1: /*
2: The ST (spectral transformation) interface routines, callable by users.
4: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
5: SLEPc - Scalable Library for Eigenvalue Problem Computations
6: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
8: This file is part of SLEPc.
10: SLEPc is free software: you can redistribute it and/or modify it under the
11: terms of version 3 of the GNU Lesser General Public License as published by
12: the Free Software Foundation.
14: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
15: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
16: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
17: more details.
19: You should have received a copy of the GNU Lesser General Public License
20: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
21: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
22: */
24: #include <slepc/private/stimpl.h> /*I "slepcst.h" I*/
28: /*@
29: STApply - Applies the spectral transformation operator to a vector, for
30: instance (A - sB)^-1 B in the case of the shift-and-invert transformation
31: and generalized eigenproblem.
33: Collective on ST and Vec
35: Input Parameters:
36: + st - the spectral transformation context
37: - x - input vector
39: Output Parameter:
40: . y - output vector
42: Level: developer
44: .seealso: STApplyTranspose()
45: @*/
46: PetscErrorCode STApply(ST st,Vec x,Vec y) 47: {
55: STCheckMatrices(st,1);
56: if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
57: VecLocked(y,3);
59: if (st->state!=ST_STATE_SETUP) { STSetUp(st); }
61: if (!st->ops->apply) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have apply");
62: VecLockPush(x);
63: PetscLogEventBegin(ST_Apply,st,x,y,0);
64: if (st->D) { /* with balancing */
65: VecPointwiseDivide(st->wb,x,st->D);
66: (*st->ops->apply)(st,st->wb,y);
67: VecPointwiseMult(y,y,st->D);
68: } else {
69: (*st->ops->apply)(st,x,y);
70: }
71: PetscLogEventEnd(ST_Apply,st,x,y,0);
72: VecLockPop(x);
73: return(0);
74: }
78: /*@
79: STApplyTranspose - Applies the transpose of the operator to a vector, for
80: instance B^T(A - sB)^-T in the case of the shift-and-invert transformation
81: and generalized eigenproblem.
83: Collective on ST and Vec
85: Input Parameters:
86: + st - the spectral transformation context
87: - x - input vector
89: Output Parameter:
90: . y - output vector
92: Level: developer
94: .seealso: STApply()
95: @*/
96: PetscErrorCode STApplyTranspose(ST st,Vec x,Vec y) 97: {
105: STCheckMatrices(st,1);
106: if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
107: VecLocked(y,3);
109: if (st->state!=ST_STATE_SETUP) { STSetUp(st); }
111: if (!st->ops->applytrans) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have applytrans");
112: VecLockPush(x);
113: PetscLogEventBegin(ST_ApplyTranspose,st,x,y,0);
114: if (st->D) { /* with balancing */
115: VecPointwiseMult(st->wb,x,st->D);
116: (*st->ops->applytrans)(st,st->wb,y);
117: VecPointwiseDivide(y,y,st->D);
118: } else {
119: (*st->ops->applytrans)(st,x,y);
120: }
121: PetscLogEventEnd(ST_ApplyTranspose,st,x,y,0);
122: VecLockPop(x);
123: return(0);
124: }
128: /*@
129: STGetBilinearForm - Returns the matrix used in the bilinear form with a
130: generalized problem with semi-definite B.
132: Not collective, though a parallel Mat may be returned
134: Input Parameters:
135: . st - the spectral transformation context
137: Output Parameter:
138: . B - output matrix
140: Notes:
141: The output matrix B must be destroyed after use. It will be NULL in
142: case of standard eigenproblems.
144: Level: developer
145: @*/
146: PetscErrorCode STGetBilinearForm(ST st,Mat *B)147: {
154: STCheckMatrices(st,1);
155: (*st->ops->getbilinearform)(st,B);
156: return(0);
157: }
161: PetscErrorCode STGetBilinearForm_Default(ST st,Mat *B)162: {
166: if (st->nmat==1) *B = NULL;
167: else {
168: *B = st->A[1];
169: PetscObjectReference((PetscObject)*B);
170: }
171: return(0);
172: }
176: /*@
177: STComputeExplicitOperator - Computes the explicit operator associated
178: to the eigenvalue problem with the specified spectral transformation.
180: Collective on ST182: Input Parameter:
183: . st - the spectral transform context
185: Output Parameter:
186: . mat - the explicit operator
188: Notes:
189: This routine builds a matrix containing the explicit operator. For
190: example, in generalized problems with shift-and-invert spectral
191: transformation the result would be matrix (A - s B)^-1 B.
193: This computation is done by applying the operator to columns of the
194: identity matrix. This is analogous to MatComputeExplicitOperator().
196: Level: advanced
198: .seealso: STApply()
199: @*/
200: PetscErrorCode STComputeExplicitOperator(ST st,Mat *mat)201: {
202: PetscErrorCode ierr;
203: Vec in,out;
204: PetscInt i,M,m,*rows,start,end;
205: const PetscScalar *array;
206: PetscScalar one = 1.0;
207: PetscMPIInt size;
212: STCheckMatrices(st,1);
213: if (st->nmat>2) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_WRONGSTATE,"Can only be used with 1 or 2 matrices");
214: MPI_Comm_size(PetscObjectComm((PetscObject)st),&size);
216: MatCreateVecs(st->A[0],&in,&out);
217: VecGetSize(out,&M);
218: VecGetLocalSize(out,&m);
219: VecSetOption(in,VEC_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE);
220: VecGetOwnershipRange(out,&start,&end);
221: PetscMalloc1(m,&rows);
222: for (i=0;i<m;i++) rows[i] = start + i;
224: MatCreate(PetscObjectComm((PetscObject)st),mat);
225: MatSetSizes(*mat,m,m,M,M);
226: if (size == 1) {
227: MatSetType(*mat,MATSEQDENSE);
228: MatSeqDenseSetPreallocation(*mat,NULL);
229: } else {
230: MatSetType(*mat,MATMPIAIJ);
231: MatMPIAIJSetPreallocation(*mat,m,NULL,M-m,NULL);
232: }
234: for (i=0;i<M;i++) {
235: VecSet(in,0.0);
236: VecSetValues(in,1,&i,&one,INSERT_VALUES);
237: VecAssemblyBegin(in);
238: VecAssemblyEnd(in);
240: STApply(st,in,out);
242: VecGetArrayRead(out,&array);
243: MatSetValues(*mat,m,rows,1,&i,array,INSERT_VALUES);
244: VecRestoreArrayRead(out,&array);
245: }
246: PetscFree(rows);
247: VecDestroy(&in);
248: VecDestroy(&out);
249: MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);
250: MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);
251: return(0);
252: }
256: /*@
257: STSetUp - Prepares for the use of a spectral transformation.
259: Collective on ST261: Input Parameter:
262: . st - the spectral transformation context
264: Level: advanced
266: .seealso: STCreate(), STApply(), STDestroy()
267: @*/
268: PetscErrorCode STSetUp(ST st)269: {
270: PetscInt i,n,k;
275: STCheckMatrices(st,1);
276: if (st->state==ST_STATE_SETUP) return(0);
277: PetscInfo(st,"Setting up new ST\n");
278: PetscLogEventBegin(ST_SetUp,st,0,0,0);
279: if (!((PetscObject)st)->type_name) {
280: STSetType(st,STSHIFT);
281: }
282: if (!st->T) {
283: PetscMalloc1(PetscMax(2,st->nmat),&st->T);
284: PetscLogObjectMemory((PetscObject)st,PetscMax(2,st->nmat)*sizeof(Mat));
285: for (i=0;i<PetscMax(2,st->nmat);i++) st->T[i] = NULL;
286: } else if (st->state!=ST_STATE_UPDATED) {
287: for (i=0;i<PetscMax(2,st->nmat);i++) {
288: MatDestroy(&st->T[i]);
289: }
290: }
291: if (st->state!=ST_STATE_UPDATED) { MatDestroy(&st->P); }
292: if (st->D) {
293: MatGetLocalSize(st->A[0],NULL,&n);
294: VecGetLocalSize(st->D,&k);
295: if (n != k) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Balance matrix has wrong dimension %D (should be %D)",k,n);
296: if (!st->wb) {
297: VecDuplicate(st->D,&st->wb);
298: PetscLogObjectParent((PetscObject)st,(PetscObject)st->wb);
299: }
300: }
301: if (st->ops->setup) { (*st->ops->setup)(st); }
302: st->state = ST_STATE_SETUP;
303: PetscLogEventEnd(ST_SetUp,st,0,0,0);
304: return(0);
305: }
309: /*
310: Computes coefficients for the transformed polynomial,
311: and stores the result in argument S.
313: alpha - value of the parameter of the transformed polynomial
314: beta - value of the previous shift (only used in inplace mode)
315: k - number of A matrices involved in the computation
316: coeffs - coefficients of the expansion
317: initial - true if this is the first time (only relevant for shell mode)
318: */
319: PetscErrorCode STMatMAXPY_Private(ST st,PetscScalar alpha,PetscScalar beta,PetscInt k,PetscScalar *coeffs,PetscBool initial,Mat *S)320: {
322: PetscInt *matIdx=NULL,nmat,i,ini=-1;
323: PetscScalar t=1.0,ta,gamma;
324: PetscBool nz=PETSC_FALSE;
327: nmat = st->nmat-k;
328: switch (st->shift_matrix) {
329: case ST_MATMODE_INPLACE:
330: if (st->nmat>2) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST_MATMODE_INPLACE not supported for polynomial eigenproblems");
331: if (initial) {
332: PetscObjectReference((PetscObject)st->A[0]);
333: *S = st->A[0];
334: gamma = alpha;
335: } else gamma = alpha-beta;
336: if (gamma != 0.0) {
337: if (st->nmat>1) {
338: MatAXPY(*S,gamma,st->A[1],st->str);
339: } else {
340: MatShift(*S,gamma);
341: }
342: }
343: break;
344: case ST_MATMODE_SHELL:
345: if (initial) {
346: if (st->nmat>2) {
347: PetscMalloc1(nmat,&matIdx);
348: for (i=0;i<nmat;i++) matIdx[i] = k+i;
349: }
350: STMatShellCreate(st,alpha,nmat,matIdx,coeffs,S);
351: PetscLogObjectParent((PetscObject)st,(PetscObject)*S);
352: if (st->nmat>2) { PetscFree(matIdx); }
353: } else {
354: STMatShellShift(*S,alpha);
355: }
356: break;
357: case ST_MATMODE_COPY:
358: if (coeffs) {
359: for (i=0;i<nmat && ini==-1;i++) {
360: if (coeffs[i]!=0.0) ini = i;
361: else t *= alpha;
362: }
363: if (coeffs[ini] != 1.0) nz = PETSC_TRUE;
364: for (i=ini+1;i<nmat&&!nz;i++) if (coeffs[i]!=0.0) nz = PETSC_TRUE;
365: } else { nz = PETSC_TRUE; ini = 0; }
366: if ((alpha == 0.0 || !nz) && t==1.0) {
367: MatDestroy(S);
368: PetscObjectReference((PetscObject)st->A[k+ini]);
369: *S = st->A[k+ini];
370: } else {
371: if (*S && *S!=st->A[k+ini]) {
372: MatSetOption(*S,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
373: MatCopy(st->A[k+ini],*S,DIFFERENT_NONZERO_PATTERN);
374: } else {
375: MatDestroy(S);
376: MatDuplicate(st->A[k+ini],MAT_COPY_VALUES,S);
377: MatSetOption(*S,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
378: PetscLogObjectParent((PetscObject)st,(PetscObject)*S);
379: }
380: if (coeffs && coeffs[ini]!=1.0) {
381: MatScale(*S,coeffs[ini]);
382: }
383: for (i=ini+k+1;i<PetscMax(2,st->nmat);i++) {
384: t *= alpha;
385: ta = t;
386: if (coeffs) ta *= coeffs[i-k];
387: if (ta!=0.0) {
388: if (st->nmat>1) {
389: MatAXPY(*S,ta,st->A[i],st->str);
390: } else {
391: MatShift(*S,ta);
392: }
393: }
394: }
395: }
396: }
397: STMatSetHermitian(st,*S);
398: return(0);
399: }
403: /*
404: Computes the values of the coefficients required by STMatMAXPY_Private
405: for the case of monomial basis.
406: */
407: PetscErrorCode STCoeffs_Monomial(ST st, PetscScalar *coeffs)408: {
409: PetscInt k,i,ini,inip;
412: /* Compute binomial coefficients */
413: ini = (st->nmat*(st->nmat-1))/2;
414: for (i=0;i<st->nmat;i++) coeffs[ini+i]=1.0;
415: for (k=st->nmat-1;k>=1;k--) {
416: inip = ini+1;
417: ini = (k*(k-1))/2;
418: coeffs[ini] = 1.0;
419: for (i=1;i<k;i++) coeffs[ini+i] = coeffs[ini+i-1]+coeffs[inip+i-1];
420: }
421: return(0);
422: }
426: /*@
427: STPostSolve - Optional post-solve phase, intended for any actions that must
428: be performed on the ST object after the eigensolver has finished.
430: Collective on ST432: Input Parameters:
433: . st - the spectral transformation context
435: Level: developer
437: .seealso: EPSSolve()
438: @*/
439: PetscErrorCode STPostSolve(ST st)440: {
446: if (st->ops->postsolve) {
447: (*st->ops->postsolve)(st);
448: }
449: return(0);
450: }
454: /*@
455: STBackTransform - Back-transformation phase, intended for
456: spectral transformations which require to transform the computed
457: eigenvalues back to the original eigenvalue problem.
459: Not Collective
461: Input Parameters:
462: st - the spectral transformation context
463: eigr - real part of a computed eigenvalue
464: eigi - imaginary part of a computed eigenvalue
466: Level: developer
467: @*/
468: PetscErrorCode STBackTransform(ST st,PetscInt n,PetscScalar* eigr,PetscScalar* eigi)469: {
475: if (st->ops->backtransform) {
476: (*st->ops->backtransform)(st,n,eigr,eigi);
477: }
478: return(0);
479: }
483: /*@
484: STMatSetUp - Build the preconditioner matrix used in STMatSolve().
486: Collective on ST488: Input Parameters:
489: + st - the spectral transformation context
490: . sigma - the shift
491: - coeffs - the coefficients (may be NULL)
493: Note:
494: This function is not intended to be called by end users, but by SLEPc
495: solvers that use ST. It builds matrix st->P as follows, then calls KSPSetUp().
496: .vb
497: If (coeffs): st->P = Sum_{i=0:nmat-1} coeffs[i]*sigma^i*A_i.
498: else st->P = Sum_{i=0:nmat-1} sigma^i*A_i
499: .ve
501: Level: developer
503: .seealso: STMatSolve()
504: @*/
505: PetscErrorCode STMatSetUp(ST st,PetscScalar sigma,PetscScalar *coeffs)506: {
508: PetscBool flg;
513: STCheckMatrices(st,1);
515: PetscLogEventBegin(ST_MatSetUp,st,0,0,0);
516: STMatMAXPY_Private(st,sigma,0.0,0,coeffs,PETSC_TRUE,&st->P);
517: if (!st->ksp) { STGetKSP(st,&st->ksp); }
518: STCheckFactorPackage(st);
519: KSPSetOperators(st->ksp,st->P,st->P);
520: PetscObjectTypeCompare((PetscObject)st,STPRECOND,&flg);
521: if (!flg) {
522: KSPSetErrorIfNotConverged(st->ksp,PETSC_TRUE);
523: }
524: KSPSetUp(st->ksp);
525: PetscLogEventEnd(ST_MatSetUp,st,0,0,0);
526: return(0);
527: }