Actual source code: stsolve.c
1: /*
2: The ST (spectral transformation) interface routines, callable by users.
4: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
5: SLEPc - Scalable Library for Eigenvalue Problem Computations
6: Copyright (c) 2002-2013, 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/>.
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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 tranformation
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: {
54: if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
56: if (!st->setupcalled) { STSetUp(st); }
58: if (!st->ops->apply) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have apply");
59: PetscLogEventBegin(ST_Apply,st,x,y,0);
60: st->applys++;
61: if (st->D) { /* with balancing */
62: VecPointwiseDivide(st->wb,x,st->D);
63: (*st->ops->apply)(st,st->wb,y);
64: VecPointwiseMult(y,y,st->D);
65: } else {
66: (*st->ops->apply)(st,x,y);
67: }
68: PetscLogEventEnd(ST_Apply,st,x,y,0);
69: return(0);
70: }
74: /*@
75: STGetBilinearForm - Returns the matrix used in the bilinear form with a
76: generalized problem with semi-definite B.
78: Not collective, though a parallel Mat may be returned
80: Input Parameters:
81: . st - the spectral transformation context
83: Output Parameter:
84: . B - output matrix
86: Notes:
87: The output matrix B must be destroyed after use. It will be NULL in
88: case of standard eigenproblems.
90: Level: developer
91: @*/
92: PetscErrorCode STGetBilinearForm(ST st,Mat *B)
93: {
99: if (!st->A) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_WRONGSTATE,"Matrices must be set first");
100: (*st->ops->getbilinearform)(st,B);
101: return(0);
102: }
106: PetscErrorCode STGetBilinearForm_Default(ST st,Mat *B)
107: {
111: if (st->nmat==1) *B = NULL;
112: else {
113: *B = st->A[1];
114: PetscObjectReference((PetscObject)*B);
115: }
116: return(0);
117: }
121: /*@
122: STApplyTranspose - Applies the transpose of the operator to a vector, for
123: instance B^T(A - sB)^-T in the case of the shift-and-invert tranformation
124: and generalized eigenproblem.
126: Collective on ST and Vec
128: Input Parameters:
129: + st - the spectral transformation context
130: - x - input vector
132: Output Parameter:
133: . y - output vector
135: Level: developer
137: .seealso: STApply()
138: @*/
139: PetscErrorCode STApplyTranspose(ST st,Vec x,Vec y)
140: {
147: if (x == y) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_IDN,"x and y must be different vectors");
149: if (!st->setupcalled) { STSetUp(st); }
151: if (!st->ops->applytrans) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"ST does not have applytrans");
152: PetscLogEventBegin(ST_ApplyTranspose,st,x,y,0);
153: st->applys++;
154: if (st->D) { /* with balancing */
155: VecPointwiseMult(st->wb,x,st->D);
156: (*st->ops->applytrans)(st,st->wb,y);
157: VecPointwiseDivide(y,y,st->D);
158: } else {
159: (*st->ops->applytrans)(st,x,y);
160: }
161: PetscLogEventEnd(ST_ApplyTranspose,st,x,y,0);
162: return(0);
163: }
167: /*@
168: STComputeExplicitOperator - Computes the explicit operator associated
169: to the eigenvalue problem with the specified spectral transformation.
171: Collective on ST
173: Input Parameter:
174: . st - the spectral transform context
176: Output Parameter:
177: . mat - the explicit operator
179: Notes:
180: This routine builds a matrix containing the explicit operator. For
181: example, in generalized problems with shift-and-invert spectral
182: transformation the result would be matrix (A - s B)^-1 B.
184: This computation is done by applying the operator to columns of the
185: identity matrix. This is analogous to MatComputeExplicitOperator().
187: Level: advanced
189: .seealso: STApply()
190: @*/
191: PetscErrorCode STComputeExplicitOperator(ST st,Mat *mat)
192: {
193: PetscErrorCode ierr;
194: Vec in,out;
195: PetscInt i,M,m,*rows,start,end;
196: const PetscScalar *array;
197: PetscScalar one = 1.0;
198: PetscMPIInt size;
203: if (!st->A) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_WRONGSTATE,"Matrices must be set first");
204: MPI_Comm_size(PetscObjectComm((PetscObject)st),&size);
206: MatGetVecs(st->A[0],&in,&out);
207: VecGetSize(out,&M);
208: VecGetLocalSize(out,&m);
209: VecSetOption(in,VEC_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE);
210: VecGetOwnershipRange(out,&start,&end);
211: PetscMalloc(m*sizeof(PetscInt),&rows);
212: for (i=0;i<m;i++) rows[i] = start + i;
214: MatCreate(PetscObjectComm((PetscObject)st),mat);
215: MatSetSizes(*mat,m,m,M,M);
216: if (size == 1) {
217: MatSetType(*mat,MATSEQDENSE);
218: MatSeqDenseSetPreallocation(*mat,NULL);
219: } else {
220: MatSetType(*mat,MATMPIAIJ);
221: MatMPIAIJSetPreallocation(*mat,m,NULL,M-m,NULL);
222: }
224: for (i=0;i<M;i++) {
225: VecSet(in,0.0);
226: VecSetValues(in,1,&i,&one,INSERT_VALUES);
227: VecAssemblyBegin(in);
228: VecAssemblyEnd(in);
230: STApply(st,in,out);
232: VecGetArrayRead(out,&array);
233: MatSetValues(*mat,m,rows,1,&i,array,INSERT_VALUES);
234: VecRestoreArrayRead(out,&array);
235: }
236: PetscFree(rows);
237: VecDestroy(&in);
238: VecDestroy(&out);
239: MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);
240: MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);
241: return(0);
242: }
246: /*@
247: STSetUp - Prepares for the use of a spectral transformation.
249: Collective on ST
251: Input Parameter:
252: . st - the spectral transformation context
254: Level: advanced
256: .seealso: STCreate(), STApply(), STDestroy()
257: @*/
258: PetscErrorCode STSetUp(ST st)
259: {
260: PetscInt i,n,k;
265: if (!st->A) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_ARG_WRONGSTATE,"Matrices must be set first");
266: if (st->setupcalled) return(0);
267: PetscInfo(st,"Setting up new ST\n");
268: PetscLogEventBegin(ST_SetUp,st,0,0,0);
269: if (!((PetscObject)st)->type_name) {
270: STSetType(st,STSHIFT);
271: }
272: if (!st->T) {
273: PetscMalloc(PetscMax(2,st->nmat)*sizeof(Mat),&st->T);
274: PetscLogObjectMemory(st,PetscMax(2,st->nmat)*sizeof(Mat));
275: }
276: for (i=0;i<PetscMax(2,st->nmat);i++) st->T[i] = NULL;
277: if (!st->w) {
278: MatGetVecs(st->A[0],&st->w,NULL);
279: PetscLogObjectParent(st,st->w);
280: }
281: if (st->D) {
282: MatGetLocalSize(st->A[0],NULL,&n);
283: VecGetLocalSize(st->D,&k);
284: if (n != k) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Balance matrix has wrong dimension %D (should be %D)",k,n);
285: if (!st->wb) {
286: VecDuplicate(st->D,&st->wb);
287: PetscLogObjectParent(st,st->wb);
288: }
289: }
290: if (st->ops->setup) { (*st->ops->setup)(st); }
291: st->setupcalled = 1;
292: PetscLogEventEnd(ST_SetUp,st,0,0,0);
293: return(0);
294: }
298: /*
299: Computes a generalized AXPY operation on the A[:] matrices provided by the user,
300: and stores the result in one of the T[:] matrices. The computation is different
301: depending on whether the ST has two or three matrices. Also, in quadratic problems
302: this function is used to compute two matrices, those corresponding to degree 1 and 2.
304: Builds matrix in T[k] as follows:
305: deg=1: T[k] = A+alpha*B (if st->nmat==2) or B+2*alpha*C (if st->nmat==3)
306: deg=2: T[k] = A+alpha*B+alpha*alpha*C
307: */
308: PetscErrorCode STMatGAXPY_Private(ST st,PetscScalar alpha,PetscScalar beta,PetscInt deg,PetscInt k,PetscBool initial)
309: {
311: PetscScalar gamma;
312: PetscInt matIdx[3],t,i;
315: if (st->nmat==3 && deg==1) t = 1;
316: else t = 0;
317: switch (st->shift_matrix) {
318: case ST_MATMODE_INPLACE:
319: if (initial) {
320: PetscObjectReference((PetscObject)st->A[t]);
321: st->T[k] = st->A[t];
322: gamma = alpha;
323: } else gamma = alpha-beta;
324: if (gamma != 0.0) {
325: if (st->nmat>1) {
326: MatAXPY(st->T[k],gamma,st->A[t+1],st->str);
327: if (st->nmat==3 && deg==2) {
328: MatAXPY(st->T[k],gamma*gamma,st->A[2],st->str);
329: }
330: } else {
331: MatShift(st->T[k],gamma);
332: }
333: }
334: break;
335: case ST_MATMODE_SHELL:
336: if (initial) {
337: if (st->nmat>1) {
338: for (i=0;i<=deg;i++) {
339: matIdx[i] = t+i;
340: }
341: STMatShellCreate(st,alpha,deg+1,matIdx,&st->T[k]);
342: } else {
343: STMatShellCreate(st,alpha,deg,NULL,&st->T[k]);
344: }
345: PetscLogObjectParent(st,st->T[k]);
346: } else {
347: STMatShellShift(st->T[k],alpha);
348: }
349: break;
350: default:
351: if (alpha == 0.0) {
352: if (!initial) {
353: MatDestroy(&st->T[k]);
354: }
355: PetscObjectReference((PetscObject)st->A[t]);
356: st->T[k] = st->A[t];
357: } else {
358: if (initial) {
359: MatDuplicate(st->A[t],MAT_COPY_VALUES,&st->T[k]);
360: PetscLogObjectParent(st,st->T[k]);
361: } else {
362: if (beta==0.0) {
363: MatDestroy(&st->T[k]);
364: MatDuplicate(st->A[t],MAT_COPY_VALUES,&st->T[k]);
365: PetscLogObjectParent(st,st->T[k]);
366: } else {
367: MatCopy(st->A[t],st->T[k],SAME_NONZERO_PATTERN);
368: }
369: }
370: if (st->nmat>1) {
371: MatAXPY(st->T[k],alpha,st->A[t+1],st->str);
372: if (st->nmat==3 && deg==2) {
373: MatAXPY(st->T[k],alpha*alpha,st->A[2],st->str);
374: }
375: } else {
376: MatShift(st->T[k],alpha);
377: }
378: }
379: }
380: STMatSetHermitian(st,st->T[k]);
381: return(0);
382: }
386: /*@
387: STPostSolve - Optional post-solve phase, intended for any actions that must
388: be performed on the ST object after the eigensolver has finished.
390: Collective on ST
392: Input Parameters:
393: . st - the spectral transformation context
395: Level: developer
397: .seealso: EPSSolve()
398: @*/
399: PetscErrorCode STPostSolve(ST st)
400: {
405: if (st->ops->postsolve) {
406: (*st->ops->postsolve)(st);
407: }
408: return(0);
409: }
413: /*@
414: STBackTransform - Back-transformation phase, intended for
415: spectral transformations which require to transform the computed
416: eigenvalues back to the original eigenvalue problem.
418: Not Collective
420: Input Parameters:
421: st - the spectral transformation context
422: eigr - real part of a computed eigenvalue
423: eigi - imaginary part of a computed eigenvalue
425: Level: developer
426: @*/
427: PetscErrorCode STBackTransform(ST st,PetscInt n,PetscScalar* eigr,PetscScalar* eigi)
428: {
433: if (st->ops->backtransform) {
434: (*st->ops->backtransform)(st,n,eigr,eigi);
435: }
436: return(0);
437: }