalScale()`, or `MAT_SHELL_NOT_ALLOWED` if the internal scaling should be `NULL`
2003 . right  - `Vec` pointer (can be `NULL`), see `MatDiagonalScale()`, or `MAT_SHELL_NOT_ALLOWED` if the internal scaling should be `NULL`
2004 . axpy   - `Mat` pointer (can be `NULL`), or `MAT_SHELL_NOT_ALLOWED` if `MatAXPY()` should have not been called on `A`
2005 . zrows  - `Vec` pointer (can be `NULL`), or `MAT_SHELL_NOT_ALLOWED` if `MatZeroRows()` should have not been called on `A`
2006 - zcols  - `Vec` pointer (can be `NULL`), or `MAT_SHELL_NOT_ALLOWED` if `MatZeroRowsColumns()` should have not been called on `A`
2007 
2008   Level: advanced
2009 
2010   Developer Notes:
2011   This is mostly useful to check for corner-cases in `MatType` deriving from
2012   `MATSHELL`, e.g, `MATCOMPOSITE` or `MATTRANSPOSEVIRTUAL`, since scaling and
2013   shifts often require extra work which is not always implemented.
2014 
2015 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShift()`, `MatScale()`, `MatDiagonalSet()`, `MatDiagonalScale()`, `MatAXPY()`, `MatZeroRows()`, `MatZeroRowsColumns()`, `MatShellSetManageScalingShifts()`
2016 @*/
2017 PetscErrorCode MatShellGetScalingShifts(Mat A, PetscScalar *vshift, PetscScalar *vscale, Vec *dshift, Vec *left, Vec *right, Mat *axpy, IS *zrows, IS *zcols)
2018 {
2019   PetscFunctionBegin;
2020   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2021   PetscTryMethod(A, "MatShellGetScalingShifts_C", (Mat, PetscScalar *, PetscScalar *, Vec *, Vec *, Vec *, Mat *, IS *, IS *), (A, vshift, vscale, dshift, left, right, axpy, zrows, zcols));
2022   PetscFunctionReturn(PETSC_SUCCESS);
2023 }
2024 
2025 /*@C
2026   MatShellTestMult - Compares the multiply routine provided to the `MATSHELL` with differencing on a given function.
2027 
2028   Logically Collective; No Fortran Support
2029 
2030   Input Parameters:
2031 + mat  - the `MATSHELL` shell matrix
2032 . f    - the function
2033 . base - differences are computed around this vector, see `MatMFFDSetBase()`, for Jacobians this is the point at which the Jacobian is being evaluated
2034 - ctx  - an optional context for the function
2035 
2036   Output Parameter:
2037 . flg - `PETSC_TRUE` if the multiply is likely correct
2038 
2039   Options Database Key:
2040 . -mat_shell_test_mult_view - print if any differences are detected between the products and print the difference
2041 
2042   Level: advanced
2043 
2044 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellTestMultTranspose()`
2045 @*/
2046 PetscErrorCode MatShellTestMult(Mat mat, PetscErrorCode (*f)(void *, Vec, Vec), Vec base, void *ctx, PetscBool *flg)
2047 {
2048   PetscInt  m, n;
2049   Mat       mf, Dmf, Dmat, Ddiff;
2050   PetscReal Diffnorm, Dmfnorm;
2051   PetscBool v = PETSC_FALSE, flag = PETSC_TRUE;
2052 
2053   PetscFunctionBegin;
2054   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2055   PetscCall(PetscOptionsHasName(NULL, ((PetscObject)mat)->prefix, "-mat_shell_test_mult_view", &v));
2056   PetscCall(MatGetLocalSize(mat, &m, &n));
2057   PetscCall(MatCreateMFFD(PetscObjectComm((PetscObject)mat), m, n, PETSC_DECIDE, PETSC_DECIDE, &mf));
2058   PetscCall(MatMFFDSetFunction(mf, f, ctx));
2059   PetscCall(MatMFFDSetBase(mf, base, NULL));
2060 
2061   PetscCall(MatComputeOperator(mf, MATAIJ, &Dmf));
2062   PetscCall(MatComputeOperator(mat, MATAIJ, &Dmat));
2063 
2064   PetscCall(MatDuplicate(Dmat, MAT_COPY_VALUES, &Ddiff));
2065   PetscCall(MatAXPY(Ddiff, -1.0, Dmf, DIFFERENT_NONZERO_PATTERN));
2066   PetscCall(MatNorm(Ddiff, NORM_FROBENIUS, &Diffnorm));
2067   PetscCall(MatNorm(Dmf, NORM_FROBENIUS, &Dmfnorm));
2068   if (Diffnorm / Dmfnorm > 10 * PETSC_SQRT_MACHINE_EPSILON) {
2069     flag = PETSC_FALSE;
2070     if (v) {
2071       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)));
2072       PetscCall(MatViewFromOptions(Ddiff, (PetscObject)mat, "-mat_shell_test_mult_view"));
2073       PetscCall(MatViewFromOptions(Dmf, (PetscObject)mat, "-mat_shell_test_mult_view"));
2074       PetscCall(MatViewFromOptions(Dmat, (PetscObject)mat, "-mat_shell_test_mult_view"));
2075     }
2076   } else if (v) {
2077     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL and matrix-free multiple appear to produce the same results\n"));
2078   }
2079   if (flg) *flg = flag;
2080   PetscCall(MatDestroy(&Ddiff));
2081   PetscCall(MatDestroy(&mf));
2082   PetscCall(MatDestroy(&Dmf));
2083   PetscCall(MatDestroy(&Dmat));
2084   PetscFunctionReturn(PETSC_SUCCESS);
2085 }
2086 
2087 /*@C
2088   MatShellTestMultTranspose - Compares the multiply transpose routine provided to the `MATSHELL` with differencing on a given function.
2089 
2090   Logically Collective; No Fortran Support
2091 
2092   Input Parameters:
2093 + mat  - the `MATSHELL` shell matrix
2094 . f    - the function
2095 . base - differences are computed around this vector, see `MatMFFDSetBase()`, for Jacobians this is the point at which the Jacobian is being evaluated
2096 - ctx  - an optional context for the function
2097 
2098   Output Parameter:
2099 . flg - `PETSC_TRUE` if the multiply is likely correct
2100 
2101   Options Database Key:
2102 . -mat_shell_test_mult_view - print if any differences are detected between the products and print the difference
2103 
2104   Level: advanced
2105 
2106 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellTestMult()`
2107 @*/
2108 PetscErrorCode MatShellTestMultTranspose(Mat mat, PetscErrorCode (*f)(void *, Vec, Vec), Vec base, void *ctx, PetscBool *flg)
2109 {
2110   Vec       x, y, z;
2111   PetscInt  m, n, M, N;
2112   Mat       mf, Dmf, Dmat, Ddiff;
2113   PetscReal Diffnorm, Dmfnorm;
2114   PetscBool v = PETSC_FALSE, flag = PETSC_TRUE;
2115 
2116   PetscFunctionBegin;
2117   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2118   PetscCall(PetscOptionsHasName(NULL, ((PetscObject)mat)->prefix, "-mat_shell_test_mult_transpose_view", &v));
2119   PetscCall(MatCreateVecs(mat, &x, &y));
2120   PetscCall(VecDuplicate(y, &z));
2121   PetscCall(MatGetLocalSize(mat, &m, &n));
2122   PetscCall(MatGetSize(mat, &M, &N));
2123   PetscCall(MatCreateMFFD(PetscObjectComm((PetscObject)mat), m, n, M, N, &mf));
2124   PetscCall(MatMFFDSetFunction(mf, f, ctx));
2125   PetscCall(MatMFFDSetBase(mf, base, NULL));
2126   PetscCall(MatComputeOperator(mf, MATAIJ, &Dmf));
2127   PetscCall(MatTranspose(Dmf, MAT_INPLACE_MATRIX, &Dmf));
2128   PetscCall(MatComputeOperatorTranspose(mat, MATAIJ, &Dmat));
2129 
2130   PetscCall(MatDuplicate(Dmat, MAT_COPY_VALUES, &Ddiff));
2131   PetscCall(MatAXPY(Ddiff, -1.0, Dmf, DIFFERENT_NONZERO_PATTERN));
2132   PetscCall(MatNorm(Ddiff, NORM_FROBENIUS, &Diffnorm));
2133   PetscCall(MatNorm(Dmf, NORM_FROBENIUS, &Dmfnorm));
2134   if (Diffnorm / Dmfnorm > 10 * PETSC_SQRT_MACHINE_EPSILON) {
2135     flag = PETSC_FALSE;
2136     if (v) {
2137       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)));
2138       PetscCall(MatViewFromOptions(Ddiff, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2139       PetscCall(MatViewFromOptions(Dmf, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2140       PetscCall(MatViewFromOptions(Dmat, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2141     }
2142   } else if (v) {
2143     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL transpose and matrix-free multiple appear to produce the same results\n"));
2144   }
2145   if (flg) *flg = flag;
2146   PetscCall(MatDestroy(&mf));
2147   PetscCall(MatDestroy(&Dmat));
2148   PetscCall(MatDestroy(&Ddiff));
2149   PetscCall(MatDestroy(&Dmf));
2150   PetscCall(VecDestroy(&x));
2151   PetscCall(VecDestroy(&y));
2152   PetscCall(VecDestroy(&z));
2153   PetscFunctionReturn(PETSC_SUCCESS);
2154 }
2155 
2156 /*@C
2157   MatShellSetOperation - Allows user to set a matrix operation for a `MATSHELL` shell matrix.
2158 
2159   Logically Collective
2160 
2161   Input Parameters:
2162 + mat - the `MATSHELL` shell matrix
2163 . op  - the name of the operation
2164 - g   - the function that provides the operation.
2165 
2166   Level: advanced
2167 
2168   Example Usage:
2169 .vb
2170   extern PetscErrorCode usermult(Mat, Vec, Vec);
2171 
2172   MatCreateShell(comm, m, n, M, N, ctx, &A);
2173   MatShellSetOperation(A, MATOP_MULT, (void(*)(void))usermult);
2174 .ve
2175 
2176   Notes:
2177   See the file include/petscmat.h for a complete list of matrix
2178   operations, which all have the form MATOP_<OPERATION>, where
2179   <OPERATION> is the name (in all capital letters) of the
2180   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).
2181 
2182   All user-provided functions (except for `MATOP_DESTROY`) should have the same calling
2183   sequence as the usual matrix interface routines, since they
2184   are intended to be accessed via the usual matrix interface
2185   routines, e.g.,
2186 .vb
2187   MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
2188 .ve
2189 
2190   In particular each function MUST return an error code of 0 on success and
2191   nonzero on failure.
2192 
2193   Within each user-defined routine, the user should call
2194   `MatShellGetContext()` to obtain the user-defined context that was
2195   set by `MatCreateShell()`.
2196 
2197   Use `MatSetOperation()` to set an operation for any matrix type. For matrix product operations (i.e. `MatMatXXX()`, `MatTransposeMatXXX()` etc)
2198   use `MatShellSetMatProductOperation()`
2199 
2200   Fortran Note:
2201   For `MatCreateVecs()` the user code should check if the input left or right matrix is -1 and in that case not
2202   generate a matrix. See src/mat/tests/ex120f.F
2203 
2204 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatSetOperation()`, `MatShellSetManageScalingShifts()`, `MatShellSetMatProductOperation()`
2205 @*/
2206 PetscErrorCode MatShellSetOperation(Mat mat, MatOperation op, void (*g)(void))
2207 {
2208   PetscFunctionBegin;
2209   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2210   PetscTryMethod(mat, "MatShellSetOperation_C", (Mat, MatOperation, void (*)(void)), (mat, op, g));
2211   PetscFunctionReturn(PETSC_SUCCESS);
2212 }
2213 
2214 /*@C
2215   MatShellGetOperation - Gets a matrix function for a `MATSHELL` shell matrix.
2216 
2217   Not Collective
2218 
2219   Input Parameters:
2220 + mat - the `MATSHELL` shell matrix
2221 - op  - the name of the operation
2222 
2223   Output Parameter:
2224 . g - the function that provides the operation.
2225 
2226   Level: advanced
2227 
2228   Notes:
2229   See the file include/petscmat.h for a complete list of matrix
2230   operations, which all have the form MATOP_<OPERATION>, where
2231   <OPERATION> is the name (in all capital letters) of the
2232   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).
2233 
2234   All user-provided functions have the same calling
2235   sequence as the usual matrix interface routines, since they
2236   are intended to be accessed via the usual matrix interface
2237   routines, e.g.,
2238 .vb
2239   MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
2240 .ve
2241 
2242   Within each user-defined routine, the user should call
2243   `MatShellGetContext()` to obtain the user-defined context that was
2244   set by `MatCreateShell()`.
2245 
2246 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellSetOperation()`, `MatShellSetContext()`
2247 @*/
2248 PetscErrorCode MatShellGetOperation(Mat mat, MatOperation op, void (**g)(void))
2249 {
2250   PetscFunctionBegin;
2251   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2252   PetscUseMethod(mat, "MatShellGetOperation_C", (Mat, MatOperation, void (**)(void)), (mat, op, g));
2253   PetscFunctionReturn(PETSC_SUCCESS);
2254 }
2255 
2256 /*@
2257   MatIsShell - Inquires if a matrix is derived from `MATSHELL`
2258 
2259   Input Parameter:
2260 . mat - the matrix
2261 
2262   Output Parameter:
2263 . flg - the Boolean value
2264 
2265   Level: developer
2266 
2267 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MATMFFD`, `MatCreateShell()`, `MATTRANSPOSEVIRTUAL`, `MATSCHURCOMPLEMENT`
2268 @*/
2269 PetscErrorCode MatIsShell(Mat mat, PetscBool *flg)
2270 {
2271   PetscFunctionBegin;
2272   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2273   PetscAssertPointer(flg, 2);
2274   *flg = (PetscBool)(mat->ops->destroy == MatDestroy_Shell);
2275   PetscFunctionReturn(PETSC_SUCCESS);
2276 }
2277