Actual source code: svdsolve.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: SVD routines related to the solution process
12: */
14: #include <slepc/private/svdimpl.h>
15: #include <slepc/private/bvimpl.h>
17: /*
18: SVDComputeVectors_Left - Compute left singular vectors as U=A*V.
19: Only done if the leftbasis flag is false. Assumes V is available.
20: */
21: PetscErrorCode SVDComputeVectors_Left(SVD svd)
22: {
23: Vec tl,omega2,u,v,w;
24: PetscInt i,oldsize;
25: VecType vtype;
26: const PetscScalar* varray;
28: PetscFunctionBegin;
29: if (!svd->leftbasis) {
30: /* generate left singular vectors on U */
31: if (!svd->U) PetscCall(SVDGetBV(svd,NULL,&svd->U));
32: PetscCall(BVGetSizes(svd->U,NULL,NULL,&oldsize));
33: if (!oldsize) {
34: if (!((PetscObject)svd->U)->type_name) PetscCall(BVSetType(svd->U,((PetscObject)svd->V)->type_name));
35: PetscCall(MatCreateVecsEmpty(svd->A,NULL,&tl));
36: PetscCall(BVSetSizesFromVec(svd->U,tl,svd->ncv));
37: PetscCall(VecDestroy(&tl));
38: }
39: PetscCall(BVSetActiveColumns(svd->V,0,svd->nconv));
40: PetscCall(BVSetActiveColumns(svd->U,0,svd->nconv));
41: if (!svd->ishyperbolic) PetscCall(BVMatMult(svd->V,svd->A,svd->U));
42: else if (svd->swapped) { /* compute right singular vectors as V=A'*Omega*U */
43: PetscCall(MatCreateVecs(svd->A,&w,NULL));
44: for (i=0;i<svd->nconv;i++) {
45: PetscCall(BVGetColumn(svd->V,i,&v));
46: PetscCall(BVGetColumn(svd->U,i,&u));
47: PetscCall(VecPointwiseMult(w,v,svd->omega));
48: PetscCall(MatMult(svd->A,w,u));
49: PetscCall(BVRestoreColumn(svd->V,i,&v));
50: PetscCall(BVRestoreColumn(svd->U,i,&u));
51: }
52: PetscCall(VecDestroy(&w));
53: } else { /* compute left singular vectors as usual U=A*V, and set-up Omega-orthogonalization of U */
54: PetscCall(BV_SetMatrixDiagonal(svd->U,svd->omega,svd->A));
55: PetscCall(BVMatMult(svd->V,svd->A,svd->U));
56: }
57: PetscCall(BVOrthogonalize(svd->U,NULL));
58: if (svd->ishyperbolic && !svd->swapped) { /* store signature after Omega-orthogonalization */
59: PetscCall(MatGetVecType(svd->A,&vtype));
60: PetscCall(VecCreate(PETSC_COMM_SELF,&omega2));
61: PetscCall(VecSetSizes(omega2,svd->nconv,svd->nconv));
62: PetscCall(VecSetType(omega2,vtype));
63: PetscCall(BVGetSignature(svd->U,omega2));
64: PetscCall(VecGetArrayRead(omega2,&varray));
65: for (i=0;i<svd->nconv;i++) {
66: svd->sign[i] = PetscRealPart(varray[i]);
67: if (PetscRealPart(varray[i])<0.0) PetscCall(BVScaleColumn(svd->U,i,-1.0));
68: }
69: PetscCall(VecRestoreArrayRead(omega2,&varray));
70: PetscCall(VecDestroy(&omega2));
71: }
72: }
73: PetscFunctionReturn(PETSC_SUCCESS);
74: }
76: PetscErrorCode SVDComputeVectors(SVD svd)
77: {
78: PetscFunctionBegin;
79: SVDCheckSolved(svd,1);
80: if (svd->state==SVD_STATE_SOLVED) PetscTryTypeMethod(svd,computevectors);
81: svd->state = SVD_STATE_VECTORS;
82: PetscFunctionReturn(PETSC_SUCCESS);
83: }
85: /*@
86: SVDSolve - Solves the singular value problem.
88: Collective
90: Input Parameter:
91: . svd - the singular value solver context
93: Options Database Keys:
94: + -svd_view - print information about the solver used
95: . -svd_view_mat0 - view the first matrix ($A$)
96: . -svd_view_mat1 - view the second matrix ($B$)
97: . -svd_view_signature - view the signature matrix ($\Omega$)
98: . -svd_view_vectors - view the computed singular vectors
99: . -svd_view_values - view the computed singular values
100: . -svd_converged_reason - print reason for convergence/divergence, and number of iterations
101: . -svd_error_absolute - print absolute errors of each singular triplet
102: . -svd_error_relative - print relative errors of each singular triplet
103: - -svd_error_norm - print errors relative to the matrix norms of each singular triplet
105: Notes:
106: The problem matrices are specified with `SVDSetOperators()`.
108: `SVDSolve()` will return without generating an error regardless of whether
109: all requested solutions were computed or not. Call `SVDGetConverged()` to get the
110: actual number of computed solutions, and `SVDGetConvergedReason()` to determine if
111: the solver converged or failed and why.
113: All the command-line options listed above admit an optional argument specifying
114: the viewer type and options. For instance, use `-svd_view_mat0 binary:amatrix.bin`
115: to save the $A$ matrix to a binary file, `-svd_view_values draw` to draw the computed
116: singular values graphically, or `-svd_error_relative :myerr.m:ascii_matlab` to save
117: the errors in a file that can be executed in Matlab.
119: Level: beginner
121: .seealso: [](ch:svd), `SVDCreate()`, `SVDSetUp()`, `SVDDestroy()`, `SVDSetOperators()`, `SVDGetConverged()`, `SVDGetConvergedReason()`
122: @*/
123: PetscErrorCode SVDSolve(SVD svd)
124: {
125: PetscInt i,m,n,*workperm;
127: PetscFunctionBegin;
129: if (svd->state>=SVD_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS);
130: PetscCall(PetscLogEventBegin(SVD_Solve,svd,0,0,0));
132: /* call setup */
133: PetscCall(SVDSetUp(svd));
135: /* safeguard for matrices with zero rows or columns */
136: PetscCall(MatGetSize(svd->OP,&m,&n));
137: if (m == 0 || n == 0) {
138: svd->nconv = 0;
139: svd->reason = SVD_CONVERGED_TOL;
140: svd->state = SVD_STATE_SOLVED;
141: PetscFunctionReturn(PETSC_SUCCESS);
142: }
144: svd->its = 0;
145: svd->nconv = 0;
146: for (i=0;i<svd->ncv;i++) {
147: svd->sigma[i] = 0.0;
148: svd->errest[i] = 0.0;
149: svd->perm[i] = i;
150: }
151: PetscCall(SVDViewFromOptions(svd,NULL,"-svd_view_pre"));
153: switch (svd->problem_type) {
154: case SVD_STANDARD:
155: PetscUseTypeMethod(svd,solve);
156: break;
157: case SVD_GENERALIZED:
158: PetscUseTypeMethod(svd,solveg);
159: break;
160: case SVD_HYPERBOLIC:
161: PetscUseTypeMethod(svd,solveh);
162: break;
163: }
164: svd->state = SVD_STATE_SOLVED;
166: /* sort singular triplets */
167: if (svd->which == SVD_SMALLEST) PetscCall(PetscSortRealWithPermutation(svd->nconv,svd->sigma,svd->perm));
168: else {
169: PetscCall(PetscMalloc1(svd->nconv,&workperm));
170: for (i=0;i<svd->nconv;i++) workperm[i] = i;
171: PetscCall(PetscSortRealWithPermutation(svd->nconv,svd->sigma,workperm));
172: for (i=0;i<svd->nconv;i++) svd->perm[i] = workperm[svd->nconv-i-1];
173: PetscCall(PetscFree(workperm));
174: }
175: PetscCall(PetscLogEventEnd(SVD_Solve,svd,0,0,0));
177: /* various viewers */
178: PetscCall(SVDViewFromOptions(svd,NULL,"-svd_view"));
179: PetscCall(SVDConvergedReasonViewFromOptions(svd));
180: PetscCall(SVDErrorViewFromOptions(svd));
181: PetscCall(SVDValuesViewFromOptions(svd));
182: PetscCall(SVDVectorsViewFromOptions(svd));
183: PetscCall(MatViewFromOptions(svd->OP,(PetscObject)svd,"-svd_view_mat0"));
184: if (svd->isgeneralized) PetscCall(MatViewFromOptions(svd->OPb,(PetscObject)svd,"-svd_view_mat1"));
185: if (svd->ishyperbolic) PetscCall(VecViewFromOptions(svd->omega,(PetscObject)svd,"-svd_view_signature"));
187: /* Remove the initial subspaces */
188: svd->nini = 0;
189: svd->ninil = 0;
190: PetscFunctionReturn(PETSC_SUCCESS);
191: }
193: /*@
194: SVDGetIterationNumber - Gets the current iteration number. If the
195: call to `SVDSolve()` is complete, then it returns the number of iterations
196: carried out by the solution method.
198: Not Collective
200: Input Parameter:
201: . svd - the singular value solver context
203: Output Parameter:
204: . its - number of iterations
206: Note:
207: During the $i$-th iteration this call returns $i-1$. If `SVDSolve()` is
208: complete, then parameter `its` contains either the iteration number at
209: which convergence was successfully reached, or failure was detected.
210: Call `SVDGetConvergedReason()` to determine if the solver converged or
211: failed and why.
213: Level: intermediate
215: .seealso: [](ch:svd), `SVDGetConvergedReason()`, `SVDSetTolerances()`
216: @*/
217: PetscErrorCode SVDGetIterationNumber(SVD svd,PetscInt *its)
218: {
219: PetscFunctionBegin;
221: PetscAssertPointer(its,2);
222: *its = svd->its;
223: PetscFunctionReturn(PETSC_SUCCESS);
224: }
226: /*@
227: SVDGetConvergedReason - Gets the reason why the `SVDSolve()` iteration was
228: stopped.
230: Not Collective
232: Input Parameter:
233: . svd - the singular value solver context
235: Output Parameter:
236: . reason - negative value indicates diverged, positive value converged, see
237: `SVDConvergedReason` for the possible values
239: Options Database Key:
240: . -svd_converged_reason - print reason for convergence/divergence, and number of iterations
242: Note:
243: If this routine is called before or doing the `SVDSolve()` the value of
244: `SVD_CONVERGED_ITERATING` is returned.
246: Level: intermediate
248: .seealso: [](ch:svd), `SVDSetTolerances()`, `SVDSolve()`, `SVDConvergedReason`
249: @*/
250: PetscErrorCode SVDGetConvergedReason(SVD svd,SVDConvergedReason *reason)
251: {
252: PetscFunctionBegin;
254: PetscAssertPointer(reason,2);
255: SVDCheckSolved(svd,1);
256: *reason = svd->reason;
257: PetscFunctionReturn(PETSC_SUCCESS);
258: }
260: /*@
261: SVDGetConverged - Gets the number of converged singular values.
263: Not Collective
265: Input Parameter:
266: . svd - the singular value solver context
268: Output Parameter:
269: . nconv - number of converged singular values
271: Notes:
272: This function should be called after `SVDSolve()` has finished.
274: The value `nconv` may be different from the number of requested solutions
275: `nsv`, but not larger than `ncv`, see `SVDSetDimensions()`.
277: Level: beginner
279: .seealso: [](ch:svd), `SVDSetDimensions()`, `SVDSolve()`, `SVDGetSingularTriplet()`
280: @*/
281: PetscErrorCode SVDGetConverged(SVD svd,PetscInt *nconv)
282: {
283: PetscFunctionBegin;
285: PetscAssertPointer(nconv,2);
286: SVDCheckSolved(svd,1);
287: *nconv = svd->nconv;
288: PetscFunctionReturn(PETSC_SUCCESS);
289: }
291: /*@
292: SVDGetSingularTriplet - Gets the `i`-th triplet of the singular value decomposition
293: as computed by `SVDSolve()`. The solution consists in the singular value and its left
294: and right singular vectors.
296: Collective
298: Input Parameters:
299: + svd - the singular value solver context
300: - i - index of the solution
302: Output Parameters:
303: + sigma - singular value
304: . u - left singular vector
305: - v - right singular vector
307: Note:
308: Both `u` or `v` can be `NULL` if singular vectors are not required.
309: Otherwise, the caller must provide valid `Vec` objects, i.e.,
310: they must be created by the calling program with e.g. `MatCreateVecs()`.
312: The index `i` should be a value between 0 and `nconv`-1 (see `SVDGetConverged()`).
313: Singular triplets are indexed according to the ordering criterion established
314: with `SVDSetWhichSingularTriplets()`.
316: In the case of GSVD, the solution consists in three vectors $u$, $v$, $x$ that are
317: returned as follows. Vector $x$ is returned in the right singular vector
318: (argument `v`) and has length equal to the number of columns of $A$ and $B$.
319: The other two vectors are returned stacked on top of each other $[u^*,v^*]^*$ in
320: the left singular vector argument `u`, with length equal to $m+n$ (number of rows
321: of $A$ plus number of rows of $B$).
323: Level: beginner
325: .seealso: [](ch:svd), `SVDSolve()`, `SVDGetConverged()`, `SVDSetWhichSingularTriplets()`
326: @*/
327: PetscErrorCode SVDGetSingularTriplet(SVD svd,PetscInt i,PetscReal *sigma,Vec u,Vec v)
328: {
329: PetscInt M,N;
330: Vec w;
332: PetscFunctionBegin;
335: SVDCheckSolved(svd,1);
338: PetscCheck(i>=0,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative");
339: PetscCheck(i<svd->nconv,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see SVDGetConverged()");
340: if (sigma) *sigma = svd->sigma[svd->perm[i]];
341: if (u || v) {
342: if (!svd->isgeneralized) {
343: PetscCall(MatGetSize(svd->OP,&M,&N));
344: if (M<N) { w = u; u = v; v = w; }
345: }
346: PetscCall(SVDComputeVectors(svd));
347: if (u) PetscCall(BVCopyVec(svd->U,svd->perm[i],u));
348: if (v) PetscCall(BVCopyVec(svd->V,svd->perm[i],v));
349: }
350: PetscFunctionReturn(PETSC_SUCCESS);
351: }
353: /*
354: SVDComputeResidualNorms_Standard - Computes the norms of the left and
355: right residuals associated with the i-th computed singular triplet.
357: Input Parameters:
358: sigma - singular value
359: u,v - singular vectors
360: x,y - two work vectors with the same dimensions as u,v
361: */
362: static PetscErrorCode SVDComputeResidualNorms_Standard(SVD svd,PetscReal sigma,Vec u,Vec v,Vec x,Vec y,PetscReal *norm1,PetscReal *norm2)
363: {
364: PetscInt M,N;
366: PetscFunctionBegin;
367: /* norm1 = ||A*v-sigma*u||_2 */
368: if (norm1) {
369: PetscCall(MatMult(svd->OP,v,x));
370: PetscCall(VecAXPY(x,-sigma,u));
371: PetscCall(VecNorm(x,NORM_2,norm1));
372: }
373: /* norm2 = ||A^T*u-sigma*v||_2 */
374: if (norm2) {
375: PetscCall(MatGetSize(svd->OP,&M,&N));
376: if (M<N) PetscCall(MatMult(svd->A,u,y));
377: else PetscCall(MatMult(svd->AT,u,y));
378: PetscCall(VecAXPY(y,-sigma,v));
379: PetscCall(VecNorm(y,NORM_2,norm2));
380: }
381: PetscFunctionReturn(PETSC_SUCCESS);
382: }
384: /*
385: SVDComputeResidualNorms_Generalized - In GSVD, compute the residual norms
386: norm1 = ||s^2*A'*u-c*B'*B*x||_2 and norm2 = ||c^2*B'*v-s*A'*A*x||_2.
388: Input Parameters:
389: sigma - singular value
390: uv - left singular vectors [u;v]
391: x - right singular vector
392: y,z - two work vectors with the same dimension as x
393: */
394: static PetscErrorCode SVDComputeResidualNorms_Generalized(SVD svd,PetscReal sigma,Vec uv,Vec x,Vec y,Vec z,PetscReal *norm1,PetscReal *norm2)
395: {
396: Vec u,v,ax,bx,nest,aux[2];
397: PetscReal c,s;
399: PetscFunctionBegin;
400: PetscCall(MatCreateVecs(svd->OP,NULL,&u));
401: PetscCall(MatCreateVecs(svd->OPb,NULL,&v));
402: aux[0] = u;
403: aux[1] = v;
404: PetscCall(VecCreateNest(PetscObjectComm((PetscObject)svd),2,NULL,aux,&nest));
405: PetscCall(VecCopy(uv,nest));
407: s = 1.0/PetscSqrtReal(1.0+sigma*sigma);
408: c = sigma*s;
410: /* norm1 = ||s^2*A'*u-c*B'*B*x||_2 */
411: if (norm1) {
412: PetscCall(VecDuplicate(v,&bx));
413: PetscCall(MatMultHermitianTranspose(svd->OP,u,z));
414: PetscCall(MatMult(svd->OPb,x,bx));
415: PetscCall(MatMultHermitianTranspose(svd->OPb,bx,y));
416: PetscCall(VecAXPBY(y,s*s,-c,z));
417: PetscCall(VecNorm(y,NORM_2,norm1));
418: PetscCall(VecDestroy(&bx));
419: }
420: /* norm2 = ||c^2*B'*v-s*A'*A*x||_2 */
421: if (norm2) {
422: PetscCall(VecDuplicate(u,&ax));
423: PetscCall(MatMultHermitianTranspose(svd->OPb,v,z));
424: PetscCall(MatMult(svd->OP,x,ax));
425: PetscCall(MatMultHermitianTranspose(svd->OP,ax,y));
426: PetscCall(VecAXPBY(y,c*c,-s,z));
427: PetscCall(VecNorm(y,NORM_2,norm2));
428: PetscCall(VecDestroy(&ax));
429: }
431: PetscCall(VecDestroy(&v));
432: PetscCall(VecDestroy(&u));
433: PetscCall(VecDestroy(&nest));
434: PetscFunctionReturn(PETSC_SUCCESS);
435: }
437: /*
438: SVDComputeResidualNorms_Hyperbolic - Computes the norms of the left and
439: right residuals associated with the i-th computed singular triplet.
441: Input Parameters:
442: sigma - singular value
443: sign - corresponding element of the signature Omega2
444: u,v - singular vectors
445: x,y,z - three work vectors with the same dimensions as u,v,u
446: */
447: static PetscErrorCode SVDComputeResidualNorms_Hyperbolic(SVD svd,PetscReal sigma,PetscReal sign,Vec u,Vec v,Vec x,Vec y,Vec z,PetscReal *norm1,PetscReal *norm2)
448: {
449: PetscInt M,N;
451: PetscFunctionBegin;
452: /* norm1 = ||A*v-sigma*u||_2 */
453: if (norm1) {
454: PetscCall(MatMult(svd->OP,v,x));
455: PetscCall(VecAXPY(x,-sigma,u));
456: PetscCall(VecNorm(x,NORM_2,norm1));
457: }
458: /* norm2 = ||A^T*Omega*u-sigma*sign*v||_2 */
459: if (norm2) {
460: PetscCall(MatGetSize(svd->OP,&M,&N));
461: PetscCall(VecPointwiseMult(z,u,svd->omega));
462: if (M<N) PetscCall(MatMult(svd->A,z,y));
463: else PetscCall(MatMult(svd->AT,z,y));
464: PetscCall(VecAXPY(y,-sigma*sign,v));
465: PetscCall(VecNorm(y,NORM_2,norm2));
466: }
467: PetscFunctionReturn(PETSC_SUCCESS);
468: }
470: /*@
471: SVDComputeError - Computes the error (based on the residual norm) associated
472: with the `i`-th singular triplet.
474: Collective
476: Input Parameters:
477: + svd - the singular value solver context
478: . i - the solution index
479: - type - the type of error to compute, see `SVDErrorType`
481: Output Parameter:
482: . error - the error
484: Notes:
485: The error can be computed in various ways, all of them based on the residual
486: norm obtained as $\sqrt{\eta_1^2+\eta_2^2}$ with $\eta_1 = \|Av-\sigma u\|_2$ and
487: $\eta_2 = \|A^*u-\sigma v\|_2$, where $(\sigma,u,v)$ is the approximate singular
488: triplet.
490: In the case of the GSVD, the two components of the residual norm are
491: $\eta_1 = \|s^2 A^*u-cB^*Bx\|_2$ and $\eta_2 = ||c^2 B^*v-sA^*Ax||_2$, where
492: $(\sigma,u,v,x)$ is the approximate generalized singular quadruple, with
493: $\sigma=c/s$.
495: Level: beginner
497: .seealso: [](ch:svd), `SVDErrorType`, `SVDSolve()`
498: @*/
499: PetscErrorCode SVDComputeError(SVD svd,PetscInt i,SVDErrorType type,PetscReal *error)
500: {
501: PetscReal sigma,norm1,norm2,c,s;
502: Vec u=NULL,v=NULL,x=NULL,y=NULL,z=NULL;
503: PetscReal vecnorm=1.0;
505: PetscFunctionBegin;
509: PetscAssertPointer(error,4);
510: SVDCheckSolved(svd,1);
512: /* allocate work vectors */
513: switch (svd->problem_type) {
514: case SVD_STANDARD:
515: PetscCall(SVDSetWorkVecs(svd,2,2));
516: u = svd->workl[0];
517: v = svd->workr[0];
518: x = svd->workl[1];
519: y = svd->workr[1];
520: break;
521: case SVD_GENERALIZED:
522: PetscCall(SVDSetWorkVecs(svd,1,3));
523: u = svd->workl[0];
524: v = svd->workr[0];
525: x = svd->workr[1];
526: y = svd->workr[2];
527: break;
528: case SVD_HYPERBOLIC:
529: PetscCall(SVDSetWorkVecs(svd,3,2));
530: u = svd->workl[0];
531: v = svd->workr[0];
532: x = svd->workl[1];
533: y = svd->workr[1];
534: z = svd->workl[2];
535: break;
536: }
538: /* compute residual norm */
539: PetscCall(SVDGetSingularTriplet(svd,i,&sigma,u,v));
540: switch (svd->problem_type) {
541: case SVD_STANDARD:
542: PetscCall(SVDComputeResidualNorms_Standard(svd,sigma,u,v,x,y,&norm1,&norm2));
543: break;
544: case SVD_GENERALIZED:
545: PetscCall(SVDComputeResidualNorms_Generalized(svd,sigma,u,v,x,y,&norm1,&norm2));
546: break;
547: case SVD_HYPERBOLIC:
548: PetscCall(SVDComputeResidualNorms_Hyperbolic(svd,sigma,svd->sign[svd->perm[i]],u,v,x,y,z,&norm1,&norm2));
549: break;
550: }
551: *error = SlepcAbs(norm1,norm2);
553: /* compute 2-norm of eigenvector of the cyclic form */
554: if (type!=SVD_ERROR_ABSOLUTE) {
555: switch (svd->problem_type) {
556: case SVD_STANDARD:
557: vecnorm = PETSC_SQRT2;
558: break;
559: case SVD_GENERALIZED:
560: PetscCall(VecNorm(v,NORM_2,&vecnorm));
561: vecnorm = PetscSqrtReal(1.0+vecnorm*vecnorm);
562: break;
563: case SVD_HYPERBOLIC:
564: PetscCall(VecNorm(u,NORM_2,&vecnorm));
565: vecnorm = PetscSqrtReal(1.0+vecnorm*vecnorm);
566: break;
567: }
568: }
570: /* compute error */
571: switch (type) {
572: case SVD_ERROR_ABSOLUTE:
573: break;
574: case SVD_ERROR_RELATIVE:
575: if (svd->isgeneralized) {
576: s = 1.0/PetscSqrtReal(1.0+sigma*sigma);
577: c = sigma*s;
578: norm1 /= c*vecnorm;
579: norm2 /= s*vecnorm;
580: *error = PetscMax(norm1,norm2);
581: } else *error /= sigma*vecnorm;
582: break;
583: case SVD_ERROR_NORM:
584: if (!svd->nrma) PetscCall(MatNorm(svd->OP,NORM_INFINITY,&svd->nrma));
585: if (svd->isgeneralized && !svd->nrmb) PetscCall(MatNorm(svd->OPb,NORM_INFINITY,&svd->nrmb));
586: *error /= PetscMax(svd->nrma,svd->nrmb)*vecnorm;
587: break;
588: default:
589: SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type");
590: }
591: PetscFunctionReturn(PETSC_SUCCESS);
592: }