xref: /petsc/src/mat/impls/shell/shell.c (revision 4ad8454beace47809662cdae21ee081016eaa39a)
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(PETSC_COMM_SELF, 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(PETSC_COMM_SELF, 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, "MatShellSetOperation_C", NULL));
475   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellGetOperation_C", NULL));
476   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatShellSetMatProductOperation_C", NULL));
477   PetscCall(PetscFree(mat->data));
478   PetscFunctionReturn(PETSC_SUCCESS);
479 }
480 
481 typedef struct {
482   PetscErrorCode (*numeric)(Mat, Mat, Mat, void *);
483   PetscErrorCode (*destroy)(void *);
484   void *userdata;
485   Mat   B;
486   Mat   Bt;
487   Mat   axpy;
488 } MatMatDataShell;
489 
490 static PetscErrorCode DestroyMatMatDataShell(void *data)
491 {
492   MatMatDataShell *mmdata = (MatMatDataShell *)data;
493 
494   PetscFunctionBegin;
495   if (mmdata->destroy) PetscCall((*mmdata->destroy)(mmdata->userdata));
496   PetscCall(MatDestroy(&mmdata->B));
497   PetscCall(MatDestroy(&mmdata->Bt));
498   PetscCall(MatDestroy(&mmdata->axpy));
499   PetscCall(PetscFree(mmdata));
500   PetscFunctionReturn(PETSC_SUCCESS);
501 }
502 
503 static PetscErrorCode MatProductNumeric_Shell_X(Mat D)
504 {
505   Mat_Product     *product;
506   Mat              A, B;
507   MatMatDataShell *mdata;
508   PetscScalar      zero = 0.0;
509 
510   PetscFunctionBegin;
511   MatCheckProduct(D, 1);
512   product = D->product;
513   PetscCheck(product->data, PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "Product data empty");
514   A     = product->A;
515   B     = product->B;
516   mdata = (MatMatDataShell *)product->data;
517   if (mdata->numeric) {
518     Mat_Shell *shell                = (Mat_Shell *)A->data;
519     PetscErrorCode (*stashsym)(Mat) = D->ops->productsymbolic;
520     PetscErrorCode (*stashnum)(Mat) = D->ops->productnumeric;
521     PetscBool useBmdata = PETSC_FALSE, newB = PETSC_TRUE;
522 
523     if (shell->managescalingshifts) {
524       PetscCheck(!shell->zcols && !shell->zrows, PetscObjectComm((PetscObject)D), PETSC_ERR_SUP, "MatProduct not supported with zeroed rows/columns");
525       if (shell->right || shell->left) {
526         useBmdata = PETSC_TRUE;
527         if (!mdata->B) {
528           PetscCall(MatDuplicate(B, MAT_SHARE_NONZERO_PATTERN, &mdata->B));
529         } else {
530           newB = PETSC_FALSE;
531         }
532         PetscCall(MatCopy(B, mdata->B, SAME_NONZERO_PATTERN));
533       }
534       switch (product->type) {
535       case MATPRODUCT_AB: /* s L A R B + v L R B + L D R B */
536         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, shell->right, NULL));
537         break;
538       case MATPRODUCT_AtB: /* s R A^t L B + v R L B + R D L B */
539         if (shell->left) PetscCall(MatDiagonalScale(mdata->B, shell->left, NULL));
540         break;
541       case MATPRODUCT_ABt: /* s L A R B^t + v L R B^t + L D R B^t */
542         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, NULL, shell->right));
543         break;
544       case MATPRODUCT_RARt: /* s B L A R B^t + v B L R B^t + B L D R B^t */
545         if (shell->right && shell->left) {
546           PetscBool flg;
547 
548           PetscCall(VecEqual(shell->right, shell->left, &flg));
549           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,
550                      ((PetscObject)B)->type_name);
551         }
552         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, NULL, shell->right));
553         break;
554       case MATPRODUCT_PtAP: /* s B^t L A R B + v B^t L R B + B^t L D R B */
555         if (shell->right && shell->left) {
556           PetscBool flg;
557 
558           PetscCall(VecEqual(shell->right, shell->left, &flg));
559           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,
560                      ((PetscObject)B)->type_name);
561         }
562         if (shell->right) PetscCall(MatDiagonalScale(mdata->B, shell->right, NULL));
563         break;
564       default:
565         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);
566       }
567     }
568     /* allow the user to call MatMat operations on D */
569     D->product              = NULL;
570     D->ops->productsymbolic = NULL;
571     D->ops->productnumeric  = NULL;
572 
573     PetscCall((*mdata->numeric)(A, useBmdata ? mdata->B : B, D, mdata->userdata));
574 
575     /* clear any leftover user data and restore D pointers */
576     PetscCall(MatProductClear(D));
577     D->ops->productsymbolic = stashsym;
578     D->ops->productnumeric  = stashnum;
579     D->product              = product;
580 
581     if (shell->managescalingshifts) {
582       PetscCall(MatScale(D, shell->vscale));
583       switch (product->type) {
584       case MATPRODUCT_AB:  /* s L A R B + v L R B + L D R B */
585       case MATPRODUCT_ABt: /* s L A R B^t + v L R B^t + L D R B^t */
586         if (shell->left) {
587           PetscCall(MatDiagonalScale(D, shell->left, NULL));
588           if (shell->dshift || shell->vshift != zero) {
589             if (!shell->left_work) PetscCall(MatCreateVecs(A, NULL, &shell->left_work));
590             if (shell->dshift) {
591               PetscCall(VecCopy(shell->dshift, shell->left_work));
592               PetscCall(VecShift(shell->left_work, shell->vshift));
593               PetscCall(VecPointwiseMult(shell->left_work, shell->left_work, shell->left));
594             } else {
595               PetscCall(VecSet(shell->left_work, shell->vshift));
596             }
597             if (product->type == MATPRODUCT_ABt) {
598               MatReuse     reuse = mdata->Bt ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;
599               MatStructure str   = mdata->Bt ? SUBSET_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN;
600 
601               PetscCall(MatTranspose(mdata->B, reuse, &mdata->Bt));
602               PetscCall(MatDiagonalScale(mdata->Bt, shell->left_work, NULL));
603               PetscCall(MatAXPY(D, 1.0, mdata->Bt, str));
604             } else {
605               MatStructure str = newB ? DIFFERENT_NONZERO_PATTERN : SUBSET_NONZERO_PATTERN;
606 
607               PetscCall(MatDiagonalScale(mdata->B, shell->left_work, NULL));
608               PetscCall(MatAXPY(D, 1.0, mdata->B, str));
609             }
610           }
611         }
612         break;
613       case MATPRODUCT_AtB: /* s R A^t L B + v R L B + R D L B */
614         if (shell->right) {
615           PetscCall(MatDiagonalScale(D, shell->right, NULL));
616           if (shell->dshift || shell->vshift != zero) {
617             MatStructure str = newB ? DIFFERENT_NONZERO_PATTERN : SUBSET_NONZERO_PATTERN;
618 
619             if (!shell->right_work) PetscCall(MatCreateVecs(A, &shell->right_work, NULL));
620             if (shell->dshift) {
621               PetscCall(VecCopy(shell->dshift, shell->right_work));
622               PetscCall(VecShift(shell->right_work, shell->vshift));
623               PetscCall(VecPointwiseMult(shell->right_work, shell->right_work, shell->right));
624             } else {
625               PetscCall(VecSet(shell->right_work, shell->vshift));
626             }
627             PetscCall(MatDiagonalScale(mdata->B, shell->right_work, NULL));
628             PetscCall(MatAXPY(D, 1.0, mdata->B, str));
629           }
630         }
631         break;
632       case MATPRODUCT_PtAP: /* s B^t L A R B + v B^t L R B + B^t L D R B */
633       case MATPRODUCT_RARt: /* s B L A R B^t + v B L R B^t + B L D R B^t */
634         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,
635                    ((PetscObject)B)->type_name);
636         break;
637       default:
638         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);
639       }
640       if (shell->axpy && shell->axpy_vscale != zero) {
641         Mat              X;
642         PetscObjectState axpy_state;
643         MatStructure     str = DIFFERENT_NONZERO_PATTERN; /* not sure it is safe to ever use SUBSET_NONZERO_PATTERN */
644 
645         PetscCall(MatShellGetContext(shell->axpy, &X));
646         PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
647         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,...)");
648         if (!mdata->axpy) {
649           str = DIFFERENT_NONZERO_PATTERN;
650           PetscCall(MatProductCreate(shell->axpy, B, NULL, &mdata->axpy));
651           PetscCall(MatProductSetType(mdata->axpy, product->type));
652           PetscCall(MatProductSetFromOptions(mdata->axpy));
653           PetscCall(MatProductSymbolic(mdata->axpy));
654         } else { /* May be that shell->axpy has changed */
655           PetscBool flg;
656 
657           PetscCall(MatProductReplaceMats(shell->axpy, B, NULL, mdata->axpy));
658           PetscCall(MatHasOperation(mdata->axpy, MATOP_PRODUCTSYMBOLIC, &flg));
659           if (!flg) {
660             str = DIFFERENT_NONZERO_PATTERN;
661             PetscCall(MatProductSetFromOptions(mdata->axpy));
662             PetscCall(MatProductSymbolic(mdata->axpy));
663           }
664         }
665         PetscCall(MatProductNumeric(mdata->axpy));
666         PetscCall(MatAXPY(D, shell->axpy_vscale, mdata->axpy, str));
667       }
668     }
669   } else SETERRQ(PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "Missing numeric operation");
670   PetscFunctionReturn(PETSC_SUCCESS);
671 }
672 
673 static PetscErrorCode MatProductSymbolic_Shell_X(Mat D)
674 {
675   Mat_Product            *product;
676   Mat                     A, B;
677   MatShellMatFunctionList matmat;
678   Mat_Shell              *shell;
679   PetscBool               flg = PETSC_FALSE;
680   char                    composedname[256];
681   MatMatDataShell        *mdata;
682 
683   PetscFunctionBegin;
684   MatCheckProduct(D, 1);
685   product = D->product;
686   PetscCheck(!product->data, PetscObjectComm((PetscObject)D), PETSC_ERR_PLIB, "Product data not empty");
687   A      = product->A;
688   B      = product->B;
689   shell  = (Mat_Shell *)A->data;
690   matmat = shell->matmat;
691   PetscCall(PetscSNPrintf(composedname, sizeof(composedname), "MatProductSetFromOptions_%s_%s_C", ((PetscObject)A)->type_name, ((PetscObject)B)->type_name));
692   while (matmat) {
693     PetscCall(PetscStrcmp(composedname, matmat->composedname, &flg));
694     flg = (PetscBool)(flg && (matmat->ptype == product->type));
695     if (flg) break;
696     matmat = matmat->next;
697   }
698   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Composedname \"%s\" for product type %s not found", composedname, MatProductTypes[product->type]);
699   switch (product->type) {
700   case MATPRODUCT_AB:
701     PetscCall(MatSetSizes(D, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
702     break;
703   case MATPRODUCT_AtB:
704     PetscCall(MatSetSizes(D, A->cmap->n, B->cmap->n, A->cmap->N, B->cmap->N));
705     break;
706   case MATPRODUCT_ABt:
707     PetscCall(MatSetSizes(D, A->rmap->n, B->rmap->n, A->rmap->N, B->rmap->N));
708     break;
709   case MATPRODUCT_RARt:
710     PetscCall(MatSetSizes(D, B->rmap->n, B->rmap->n, B->rmap->N, B->rmap->N));
711     break;
712   case MATPRODUCT_PtAP:
713     PetscCall(MatSetSizes(D, B->cmap->n, B->cmap->n, B->cmap->N, B->cmap->N));
714     break;
715   default:
716     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);
717   }
718   /* respect users who passed in a matrix for which resultname is the base type */
719   if (matmat->resultname) {
720     PetscCall(PetscObjectBaseTypeCompare((PetscObject)D, matmat->resultname, &flg));
721     if (!flg) PetscCall(MatSetType(D, matmat->resultname));
722   }
723   /* If matrix type was not set or different, we need to reset this pointers */
724   D->ops->productsymbolic = MatProductSymbolic_Shell_X;
725   D->ops->productnumeric  = MatProductNumeric_Shell_X;
726   /* attach product data */
727   PetscCall(PetscNew(&mdata));
728   mdata->numeric = matmat->numeric;
729   mdata->destroy = matmat->destroy;
730   if (matmat->symbolic) {
731     PetscCall((*matmat->symbolic)(A, B, D, &mdata->userdata));
732   } else { /* call general setup if symbolic operation not provided */
733     PetscCall(MatSetUp(D));
734   }
735   PetscCheck(D->product, PetscObjectComm((PetscObject)D), PETSC_ERR_COR, "Product disappeared after user symbolic phase");
736   PetscCheck(!D->product->data, PetscObjectComm((PetscObject)D), PETSC_ERR_COR, "Product data not empty after user symbolic phase");
737   D->product->data    = mdata;
738   D->product->destroy = DestroyMatMatDataShell;
739   /* Be sure to reset these pointers if the user did something unexpected */
740   D->ops->productsymbolic = MatProductSymbolic_Shell_X;
741   D->ops->productnumeric  = MatProductNumeric_Shell_X;
742   PetscFunctionReturn(PETSC_SUCCESS);
743 }
744 
745 static PetscErrorCode MatProductSetFromOptions_Shell_X(Mat D)
746 {
747   Mat_Product            *product;
748   Mat                     A, B;
749   MatShellMatFunctionList matmat;
750   Mat_Shell              *shell;
751   PetscBool               flg;
752   char                    composedname[256];
753 
754   PetscFunctionBegin;
755   MatCheckProduct(D, 1);
756   product = D->product;
757   A       = product->A;
758   B       = product->B;
759   PetscCall(MatIsShell(A, &flg));
760   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);
761   shell  = (Mat_Shell *)A->data;
762   matmat = shell->matmat;
763   PetscCall(PetscSNPrintf(composedname, sizeof(composedname), "MatProductSetFromOptions_%s_%s_C", ((PetscObject)A)->type_name, ((PetscObject)B)->type_name));
764   while (matmat) {
765     PetscCall(PetscStrcmp(composedname, matmat->composedname, &flg));
766     flg = (PetscBool)(flg && (matmat->ptype == product->type));
767     if (flg) break;
768     matmat = matmat->next;
769   }
770   if (flg) {
771     D->ops->productsymbolic = MatProductSymbolic_Shell_X;
772   } else PetscCall(PetscInfo(D, "  symbolic product %s not registered for product type %s\n", composedname, MatProductTypes[product->type]));
773   PetscFunctionReturn(PETSC_SUCCESS);
774 }
775 
776 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)
777 {
778   PetscBool               flg;
779   Mat_Shell              *shell;
780   MatShellMatFunctionList matmat;
781 
782   PetscFunctionBegin;
783   PetscCheck(numeric, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing numeric routine");
784   PetscCheck(composedname, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing composed name");
785 
786   /* add product callback */
787   shell  = (Mat_Shell *)A->data;
788   matmat = shell->matmat;
789   if (!matmat) {
790     PetscCall(PetscNew(&shell->matmat));
791     matmat = shell->matmat;
792   } else {
793     MatShellMatFunctionList entry = matmat;
794     while (entry) {
795       PetscCall(PetscStrcmp(composedname, entry->composedname, &flg));
796       flg    = (PetscBool)(flg && (entry->ptype == ptype));
797       matmat = entry;
798       if (flg) goto set;
799       entry = entry->next;
800     }
801     PetscCall(PetscNew(&matmat->next));
802     matmat = matmat->next;
803   }
804 
805 set:
806   matmat->symbolic = symbolic;
807   matmat->numeric  = numeric;
808   matmat->destroy  = destroy;
809   matmat->ptype    = ptype;
810   PetscCall(PetscFree(matmat->composedname));
811   PetscCall(PetscFree(matmat->resultname));
812   PetscCall(PetscStrallocpy(composedname, &matmat->composedname));
813   PetscCall(PetscStrallocpy(resultname, &matmat->resultname));
814   PetscCall(PetscInfo(A, "Composing %s for product type %s with result %s\n", matmat->composedname, MatProductTypes[matmat->ptype], matmat->resultname ? matmat->resultname : "not specified"));
815   PetscCall(PetscObjectComposeFunction((PetscObject)A, matmat->composedname, MatProductSetFromOptions_Shell_X));
816   PetscFunctionReturn(PETSC_SUCCESS);
817 }
818 
819 /*@C
820   MatShellSetMatProductOperation - Allows user to set a matrix matrix operation for a `MATSHELL` shell matrix.
821 
822   Logically Collective; No Fortran Support
823 
824   Input Parameters:
825 + A        - the `MATSHELL` shell matrix
826 . ptype    - the product type
827 . symbolic - the function for the symbolic phase (can be `NULL`)
828 . numeric  - the function for the numerical phase
829 . destroy  - the function for the destruction of the needed data generated during the symbolic phase (can be `NULL`)
830 . Btype    - the matrix type for the matrix to be multiplied against
831 - Ctype    - the matrix type for the result (can be `NULL`)
832 
833   Level: advanced
834 
835   Example Usage:
836 .vb
837   extern PetscErrorCode usersymbolic(Mat, Mat, Mat, void**);
838   extern PetscErrorCode usernumeric(Mat, Mat, Mat, void*);
839   extern PetscErrorCode userdestroy(void*);
840 
841   MatCreateShell(comm, m, n, M, N, ctx, &A);
842   MatShellSetMatProductOperation(
843     A, MATPRODUCT_AB, usersymbolic, usernumeric, userdestroy,MATSEQAIJ, MATDENSE
844   );
845   // create B of type SEQAIJ etc..
846   MatProductCreate(A, B, PETSC_NULLPTR, &C);
847   MatProductSetType(C, MATPRODUCT_AB);
848   MatProductSetFromOptions(C);
849   MatProductSymbolic(C); // actually runs the user defined symbolic operation
850   MatProductNumeric(C); // actually runs the user defined numeric operation
851   // use C = A * B
852 .ve
853 
854   Notes:
855   `MATPRODUCT_ABC` is not supported yet.
856 
857   If the symbolic phase is not specified, `MatSetUp()` is called on the result matrix that must have its type set if Ctype is `NULL`.
858 
859   Any additional data needed by the matrix product needs to be returned during the symbolic phase and destroyed with the destroy callback.
860   PETSc will take care of calling the user-defined callbacks.
861   It is allowed to specify the same callbacks for different Btype matrix types.
862   The couple (Btype,ptype) uniquely identifies the operation, the last specified callbacks takes precedence.
863 
864 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatSetOperation()`, `MatProductType`, `MatType`, `MatSetUp()`
865 @*/
866 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)
867 {
868   PetscFunctionBegin;
869   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
870   PetscValidLogicalCollectiveEnum(A, ptype, 2);
871   PetscCheck(ptype != MATPRODUCT_ABC, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for product type %s", MatProductTypes[ptype]);
872   PetscCheck(numeric, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "Missing numeric routine, argument 4");
873   PetscAssertPointer(Btype, 6);
874   if (Ctype) PetscAssertPointer(Ctype, 7);
875   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));
876   PetscFunctionReturn(PETSC_SUCCESS);
877 }
878 
879 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)
880 {
881   PetscBool   flg;
882   char        composedname[256];
883   MatRootName Bnames = MatRootNameList, Cnames = MatRootNameList;
884   PetscMPIInt size;
885 
886   PetscFunctionBegin;
887   PetscValidType(A, 1);
888   while (Bnames) { /* user passed in the root name */
889     PetscCall(PetscStrcmp(Btype, Bnames->rname, &flg));
890     if (flg) break;
891     Bnames = Bnames->next;
892   }
893   while (Cnames) { /* user passed in the root name */
894     PetscCall(PetscStrcmp(Ctype, Cnames->rname, &flg));
895     if (flg) break;
896     Cnames = Cnames->next;
897   }
898   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
899   Btype = Bnames ? (size > 1 ? Bnames->mname : Bnames->sname) : Btype;
900   Ctype = Cnames ? (size > 1 ? Cnames->mname : Cnames->sname) : Ctype;
901   PetscCall(PetscSNPrintf(composedname, sizeof(composedname), "MatProductSetFromOptions_%s_%s_C", ((PetscObject)A)->type_name, Btype));
902   PetscCall(MatShellSetMatProductOperation_Private(A, ptype, symbolic, numeric, destroy, composedname, Ctype));
903   PetscFunctionReturn(PETSC_SUCCESS);
904 }
905 
906 static PetscErrorCode MatCopy_Shell(Mat A, Mat B, MatStructure str)
907 {
908   Mat_Shell              *shellA = (Mat_Shell *)A->data, *shellB = (Mat_Shell *)B->data;
909   PetscBool               matflg;
910   MatShellMatFunctionList matmatA;
911 
912   PetscFunctionBegin;
913   PetscCall(MatIsShell(B, &matflg));
914   PetscCheck(matflg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Matrix %s not derived from MATSHELL", ((PetscObject)B)->type_name);
915 
916   B->ops[0]      = A->ops[0];
917   shellB->ops[0] = shellA->ops[0];
918 
919   if (shellA->ops->copy) PetscCall((*shellA->ops->copy)(A, B, str));
920   shellB->vscale = shellA->vscale;
921   shellB->vshift = shellA->vshift;
922   if (shellA->dshift) {
923     if (!shellB->dshift) PetscCall(VecDuplicate(shellA->dshift, &shellB->dshift));
924     PetscCall(VecCopy(shellA->dshift, shellB->dshift));
925   } else {
926     PetscCall(VecDestroy(&shellB->dshift));
927   }
928   if (shellA->left) {
929     if (!shellB->left) PetscCall(VecDuplicate(shellA->left, &shellB->left));
930     PetscCall(VecCopy(shellA->left, shellB->left));
931   } else {
932     PetscCall(VecDestroy(&shellB->left));
933   }
934   if (shellA->right) {
935     if (!shellB->right) PetscCall(VecDuplicate(shellA->right, &shellB->right));
936     PetscCall(VecCopy(shellA->right, shellB->right));
937   } else {
938     PetscCall(VecDestroy(&shellB->right));
939   }
940   PetscCall(MatDestroy(&shellB->axpy));
941   shellB->axpy_vscale = 0.0;
942   shellB->axpy_state  = 0;
943   if (shellA->axpy) {
944     PetscCall(PetscObjectReference((PetscObject)shellA->axpy));
945     shellB->axpy        = shellA->axpy;
946     shellB->axpy_vscale = shellA->axpy_vscale;
947     shellB->axpy_state  = shellA->axpy_state;
948   }
949   if (shellA->zrows) {
950     PetscCall(ISDuplicate(shellA->zrows, &shellB->zrows));
951     if (shellA->zcols) PetscCall(ISDuplicate(shellA->zcols, &shellB->zcols));
952     PetscCall(VecDuplicate(shellA->zvals, &shellB->zvals));
953     PetscCall(VecCopy(shellA->zvals, shellB->zvals));
954     PetscCall(VecDuplicate(shellA->zvals_w, &shellB->zvals_w));
955     PetscCall(PetscObjectReference((PetscObject)shellA->zvals_sct_r));
956     PetscCall(PetscObjectReference((PetscObject)shellA->zvals_sct_c));
957     shellB->zvals_sct_r = shellA->zvals_sct_r;
958     shellB->zvals_sct_c = shellA->zvals_sct_c;
959   }
960 
961   matmatA = shellA->matmat;
962   if (matmatA) {
963     while (matmatA->next) {
964       PetscCall(MatShellSetMatProductOperation_Private(B, matmatA->ptype, matmatA->symbolic, matmatA->numeric, matmatA->destroy, matmatA->composedname, matmatA->resultname));
965       matmatA = matmatA->next;
966     }
967   }
968   PetscFunctionReturn(PETSC_SUCCESS);
969 }
970 
971 static PetscErrorCode MatDuplicate_Shell(Mat mat, MatDuplicateOption op, Mat *M)
972 {
973   PetscFunctionBegin;
974   PetscCall(MatCreateShell(PetscObjectComm((PetscObject)mat), mat->rmap->n, mat->cmap->n, mat->rmap->N, mat->cmap->N, NULL, M));
975   ((Mat_Shell *)(*M)->data)->ctxcontainer = ((Mat_Shell *)mat->data)->ctxcontainer;
976   PetscCall(PetscObjectCompose((PetscObject)*M, "MatShell ctx", (PetscObject)((Mat_Shell *)(*M)->data)->ctxcontainer));
977   PetscCall(PetscObjectChangeTypeName((PetscObject)*M, ((PetscObject)mat)->type_name));
978   if (op == MAT_COPY_VALUES) PetscCall(MatCopy(mat, *M, SAME_NONZERO_PATTERN));
979   PetscCall(PetscObjectCopyFortranFunctionPointers((PetscObject)mat, (PetscObject)*M));
980   PetscFunctionReturn(PETSC_SUCCESS);
981 }
982 
983 static PetscErrorCode MatMult_Shell(Mat A, Vec x, Vec y)
984 {
985   Mat_Shell       *shell = (Mat_Shell *)A->data;
986   Vec              xx;
987   PetscObjectState instate, outstate;
988 
989   PetscFunctionBegin;
990   PetscCall(MatShellPreZeroRight(A, x, &xx));
991   PetscCall(MatShellPreScaleRight(A, xx, &xx));
992   PetscCall(PetscObjectStateGet((PetscObject)y, &instate));
993   PetscCall((*shell->ops->mult)(A, xx, y));
994   PetscCall(PetscObjectStateGet((PetscObject)y, &outstate));
995   if (instate == outstate) {
996     /* increase the state of the output vector since the user did not update its state themself as should have been done */
997     PetscCall(PetscObjectStateIncrease((PetscObject)y));
998   }
999   PetscCall(MatShellShiftAndScale(A, xx, y, PETSC_FALSE));
1000   PetscCall(MatShellPostScaleLeft(A, y));
1001   PetscCall(MatShellPostZeroLeft(A, y));
1002 
1003   if (shell->axpy) {
1004     Mat              X;
1005     PetscObjectState axpy_state;
1006 
1007     PetscCall(MatShellGetContext(shell->axpy, &X));
1008     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1009     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,...)");
1010 
1011     PetscCall(MatCreateVecs(shell->axpy, shell->axpy_right ? NULL : &shell->axpy_right, shell->axpy_left ? NULL : &shell->axpy_left));
1012     PetscCall(VecCopy(x, shell->axpy_right));
1013     PetscCall(MatMult(shell->axpy, shell->axpy_right, shell->axpy_left));
1014     PetscCall(VecAXPY(y, shell->axpy_vscale, shell->axpy_left));
1015   }
1016   PetscFunctionReturn(PETSC_SUCCESS);
1017 }
1018 
1019 static PetscErrorCode MatMultAdd_Shell(Mat A, Vec x, Vec y, Vec z)
1020 {
1021   Mat_Shell *shell = (Mat_Shell *)A->data;
1022 
1023   PetscFunctionBegin;
1024   if (y == z) {
1025     if (!shell->right_add_work) PetscCall(VecDuplicate(z, &shell->right_add_work));
1026     PetscCall(MatMult(A, x, shell->right_add_work));
1027     PetscCall(VecAXPY(z, 1.0, shell->right_add_work));
1028   } else {
1029     PetscCall(MatMult(A, x, z));
1030     PetscCall(VecAXPY(z, 1.0, y));
1031   }
1032   PetscFunctionReturn(PETSC_SUCCESS);
1033 }
1034 
1035 static PetscErrorCode MatMultTranspose_Shell(Mat A, Vec x, Vec y)
1036 {
1037   Mat_Shell       *shell = (Mat_Shell *)A->data;
1038   Vec              xx;
1039   PetscObjectState instate, outstate;
1040 
1041   PetscFunctionBegin;
1042   PetscCall(MatShellPreZeroLeft(A, x, &xx));
1043   PetscCall(MatShellPreScaleLeft(A, xx, &xx, PETSC_FALSE));
1044   PetscCall(PetscObjectStateGet((PetscObject)y, &instate));
1045   PetscCall((*shell->ops->multtranspose)(A, xx, y));
1046   PetscCall(PetscObjectStateGet((PetscObject)y, &outstate));
1047   if (instate == outstate) {
1048     /* increase the state of the output vector since the user did not update its state themself as should have been done */
1049     PetscCall(PetscObjectStateIncrease((PetscObject)y));
1050   }
1051   PetscCall(MatShellShiftAndScale(A, xx, y, PETSC_FALSE));
1052   PetscCall(MatShellPostScaleRight(A, y, PETSC_FALSE));
1053   PetscCall(MatShellPostZeroRight(A, y));
1054 
1055   if (shell->axpy) {
1056     Mat              X;
1057     PetscObjectState axpy_state;
1058 
1059     PetscCall(MatShellGetContext(shell->axpy, &X));
1060     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1061     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,...)");
1062     PetscCall(MatCreateVecs(shell->axpy, shell->axpy_right ? NULL : &shell->axpy_right, shell->axpy_left ? NULL : &shell->axpy_left));
1063     PetscCall(VecCopy(x, shell->axpy_left));
1064     PetscCall(MatMultTranspose(shell->axpy, shell->axpy_left, shell->axpy_right));
1065     PetscCall(VecAXPY(y, shell->axpy_vscale, shell->axpy_right));
1066   }
1067   PetscFunctionReturn(PETSC_SUCCESS);
1068 }
1069 
1070 static PetscErrorCode MatMultHermitianTranspose_Shell(Mat A, Vec x, Vec y)
1071 {
1072   Mat_Shell       *shell = (Mat_Shell *)A->data;
1073   Vec              xx;
1074   PetscObjectState instate, outstate;
1075 
1076   PetscFunctionBegin;
1077   PetscCall(MatShellPreZeroLeft(A, x, &xx));
1078   PetscCall(MatShellPreScaleLeft(A, xx, &xx, PETSC_TRUE));
1079   PetscCall(PetscObjectStateGet((PetscObject)y, &instate));
1080   PetscCall((*shell->ops->multhermitiantranspose)(A, xx, y));
1081   PetscCall(PetscObjectStateGet((PetscObject)y, &outstate));
1082   if (instate == outstate) {
1083     /* increase the state of the output vector since the user did not update its state themself as should have been done */
1084     PetscCall(PetscObjectStateIncrease((PetscObject)y));
1085   }
1086   PetscCall(MatShellShiftAndScale(A, xx, y, PETSC_TRUE));
1087   PetscCall(MatShellPostScaleRight(A, y, PETSC_TRUE));
1088   PetscCall(MatShellPostZeroRight(A, y));
1089 
1090   if (shell->axpy) {
1091     Mat              X;
1092     PetscObjectState axpy_state;
1093 
1094     PetscCall(MatShellGetContext(shell->axpy, &X));
1095     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1096     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,...)");
1097     PetscCall(MatCreateVecs(shell->axpy, shell->axpy_right ? NULL : &shell->axpy_right, shell->axpy_left ? NULL : &shell->axpy_left));
1098     PetscCall(VecCopy(x, shell->axpy_left));
1099     PetscCall(MatMultHermitianTranspose(shell->axpy, shell->axpy_left, shell->axpy_right));
1100     PetscCall(VecAXPY(y, PetscConj(shell->axpy_vscale), shell->axpy_right));
1101   }
1102   PetscFunctionReturn(PETSC_SUCCESS);
1103 }
1104 
1105 static PetscErrorCode MatMultTransposeAdd_Shell(Mat A, Vec x, Vec y, Vec z)
1106 {
1107   Mat_Shell *shell = (Mat_Shell *)A->data;
1108 
1109   PetscFunctionBegin;
1110   if (y == z) {
1111     if (!shell->left_add_work) PetscCall(VecDuplicate(z, &shell->left_add_work));
1112     PetscCall(MatMultTranspose(A, x, shell->left_add_work));
1113     PetscCall(VecAXPY(z, 1.0, shell->left_add_work));
1114   } else {
1115     PetscCall(MatMultTranspose(A, x, z));
1116     PetscCall(VecAXPY(z, 1.0, y));
1117   }
1118   PetscFunctionReturn(PETSC_SUCCESS);
1119 }
1120 
1121 static PetscErrorCode MatMultHermitianTransposeAdd_Shell(Mat A, Vec x, Vec y, Vec z)
1122 {
1123   Mat_Shell *shell = (Mat_Shell *)A->data;
1124 
1125   PetscFunctionBegin;
1126   if (y == z) {
1127     if (!shell->left_add_work) PetscCall(VecDuplicate(z, &shell->left_add_work));
1128     PetscCall(MatMultHermitianTranspose(A, x, shell->left_add_work));
1129     PetscCall(VecAXPY(z, 1.0, shell->left_add_work));
1130   } else {
1131     PetscCall(MatMultHermitianTranspose(A, x, z));
1132     PetscCall(VecAXPY(z, 1.0, y));
1133   }
1134   PetscFunctionReturn(PETSC_SUCCESS);
1135 }
1136 
1137 /*
1138           diag(left)(vscale*A + diag(dshift) + vshift I)diag(right)
1139 */
1140 static PetscErrorCode MatGetDiagonal_Shell(Mat A, Vec v)
1141 {
1142   Mat_Shell *shell = (Mat_Shell *)A->data;
1143 
1144   PetscFunctionBegin;
1145   if (shell->ops->getdiagonal) {
1146     PetscCall((*shell->ops->getdiagonal)(A, v));
1147   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Must provide shell matrix with routine to return diagonal using\nMatShellSetOperation(S,MATOP_GET_DIAGONAL,...)");
1148   PetscCall(VecScale(v, shell->vscale));
1149   if (shell->dshift) PetscCall(VecAXPY(v, 1.0, shell->dshift));
1150   PetscCall(VecShift(v, shell->vshift));
1151   if (shell->left) PetscCall(VecPointwiseMult(v, v, shell->left));
1152   if (shell->right) PetscCall(VecPointwiseMult(v, v, shell->right));
1153   if (shell->zrows) {
1154     PetscCall(VecScatterBegin(shell->zvals_sct_r, shell->zvals, v, INSERT_VALUES, SCATTER_REVERSE));
1155     PetscCall(VecScatterEnd(shell->zvals_sct_r, shell->zvals, v, INSERT_VALUES, SCATTER_REVERSE));
1156   }
1157   if (shell->axpy) {
1158     Mat              X;
1159     PetscObjectState axpy_state;
1160 
1161     PetscCall(MatShellGetContext(shell->axpy, &X));
1162     PetscCall(PetscObjectStateGet((PetscObject)X, &axpy_state));
1163     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,...)");
1164     PetscCall(MatCreateVecs(shell->axpy, NULL, shell->axpy_left ? NULL : &shell->axpy_left));
1165     PetscCall(MatGetDiagonal(shell->axpy, shell->axpy_left));
1166     PetscCall(VecAXPY(v, shell->axpy_vscale, shell->axpy_left));
1167   }
1168   PetscFunctionReturn(PETSC_SUCCESS);
1169 }
1170 
1171 static PetscErrorCode MatShift_Shell(Mat Y, PetscScalar a)
1172 {
1173   Mat_Shell *shell = (Mat_Shell *)Y->data;
1174   PetscBool  flg;
1175 
1176   PetscFunctionBegin;
1177   PetscCall(MatHasCongruentLayouts(Y, &flg));
1178   PetscCheck(flg, PetscObjectComm((PetscObject)Y), PETSC_ERR_SUP, "Cannot shift shell matrix if it is not congruent");
1179   if (shell->left || shell->right) {
1180     if (!shell->dshift) {
1181       PetscCall(VecDuplicate(shell->left ? shell->left : shell->right, &shell->dshift));
1182       PetscCall(VecSet(shell->dshift, a));
1183     } else {
1184       if (shell->left) PetscCall(VecPointwiseMult(shell->dshift, shell->dshift, shell->left));
1185       if (shell->right) PetscCall(VecPointwiseMult(shell->dshift, shell->dshift, shell->right));
1186       PetscCall(VecShift(shell->dshift, a));
1187     }
1188     if (shell->left) PetscCall(VecPointwiseDivide(shell->dshift, shell->dshift, shell->left));
1189     if (shell->right) PetscCall(VecPointwiseDivide(shell->dshift, shell->dshift, shell->right));
1190   } else shell->vshift += a;
1191   if (shell->zrows) PetscCall(VecShift(shell->zvals, a));
1192   PetscFunctionReturn(PETSC_SUCCESS);
1193 }
1194 
1195 static PetscErrorCode MatDiagonalSet_Shell_Private(Mat A, Vec D, PetscScalar s)
1196 {
1197   Mat_Shell *shell = (Mat_Shell *)A->data;
1198 
1199   PetscFunctionBegin;
1200   if (!shell->dshift) PetscCall(VecDuplicate(D, &shell->dshift));
1201   if (shell->left || shell->right) {
1202     if (!shell->right_work) PetscCall(VecDuplicate(shell->left ? shell->left : shell->right, &shell->right_work));
1203     if (shell->left && shell->right) {
1204       PetscCall(VecPointwiseDivide(shell->right_work, D, shell->left));
1205       PetscCall(VecPointwiseDivide(shell->right_work, shell->right_work, shell->right));
1206     } else if (shell->left) {
1207       PetscCall(VecPointwiseDivide(shell->right_work, D, shell->left));
1208     } else {
1209       PetscCall(VecPointwiseDivide(shell->right_work, D, shell->right));
1210     }
1211     PetscCall(VecAXPY(shell->dshift, s, shell->right_work));
1212   } else {
1213     PetscCall(VecAXPY(shell->dshift, s, D));
1214   }
1215   PetscFunctionReturn(PETSC_SUCCESS);
1216 }
1217 
1218 static PetscErrorCode MatDiagonalSet_Shell(Mat A, Vec D, InsertMode ins)
1219 {
1220   Mat_Shell *shell = (Mat_Shell *)A->data;
1221   Vec        d;
1222   PetscBool  flg;
1223 
1224   PetscFunctionBegin;
1225   PetscCall(MatHasCongruentLayouts(A, &flg));
1226   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot diagonal set or shift shell matrix if it is not congruent");
1227   if (ins == INSERT_VALUES) {
1228     PetscCall(VecDuplicate(D, &d));
1229     PetscCall(MatGetDiagonal(A, d));
1230     PetscCall(MatDiagonalSet_Shell_Private(A, d, -1.));
1231     PetscCall(MatDiagonalSet_Shell_Private(A, D, 1.));
1232     PetscCall(VecDestroy(&d));
1233     if (shell->zrows) PetscCall(VecCopy(D, shell->zvals));
1234   } else {
1235     PetscCall(MatDiagonalSet_Shell_Private(A, D, 1.));
1236     if (shell->zrows) PetscCall(VecAXPY(shell->zvals, 1.0, D));
1237   }
1238   PetscFunctionReturn(PETSC_SUCCESS);
1239 }
1240 
1241 static PetscErrorCode MatScale_Shell(Mat Y, PetscScalar a)
1242 {
1243   Mat_Shell *shell = (Mat_Shell *)Y->data;
1244 
1245   PetscFunctionBegin;
1246   shell->vscale *= a;
1247   shell->vshift *= a;
1248   if (shell->dshift) PetscCall(VecScale(shell->dshift, a));
1249   shell->axpy_vscale *= a;
1250   if (shell->zrows) PetscCall(VecScale(shell->zvals, a));
1251   PetscFunctionReturn(PETSC_SUCCESS);
1252 }
1253 
1254 static PetscErrorCode MatDiagonalScale_Shell(Mat Y, Vec left, Vec right)
1255 {
1256   Mat_Shell *shell = (Mat_Shell *)Y->data;
1257 
1258   PetscFunctionBegin;
1259   if (left) {
1260     if (!shell->left) {
1261       PetscCall(VecDuplicate(left, &shell->left));
1262       PetscCall(VecCopy(left, shell->left));
1263     } else {
1264       PetscCall(VecPointwiseMult(shell->left, shell->left, left));
1265     }
1266     if (shell->zrows) PetscCall(VecPointwiseMult(shell->zvals, shell->zvals, left));
1267   }
1268   if (right) {
1269     if (!shell->right) {
1270       PetscCall(VecDuplicate(right, &shell->right));
1271       PetscCall(VecCopy(right, shell->right));
1272     } else {
1273       PetscCall(VecPointwiseMult(shell->right, shell->right, right));
1274     }
1275     if (shell->zrows) {
1276       if (!shell->left_work) PetscCall(MatCreateVecs(Y, NULL, &shell->left_work));
1277       PetscCall(VecSet(shell->zvals_w, 1.0));
1278       PetscCall(VecScatterBegin(shell->zvals_sct_c, right, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
1279       PetscCall(VecScatterEnd(shell->zvals_sct_c, right, shell->zvals_w, INSERT_VALUES, SCATTER_FORWARD));
1280       PetscCall(VecPointwiseMult(shell->zvals, shell->zvals, shell->zvals_w));
1281     }
1282   }
1283   if (shell->axpy) PetscCall(MatDiagonalScale(shell->axpy, left, right));
1284   PetscFunctionReturn(PETSC_SUCCESS);
1285 }
1286 
1287 PETSC_INTERN PetscErrorCode MatAssemblyEnd_Shell(Mat Y, MatAssemblyType t)
1288 {
1289   Mat_Shell *shell = (Mat_Shell *)Y->data;
1290 
1291   PetscFunctionBegin;
1292   if (t == MAT_FINAL_ASSEMBLY) {
1293     shell->vshift      = 0.0;
1294     shell->vscale      = 1.0;
1295     shell->axpy_vscale = 0.0;
1296     shell->axpy_state  = 0;
1297     PetscCall(VecDestroy(&shell->dshift));
1298     PetscCall(VecDestroy(&shell->left));
1299     PetscCall(VecDestroy(&shell->right));
1300     PetscCall(MatDestroy(&shell->axpy));
1301     PetscCall(VecDestroy(&shell->axpy_left));
1302     PetscCall(VecDestroy(&shell->axpy_right));
1303     PetscCall(VecScatterDestroy(&shell->zvals_sct_c));
1304     PetscCall(VecScatterDestroy(&shell->zvals_sct_r));
1305     PetscCall(ISDestroy(&shell->zrows));
1306     PetscCall(ISDestroy(&shell->zcols));
1307   }
1308   PetscFunctionReturn(PETSC_SUCCESS);
1309 }
1310 
1311 static PetscErrorCode MatMissingDiagonal_Shell(Mat A, PetscBool *missing, PetscInt *d)
1312 {
1313   PetscFunctionBegin;
1314   *missing = PETSC_FALSE;
1315   PetscFunctionReturn(PETSC_SUCCESS);
1316 }
1317 
1318 static PetscErrorCode MatAXPY_Shell(Mat Y, PetscScalar a, Mat X, MatStructure str)
1319 {
1320   Mat_Shell *shell = (Mat_Shell *)Y->data;
1321 
1322   PetscFunctionBegin;
1323   if (X == Y) {
1324     PetscCall(MatScale(Y, 1.0 + a));
1325     PetscFunctionReturn(PETSC_SUCCESS);
1326   }
1327   if (!shell->axpy) {
1328     PetscCall(MatConvertFrom_Shell(X, MATSHELL, MAT_INITIAL_MATRIX, &shell->axpy));
1329     shell->axpy_vscale = a;
1330     PetscCall(PetscObjectStateGet((PetscObject)X, &shell->axpy_state));
1331   } else {
1332     PetscCall(MatAXPY(shell->axpy, a / shell->axpy_vscale, X, str));
1333   }
1334   PetscFunctionReturn(PETSC_SUCCESS);
1335 }
1336 
1337 static struct _MatOps MatOps_Values = {NULL,
1338                                        NULL,
1339                                        NULL,
1340                                        NULL,
1341                                        /* 4*/ MatMultAdd_Shell,
1342                                        NULL,
1343                                        MatMultTransposeAdd_Shell,
1344                                        NULL,
1345                                        NULL,
1346                                        NULL,
1347                                        /*10*/ NULL,
1348                                        NULL,
1349                                        NULL,
1350                                        NULL,
1351                                        NULL,
1352                                        /*15*/ NULL,
1353                                        NULL,
1354                                        NULL,
1355                                        MatDiagonalScale_Shell,
1356                                        NULL,
1357                                        /*20*/ NULL,
1358                                        MatAssemblyEnd_Shell,
1359                                        NULL,
1360                                        NULL,
1361                                        /*24*/ MatZeroRows_Shell,
1362                                        NULL,
1363                                        NULL,
1364                                        NULL,
1365                                        NULL,
1366                                        /*29*/ NULL,
1367                                        NULL,
1368                                        NULL,
1369                                        NULL,
1370                                        NULL,
1371                                        /*34*/ MatDuplicate_Shell,
1372                                        NULL,
1373                                        NULL,
1374                                        NULL,
1375                                        NULL,
1376                                        /*39*/ MatAXPY_Shell,
1377                                        NULL,
1378                                        NULL,
1379                                        NULL,
1380                                        MatCopy_Shell,
1381                                        /*44*/ NULL,
1382                                        MatScale_Shell,
1383                                        MatShift_Shell,
1384                                        MatDiagonalSet_Shell,
1385                                        MatZeroRowsColumns_Shell,
1386                                        /*49*/ NULL,
1387                                        NULL,
1388                                        NULL,
1389                                        NULL,
1390                                        NULL,
1391                                        /*54*/ NULL,
1392                                        NULL,
1393                                        NULL,
1394                                        NULL,
1395                                        NULL,
1396                                        /*59*/ NULL,
1397                                        MatDestroy_Shell,
1398                                        NULL,
1399                                        MatConvertFrom_Shell,
1400                                        NULL,
1401                                        /*64*/ NULL,
1402                                        NULL,
1403                                        NULL,
1404                                        NULL,
1405                                        NULL,
1406                                        /*69*/ NULL,
1407                                        NULL,
1408                                        MatConvert_Shell,
1409                                        NULL,
1410                                        NULL,
1411                                        /*74*/ NULL,
1412                                        NULL,
1413                                        NULL,
1414                                        NULL,
1415                                        NULL,
1416                                        /*79*/ NULL,
1417                                        NULL,
1418                                        NULL,
1419                                        NULL,
1420                                        NULL,
1421                                        /*84*/ NULL,
1422                                        NULL,
1423                                        NULL,
1424                                        NULL,
1425                                        NULL,
1426                                        /*89*/ NULL,
1427                                        NULL,
1428                                        NULL,
1429                                        NULL,
1430                                        NULL,
1431                                        /*94*/ NULL,
1432                                        NULL,
1433                                        NULL,
1434                                        NULL,
1435                                        NULL,
1436                                        /*99*/ NULL,
1437                                        NULL,
1438                                        NULL,
1439                                        NULL,
1440                                        NULL,
1441                                        /*104*/ NULL,
1442                                        NULL,
1443                                        NULL,
1444                                        NULL,
1445                                        NULL,
1446                                        /*109*/ NULL,
1447                                        NULL,
1448                                        NULL,
1449                                        NULL,
1450                                        MatMissingDiagonal_Shell,
1451                                        /*114*/ NULL,
1452                                        NULL,
1453                                        NULL,
1454                                        NULL,
1455                                        NULL,
1456                                        /*119*/ NULL,
1457                                        NULL,
1458                                        NULL,
1459                                        MatMultHermitianTransposeAdd_Shell,
1460                                        NULL,
1461                                        /*124*/ NULL,
1462                                        NULL,
1463                                        NULL,
1464                                        NULL,
1465                                        NULL,
1466                                        /*129*/ NULL,
1467                                        NULL,
1468                                        NULL,
1469                                        NULL,
1470                                        NULL,
1471                                        /*134*/ NULL,
1472                                        NULL,
1473                                        NULL,
1474                                        NULL,
1475                                        NULL,
1476                                        /*139*/ NULL,
1477                                        NULL,
1478                                        NULL,
1479                                        NULL,
1480                                        NULL,
1481                                        /*144*/ NULL,
1482                                        NULL,
1483                                        NULL,
1484                                        NULL,
1485                                        NULL,
1486                                        NULL,
1487                                        /*150*/ NULL,
1488                                        NULL,
1489                                        NULL};
1490 
1491 static PetscErrorCode MatShellSetContext_Shell(Mat mat, void *ctx)
1492 {
1493   Mat_Shell *shell = (Mat_Shell *)mat->data;
1494 
1495   PetscFunctionBegin;
1496   if (ctx) {
1497     PetscContainer ctxcontainer;
1498     PetscCall(PetscContainerCreate(PetscObjectComm((PetscObject)mat), &ctxcontainer));
1499     PetscCall(PetscContainerSetPointer(ctxcontainer, ctx));
1500     PetscCall(PetscObjectCompose((PetscObject)mat, "MatShell ctx", (PetscObject)ctxcontainer));
1501     shell->ctxcontainer = ctxcontainer;
1502     PetscCall(PetscContainerDestroy(&ctxcontainer));
1503   } else {
1504     PetscCall(PetscObjectCompose((PetscObject)mat, "MatShell ctx", NULL));
1505     shell->ctxcontainer = NULL;
1506   }
1507   PetscFunctionReturn(PETSC_SUCCESS);
1508 }
1509 
1510 static PetscErrorCode MatShellSetContextDestroy_Shell(Mat mat, PetscErrorCode (*f)(void *))
1511 {
1512   Mat_Shell *shell = (Mat_Shell *)mat->data;
1513 
1514   PetscFunctionBegin;
1515   if (shell->ctxcontainer) PetscCall(PetscContainerSetUserDestroy(shell->ctxcontainer, f));
1516   PetscFunctionReturn(PETSC_SUCCESS);
1517 }
1518 
1519 PetscErrorCode MatShellSetContext_Immutable(Mat mat, void *ctx)
1520 {
1521   PetscFunctionBegin;
1522   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);
1523   PetscFunctionReturn(PETSC_SUCCESS);
1524 }
1525 
1526 PetscErrorCode MatShellSetContextDestroy_Immutable(Mat mat, PetscErrorCode (*f)(void *))
1527 {
1528   PetscFunctionBegin;
1529   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);
1530   PetscFunctionReturn(PETSC_SUCCESS);
1531 }
1532 
1533 PetscErrorCode MatShellSetManageScalingShifts_Immutable(Mat mat)
1534 {
1535   PetscFunctionBegin;
1536   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);
1537   PetscFunctionReturn(PETSC_SUCCESS);
1538 }
1539 
1540 static PetscErrorCode MatShellSetVecType_Shell(Mat mat, VecType vtype)
1541 {
1542   PetscFunctionBegin;
1543   PetscCall(PetscFree(mat->defaultvectype));
1544   PetscCall(PetscStrallocpy(vtype, (char **)&mat->defaultvectype));
1545   PetscFunctionReturn(PETSC_SUCCESS);
1546 }
1547 
1548 static PetscErrorCode MatShellSetManageScalingShifts_Shell(Mat A)
1549 {
1550   Mat_Shell *shell = (Mat_Shell *)A->data;
1551 
1552   PetscFunctionBegin;
1553   shell->managescalingshifts = PETSC_FALSE;
1554   A->ops->diagonalset        = NULL;
1555   A->ops->diagonalscale      = NULL;
1556   A->ops->scale              = NULL;
1557   A->ops->shift              = NULL;
1558   A->ops->axpy               = NULL;
1559   PetscFunctionReturn(PETSC_SUCCESS);
1560 }
1561 
1562 static PetscErrorCode MatShellSetOperation_Shell(Mat mat, MatOperation op, void (*f)(void))
1563 {
1564   Mat_Shell *shell = (Mat_Shell *)mat->data;
1565 
1566   PetscFunctionBegin;
1567   switch (op) {
1568   case MATOP_DESTROY:
1569     shell->ops->destroy = (PetscErrorCode(*)(Mat))f;
1570     break;
1571   case MATOP_VIEW:
1572     if (!mat->ops->viewnative) mat->ops->viewnative = mat->ops->view;
1573     mat->ops->view = (PetscErrorCode(*)(Mat, PetscViewer))f;
1574     break;
1575   case MATOP_COPY:
1576     shell->ops->copy = (PetscErrorCode(*)(Mat, Mat, MatStructure))f;
1577     break;
1578   case MATOP_DIAGONAL_SET:
1579   case MATOP_DIAGONAL_SCALE:
1580   case MATOP_SHIFT:
1581   case MATOP_SCALE:
1582   case MATOP_AXPY:
1583   case MATOP_ZERO_ROWS:
1584   case MATOP_ZERO_ROWS_COLUMNS:
1585     PetscCheck(!shell->managescalingshifts, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MATSHELL is managing scalings and shifts, see MatShellSetManageScalingShifts()");
1586     (((void (**)(void))mat->ops)[op]) = f;
1587     break;
1588   case MATOP_GET_DIAGONAL:
1589     if (shell->managescalingshifts) {
1590       shell->ops->getdiagonal = (PetscErrorCode(*)(Mat, Vec))f;
1591       mat->ops->getdiagonal   = MatGetDiagonal_Shell;
1592     } else {
1593       shell->ops->getdiagonal = NULL;
1594       mat->ops->getdiagonal   = (PetscErrorCode(*)(Mat, Vec))f;
1595     }
1596     break;
1597   case MATOP_MULT:
1598     if (shell->managescalingshifts) {
1599       shell->ops->mult = (PetscErrorCode(*)(Mat, Vec, Vec))f;
1600       mat->ops->mult   = MatMult_Shell;
1601     } else {
1602       shell->ops->mult = NULL;
1603       mat->ops->mult   = (PetscErrorCode(*)(Mat, Vec, Vec))f;
1604     }
1605     break;
1606   case MATOP_MULT_TRANSPOSE:
1607     if (shell->managescalingshifts) {
1608       shell->ops->multtranspose = (PetscErrorCode(*)(Mat, Vec, Vec))f;
1609       mat->ops->multtranspose   = MatMultTranspose_Shell;
1610     } else {
1611       shell->ops->multtranspose = NULL;
1612       mat->ops->multtranspose   = (PetscErrorCode(*)(Mat, Vec, Vec))f;
1613     }
1614     break;
1615   case MATOP_MULT_HERMITIAN_TRANSPOSE:
1616     if (shell->managescalingshifts) {
1617       shell->ops->multhermitiantranspose = (PetscErrorCode(*)(Mat, Vec, Vec))f;
1618       mat->ops->multhermitiantranspose   = MatMultHermitianTranspose_Shell;
1619     } else {
1620       shell->ops->multhermitiantranspose = NULL;
1621       mat->ops->multhermitiantranspose   = (PetscErrorCode(*)(Mat, Vec, Vec))f;
1622     }
1623     break;
1624   default:
1625     (((void (**)(void))mat->ops)[op]) = f;
1626     break;
1627   }
1628   PetscFunctionReturn(PETSC_SUCCESS);
1629 }
1630 
1631 static PetscErrorCode MatShellGetOperation_Shell(Mat mat, MatOperation op, void (**f)(void))
1632 {
1633   Mat_Shell *shell = (Mat_Shell *)mat->data;
1634 
1635   PetscFunctionBegin;
1636   switch (op) {
1637   case MATOP_DESTROY:
1638     *f = (void (*)(void))shell->ops->destroy;
1639     break;
1640   case MATOP_VIEW:
1641     *f = (void (*)(void))mat->ops->view;
1642     break;
1643   case MATOP_COPY:
1644     *f = (void (*)(void))shell->ops->copy;
1645     break;
1646   case MATOP_DIAGONAL_SET:
1647   case MATOP_DIAGONAL_SCALE:
1648   case MATOP_SHIFT:
1649   case MATOP_SCALE:
1650   case MATOP_AXPY:
1651   case MATOP_ZERO_ROWS:
1652   case MATOP_ZERO_ROWS_COLUMNS:
1653     *f = (((void (**)(void))mat->ops)[op]);
1654     break;
1655   case MATOP_GET_DIAGONAL:
1656     if (shell->ops->getdiagonal) *f = (void (*)(void))shell->ops->getdiagonal;
1657     else *f = (((void (**)(void))mat->ops)[op]);
1658     break;
1659   case MATOP_MULT:
1660     if (shell->ops->mult) *f = (void (*)(void))shell->ops->mult;
1661     else *f = (((void (**)(void))mat->ops)[op]);
1662     break;
1663   case MATOP_MULT_TRANSPOSE:
1664     if (shell->ops->multtranspose) *f = (void (*)(void))shell->ops->multtranspose;
1665     else *f = (((void (**)(void))mat->ops)[op]);
1666     break;
1667   case MATOP_MULT_HERMITIAN_TRANSPOSE:
1668     if (shell->ops->multhermitiantranspose) *f = (void (*)(void))shell->ops->multhermitiantranspose;
1669     else *f = (((void (**)(void))mat->ops)[op]);
1670     break;
1671   default:
1672     *f = (((void (**)(void))mat->ops)[op]);
1673   }
1674   PetscFunctionReturn(PETSC_SUCCESS);
1675 }
1676 
1677 /*MC
1678    MATSHELL - MATSHELL = "shell" - A matrix type to be used to define your own matrix type -- perhaps matrix-free.
1679 
1680   Level: advanced
1681 
1682 .seealso: [](ch_matrices), `Mat`, `MatCreateShell()`
1683 M*/
1684 
1685 PETSC_EXTERN PetscErrorCode MatCreate_Shell(Mat A)
1686 {
1687   Mat_Shell *b;
1688 
1689   PetscFunctionBegin;
1690   PetscCall(PetscNew(&b));
1691   A->data   = (void *)b;
1692   A->ops[0] = MatOps_Values;
1693 
1694   b->ctxcontainer        = NULL;
1695   b->vshift              = 0.0;
1696   b->vscale              = 1.0;
1697   b->managescalingshifts = PETSC_TRUE;
1698   A->assembled           = PETSC_TRUE;
1699   A->preallocated        = PETSC_FALSE;
1700 
1701   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetContext_C", MatShellGetContext_Shell));
1702   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", MatShellSetContext_Shell));
1703   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContextDestroy_C", MatShellSetContextDestroy_Shell));
1704   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetVecType_C", MatShellSetVecType_Shell));
1705   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetManageScalingShifts_C", MatShellSetManageScalingShifts_Shell));
1706   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetOperation_C", MatShellSetOperation_Shell));
1707   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellGetOperation_C", MatShellGetOperation_Shell));
1708   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetMatProductOperation_C", MatShellSetMatProductOperation_Shell));
1709   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATSHELL));
1710   PetscFunctionReturn(PETSC_SUCCESS);
1711 }
1712 
1713 /*@C
1714   MatCreateShell - Creates a new matrix of `MatType` `MATSHELL` for use with a user-defined
1715   private data storage format.
1716 
1717   Collective
1718 
1719   Input Parameters:
1720 + comm - MPI communicator
1721 . m    - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
1722 . n    - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
1723 . M    - number of global rows (may be `PETSC_DETERMINE` to have calculated if `m` is given)
1724 . N    - number of global columns (may be `PETSC_DETERMINE` to have calculated if `n` is given)
1725 - ctx  - pointer to data needed by the shell matrix routines
1726 
1727   Output Parameter:
1728 . A - the matrix
1729 
1730   Level: advanced
1731 
1732   Example Usage:
1733 .vb
1734   extern PetscErrorCode mult(Mat, Vec, Vec);
1735 
1736   MatCreateShell(comm, m, n, M, N, ctx, &mat);
1737   MatShellSetOperation(mat, MATOP_MULT, (void(*)(void))mult);
1738   // Use matrix for operations that have been set
1739   MatDestroy(mat);
1740 .ve
1741 
1742   Notes:
1743   The shell matrix type is intended to provide a simple class to use
1744   with `KSP` (such as, for use with matrix-free methods). You should not
1745   use the shell type if you plan to define a complete matrix class.
1746 
1747   PETSc requires that matrices and vectors being used for certain
1748   operations are partitioned accordingly.  For example, when
1749   creating a shell matrix, `A`, that supports parallel matrix-vector
1750   products using `MatMult`(A,x,y) the user should set the number
1751   of local matrix rows to be the number of local elements of the
1752   corresponding result vector, y. Note that this is information is
1753   required for use of the matrix interface routines, even though
1754   the shell matrix may not actually be physically partitioned.
1755   For example,
1756 
1757 .vb
1758      Vec x, y
1759      extern PetscErrorCode mult(Mat,Vec,Vec);
1760      Mat A
1761 
1762      VecCreateMPI(comm,PETSC_DECIDE,M,&y);
1763      VecCreateMPI(comm,PETSC_DECIDE,N,&x);
1764      VecGetLocalSize(y,&m);
1765      VecGetLocalSize(x,&n);
1766      MatCreateShell(comm,m,n,M,N,ctx,&A);
1767      MatShellSetOperation(mat,MATOP_MULT,(void(*)(void))mult);
1768      MatMult(A,x,y);
1769      MatDestroy(&A);
1770      VecDestroy(&y);
1771      VecDestroy(&x);
1772 .ve
1773 
1774   `MATSHELL` handles `MatShift()`, `MatDiagonalSet()`, `MatDiagonalScale()`, `MatAXPY()`, `MatScale()`, `MatZeroRows()` and `MatZeroRowsColumns()`
1775   internally, so these  operations cannot be overwritten unless `MatShellSetManageScalingShifts()` is called.
1776 
1777   Developer Notes:
1778   For rectangular matrices do all the scalings and shifts make sense?
1779 
1780   Regarding shifting and scaling. The general form is
1781 
1782   diag(left)(vscale*A + diag(dshift) + vshift I)diag(right)
1783 
1784   The order you apply the operations is important. For example if you have a dshift then
1785   apply a MatScale(s) you get s*vscale*A + s*diag(shift). But if you first scale and then shift
1786   you get s*vscale*A + diag(shift)
1787 
1788   A is the user provided function.
1789 
1790   `KSP`/`PC` uses changes in the `Mat`'s "state" to decide if preconditioners need to be rebuilt `PCSetUp()` only calls the setup() for
1791   for the `PC` implementation if the `Mat` state has increased from the previous call. Thus to get changes in a `MATSHELL` to trigger
1792   an update in the preconditioner you must call `MatAssemblyBegin()` and `MatAssemblyEnd()` or `PetscObjectStateIncrease`((`PetscObject`)mat);
1793   each time the `MATSHELL` matrix has changed.
1794 
1795   Matrix product operations (i.e. `MatMat()`, `MatTransposeMat()` etc) can be specified using `MatShellSetMatProductOperation()`
1796 
1797   Calling `MatAssemblyBegin()`/`MatAssemblyEnd()` on a `MATSHELL` removes any previously supplied shift and scales that were provided
1798   with `MatDiagonalSet()`, `MatShift()`, `MatScale()`, or `MatDiagonalScale()`.
1799 
1800   Fortran Notes:
1801   To use this from Fortran with a `ctx` you must write an interface definition for this
1802   function and for `MatShellGetContext()` that tells Fortran the Fortran derived data type you are passing
1803   in as the `ctx` argument.
1804 
1805 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatShellSetOperation()`, `MatHasOperation()`, `MatShellGetContext()`, `MatShellSetContext()`, `MatShellSetManageScalingShifts()`, `MatShellSetMatProductOperation()`
1806 @*/
1807 PetscErrorCode MatCreateShell(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, void *ctx, Mat *A)
1808 {
1809   PetscFunctionBegin;
1810   PetscCall(MatCreate(comm, A));
1811   PetscCall(MatSetSizes(*A, m, n, M, N));
1812   PetscCall(MatSetType(*A, MATSHELL));
1813   PetscCall(MatShellSetContext(*A, ctx));
1814   PetscCall(MatSetUp(*A));
1815   PetscFunctionReturn(PETSC_SUCCESS);
1816 }
1817 
1818 /*@
1819   MatShellSetContext - sets the context for a `MATSHELL` shell matrix
1820 
1821   Logically Collective
1822 
1823   Input Parameters:
1824 + mat - the `MATSHELL` shell matrix
1825 - ctx - the context
1826 
1827   Level: advanced
1828 
1829   Fortran Notes:
1830   You must write a Fortran interface definition for this
1831   function that tells Fortran the Fortran derived data type that you are passing in as the `ctx` argument.
1832 
1833 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`
1834 @*/
1835 PetscErrorCode MatShellSetContext(Mat mat, void *ctx)
1836 {
1837   PetscFunctionBegin;
1838   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1839   PetscTryMethod(mat, "MatShellSetContext_C", (Mat, void *), (mat, ctx));
1840   PetscFunctionReturn(PETSC_SUCCESS);
1841 }
1842 
1843 /*@C
1844   MatShellSetContextDestroy - sets the destroy function for a `MATSHELL` shell matrix context
1845 
1846   Logically Collective
1847 
1848   Input Parameters:
1849 + mat - the shell matrix
1850 - f   - the context destroy function
1851 
1852   Level: advanced
1853 
1854   Note:
1855   If the `MatShell` is never duplicated, the behavior of this function is equivalent
1856   to `MatShellSetOperation`(`Mat`,`MATOP_DESTROY`,f). However, `MatShellSetContextDestroy()`
1857   ensures proper reference counting for the user provided context data in the case that
1858   the `MATSHELL` is duplicated.
1859 
1860 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellSetContext()`
1861 @*/
1862 PetscErrorCode MatShellSetContextDestroy(Mat mat, PetscErrorCode (*f)(void *))
1863 {
1864   PetscFunctionBegin;
1865   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1866   PetscTryMethod(mat, "MatShellSetContextDestroy_C", (Mat, PetscErrorCode(*)(void *)), (mat, f));
1867   PetscFunctionReturn(PETSC_SUCCESS);
1868 }
1869 
1870 /*@C
1871   MatShellSetVecType - Sets the `VecType` of `Vec` returned by `MatCreateVecs()`
1872 
1873   Logically Collective
1874 
1875   Input Parameters:
1876 + mat   - the `MATSHELL` shell matrix
1877 - vtype - type to use for creating vectors
1878 
1879   Level: advanced
1880 
1881 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateVecs()`
1882 @*/
1883 PetscErrorCode MatShellSetVecType(Mat mat, VecType vtype)
1884 {
1885   PetscFunctionBegin;
1886   PetscTryMethod(mat, "MatShellSetVecType_C", (Mat, VecType), (mat, vtype));
1887   PetscFunctionReturn(PETSC_SUCCESS);
1888 }
1889 
1890 /*@
1891   MatShellSetManageScalingShifts - Allows the user to control the scaling and shift operations of the `MATSHELL`. Must be called immediately
1892   after `MatCreateShell()`
1893 
1894   Logically Collective
1895 
1896   Input Parameter:
1897 . A - the `MATSHELL` shell matrix
1898 
1899   Level: advanced
1900 
1901 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatShellSetOperation()`
1902 @*/
1903 PetscErrorCode MatShellSetManageScalingShifts(Mat A)
1904 {
1905   PetscFunctionBegin;
1906   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
1907   PetscTryMethod(A, "MatShellSetManageScalingShifts_C", (Mat), (A));
1908   PetscFunctionReturn(PETSC_SUCCESS);
1909 }
1910 
1911 /*@C
1912   MatShellTestMult - Compares the multiply routine provided to the `MATSHELL` with differencing on a given function.
1913 
1914   Logically Collective; No Fortran Support
1915 
1916   Input Parameters:
1917 + mat  - the `MATSHELL` shell matrix
1918 . f    - the function
1919 . base - differences are computed around this vector, see `MatMFFDSetBase()`, for Jacobians this is the point at which the Jacobian is being evaluated
1920 - ctx  - an optional context for the function
1921 
1922   Output Parameter:
1923 . flg - `PETSC_TRUE` if the multiply is likely correct
1924 
1925   Options Database Key:
1926 . -mat_shell_test_mult_view - print if any differences are detected between the products and print the difference
1927 
1928   Level: advanced
1929 
1930 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellTestMultTranspose()`
1931 @*/
1932 PetscErrorCode MatShellTestMult(Mat mat, PetscErrorCode (*f)(void *, Vec, Vec), Vec base, void *ctx, PetscBool *flg)
1933 {
1934   PetscInt  m, n;
1935   Mat       mf, Dmf, Dmat, Ddiff;
1936   PetscReal Diffnorm, Dmfnorm;
1937   PetscBool v = PETSC_FALSE, flag = PETSC_TRUE;
1938 
1939   PetscFunctionBegin;
1940   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1941   PetscCall(PetscOptionsHasName(NULL, ((PetscObject)mat)->prefix, "-mat_shell_test_mult_view", &v));
1942   PetscCall(MatGetLocalSize(mat, &m, &n));
1943   PetscCall(MatCreateMFFD(PetscObjectComm((PetscObject)mat), m, n, PETSC_DECIDE, PETSC_DECIDE, &mf));
1944   PetscCall(MatMFFDSetFunction(mf, f, ctx));
1945   PetscCall(MatMFFDSetBase(mf, base, NULL));
1946 
1947   PetscCall(MatComputeOperator(mf, MATAIJ, &Dmf));
1948   PetscCall(MatComputeOperator(mat, MATAIJ, &Dmat));
1949 
1950   PetscCall(MatDuplicate(Dmat, MAT_COPY_VALUES, &Ddiff));
1951   PetscCall(MatAXPY(Ddiff, -1.0, Dmf, DIFFERENT_NONZERO_PATTERN));
1952   PetscCall(MatNorm(Ddiff, NORM_FROBENIUS, &Diffnorm));
1953   PetscCall(MatNorm(Dmf, NORM_FROBENIUS, &Dmfnorm));
1954   if (Diffnorm / Dmfnorm > 10 * PETSC_SQRT_MACHINE_EPSILON) {
1955     flag = PETSC_FALSE;
1956     if (v) {
1957       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)));
1958       PetscCall(MatViewFromOptions(Ddiff, (PetscObject)mat, "-mat_shell_test_mult_view"));
1959       PetscCall(MatViewFromOptions(Dmf, (PetscObject)mat, "-mat_shell_test_mult_view"));
1960       PetscCall(MatViewFromOptions(Dmat, (PetscObject)mat, "-mat_shell_test_mult_view"));
1961     }
1962   } else if (v) {
1963     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL and matrix-free multiple appear to produce the same results\n"));
1964   }
1965   if (flg) *flg = flag;
1966   PetscCall(MatDestroy(&Ddiff));
1967   PetscCall(MatDestroy(&mf));
1968   PetscCall(MatDestroy(&Dmf));
1969   PetscCall(MatDestroy(&Dmat));
1970   PetscFunctionReturn(PETSC_SUCCESS);
1971 }
1972 
1973 /*@C
1974   MatShellTestMultTranspose - Compares the multiply transpose routine provided to the `MATSHELL` with differencing on a given function.
1975 
1976   Logically Collective; No Fortran Support
1977 
1978   Input Parameters:
1979 + mat  - the `MATSHELL` shell matrix
1980 . f    - the function
1981 . base - differences are computed around this vector, see `MatMFFDSetBase()`, for Jacobians this is the point at which the Jacobian is being evaluated
1982 - ctx  - an optional context for the function
1983 
1984   Output Parameter:
1985 . flg - `PETSC_TRUE` if the multiply is likely correct
1986 
1987   Options Database Key:
1988 . -mat_shell_test_mult_view - print if any differences are detected between the products and print the difference
1989 
1990   Level: advanced
1991 
1992 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellTestMult()`
1993 @*/
1994 PetscErrorCode MatShellTestMultTranspose(Mat mat, PetscErrorCode (*f)(void *, Vec, Vec), Vec base, void *ctx, PetscBool *flg)
1995 {
1996   Vec       x, y, z;
1997   PetscInt  m, n, M, N;
1998   Mat       mf, Dmf, Dmat, Ddiff;
1999   PetscReal Diffnorm, Dmfnorm;
2000   PetscBool v = PETSC_FALSE, flag = PETSC_TRUE;
2001 
2002   PetscFunctionBegin;
2003   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2004   PetscCall(PetscOptionsHasName(NULL, ((PetscObject)mat)->prefix, "-mat_shell_test_mult_transpose_view", &v));
2005   PetscCall(MatCreateVecs(mat, &x, &y));
2006   PetscCall(VecDuplicate(y, &z));
2007   PetscCall(MatGetLocalSize(mat, &m, &n));
2008   PetscCall(MatGetSize(mat, &M, &N));
2009   PetscCall(MatCreateMFFD(PetscObjectComm((PetscObject)mat), m, n, M, N, &mf));
2010   PetscCall(MatMFFDSetFunction(mf, f, ctx));
2011   PetscCall(MatMFFDSetBase(mf, base, NULL));
2012   PetscCall(MatComputeOperator(mf, MATAIJ, &Dmf));
2013   PetscCall(MatTranspose(Dmf, MAT_INPLACE_MATRIX, &Dmf));
2014   PetscCall(MatComputeOperatorTranspose(mat, MATAIJ, &Dmat));
2015 
2016   PetscCall(MatDuplicate(Dmat, MAT_COPY_VALUES, &Ddiff));
2017   PetscCall(MatAXPY(Ddiff, -1.0, Dmf, DIFFERENT_NONZERO_PATTERN));
2018   PetscCall(MatNorm(Ddiff, NORM_FROBENIUS, &Diffnorm));
2019   PetscCall(MatNorm(Dmf, NORM_FROBENIUS, &Dmfnorm));
2020   if (Diffnorm / Dmfnorm > 10 * PETSC_SQRT_MACHINE_EPSILON) {
2021     flag = PETSC_FALSE;
2022     if (v) {
2023       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)));
2024       PetscCall(MatViewFromOptions(Ddiff, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2025       PetscCall(MatViewFromOptions(Dmf, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2026       PetscCall(MatViewFromOptions(Dmat, (PetscObject)mat, "-mat_shell_test_mult_transpose_view"));
2027     }
2028   } else if (v) {
2029     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "MATSHELL transpose and matrix-free multiple appear to produce the same results\n"));
2030   }
2031   if (flg) *flg = flag;
2032   PetscCall(MatDestroy(&mf));
2033   PetscCall(MatDestroy(&Dmat));
2034   PetscCall(MatDestroy(&Ddiff));
2035   PetscCall(MatDestroy(&Dmf));
2036   PetscCall(VecDestroy(&x));
2037   PetscCall(VecDestroy(&y));
2038   PetscCall(VecDestroy(&z));
2039   PetscFunctionReturn(PETSC_SUCCESS);
2040 }
2041 
2042 /*@C
2043   MatShellSetOperation - Allows user to set a matrix operation for a `MATSHELL` shell matrix.
2044 
2045   Logically Collective
2046 
2047   Input Parameters:
2048 + mat - the `MATSHELL` shell matrix
2049 . op  - the name of the operation
2050 - g   - the function that provides the operation.
2051 
2052   Level: advanced
2053 
2054   Example Usage:
2055 .vb
2056   extern PetscErrorCode usermult(Mat, Vec, Vec);
2057 
2058   MatCreateShell(comm, m, n, M, N, ctx, &A);
2059   MatShellSetOperation(A, MATOP_MULT, (void(*)(void))usermult);
2060 .ve
2061 
2062   Notes:
2063   See the file include/petscmat.h for a complete list of matrix
2064   operations, which all have the form MATOP_<OPERATION>, where
2065   <OPERATION> is the name (in all capital letters) of the
2066   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).
2067 
2068   All user-provided functions (except for `MATOP_DESTROY`) should have the same calling
2069   sequence as the usual matrix interface routines, since they
2070   are intended to be accessed via the usual matrix interface
2071   routines, e.g.,
2072 $       MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
2073 
2074   In particular each function MUST return an error code of 0 on success and
2075   nonzero on failure.
2076 
2077   Within each user-defined routine, the user should call
2078   `MatShellGetContext()` to obtain the user-defined context that was
2079   set by `MatCreateShell()`.
2080 
2081   Use `MatSetOperation()` to set an operation for any matrix type. For matrix product operations (i.e. `MatMatXXX()`, `MatTransposeMatXXX()` etc)
2082   use `MatShellSetMatProductOperation()`
2083 
2084   Fortran Notes:
2085   For `MatCreateVecs()` the user code should check if the input left or right matrix is -1 and in that case not
2086   generate a matrix. See src/mat/tests/ex120f.F
2087 
2088 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`, `MatShellSetContext()`, `MatSetOperation()`, `MatShellSetManageScalingShifts()`, `MatShellSetMatProductOperation()`
2089 @*/
2090 PetscErrorCode MatShellSetOperation(Mat mat, MatOperation op, void (*g)(void))
2091 {
2092   PetscFunctionBegin;
2093   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2094   PetscTryMethod(mat, "MatShellSetOperation_C", (Mat, MatOperation, void (*)(void)), (mat, op, g));
2095   PetscFunctionReturn(PETSC_SUCCESS);
2096 }
2097 
2098 /*@C
2099   MatShellGetOperation - Gets a matrix function for a `MATSHELL` shell matrix.
2100 
2101   Not Collective
2102 
2103   Input Parameters:
2104 + mat - the `MATSHELL` shell matrix
2105 - op  - the name of the operation
2106 
2107   Output Parameter:
2108 . g - the function that provides the operation.
2109 
2110   Level: advanced
2111 
2112   Notes:
2113   See the file include/petscmat.h for a complete list of matrix
2114   operations, which all have the form MATOP_<OPERATION>, where
2115   <OPERATION> is the name (in all capital letters) of the
2116   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).
2117 
2118   All user-provided functions have the same calling
2119   sequence as the usual matrix interface routines, since they
2120   are intended to be accessed via the usual matrix interface
2121   routines, e.g.,
2122 $       MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
2123 
2124   Within each user-defined routine, the user should call
2125   `MatShellGetContext()` to obtain the user-defined context that was
2126   set by `MatCreateShell()`.
2127 
2128 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellSetOperation()`, `MatShellSetContext()`
2129 @*/
2130 PetscErrorCode MatShellGetOperation(Mat mat, MatOperation op, void (**g)(void))
2131 {
2132   PetscFunctionBegin;
2133   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2134   PetscUseMethod(mat, "MatShellGetOperation_C", (Mat, MatOperation, void (**)(void)), (mat, op, g));
2135   PetscFunctionReturn(PETSC_SUCCESS);
2136 }
2137 
2138 /*@
2139   MatIsShell - Inquires if a matrix is derived from `MATSHELL`
2140 
2141   Input Parameter:
2142 . mat - the matrix
2143 
2144   Output Parameter:
2145 . flg - the boolean value
2146 
2147   Level: developer
2148 
2149   Developer Notes:
2150   In the future, we should allow the object type name to be changed still using the `MATSHELL` data structure for other matrices
2151   (i.e. `MATTRANSPOSEVIRTUAL`, `MATSCHURCOMPLEMENT` etc)
2152 
2153 .seealso: [](ch_matrices), `Mat`, `MATSHELL`, `MATMFFD`, `MatCreateShell()`, `MATTRANSPOSEVIRTUAL`, `MATSCHURCOMPLEMENT`
2154 @*/
2155 PetscErrorCode MatIsShell(Mat mat, PetscBool *flg)
2156 {
2157   PetscFunctionBegin;
2158   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
2159   PetscAssertPointer(flg, 2);
2160   *flg = (PetscBool)(mat->ops->destroy == MatDestroy_Shell);
2161   PetscFunctionReturn(PETSC_SUCCESS);
2162 }
2163