Actual source code: schurm.c

petsc-3.8.3 2017-12-09
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  1:  #include <petsc/private/matimpl.h>
  2:  #include <petscksp.h>
  3: const char *const MatSchurComplementAinvTypes[] = {"DIAG","LUMP","MatSchurComplementAinvType","MAT_SCHUR_COMPLEMENT_AINV_",0};

  5: typedef struct {
  6:   Mat                        A,Ap,B,C,D;
  7:   KSP                        ksp;
  8:   Vec                        work1,work2;
  9:   MatSchurComplementAinvType ainvtype;
 10: } Mat_SchurComplement;

 12: PetscErrorCode MatCreateVecs_SchurComplement(Mat N,Vec *right,Vec *left)
 13: {
 14:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
 15:   PetscErrorCode      ierr;

 18:   if (Na->D) {
 19:     MatCreateVecs(Na->D,right,left);
 20:     return(0);
 21:   }
 22:   if (right) {
 23:     MatCreateVecs(Na->B,right,NULL);
 24:   }
 25:   if (left) {
 26:     MatCreateVecs(Na->C,NULL,left);
 27:   }
 28:   return(0);
 29: }

 31: PetscErrorCode MatView_SchurComplement(Mat N,PetscViewer viewer)
 32: {
 33:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
 34:   PetscErrorCode      ierr;

 37:   PetscViewerASCIIPrintf(viewer,"Schur complement A11 - A10 inv(A00) A01\n");
 38:   if (Na->D) {
 39:     PetscViewerASCIIPrintf(viewer,"A11\n");
 40:     PetscViewerASCIIPushTab(viewer);
 41:     MatView(Na->D,viewer);
 42:     PetscViewerASCIIPopTab(viewer);
 43:   } else {
 44:     PetscViewerASCIIPrintf(viewer,"A11 = 0\n");
 45:   }
 46:   PetscViewerASCIIPrintf(viewer,"A10\n");
 47:   PetscViewerASCIIPushTab(viewer);
 48:   MatView(Na->C,viewer);
 49:   PetscViewerASCIIPopTab(viewer);
 50:   PetscViewerASCIIPrintf(viewer,"KSP of A00\n");
 51:   PetscViewerASCIIPushTab(viewer);
 52:   KSPView(Na->ksp,viewer);
 53:   PetscViewerASCIIPopTab(viewer);
 54:   PetscViewerASCIIPrintf(viewer,"A01\n");
 55:   PetscViewerASCIIPushTab(viewer);
 56:   MatView(Na->B,viewer);
 57:   PetscViewerASCIIPopTab(viewer);
 58:   return(0);
 59: }

 61: /*
 62:            A11^T - A01^T ksptrans(A00,Ap00) A10^T
 63: */
 64: PetscErrorCode MatMultTranspose_SchurComplement(Mat N,Vec x,Vec y)
 65: {
 66:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
 67:   PetscErrorCode      ierr;

 70:   if (!Na->work1) {MatCreateVecs(Na->A,&Na->work1,NULL);}
 71:   if (!Na->work2) {MatCreateVecs(Na->A,&Na->work2,NULL);}
 72:   MatMultTranspose(Na->C,x,Na->work1);
 73:   KSPSolveTranspose(Na->ksp,Na->work1,Na->work2);
 74:   MatMultTranspose(Na->B,Na->work2,y);
 75:   VecScale(y,-1.0);
 76:   if (Na->D) {
 77:     MatMultTransposeAdd(Na->D,x,y,y);
 78:   }
 79:   return(0);
 80: }

 82: /*
 83:            A11 - A10 ksp(A00,Ap00) A01
 84: */
 85: PetscErrorCode MatMult_SchurComplement(Mat N,Vec x,Vec y)
 86: {
 87:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
 88:   PetscErrorCode      ierr;

 91:   if (!Na->work1) {MatCreateVecs(Na->A,&Na->work1,NULL);}
 92:   if (!Na->work2) {MatCreateVecs(Na->A,&Na->work2,NULL);}
 93:   MatMult(Na->B,x,Na->work1);
 94:   KSPSolve(Na->ksp,Na->work1,Na->work2);
 95:   MatMult(Na->C,Na->work2,y);
 96:   VecScale(y,-1.0);
 97:   if (Na->D) {
 98:     MatMultAdd(Na->D,x,y,y);
 99:   }
100:   return(0);
101: }

103: /*
104:            A11 - A10 ksp(A00,Ap00) A01
105: */
106: PetscErrorCode MatMultAdd_SchurComplement(Mat N,Vec x,Vec y,Vec z)
107: {
108:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
109:   PetscErrorCode      ierr;

112:   if (!Na->work1) {MatCreateVecs(Na->A,&Na->work1,NULL);}
113:   if (!Na->work2) {MatCreateVecs(Na->A,&Na->work2,NULL);}
114:   MatMult(Na->B,x,Na->work1);
115:   KSPSolve(Na->ksp,Na->work1,Na->work2);
116:   if (y == z) {
117:     VecScale(Na->work2,-1.0);
118:     MatMultAdd(Na->C,Na->work2,z,z);
119:   } else {
120:     MatMult(Na->C,Na->work2,z);
121:     VecAYPX(z,-1.0,y);
122:   }
123:   if (Na->D) {
124:     MatMultAdd(Na->D,x,z,z);
125:   }
126:   return(0);
127: }

129: PetscErrorCode MatSetFromOptions_SchurComplement(PetscOptionItems *PetscOptionsObject,Mat N)
130: {
131:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
132:   PetscErrorCode      ierr;

135:   PetscOptionsHead(PetscOptionsObject,"MatSchurComplementOptions");
136:   Na->ainvtype = MAT_SCHUR_COMPLEMENT_AINV_DIAG;
137:   PetscOptionsEnum("-mat_schur_complement_ainv_type","Type of approximation for inv(A00) used when assembling Sp = A11 - A10 inv(A00) A01","MatSchurComplementSetAinvType",MatSchurComplementAinvTypes,(PetscEnum)Na->ainvtype,(PetscEnum*)&Na->ainvtype,NULL);
138:   PetscOptionsTail();
139:   KSPSetFromOptions(Na->ksp);
140:   return(0);
141: }

143: PetscErrorCode MatDestroy_SchurComplement(Mat N)
144: {
145:   Mat_SchurComplement *Na = (Mat_SchurComplement*)N->data;
146:   PetscErrorCode      ierr;

149:   MatDestroy(&Na->A);
150:   MatDestroy(&Na->Ap);
151:   MatDestroy(&Na->B);
152:   MatDestroy(&Na->C);
153:   MatDestroy(&Na->D);
154:   VecDestroy(&Na->work1);
155:   VecDestroy(&Na->work2);
156:   KSPDestroy(&Na->ksp);
157:   PetscFree(N->data);
158:   return(0);
159: }

161: /*@
162:       MatCreateSchurComplement - Creates a new matrix object that behaves like the Schur complement of a matrix

164:    Collective on Mat

166:    Input Parameters:
167: +   A00,A01,A10,A11  - the four parts of the original matrix A = [A00 A01; A10 A11] (A11 is optional)
168: -   Ap00             - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}

170:    Output Parameter:
171: .   S - the matrix that the Schur complement S = A11 - A10 ksp(A00,Ap00) A01

173:    Level: intermediate

175:    Notes: The Schur complement is NOT actually formed! Rather, this
176:           object performs the matrix-vector product by using formula S = A11 - A10 A^{-1} A01
177:           for Schur complement S and a KSP solver to approximate the action of A^{-1}.

179:           All four matrices must have the same MPI communicator.

181:           A00 and  A11 must be square matrices.

183:           MatGetSchurComplement() takes as arguments the index sets for the submatrices and returns both the virtual Schur complement (what this returns) plus
184:           a sparse approximation to the true Schur complement (useful for building a preconditioner for the Schur complement).

186:           MatSchurComplementGetPmat() can be called on the output of this function to generate an explicit approximation to the Schur complement.

188:     Developer Notes: The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to
189:     remove redundancy and be clearer and simplier.


192: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatSchurComplementUpdateSubMatrices(), MatCreateTranspose(), MatGetSchurComplement(),
193:           MatSchurComplementGetPmat()

195: @*/
196: PetscErrorCode  MatCreateSchurComplement(Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11,Mat *S)
197: {

201:   KSPInitializePackage();
202:   MatCreate(((PetscObject)A00)->comm,S);
203:   MatSetType(*S,MATSCHURCOMPLEMENT);
204:   MatSchurComplementSetSubMatrices(*S,A00,Ap00,A01,A10,A11);
205:   return(0);
206: }

208: /*@
209:       MatSchurComplementSetSubMatrices - Sets the matrices that define the Schur complement

211:    Collective on Mat

213:    Input Parameter:
214: +   S                - matrix obtained with MatCreateSchurComplement (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
215: .   A00,A01,A10,A11  - the four parts of A = [A00 A01; A10 A11] (A11 is optional)
216: -   Ap00             - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}.

218:    Level: intermediate

220:    Notes: The Schur complement is NOT actually formed! Rather, this
221:           object performs the matrix-vector product by using formula S = A11 - A10 A^{-1} A01
222:           for Schur complement S and a KSP solver to approximate the action of A^{-1}.

224:           All four matrices must have the same MPI communicator.

226:           A00 and  A11 must be square matrices.

228: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatSchurComplementUpdateSubMatrices(), MatCreateTranspose(), MatCreateSchurComplement(), MatGetSchurComplement()

230: @*/
231: PetscErrorCode  MatSchurComplementSetSubMatrices(Mat S,Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11)
232: {
233:   PetscErrorCode      ierr;
234:   PetscInt            m,n;
235:   Mat_SchurComplement *Na = (Mat_SchurComplement*)S->data;

238:   if (S->assembled) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Use MatSchurComplementUpdateSubMatrices() for already used matrix");
246:   if (A00->rmap->n != A00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local columns %D",A00->rmap->n,A00->cmap->n);
247:   if (A00->rmap->n != Ap00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local rows of Ap00 %D",A00->rmap->n,Ap00->rmap->n);
248:   if (Ap00->rmap->n != Ap00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of Ap00 %D do not equal local columns %D",Ap00->rmap->n,Ap00->cmap->n);
249:   if (A00->cmap->n != A01->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A00 %D do not equal local rows of A01 %D",A00->cmap->n,A01->rmap->n);
250:   if (A10->cmap->n != A00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A10 %D do not equal local rows of A00 %D",A10->cmap->n,A00->rmap->n);
251:   if (A11) {
254:     if (A10->rmap->n != A11->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A10 %D do not equal local rows A11 %D",A10->rmap->n,A11->rmap->n);
255:   }

257:   MatGetLocalSize(A01,NULL,&n);
258:   MatGetLocalSize(A10,&m,NULL);
259:   MatSetSizes(S,m,n,PETSC_DECIDE,PETSC_DECIDE);
260:   PetscObjectReference((PetscObject)A00);
261:   PetscObjectReference((PetscObject)Ap00);
262:   PetscObjectReference((PetscObject)A01);
263:   PetscObjectReference((PetscObject)A10);
264:   Na->A  = A00;
265:   Na->Ap = Ap00;
266:   Na->B  = A01;
267:   Na->C  = A10;
268:   Na->D  = A11;
269:   if (A11) {
270:     PetscObjectReference((PetscObject)A11);
271:   }
272:   S->assembled    = PETSC_TRUE;
273:   S->preallocated = PETSC_TRUE;

275:   PetscLayoutSetUp((S)->rmap);
276:   PetscLayoutSetUp((S)->cmap);
277:   KSPSetOperators(Na->ksp,A00,Ap00);
278:   return(0);
279: }

281: /*@
282:   MatSchurComplementGetKSP - Gets the KSP object that is used to invert A00 in the Schur complement matrix S = A11 - A10 ksp(A00,Ap00) A01

284:   Not Collective

286:   Input Parameter:
287: . S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01

289:   Output Parameter:
290: . ksp - the linear solver object

292:   Options Database:
293: . -fieldsplit_<splitname_0>_XXX sets KSP and PC options for the 0-split solver inside the Schur complement used in PCFieldSplit; default <splitname_0> is 0.

295:   Level: intermediate

297: .seealso: MatSchurComplementSetKSP(), MatCreateSchurComplement(), MatCreateNormal(), MatMult(), MatCreate()
298: @*/
299: PetscErrorCode MatSchurComplementGetKSP(Mat S, KSP *ksp)
300: {
301:   Mat_SchurComplement *Na;

306:   Na   = (Mat_SchurComplement*) S->data;
307:   *ksp = Na->ksp;
308:   return(0);
309: }

311: /*@
312:   MatSchurComplementSetKSP - Sets the KSP object that is used to invert A00 in the Schur complement matrix S = A11 - A10 ksp(A00,Ap00) A01

314:   Not Collective

316:   Input Parameters:
317: + S   - matrix created with MatCreateSchurComplement()
318: - ksp - the linear solver object

320:   Level: developer

322:   Developer Notes:
323:     This is used in PCFieldSplit to reuse the 0-split KSP to implement ksp(A00,Ap00) in S.

325: .seealso: MatSchurComplementGetKSP(), MatCreateSchurComplement(), MatCreateNormal(), MatMult(), MatCreate(), MATSCHURCOMPLEMENT
326: @*/
327: PetscErrorCode MatSchurComplementSetKSP(Mat S, KSP ksp)
328: {
329:   Mat_SchurComplement *Na;
330:   PetscErrorCode      ierr;

335:   Na      = (Mat_SchurComplement*) S->data;
336:   PetscObjectReference((PetscObject)ksp);
337:   KSPDestroy(&Na->ksp);
338:   Na->ksp = ksp;
339:   KSPSetOperators(Na->ksp, Na->A, Na->Ap);
340:   return(0);
341: }

343: /*@
344:       MatSchurComplementUpdateSubMatrices - Updates the Schur complement matrix object with new submatrices

346:    Collective on Mat

348:    Input Parameters:
349: +   S                - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
350: .   A00,A01,A10,A11  - the four parts of A = [A00 A01; A10 A11] (A11 is optional)
351: -   Ap00             - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}.

353:    Level: intermediate

355:    Notes: All four matrices must have the same MPI communicator

357:           A00 and  A11 must be square matrices

359:           All of the matrices provided must have the same sizes as was used with MatCreateSchurComplement() or MatSchurComplementSetSubMatrices()
360:           though they need not be the same matrices.

362: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatCreateSchurComplement()

364: @*/
365: PetscErrorCode  MatSchurComplementUpdateSubMatrices(Mat S,Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11)
366: {
367:   PetscErrorCode      ierr;
368:   Mat_SchurComplement *Na = (Mat_SchurComplement*)S->data;

371:   if (!S->assembled) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Use MatSchurComplementSetSubMatrices() for a new matrix");
378:   if (A00->rmap->n != A00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local columns %D",A00->rmap->n,A00->cmap->n);
379:   if (A00->rmap->n != Ap00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A00 %D do not equal local rows of Ap00 %D",A00->rmap->n,Ap00->rmap->n);
380:   if (Ap00->rmap->n != Ap00->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of Ap00 %D do not equal local columns %D",Ap00->rmap->n,Ap00->cmap->n);
381:   if (A00->cmap->n != A01->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A00 %D do not equal local rows of A01 %D",A00->cmap->n,A01->rmap->n);
382:   if (A10->cmap->n != A00->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local columns of A10 %D do not equal local rows of A00 %D",A10->cmap->n,A00->rmap->n);
383:   if (A11) {
386:     if (A10->rmap->n != A11->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local rows of A10 %D do not equal local rows A11 %D",A10->rmap->n,A11->rmap->n);
387:   }

389:   PetscObjectReference((PetscObject)A00);
390:   PetscObjectReference((PetscObject)Ap00);
391:   PetscObjectReference((PetscObject)A01);
392:   PetscObjectReference((PetscObject)A10);
393:   if (A11) {
394:     PetscObjectReference((PetscObject)A11);
395:   }

397:   MatDestroy(&Na->A);
398:   MatDestroy(&Na->Ap);
399:   MatDestroy(&Na->B);
400:   MatDestroy(&Na->C);
401:   MatDestroy(&Na->D);

403:   Na->A  = A00;
404:   Na->Ap = Ap00;
405:   Na->B  = A01;
406:   Na->C  = A10;
407:   Na->D  = A11;

409:   KSPSetOperators(Na->ksp,A00,Ap00);
410:   return(0);
411: }


414: /*@C
415:   MatSchurComplementGetSubMatrices - Get the individual submatrices in the Schur complement

417:   Collective on Mat

419:   Input Parameter:
420: . S                - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01

422:   Output Paramters:
423: + A00,A01,A10,A11  - the four parts of the original matrix A = [A00 A01; A10 A11] (A11 is optional)
424: - Ap00             - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}.

426:   Note: A11 is optional, and thus can be NULL.  The submatrices are not increfed before they are returned and should not be modified or destroyed.

428:   Level: intermediate

430: .seealso: MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatCreateSchurComplement(), MatSchurComplementUpdateSubMatrices()
431: @*/
432: PetscErrorCode  MatSchurComplementGetSubMatrices(Mat S,Mat *A00,Mat *Ap00,Mat *A01,Mat *A10,Mat *A11)
433: {
434:   Mat_SchurComplement *Na = (Mat_SchurComplement*) S->data;
435:   PetscErrorCode      ierr;
436:   PetscBool           flg;

440:   PetscObjectTypeCompare((PetscObject)S,MATSCHURCOMPLEMENT,&flg);
441:   if (flg) {
442:     if (A00) *A00 = Na->A;
443:     if (Ap00) *Ap00 = Na->Ap;
444:     if (A01) *A01 = Na->B;
445:     if (A10) *A10 = Na->C;
446:     if (A11) *A11 = Na->D;
447:   } else {
448:     if (A00) *A00 = 0;
449:     if (Ap00) *Ap00 = 0;
450:     if (A01) *A01 = 0;
451:     if (A10) *A10 = 0;
452:     if (A11) *A11 = 0;
453:   }
454:   return(0);
455: }

457:  #include <petsc/private/kspimpl.h>

459: /*@
460:   MatSchurComplementComputeExplicitOperator - Compute the Schur complement matrix explicitly

462:   Collective on Mat

464:   Input Parameter:
465: . M - the matrix obtained with MatCreateSchurComplement()

467:   Output Parameter:
468: . S - the Schur complement matrix

470:   Note: This can be expensive, so it is mainly for testing

472:   Level: advanced

474: .seealso: MatCreateSchurComplement(), MatSchurComplementUpdate()
475: @*/
476: PetscErrorCode MatSchurComplementComputeExplicitOperator(Mat M, Mat *S)
477: {
478:   Mat            B, C, D;
479:   KSP            ksp;
480:   PC             pc;
481:   PetscBool      isLU, isILU;
482:   PetscReal      fill = 2.0;

486:   MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);
487:   MatSchurComplementGetKSP(M, &ksp);
488:   KSPGetPC(ksp, &pc);
489:   PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);
490:   PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);
491:   if (isLU || isILU) {
492:     Mat       fact, Bd, AinvB, AinvBd;
493:     PetscReal eps = 1.0e-10;

495:     /* This can be sped up for banded LU */
496:     KSPSetUp(ksp);
497:     PCFactorGetMatrix(pc, &fact);
498:     MatConvert(B, MATDENSE, MAT_INITIAL_MATRIX, &Bd);
499:     MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);
500:     MatMatSolve(fact, Bd, AinvBd);
501:     MatDestroy(&Bd);
502:     MatChop(AinvBd, eps);
503:     MatConvert(AinvBd, MATAIJ, MAT_INITIAL_MATRIX, &AinvB);
504:     MatDestroy(&AinvBd);
505:     MatMatMult(C, AinvB, MAT_INITIAL_MATRIX, fill, S);
506:     MatDestroy(&AinvB);
507:   } else {
508:     Mat Ainvd, Ainv;

510:     PCComputeExplicitOperator(pc, &Ainvd);
511:     MatConvert(Ainvd, MATAIJ, MAT_INITIAL_MATRIX, &Ainv);
512:     MatDestroy(&Ainvd);
513: #if 0
514:     /* Symmetric version */
515:     MatPtAP(Ainv, B, MAT_INITIAL_MATRIX, fill, S);
516: #else
517:     /* Nonsymmetric version */
518:     MatMatMatMult(C, Ainv, B, MAT_INITIAL_MATRIX, fill, S);
519: #endif
520:     MatDestroy(&Ainv);
521:   }
522:   if (D) {
523:     MatAXPY(*S, -1.0, D, DIFFERENT_NONZERO_PATTERN);
524:    }
525:   MatScale(*S,-1.0);
526:   return(0);
527: }

529: /* Developer Notes: This should be implemented with a MatCreate_SchurComplement() as that is the standard design for new Mat classes. */
530: PetscErrorCode MatGetSchurComplement_Basic(Mat mat,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *newmat,MatSchurComplementAinvType ainvtype, MatReuse preuse,Mat *newpmat)
531: {
533:   Mat            A=0,Ap=0,B=0,C=0,D=0;
534:   MatReuse       reuse;

543:   if (mreuse == MAT_IGNORE_MATRIX && preuse == MAT_IGNORE_MATRIX) return(0);

547:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

549:   reuse = MAT_INITIAL_MATRIX;
550:   if (mreuse == MAT_REUSE_MATRIX) {
551:     MatSchurComplementGetSubMatrices(*newmat,&A,&Ap,&B,&C,&D);
552:     if (!A || !Ap || !B || !C) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Attempting to reuse matrix but Schur complement matrices unset");
553:     if (A != Ap) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Preconditioning matrix does not match operator");
554:     MatDestroy(&Ap); /* get rid of extra reference */
555:     reuse = MAT_REUSE_MATRIX;
556:   }
557:   MatCreateSubMatrix(mat,isrow0,iscol0,reuse,&A);
558:   MatCreateSubMatrix(mat,isrow0,iscol1,reuse,&B);
559:   MatCreateSubMatrix(mat,isrow1,iscol0,reuse,&C);
560:   MatCreateSubMatrix(mat,isrow1,iscol1,reuse,&D);
561:   switch (mreuse) {
562:   case MAT_INITIAL_MATRIX:
563:     MatCreateSchurComplement(A,A,B,C,D,newmat);
564:     break;
565:   case MAT_REUSE_MATRIX:
566:     MatSchurComplementUpdateSubMatrices(*newmat,A,A,B,C,D);
567:     break;
568:   default:
569:     if (mreuse != MAT_IGNORE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Unrecognized value of mreuse");
570:   }
571:   if (preuse != MAT_IGNORE_MATRIX) {
572:     MatCreateSchurComplementPmat(A,B,C,D,ainvtype,preuse,newpmat);
573:   }
574:   MatDestroy(&A);
575:   MatDestroy(&B);
576:   MatDestroy(&C);
577:   MatDestroy(&D);
578:   return(0);
579: }

581: /*@
582:     MatGetSchurComplement - Obtain the Schur complement from eliminating part of the matrix in another part.

584:     Collective on Mat

586:     Input Parameters:
587: +   A      - matrix in which the complement is to be taken
588: .   isrow0 - rows to eliminate
589: .   iscol0 - columns to eliminate, (isrow0,iscol0) should be square and nonsingular
590: .   isrow1 - rows in which the Schur complement is formed
591: .   iscol1 - columns in which the Schur complement is formed
592: .   mreuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in S
593: .   ainvtype - the type of approximation used for the inverse of the (0,0) block used in forming Sp:
594:                        MAT_SCHUR_COMPLEMENT_AINV_DIAG or MAT_SCHUR_COMPLEMENT_AINV_LUMP
595: -   preuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in Sp

597:     Output Parameters:
598: +   S      - exact Schur complement, often of type MATSCHURCOMPLEMENT which is difficult to use for preconditioning
599: -   Sp     - approximate Schur complement from which a preconditioner can be built

601:     Note:
602:     Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
603:     application-specific information.  The default for assembled matrices is to use the inverse of the diagonal of
604:     the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
605:     before forming inv(diag(A00)).

607:     Sometimes users would like to provide problem-specific data in the Schur complement, usually only for special row
608:     and column index sets.  In that case, the user should call PetscObjectComposeFunction() on the *S matrix and pass mreuse of MAT_REUSE_MATRIX to set
609:     "MatGetSchurComplement_C" to their function.  If their function needs to fall back to the default implementation, it
610:     should call MatGetSchurComplement_Basic().

612:     MatCreateSchurComplement() takes as arguments the four submatrices and returns the virtual Schur complement (what this returns in S).

614:     MatSchurComplementGetPmat() takes the virtual Schur complement and returns an explicit approximate Schur complement (what this returns in Sp).

616:     In other words calling MatCreateSchurComplement() followed by MatSchurComplementGetPmat() produces the same output as this function but with slightly different
617:     inputs. The actually submatrices of the original block matrix instead of index sets to the submatrices.

619:     Developer Notes: The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to
620:     remove redundancy and be clearer and simplier.

622:     Level: advanced

624:     Concepts: matrices^submatrices

626: .seealso: MatCreateSubMatrix(), PCFIELDSPLIT, MatCreateSchurComplement(), MatSchurComplementAinvType
627: @*/
628: PetscErrorCode  MatGetSchurComplement(Mat A,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *S,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Sp)
629: {
630:   PetscErrorCode ierr,(*f)(Mat,IS,IS,IS,IS,MatReuse,Mat*,MatReuse,Mat*) = NULL;

641:   if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
642:   f = NULL;
643:   if (mreuse == MAT_REUSE_MATRIX) { /* This is the only situation, in which we can demand that the user pass a non-NULL pointer to non-garbage in S. */
644:     PetscObjectQueryFunction((PetscObject)*S,"MatGetSchurComplement_C",&f);
645:   }
646:   if (f) {
647:       (*f)(A,isrow0,iscol0,isrow1,iscol1,mreuse,S,preuse,Sp);
648:   } else {
649:     MatGetSchurComplement_Basic(A,isrow0,iscol0,isrow1,iscol1,mreuse,S,ainvtype,preuse,Sp);
650:   }
651:   return(0);
652: }

654: /*@
655:     MatSchurComplementSetAinvType - set the type of approximation used for the inverse of the (0,0) block used in forming Sp in MatSchurComplementGetPmat()

657:     Not collective.

659:     Input Parameters:
660: +   S        - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
661: -   ainvtype - type of approximation used to form A00inv from A00 when assembling Sp = A11 - A10 A00inv A01:
662:                       MAT_SCHUR_COMPLEMENT_AINV_DIAG or MAT_SCHUR_COMPLEMENT_AINV_LUMP

664:     Options database:
665:     -mat_schur_complement_ainv_type diag | lump

667:     Note:
668:     Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
669:     application-specific information.  The default for assembled matrices is to use the inverse of the diagonal of
670:     the (0,0) block A00 in place of A00^{-1}. This rarely produces a scalable algorithm. Optionally, A00 can be lumped
671:     before forming inv(diag(A00)).

673:     Level: advanced

675:     Concepts: matrices^submatrices

677: .seealso: MatSchurComplementAinvType, MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementGetAinvType()
678: @*/
679: PetscErrorCode  MatSchurComplementSetAinvType(Mat S,MatSchurComplementAinvType ainvtype)
680: {
681:   PetscErrorCode      ierr;
682:   const char*         t;
683:   PetscBool           isschur;
684:   Mat_SchurComplement *schur;

688:   PetscObjectGetType((PetscObject)S,&t);
689:   PetscStrcmp(t,MATSCHURCOMPLEMENT,&isschur);
690:   if (!isschur) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected Mat of type MATSCHURCOMPLEMENT, got %s instead",t);
691:   schur = (Mat_SchurComplement*)S->data;
692:   if (ainvtype != MAT_SCHUR_COMPLEMENT_AINV_DIAG && ainvtype != MAT_SCHUR_COMPLEMENT_AINV_LUMP) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown MatSchurComplementAinvType: %D",ainvtype);
693:   schur->ainvtype = ainvtype;
694:   return(0);
695: }

697: /*@
698:     MatSchurComplementGetAinvType - get the type of approximation for the inverse of the (0,0) block used in forming Sp in MatSchurComplementGetPmat()

700:     Not collective.

702:     Input Parameter:
703: .   S      - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01

705:     Output Parameter:
706: .   ainvtype - type of approximation used to form A00inv from A00 when assembling Sp = A11 - A10 A00inv A01:
707:                       MAT_SCHUR_COMPLEMENT_AINV_DIAG or MAT_SCHUR_COMPLEMENT_AINV_LUMP

709:     Note:
710:     Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
711:     application-specific information.  The default for assembled matrices is to use the inverse of the diagonal of
712:     the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
713:     before forming inv(diag(A00)).

715:     Level: advanced

717:     Concepts: matrices^submatrices

719: .seealso: MatSchurComplementAinvType, MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementSetAinvType()
720: @*/
721: PetscErrorCode  MatSchurComplementGetAinvType(Mat S,MatSchurComplementAinvType *ainvtype)
722: {
723:   PetscErrorCode      ierr;
724:   const char*         t;
725:   PetscBool           isschur;
726:   Mat_SchurComplement *schur;

730:   PetscObjectGetType((PetscObject)S,&t);
731:   PetscStrcmp(t,MATSCHURCOMPLEMENT,&isschur);
732:   if (!isschur) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected Mat of type MATSCHURCOMPLEMENT, got %s instead",t);
733:   schur = (Mat_SchurComplement*)S->data;
734:   if (ainvtype) *ainvtype = schur->ainvtype;
735:   return(0);
736: }

738: /*@
739:     MatCreateSchurComplementPmat - create a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01

741:     Collective on Mat

743:     Input Parameters:
744: +   A00,A01,A10,A11      - the four parts of the original matrix A = [A00 A01; A10 A11] (A01,A10, and A11 are optional, implying zero matrices)
745: .   ainvtype             - type of approximation for inv(A00) used when forming Sp = A11 - A10 inv(A00) A01
746: -   preuse               - MAT_INITIAL_MATRIX for a new Sp, or MAT_REUSE_MATRIX to reuse an existing Sp, or MAT_IGNORE_MATRIX to put nothing in Sp

748:     Output Parameter:
749: -   Spmat                - approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01

751:     Note:
752:     Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
753:     application-specific information.  The default for assembled matrices is to use the inverse of the diagonal of
754:     the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
755:     before forming inv(diag(A00)).

757:     Level: advanced

759:     Concepts: matrices^submatrices

761: .seealso: MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementAinvType
762: @*/
763: PetscErrorCode  MatCreateSchurComplementPmat(Mat A00,Mat A01,Mat A10,Mat A11,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Spmat)
764: {

767:   PetscInt       N00;

770:   /* Use an appropriate approximate inverse of A00 to form A11 - A10 inv(diag(A00)) A01; a NULL A01, A10 or A11 indicates a zero matrix. */
771:   /* TODO: Perhaps should create an appropriately-sized zero matrix of the same type as A00? */
772:   if ((!A01 || !A10) & !A11) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot assemble Spmat: A01, A10 and A11 are all NULL.");

774:   if (preuse == MAT_IGNORE_MATRIX) return(0);

776:   /* A zero size A00 or empty A01 or A10 imply S = A11. */
777:   MatGetSize(A00,&N00,NULL);
778:   if (!A01 || !A10 || !N00) {
779:     if (preuse == MAT_INITIAL_MATRIX) {
780:       MatDuplicate(A11,MAT_COPY_VALUES,Spmat);
781:     } else { /* MAT_REUSE_MATRIX */
782:       /* TODO: when can we pass SAME_NONZERO_PATTERN? */
783:       MatCopy(A11,*Spmat,DIFFERENT_NONZERO_PATTERN);
784:     }

786:   } else {
787:     Mat         AdB;
788:     Vec         diag;

790:     MatCreateVecs(A00,&diag,NULL);
791:     if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_LUMP) {
792:       MatGetRowSum(A00,diag);
793:     } else if (ainvtype == MAT_SCHUR_COMPLEMENT_AINV_DIAG) {
794:       MatGetDiagonal(A00,diag);
795:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown MatSchurComplementAinvType: %D", ainvtype);
796:     VecReciprocal(diag);
797:     MatDuplicate(A01,MAT_COPY_VALUES,&AdB);
798:     MatDiagonalScale(AdB,diag,NULL);
799:     VecDestroy(&diag);
800:     /* Cannot really reuse Spmat in MatMatMult() because of MatAYPX() -->
801:          MatAXPY() --> MatHeaderReplace() --> MatDestroy_XXX_MatMatMult()  */
802:     MatDestroy(Spmat);
803:     MatMatMult(A10,AdB,MAT_INITIAL_MATRIX,PETSC_DEFAULT,Spmat);
804:     if (!A11) {
805:       MatScale(*Spmat,-1.0);
806:     } else {
807:       /* TODO: when can we pass SAME_NONZERO_PATTERN? */
808:       MatAYPX(*Spmat,-1,A11,DIFFERENT_NONZERO_PATTERN);
809:     }
810:     MatDestroy(&AdB);
811:   }
812:   return(0);
813: }

815: PetscErrorCode  MatSchurComplementGetPmat_Basic(Mat S,MatReuse preuse,Mat *Spmat)
816: {
817:   Mat A,B,C,D;
818:   Mat_SchurComplement *schur = (Mat_SchurComplement *)S->data;
819:   PetscErrorCode      ierr;

822:   if (preuse == MAT_IGNORE_MATRIX) return(0);

824:   MatSchurComplementGetSubMatrices(S,&A,NULL,&B,&C,&D);
825:   if (!A) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Schur complement component matrices unset");
826:   MatCreateSchurComplementPmat(A,B,C,D,schur->ainvtype,preuse,Spmat);
827:   return(0);
828: }

830: /*@
831:     MatSchurComplementGetPmat - Obtain a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01

833:     Collective on Mat

835:     Input Parameters:
836: +   S      - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) A01
837: -   preuse - MAT_INITIAL_MATRIX for a new Sp, or MAT_REUSE_MATRIX to reuse an existing Sp, or MAT_IGNORE_MATRIX to put nothing in Sp

839:     Output Parameter:
840: -   Sp     - approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01

842:     Note:
843:     Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
844:     application-specific information.  The default for assembled matrices is to use the inverse of the diagonal of
845:     the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
846:     before forming inv(diag(A00)).

848:     Sometimes users would like to provide problem-specific data in the Schur complement, usually only
849:     for special row and column index sets.  In that case, the user should call PetscObjectComposeFunction() to set
850:     "MatSchurComplementGetPmat_C" to their function.  If their function needs to fall back to the default implementation,
851:     it should call MatSchurComplementGetPmat_Basic().

853:     Developer Notes: The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to
854:     remove redundancy and be clearer and simplier.

856:     Level: advanced

858:     Concepts: matrices^submatrices

860: .seealso: MatCreateSubMatrix(), PCFIELDSPLIT, MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementSetAinvType()
861: @*/
862: PetscErrorCode  MatSchurComplementGetPmat(Mat S,MatReuse preuse,Mat *Sp)
863: {
864:   PetscErrorCode ierr,(*f)(Mat,MatReuse,Mat*);

870:   if (S->factortype) SETERRQ(PetscObjectComm((PetscObject)S),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

872:   PetscObjectQueryFunction((PetscObject)S,"MatSchurComplementGetPmat_C",&f);
873:   if (f) {
874:     (*f)(S,preuse,Sp);
875:   } else {
876:     MatSchurComplementGetPmat_Basic(S,preuse,Sp);
877:   }
878:   return(0);
879: }

881: PETSC_EXTERN PetscErrorCode MatCreate_SchurComplement(Mat N)
882: {
883:   PetscErrorCode      ierr;
884:   Mat_SchurComplement *Na;

887:   PetscNewLog(N,&Na);
888:   N->data = (void*) Na;

890:   N->ops->destroy        = MatDestroy_SchurComplement;
891:   N->ops->getvecs        = MatCreateVecs_SchurComplement;
892:   N->ops->view           = MatView_SchurComplement;
893:   N->ops->mult           = MatMult_SchurComplement;
894:   N->ops->multtranspose  = MatMultTranspose_SchurComplement;
895:   N->ops->multadd        = MatMultAdd_SchurComplement;
896:   N->ops->setfromoptions = MatSetFromOptions_SchurComplement;
897:   N->assembled           = PETSC_FALSE;
898:   N->preallocated        = PETSC_FALSE;

900:   KSPCreate(PetscObjectComm((PetscObject)N),&Na->ksp);
901:   PetscObjectChangeTypeName((PetscObject)N,MATSCHURCOMPLEMENT);
902:   return(0);
903: }

905: static PetscBool KSPMatRegisterAllCalled;

907: /*@C
908:   KSPMatRegisterAll - Registers all matrix implementations in the KSP package.

910:   Not Collective

912:   Level: advanced

914: .keywords: Mat, KSP, register, all

916: .seealso: MatRegisterAll(),  KSPInitializePackage()
917: @*/
918: PetscErrorCode KSPMatRegisterAll(void)
919: {

923:   if (KSPMatRegisterAllCalled) return(0);
924:   KSPMatRegisterAllCalled = PETSC_TRUE;
925:   MatRegister(MATSCHURCOMPLEMENT,MatCreate_SchurComplement);
926:   return(0);
927: }