Actual source code: trlanczos.c
slepc-3.19.2 2023-09-05
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: SLEPc singular value solver: "trlanczos"
13: Method: Thick-restart Lanczos
15: Algorithm:
17: Golub-Kahan-Lanczos bidiagonalization with thick-restart.
19: References:
21: [1] G.H. Golub and W. Kahan, "Calculating the singular values
22: and pseudo-inverse of a matrix", SIAM J. Numer. Anal. Ser.
23: B 2:205-224, 1965.
25: [2] V. Hernandez, J.E. Roman, and A. Tomas, "A robust and
26: efficient parallel SVD solver based on restarted Lanczos
27: bidiagonalization", Elec. Trans. Numer. Anal. 31:68-85,
28: 2008.
29: */
31: #include <slepc/private/svdimpl.h>
32: #include <slepc/private/bvimpl.h>
34: static PetscBool cited = PETSC_FALSE,citedg = PETSC_FALSE;
35: static const char citation[] =
36: "@Article{slepc-svd,\n"
37: " author = \"V. Hern{\\'a}ndez and J. E. Rom{\\'a}n and A. Tom{\\'a}s\",\n"
38: " title = \"A robust and efficient parallel {SVD} solver based on restarted {Lanczos} bidiagonalization\",\n"
39: " journal = \"Electron. Trans. Numer. Anal.\",\n"
40: " volume = \"31\",\n"
41: " pages = \"68--85\",\n"
42: " year = \"2008\"\n"
43: "}\n";
44: static const char citationg[] =
45: "@Article{slepc-gsvd,\n"
46: " author = \"F. Alvarruiz and C. Campos and J. E. Roman\",\n"
47: " title = \"Thick-restarted {Lanczos} bidiagonalization methods for the {GSVD}\",\n"
48: " note = \"arXiv:2206.03768\",\n"
49: " year = \"2022\"\n"
50: "}\n";
52: typedef struct {
53: /* user parameters */
54: PetscBool oneside; /* one-sided variant */
55: PetscReal keep; /* restart parameter */
56: PetscBool lock; /* locking/non-locking variant */
57: KSP ksp; /* solver for least-squares problem in GSVD */
58: SVDTRLanczosGBidiag bidiag; /* bidiagonalization variant for GSVD */
59: PetscReal scalef; /* scale factor for matrix B */
60: PetscReal scaleth; /* scale threshold for automatic scaling */
61: PetscBool explicitmatrix;
62: /* auxiliary variables */
63: Mat Z; /* aux matrix for GSVD, Z=[A;B] */
64: } SVD_TRLANCZOS;
66: /* Context for shell matrix [A; B] */
67: typedef struct {
68: Mat A,B,AT,BT;
69: Vec y1,y2,y;
70: PetscInt m;
71: PetscReal scalef;
72: } MatZData;
74: static PetscErrorCode MatZCreateContext(SVD svd,MatZData **zdata)
75: {
76: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
78: PetscFunctionBegin;
79: PetscCall(PetscNew(zdata));
80: (*zdata)->A = svd->A;
81: (*zdata)->B = svd->B;
82: (*zdata)->AT = svd->AT;
83: (*zdata)->BT = svd->BT;
84: (*zdata)->scalef = lanczos->scalef;
85: PetscCall(MatCreateVecsEmpty(svd->A,NULL,&(*zdata)->y1));
86: PetscCall(MatCreateVecsEmpty(svd->B,NULL,&(*zdata)->y2));
87: PetscCall(VecGetLocalSize((*zdata)->y1,&(*zdata)->m));
88: PetscCall(BVCreateVec(svd->U,&(*zdata)->y));
89: PetscFunctionReturn(PETSC_SUCCESS);
90: }
92: /* Update scale factor for B in Z=[A;B]
93: If matrices are swapped, the scale factor is inverted.*/
94: static PetscErrorCode MatZUpdateScale(SVD svd)
95: {
96: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
97: MatZData *zdata;
98: Mat mats[2],normal;
99: MatType Atype;
100: PetscBool sametype;
101: PetscReal scalef = svd->swapped? 1.0/lanczos->scalef : lanczos->scalef;
103: PetscFunctionBegin;
104: if (lanczos->explicitmatrix) {
105: /* Destroy the matrix Z and create it again */
106: PetscCall(MatDestroy(&lanczos->Z));
107: mats[0] = svd->A;
108: if (scalef == 1.0) {
109: mats[1] = svd->B;
110: } else {
111: PetscCall(MatDuplicate(svd->B,MAT_COPY_VALUES,&mats[1]));
112: PetscCall(MatScale(mats[1],scalef));
113: }
114: PetscCall(MatCreateNest(PetscObjectComm((PetscObject)svd),2,NULL,1,NULL,mats,&lanczos->Z));
115: PetscCall(MatGetType(svd->A,&Atype));
116: PetscCall(PetscObjectTypeCompare((PetscObject)svd->B,Atype,&sametype));
117: if (!sametype) Atype = MATAIJ;
118: PetscCall(MatConvert(lanczos->Z,Atype,MAT_INPLACE_MATRIX,&lanczos->Z));
119: if (scalef != 1.0) PetscCall(MatDestroy(&mats[1]));
120: } else {
121: PetscCall(MatShellGetContext(lanczos->Z,&zdata));
122: zdata->scalef = scalef;
123: }
125: /* create normal equations matrix, to build the preconditioner in LSQR */
126: PetscCall(MatCreateNormalHermitian(lanczos->Z,&normal));
128: if (!lanczos->ksp) PetscCall(SVDTRLanczosGetKSP(svd,&lanczos->ksp));
129: PetscCall(SVD_KSPSetOperators(lanczos->ksp,lanczos->Z,normal));
130: PetscCall(KSPSetUp(lanczos->ksp));
131: PetscCall(MatDestroy(&normal));
132: PetscFunctionReturn(PETSC_SUCCESS);
133: }
135: static PetscErrorCode MatDestroy_Z(Mat Z)
136: {
137: MatZData *zdata;
139: PetscFunctionBegin;
140: PetscCall(MatShellGetContext(Z,&zdata));
141: PetscCall(VecDestroy(&zdata->y1));
142: PetscCall(VecDestroy(&zdata->y2));
143: PetscCall(VecDestroy(&zdata->y));
144: PetscCall(PetscFree(zdata));
145: PetscFunctionReturn(PETSC_SUCCESS);
146: }
148: static PetscErrorCode MatMult_Z(Mat Z,Vec x,Vec y)
149: {
150: MatZData *zdata;
151: PetscScalar *y_elems;
153: PetscFunctionBegin;
154: PetscCall(MatShellGetContext(Z,&zdata));
155: PetscCall(VecGetArray(y,&y_elems));
156: PetscCall(VecPlaceArray(zdata->y1,y_elems));
157: PetscCall(VecPlaceArray(zdata->y2,y_elems+zdata->m));
159: PetscCall(MatMult(zdata->A,x,zdata->y1));
160: PetscCall(MatMult(zdata->B,x,zdata->y2));
161: PetscCall(VecScale(zdata->y2,zdata->scalef));
163: PetscCall(VecResetArray(zdata->y1));
164: PetscCall(VecResetArray(zdata->y2));
165: PetscCall(VecRestoreArray(y,&y_elems));
166: PetscFunctionReturn(PETSC_SUCCESS);
167: }
169: static PetscErrorCode MatMultTranspose_Z(Mat Z,Vec y,Vec x)
170: {
171: MatZData *zdata;
172: const PetscScalar *y_elems;
174: PetscFunctionBegin;
175: PetscCall(MatShellGetContext(Z,&zdata));
176: PetscCall(VecGetArrayRead(y,&y_elems));
177: PetscCall(VecPlaceArray(zdata->y1,y_elems));
178: PetscCall(VecPlaceArray(zdata->y2,y_elems+zdata->m));
180: PetscCall(MatMult(zdata->BT,zdata->y2,x));
181: PetscCall(VecScale(x,zdata->scalef));
182: PetscCall(MatMultAdd(zdata->AT,zdata->y1,x,x));
184: PetscCall(VecResetArray(zdata->y1));
185: PetscCall(VecResetArray(zdata->y2));
186: PetscCall(VecRestoreArrayRead(y,&y_elems));
187: PetscFunctionReturn(PETSC_SUCCESS);
188: }
190: static PetscErrorCode MatCreateVecs_Z(Mat Z,Vec *right,Vec *left)
191: {
192: MatZData *zdata;
194: PetscFunctionBegin;
195: PetscCall(MatShellGetContext(Z,&zdata));
196: if (right) PetscCall(MatCreateVecs(zdata->A,right,NULL));
197: if (left) PetscCall(VecDuplicate(zdata->y,left));
198: PetscFunctionReturn(PETSC_SUCCESS);
199: }
201: #define SWAP(a,b,t) do {t=a;a=b;b=t;} while (0)
203: PetscErrorCode SVDSetUp_TRLanczos(SVD svd)
204: {
205: PetscInt M,N,P,m,n,p;
206: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
207: MatZData *zdata;
208: Mat aux;
210: PetscFunctionBegin;
211: PetscCall(MatGetSize(svd->A,&M,&N));
212: PetscCall(SVDSetDimensions_Default(svd));
213: PetscCheck(svd->ncv<=svd->nsv+svd->mpd,PetscObjectComm((PetscObject)svd),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nsv+mpd");
214: PetscCheck(lanczos->lock || svd->mpd>=svd->ncv,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
215: if (svd->max_it==PETSC_DEFAULT) svd->max_it = PetscMax(N/svd->ncv,100);
216: if (!lanczos->keep) lanczos->keep = 0.5;
217: svd->leftbasis = PETSC_TRUE;
218: PetscCall(SVDAllocateSolution(svd,1));
219: if (svd->isgeneralized) {
220: PetscCall(MatGetSize(svd->B,&P,NULL));
221: if (lanczos->bidiag == SVD_TRLANCZOS_GBIDIAG_LOWER && ((svd->which==SVD_LARGEST && P<=N) || (svd->which==SVD_SMALLEST && M>N && P<=N))) {
222: SWAP(svd->A,svd->B,aux);
223: SWAP(svd->AT,svd->BT,aux);
224: svd->swapped = PETSC_TRUE;
225: } else svd->swapped = PETSC_FALSE;
227: PetscCall(SVDSetWorkVecs(svd,1,1));
229: if (svd->conv==SVD_CONV_ABS) { /* Residual norms are multiplied by matrix norms */
230: if (!svd->nrma) PetscCall(MatNorm(svd->A,NORM_INFINITY,&svd->nrma));
231: if (!svd->nrmb) PetscCall(MatNorm(svd->B,NORM_INFINITY,&svd->nrmb));
232: }
234: /* Create the matrix Z=[A;B] */
235: PetscCall(MatGetLocalSize(svd->A,&m,&n));
236: PetscCall(MatGetLocalSize(svd->B,&p,NULL));
237: if (!lanczos->explicitmatrix) {
238: PetscCall(MatDestroy(&lanczos->Z));
239: PetscCall(MatZCreateContext(svd,&zdata));
240: PetscCall(MatCreateShell(PetscObjectComm((PetscObject)svd),m+p,n,PETSC_DECIDE,PETSC_DECIDE,zdata,&lanczos->Z));
241: PetscCall(MatShellSetOperation(lanczos->Z,MATOP_MULT,(void(*)(void))MatMult_Z));
242: #if defined(PETSC_USE_COMPLEX)
243: PetscCall(MatShellSetOperation(lanczos->Z,MATOP_MULT_HERMITIAN_TRANSPOSE,(void(*)(void))MatMultTranspose_Z));
244: #else
245: PetscCall(MatShellSetOperation(lanczos->Z,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Z));
246: #endif
247: PetscCall(MatShellSetOperation(lanczos->Z,MATOP_CREATE_VECS,(void(*)(void))MatCreateVecs_Z));
248: PetscCall(MatShellSetOperation(lanczos->Z,MATOP_DESTROY,(void(*)(void))MatDestroy_Z));
249: }
250: /* Explicit matrix is created here, when updating the scale */
251: PetscCall(MatZUpdateScale(svd));
253: } else if (svd->ishyperbolic) {
254: PetscCall(BV_SetMatrixDiagonal(svd->swapped?svd->V:svd->U,svd->omega,svd->OP));
255: PetscCall(SVDSetWorkVecs(svd,1,0));
256: }
257: PetscCall(DSSetCompact(svd->ds,PETSC_TRUE));
258: PetscCall(DSSetExtraRow(svd->ds,PETSC_TRUE));
259: PetscCall(DSAllocate(svd->ds,svd->ncv+1));
260: PetscFunctionReturn(PETSC_SUCCESS);
261: }
263: static PetscErrorCode SVDOneSideTRLanczosMGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
264: {
265: PetscReal a,b;
266: PetscInt i,k=nconv+l;
267: Vec ui,ui1,vi;
269: PetscFunctionBegin;
270: PetscCall(BVGetColumn(V,k,&vi));
271: PetscCall(BVGetColumn(U,k,&ui));
272: PetscCall(MatMult(svd->A,vi,ui));
273: PetscCall(BVRestoreColumn(V,k,&vi));
274: PetscCall(BVRestoreColumn(U,k,&ui));
275: if (l>0) {
276: PetscCall(BVSetActiveColumns(U,nconv,n));
277: for (i=0;i<l;i++) work[i]=beta[i+nconv];
278: PetscCall(BVMultColumn(U,-1.0,1.0,k,work));
279: }
280: PetscCall(BVNormColumn(U,k,NORM_2,&a));
281: PetscCall(BVScaleColumn(U,k,1.0/a));
282: alpha[k] = a;
284: for (i=k+1;i<n;i++) {
285: PetscCall(BVGetColumn(V,i,&vi));
286: PetscCall(BVGetColumn(U,i-1,&ui1));
287: PetscCall(MatMult(svd->AT,ui1,vi));
288: PetscCall(BVRestoreColumn(V,i,&vi));
289: PetscCall(BVRestoreColumn(U,i-1,&ui1));
290: PetscCall(BVOrthonormalizeColumn(V,i,PETSC_FALSE,&b,NULL));
291: beta[i-1] = b;
293: PetscCall(BVGetColumn(V,i,&vi));
294: PetscCall(BVGetColumn(U,i,&ui));
295: PetscCall(MatMult(svd->A,vi,ui));
296: PetscCall(BVRestoreColumn(V,i,&vi));
297: PetscCall(BVGetColumn(U,i-1,&ui1));
298: PetscCall(VecAXPY(ui,-b,ui1));
299: PetscCall(BVRestoreColumn(U,i-1,&ui1));
300: PetscCall(BVRestoreColumn(U,i,&ui));
301: PetscCall(BVNormColumn(U,i,NORM_2,&a));
302: PetscCall(BVScaleColumn(U,i,1.0/a));
303: alpha[i] = a;
304: }
306: PetscCall(BVGetColumn(V,n,&vi));
307: PetscCall(BVGetColumn(U,n-1,&ui1));
308: PetscCall(MatMult(svd->AT,ui1,vi));
309: PetscCall(BVRestoreColumn(V,n,&vi));
310: PetscCall(BVRestoreColumn(U,n-1,&ui1));
311: PetscCall(BVOrthogonalizeColumn(V,n,NULL,&b,NULL));
312: beta[n-1] = b;
313: PetscFunctionReturn(PETSC_SUCCESS);
314: }
316: /*
317: Custom CGS orthogonalization, preprocess after first orthogonalization
318: */
319: static PetscErrorCode SVDOrthogonalizeCGS(BV V,PetscInt i,PetscScalar* h,PetscReal a,BVOrthogRefineType refine,PetscReal eta,PetscReal *norm)
320: {
321: PetscReal sum,onorm;
322: PetscScalar dot;
323: PetscInt j;
325: PetscFunctionBegin;
326: switch (refine) {
327: case BV_ORTHOG_REFINE_NEVER:
328: PetscCall(BVNormColumn(V,i,NORM_2,norm));
329: break;
330: case BV_ORTHOG_REFINE_ALWAYS:
331: PetscCall(BVSetActiveColumns(V,0,i));
332: PetscCall(BVDotColumn(V,i,h));
333: PetscCall(BVMultColumn(V,-1.0,1.0,i,h));
334: PetscCall(BVNormColumn(V,i,NORM_2,norm));
335: break;
336: case BV_ORTHOG_REFINE_IFNEEDED:
337: dot = h[i];
338: onorm = PetscSqrtReal(PetscRealPart(dot)) / a;
339: sum = 0.0;
340: for (j=0;j<i;j++) {
341: sum += PetscRealPart(h[j] * PetscConj(h[j]));
342: }
343: *norm = PetscRealPart(dot)/(a*a) - sum;
344: if (*norm>0.0) *norm = PetscSqrtReal(*norm);
345: else PetscCall(BVNormColumn(V,i,NORM_2,norm));
346: if (*norm < eta*onorm) {
347: PetscCall(BVSetActiveColumns(V,0,i));
348: PetscCall(BVDotColumn(V,i,h));
349: PetscCall(BVMultColumn(V,-1.0,1.0,i,h));
350: PetscCall(BVNormColumn(V,i,NORM_2,norm));
351: }
352: break;
353: }
354: PetscFunctionReturn(PETSC_SUCCESS);
355: }
357: static PetscErrorCode SVDOneSideTRLanczosCGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
358: {
359: PetscReal a,b,eta;
360: PetscInt i,j,k=nconv+l;
361: Vec ui,ui1,vi;
362: BVOrthogRefineType refine;
364: PetscFunctionBegin;
365: PetscCall(BVGetColumn(V,k,&vi));
366: PetscCall(BVGetColumn(U,k,&ui));
367: PetscCall(MatMult(svd->A,vi,ui));
368: PetscCall(BVRestoreColumn(V,k,&vi));
369: PetscCall(BVRestoreColumn(U,k,&ui));
370: if (l>0) {
371: PetscCall(BVSetActiveColumns(U,nconv,n));
372: for (i=0;i<l;i++) work[i]=beta[i+nconv];
373: PetscCall(BVMultColumn(U,-1.0,1.0,k,work));
374: }
375: PetscCall(BVGetOrthogonalization(V,NULL,&refine,&eta,NULL));
377: for (i=k+1;i<n;i++) {
378: PetscCall(BVGetColumn(V,i,&vi));
379: PetscCall(BVGetColumn(U,i-1,&ui1));
380: PetscCall(MatMult(svd->AT,ui1,vi));
381: PetscCall(BVRestoreColumn(V,i,&vi));
382: PetscCall(BVRestoreColumn(U,i-1,&ui1));
383: PetscCall(BVNormColumnBegin(U,i-1,NORM_2,&a));
384: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
385: PetscCall(BVSetActiveColumns(V,0,i+1));
386: PetscCall(BVGetColumn(V,i,&vi));
387: PetscCall(BVDotVecBegin(V,vi,work));
388: } else {
389: PetscCall(BVSetActiveColumns(V,0,i));
390: PetscCall(BVDotColumnBegin(V,i,work));
391: }
392: PetscCall(BVNormColumnEnd(U,i-1,NORM_2,&a));
393: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
394: PetscCall(BVDotVecEnd(V,vi,work));
395: PetscCall(BVRestoreColumn(V,i,&vi));
396: PetscCall(BVSetActiveColumns(V,0,i));
397: } else PetscCall(BVDotColumnEnd(V,i,work));
399: PetscCall(BVScaleColumn(U,i-1,1.0/a));
400: for (j=0;j<i;j++) work[j] = work[j] / a;
401: PetscCall(BVMultColumn(V,-1.0,1.0/a,i,work));
402: PetscCall(SVDOrthogonalizeCGS(V,i,work,a,refine,eta,&b));
403: PetscCall(BVScaleColumn(V,i,1.0/b));
404: PetscCheck(PetscAbsReal(b)>10*PETSC_MACHINE_EPSILON,PetscObjectComm((PetscObject)svd),PETSC_ERR_PLIB,"Recurrence generated a zero vector; use a two-sided variant");
406: PetscCall(BVGetColumn(V,i,&vi));
407: PetscCall(BVGetColumn(U,i,&ui));
408: PetscCall(BVGetColumn(U,i-1,&ui1));
409: PetscCall(MatMult(svd->A,vi,ui));
410: PetscCall(VecAXPY(ui,-b,ui1));
411: PetscCall(BVRestoreColumn(V,i,&vi));
412: PetscCall(BVRestoreColumn(U,i,&ui));
413: PetscCall(BVRestoreColumn(U,i-1,&ui1));
415: alpha[i-1] = a;
416: beta[i-1] = b;
417: }
419: PetscCall(BVGetColumn(V,n,&vi));
420: PetscCall(BVGetColumn(U,n-1,&ui1));
421: PetscCall(MatMult(svd->AT,ui1,vi));
422: PetscCall(BVRestoreColumn(V,n,&vi));
423: PetscCall(BVRestoreColumn(U,n-1,&ui1));
425: PetscCall(BVNormColumnBegin(svd->U,n-1,NORM_2,&a));
426: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
427: PetscCall(BVSetActiveColumns(V,0,n+1));
428: PetscCall(BVGetColumn(V,n,&vi));
429: PetscCall(BVDotVecBegin(V,vi,work));
430: } else {
431: PetscCall(BVSetActiveColumns(V,0,n));
432: PetscCall(BVDotColumnBegin(V,n,work));
433: }
434: PetscCall(BVNormColumnEnd(svd->U,n-1,NORM_2,&a));
435: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
436: PetscCall(BVDotVecEnd(V,vi,work));
437: PetscCall(BVRestoreColumn(V,n,&vi));
438: } else PetscCall(BVDotColumnEnd(V,n,work));
440: PetscCall(BVScaleColumn(U,n-1,1.0/a));
441: for (j=0;j<n;j++) work[j] = work[j] / a;
442: PetscCall(BVMultColumn(V,-1.0,1.0/a,n,work));
443: PetscCall(SVDOrthogonalizeCGS(V,n,work,a,refine,eta,&b));
444: PetscCall(BVSetActiveColumns(V,nconv,n));
445: alpha[n-1] = a;
446: beta[n-1] = b;
447: PetscFunctionReturn(PETSC_SUCCESS);
448: }
450: PetscErrorCode SVDSolve_TRLanczos(SVD svd)
451: {
452: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
453: PetscReal *alpha,*beta;
454: PetscScalar *swork=NULL,*w;
455: PetscInt i,k,l,nv,ld;
456: Mat U,V;
457: PetscBool breakdown=PETSC_FALSE;
458: BVOrthogType orthog;
460: PetscFunctionBegin;
461: PetscCall(PetscCitationsRegister(citation,&cited));
462: /* allocate working space */
463: PetscCall(DSGetLeadingDimension(svd->ds,&ld));
464: PetscCall(BVGetOrthogonalization(svd->V,&orthog,NULL,NULL,NULL));
465: PetscCall(PetscMalloc1(ld,&w));
466: if (lanczos->oneside) PetscCall(PetscMalloc1(svd->ncv+1,&swork));
468: /* normalize start vector */
469: if (!svd->nini) {
470: PetscCall(BVSetRandomColumn(svd->V,0));
471: PetscCall(BVOrthonormalizeColumn(svd->V,0,PETSC_TRUE,NULL,NULL));
472: }
474: l = 0;
475: while (svd->reason == SVD_CONVERGED_ITERATING) {
476: svd->its++;
478: /* inner loop */
479: nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
480: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
481: beta = alpha + ld;
482: if (lanczos->oneside) {
483: if (orthog == BV_ORTHOG_MGS) PetscCall(SVDOneSideTRLanczosMGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv,swork));
484: else PetscCall(SVDOneSideTRLanczosCGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv,swork));
485: } else PetscCall(SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv+l,&nv,&breakdown));
486: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
487: PetscCall(BVScaleColumn(svd->V,nv,1.0/beta[nv-1]));
488: PetscCall(BVSetActiveColumns(svd->V,svd->nconv,nv));
489: PetscCall(BVSetActiveColumns(svd->U,svd->nconv,nv));
491: /* solve projected problem */
492: PetscCall(DSSetDimensions(svd->ds,nv,svd->nconv,svd->nconv+l));
493: PetscCall(DSSVDSetDimensions(svd->ds,nv));
494: PetscCall(DSSetState(svd->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
495: PetscCall(DSSolve(svd->ds,w,NULL));
496: PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
497: PetscCall(DSUpdateExtraRow(svd->ds));
498: PetscCall(DSSynchronize(svd->ds,w,NULL));
499: for (i=svd->nconv;i<nv;i++) svd->sigma[i] = PetscRealPart(w[i]);
501: /* check convergence */
502: PetscCall(SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,1.0,&k));
503: PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));
505: /* update l */
506: if (svd->reason != SVD_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
507: else l = PetscMax(1,(PetscInt)((nv-k)*lanczos->keep));
508: if (!lanczos->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged triplets */
509: if (l) PetscCall(PetscInfo(svd,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
511: if (svd->reason == SVD_CONVERGED_ITERATING) {
512: if (PetscUnlikely(breakdown || k==nv)) {
513: /* Start a new bidiagonalization */
514: PetscCall(PetscInfo(svd,"Breakdown in bidiagonalization (it=%" PetscInt_FMT ")\n",svd->its));
515: if (k<svd->nsv) {
516: PetscCall(BVSetRandomColumn(svd->V,k));
517: PetscCall(BVOrthonormalizeColumn(svd->V,k,PETSC_FALSE,NULL,&breakdown));
518: if (breakdown) {
519: svd->reason = SVD_DIVERGED_BREAKDOWN;
520: PetscCall(PetscInfo(svd,"Unable to generate more start vectors\n"));
521: }
522: }
523: } else PetscCall(DSTruncate(svd->ds,k+l,PETSC_FALSE));
524: }
526: /* compute converged singular vectors and restart vectors */
527: PetscCall(DSGetMat(svd->ds,DS_MAT_V,&V));
528: PetscCall(BVMultInPlace(svd->V,V,svd->nconv,k+l));
529: PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&V));
530: PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
531: PetscCall(BVMultInPlace(svd->U,U,svd->nconv,k+l));
532: PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
534: /* copy the last vector to be the next initial vector */
535: if (svd->reason == SVD_CONVERGED_ITERATING && !breakdown) PetscCall(BVCopyColumn(svd->V,nv,k+l));
537: svd->nconv = k;
538: PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv));
539: }
541: /* orthonormalize U columns in one side method */
542: if (lanczos->oneside) {
543: for (i=0;i<svd->nconv;i++) PetscCall(BVOrthonormalizeColumn(svd->U,i,PETSC_FALSE,NULL,NULL));
544: }
546: /* free working space */
547: PetscCall(PetscFree(w));
548: if (swork) PetscCall(PetscFree(swork));
549: PetscCall(DSTruncate(svd->ds,svd->nconv,PETSC_TRUE));
550: PetscFunctionReturn(PETSC_SUCCESS);
551: }
553: PetscErrorCode SVDLanczosHSVD(SVD svd,PetscReal *alpha,PetscReal *beta,PetscReal *omega,Mat A,Mat AT,BV V,BV U,PetscInt k,PetscInt *n,PetscBool *breakdown)
554: {
555: PetscInt i;
556: Vec u,v,ou=svd->workl[0];
557: PetscBool lindep=PETSC_FALSE;
558: PetscReal norm;
560: PetscFunctionBegin;
561: for (i=k;i<*n;i++) {
562: PetscCall(BVGetColumn(V,i,&v));
563: PetscCall(BVGetColumn(U,i,&u));
564: PetscCall(MatMult(A,v,u));
565: PetscCall(BVRestoreColumn(V,i,&v));
566: PetscCall(BVRestoreColumn(U,i,&u));
567: PetscCall(BVOrthonormalizeColumn(U,i,PETSC_FALSE,alpha+i,&lindep));
568: omega[i] = PetscSign(alpha[i]);
569: if (PetscUnlikely(lindep)) {
570: *n = i;
571: break;
572: }
574: PetscCall(BVGetColumn(V,i+1,&v));
575: PetscCall(BVGetColumn(U,i,&u));
576: PetscCall(VecPointwiseMult(ou,svd->omega,u));
577: PetscCall(MatMult(AT,ou,v));
578: PetscCall(BVRestoreColumn(V,i+1,&v));
579: PetscCall(BVRestoreColumn(U,i,&u));
580: PetscCall(BVOrthonormalizeColumn(V,i+1,PETSC_FALSE,&norm,&lindep));
581: beta[i] = omega[i]*norm;
582: if (PetscUnlikely(lindep)) {
583: *n = i+1;
584: break;
585: }
586: }
588: if (breakdown) *breakdown = lindep;
589: PetscFunctionReturn(PETSC_SUCCESS);
590: }
592: PetscErrorCode SVDSolve_TRLanczos_HSVD(SVD svd)
593: {
594: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
595: PetscReal *alpha,*beta,*omega;
596: PetscScalar *w;
597: PetscInt i,k,l,nv,ld,nini;
598: Mat UU,VV,D,A,AT;
599: BV U,V;
600: PetscBool breakdown=PETSC_FALSE;
601: BVOrthogType orthog;
602: Vec vomega;
604: PetscFunctionBegin;
605: /* undo the effect of swapping in this function */
606: if (svd->swapped) {
607: A = svd->AT;
608: AT = svd->A;
609: U = svd->V;
610: V = svd->U;
611: nini = svd->ninil;
612: } else {
613: A = svd->A;
614: AT = svd->AT;
615: U = svd->U;
616: V = svd->V;
617: nini = svd->nini;
618: }
619: /* allocate working space */
620: PetscCall(DSGetLeadingDimension(svd->ds,&ld));
621: PetscCall(BVGetOrthogonalization(V,&orthog,NULL,NULL,NULL));
622: PetscCall(PetscMalloc1(ld,&w));
623: PetscCheck(!lanczos->oneside,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Oneside orthogonalization not supported for HSVD");
625: /* normalize start vector */
626: if (!nini) {
627: PetscCall(BVSetRandomColumn(V,0));
628: PetscCall(BVOrthonormalizeColumn(V,0,PETSC_TRUE,NULL,NULL));
629: }
631: l = 0;
632: while (svd->reason == SVD_CONVERGED_ITERATING) {
633: svd->its++;
635: /* inner loop */
636: nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
637: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
638: beta = alpha + ld;
639: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_D,&omega));
640: PetscCall(SVDLanczosHSVD(svd,alpha,beta,omega,A,AT,V,U,svd->nconv+l,&nv,&breakdown));
641: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
642: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_D,&omega));
643: PetscCall(BVSetActiveColumns(V,svd->nconv,nv));
644: PetscCall(BVSetActiveColumns(U,svd->nconv,nv));
646: /* solve projected problem */
647: PetscCall(DSSetDimensions(svd->ds,nv,svd->nconv,svd->nconv+l));
648: PetscCall(DSHSVDSetDimensions(svd->ds,nv));
649: PetscCall(DSSetState(svd->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
650: PetscCall(DSSolve(svd->ds,w,NULL));
651: PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
652: PetscCall(DSUpdateExtraRow(svd->ds));
653: PetscCall(DSSynchronize(svd->ds,w,NULL));
654: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_D,&omega));
655: for (i=svd->nconv;i<nv;i++) {
656: svd->sigma[i] = PetscRealPart(w[i]);
657: svd->sign[i] = omega[i];
658: }
659: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_D,&omega));
661: /* check convergence */
662: PetscCall(SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,1.0,&k));
663: PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));
665: /* update l */
666: if (svd->reason != SVD_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
667: else l = PetscMax(1,(PetscInt)((nv-k)*lanczos->keep));
668: if (!lanczos->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged triplets */
669: if (l) PetscCall(PetscInfo(svd,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
671: if (svd->reason == SVD_CONVERGED_ITERATING) {
672: if (PetscUnlikely(breakdown || k==nv)) {
673: /* Start a new bidiagonalization */
674: PetscCall(PetscInfo(svd,"Breakdown in bidiagonalization (it=%" PetscInt_FMT ")\n",svd->its));
675: if (k<svd->nsv) {
676: PetscCall(BVSetRandomColumn(V,k));
677: PetscCall(BVOrthonormalizeColumn(V,k,PETSC_FALSE,NULL,&breakdown));
678: if (breakdown) {
679: svd->reason = SVD_DIVERGED_BREAKDOWN;
680: PetscCall(PetscInfo(svd,"Unable to generate more start vectors\n"));
681: }
682: }
683: } else PetscCall(DSTruncate(svd->ds,k+l,PETSC_FALSE));
684: }
686: /* compute converged singular vectors and restart vectors */
687: PetscCall(DSGetMat(svd->ds,DS_MAT_V,&VV));
688: PetscCall(BVMultInPlace(V,VV,svd->nconv,k+l));
689: PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&VV));
690: PetscCall(DSGetMat(svd->ds,DS_MAT_U,&UU));
691: PetscCall(BVMultInPlace(U,UU,svd->nconv,k+l));
692: PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&UU));
694: /* copy the last vector of V to be the next initial vector
695: and change signature matrix of U */
696: if (svd->reason == SVD_CONVERGED_ITERATING && !breakdown) {
697: PetscCall(BVCopyColumn(V,nv,k+l));
698: PetscCall(BVSetActiveColumns(U,0,k+l));
699: PetscCall(DSGetMatAndColumn(svd->ds,DS_MAT_D,0,&D,&vomega));
700: PetscCall(BVSetSignature(U,vomega));
701: PetscCall(DSRestoreMatAndColumn(svd->ds,DS_MAT_D,0,&D,&vomega));
702: }
704: svd->nconv = k;
705: PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv));
706: }
708: /* free working space */
709: PetscCall(PetscFree(w));
710: PetscCall(DSTruncate(svd->ds,svd->nconv,PETSC_TRUE));
711: PetscFunctionReturn(PETSC_SUCCESS);
712: }
714: /* Given n computed generalized singular values in sigmain, backtransform them
715: in sigmaout by undoing scaling and reciprocating if swapped=true. Also updates vectors V
716: if given. If sigmaout=NULL then the result overwrites sigmain. */
717: static PetscErrorCode SVDLanczosBackTransform(SVD svd,PetscInt n,PetscReal *sigmain,PetscReal *sigmaout,BV V)
718: {
719: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
720: PetscInt i;
721: PetscReal c,s,r,f,scalef;
723: PetscFunctionBegin;
724: scalef = svd->swapped? 1.0/lanczos->scalef: lanczos->scalef;
725: for (i=0;i<n;i++) {
726: if (V && scalef != 1.0) {
727: s = 1.0/PetscSqrtReal(1.0+sigmain[i]*sigmain[i]);
728: c = sigmain[i]*s;
729: r = s/scalef;
730: f = 1.0/PetscSqrtReal(c*c+r*r);
731: PetscCall(BVScaleColumn(V,i,f));
732: }
733: if (sigmaout) {
734: if (svd->swapped) sigmaout[i] = 1.0/(sigmain[i]*scalef);
735: else sigmaout[i] = sigmain[i]*scalef;
736: } else {
737: sigmain[i] *= scalef;
738: if (svd->swapped) sigmain[i] = 1.0/sigmain[i];
739: }
740: }
741: PetscFunctionReturn(PETSC_SUCCESS);
742: }
744: static PetscErrorCode SVDLanczosGSingle(SVD svd,PetscReal *alpha,PetscReal *beta,Mat Z,BV V,BV U,KSP ksp,PetscInt k,PetscInt *n,PetscBool *breakdown)
745: {
746: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
747: PetscInt i,j,m;
748: const PetscScalar *carr;
749: PetscScalar *arr;
750: Vec u,v,ut=svd->workl[0],x=svd->workr[0],v1,u1,u2;
751: PetscBool lindep=PETSC_FALSE;
753: PetscFunctionBegin;
754: PetscCall(MatCreateVecsEmpty(svd->A,NULL,&v1));
755: PetscCall(BVGetColumn(V,k,&v));
756: PetscCall(BVGetColumn(U,k,&u));
758: /* Form ut=[u;0] */
759: PetscCall(VecZeroEntries(ut));
760: PetscCall(VecGetLocalSize(u,&m));
761: PetscCall(VecGetArrayRead(u,&carr));
762: PetscCall(VecGetArray(ut,&arr));
763: for (j=0; j<m; j++) arr[j] = carr[j];
764: PetscCall(VecRestoreArrayRead(u,&carr));
765: PetscCall(VecRestoreArray(ut,&arr));
767: /* Solve least squares problem */
768: PetscCall(KSPSolve(ksp,ut,x));
770: PetscCall(MatMult(Z,x,v));
772: PetscCall(BVRestoreColumn(U,k,&u));
773: PetscCall(BVRestoreColumn(V,k,&v));
774: PetscCall(BVOrthonormalizeColumn(V,k,PETSC_FALSE,alpha+k,&lindep));
775: if (PetscUnlikely(lindep)) {
776: *n = k;
777: if (breakdown) *breakdown = lindep;
778: PetscFunctionReturn(PETSC_SUCCESS);
779: }
781: for (i=k+1; i<*n; i++) {
783: /* Compute vector i of BV U */
784: PetscCall(BVGetColumn(V,i-1,&v));
785: PetscCall(VecGetArray(v,&arr));
786: PetscCall(VecPlaceArray(v1,arr));
787: PetscCall(VecRestoreArray(v,&arr));
788: PetscCall(BVRestoreColumn(V,i-1,&v));
789: PetscCall(BVInsertVec(U,i,v1));
790: PetscCall(VecResetArray(v1));
791: PetscCall(BVOrthonormalizeColumn(U,i,PETSC_FALSE,beta+i-1,&lindep));
792: if (PetscUnlikely(lindep)) {
793: *n = i;
794: break;
795: }
797: /* Compute vector i of BV V */
799: PetscCall(BVGetColumn(V,i,&v));
800: PetscCall(BVGetColumn(U,i,&u));
802: /* Form ut=[u;0] */
803: PetscCall(VecGetArrayRead(u,&carr));
804: PetscCall(VecGetArray(ut,&arr));
805: for (j=0; j<m; j++) arr[j] = carr[j];
806: PetscCall(VecRestoreArrayRead(u,&carr));
807: PetscCall(VecRestoreArray(ut,&arr));
809: /* Solve least squares problem */
810: PetscCall(KSPSolve(ksp,ut,x));
812: PetscCall(MatMult(Z,x,v));
814: PetscCall(BVRestoreColumn(U,i,&u));
815: PetscCall(BVRestoreColumn(V,i,&v));
816: if (!lanczos->oneside || i==k+1) PetscCall(BVOrthonormalizeColumn(V,i,PETSC_FALSE,alpha+i,&lindep));
817: else { /* cheap computation of V[i], if restart (i==k+1) do a full reorthogonalization */
818: PetscCall(BVGetColumn(V,i,&u2));
819: PetscCall(BVGetColumn(V,i-1,&u1));
820: PetscCall(VecAXPY(u2,-beta[i-1],u1));
821: PetscCall(BVRestoreColumn(V,i-1,&u1));
822: PetscCall(VecNorm(u2,NORM_2,&alpha[i]));
823: if (alpha[i]==0.0) lindep = PETSC_TRUE;
824: else PetscCall(VecScale(u2,1.0/alpha[i]));
825: PetscCall(BVRestoreColumn(V,i,&u2));
826: }
827: if (PetscUnlikely(lindep)) {
828: *n = i;
829: break;
830: }
831: }
833: /* Compute vector n of BV U */
834: if (!lindep) {
835: PetscCall(BVGetColumn(V,*n-1,&v));
836: PetscCall(VecGetArray(v,&arr));
837: PetscCall(VecPlaceArray(v1,arr));
838: PetscCall(VecRestoreArray(v,&arr));
839: PetscCall(BVRestoreColumn(V,*n-1,&v));
840: PetscCall(BVInsertVec(U,*n,v1));
841: PetscCall(VecResetArray(v1));
842: PetscCall(BVOrthonormalizeColumn(U,*n,PETSC_FALSE,beta+*n-1,&lindep));
843: }
844: if (breakdown) *breakdown = lindep;
845: PetscCall(VecDestroy(&v1));
846: PetscFunctionReturn(PETSC_SUCCESS);
847: }
849: /* solve generalized problem with single bidiagonalization of Q_A */
850: PetscErrorCode SVDSolve_TRLanczosGSingle(SVD svd,BV U1,BV V)
851: {
852: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
853: PetscReal *alpha,*beta,normr,scaleth,sigma0,*sigma;
854: PetscScalar *w;
855: PetscInt i,k,l,nv,ld;
856: Mat U,VV;
857: PetscBool breakdown=PETSC_FALSE;
859: PetscFunctionBegin;
860: PetscCall(DSGetLeadingDimension(svd->ds,&ld));
861: PetscCall(PetscMalloc2(ld,&w,ld,&sigma));
862: normr = (svd->conv==SVD_CONV_ABS)? PetscMax(svd->nrma,svd->nrmb*lanczos->scalef): 1.0;
863: /* Convert scale threshold th=c/s to the corresponding c */
864: scaleth = (lanczos->scaleth!=0)? lanczos->scaleth/PetscSqrtReal(lanczos->scaleth*lanczos->scaleth+1): 0.0;
866: /* normalize start vector */
867: if (!svd->ninil) {
868: PetscCall(BVSetRandomColumn(U1,0));
869: PetscCall(BVOrthonormalizeColumn(U1,0,PETSC_TRUE,NULL,NULL));
870: }
872: l = 0;
873: while (svd->reason == SVD_CONVERGED_ITERATING) {
874: svd->its++;
876: /* inner loop */
877: nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
878: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
879: beta = alpha + ld;
880: PetscCall(SVDLanczosGSingle(svd,alpha,beta,lanczos->Z,V,U1,lanczos->ksp,svd->nconv+l,&nv,&breakdown));
881: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
882: PetscCall(BVSetActiveColumns(V,svd->nconv,nv));
883: PetscCall(BVSetActiveColumns(U1,svd->nconv,nv));
885: /* solve projected problem */
886: PetscCall(DSSetDimensions(svd->ds,nv,svd->nconv,svd->nconv+l));
887: PetscCall(DSSVDSetDimensions(svd->ds,nv));
888: PetscCall(DSSetState(svd->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
889: PetscCall(DSSolve(svd->ds,w,NULL));
890: PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
891: PetscCall(DSUpdateExtraRow(svd->ds));
892: PetscCall(DSSynchronize(svd->ds,w,NULL));
893: for (i=svd->nconv;i<nv;i++) svd->sigma[i] = PetscRealPart(w[i]);
895: /* check convergence */
896: PetscCall(SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,normr,&k));
897: PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));
899: sigma0 = svd->which==SVD_LARGEST? svd->sigma[0] : 1.0/svd->sigma[0];
900: if (scaleth!=0 && k==0 && sigma0>scaleth) {
902: /* Scale and start from scratch */
903: lanczos->scalef *= svd->sigma[0]/PetscSqrtReal(1-svd->sigma[0]*svd->sigma[0]);
904: PetscCall(PetscInfo(svd,"Scaling by factor %g and starting from scratch\n",(double)lanczos->scalef));
905: PetscCall(MatZUpdateScale(svd));
906: if (svd->conv==SVD_CONV_ABS) normr = PetscMax(svd->nrma,svd->nrmb*lanczos->scalef);
907: l = 0;
909: } else {
911: /* update l */
912: if (svd->reason != SVD_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
913: else l = PetscMax(1,(PetscInt)((nv-k)*lanczos->keep));
914: if (!lanczos->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged triplets */
915: if (l) PetscCall(PetscInfo(svd,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
917: if (svd->reason == SVD_CONVERGED_ITERATING) {
918: if (PetscUnlikely(breakdown || k==nv)) {
919: /* Start a new bidiagonalization */
920: PetscCall(PetscInfo(svd,"Breakdown in bidiagonalization (it=%" PetscInt_FMT ")\n",svd->its));
921: if (k<svd->nsv) {
922: PetscCall(BVSetRandomColumn(U1,k));
923: PetscCall(BVOrthonormalizeColumn(U1,k,PETSC_FALSE,NULL,&breakdown));
924: if (breakdown) {
925: svd->reason = SVD_DIVERGED_BREAKDOWN;
926: PetscCall(PetscInfo(svd,"Unable to generate more start vectors\n"));
927: }
928: }
929: } else PetscCall(DSTruncate(svd->ds,k+l,PETSC_FALSE));
930: }
932: /* compute converged singular vectors and restart vectors */
933: PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
934: PetscCall(BVMultInPlace(V,U,svd->nconv,k+l));
935: PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
936: PetscCall(DSGetMat(svd->ds,DS_MAT_V,&VV));
937: PetscCall(BVMultInPlace(U1,VV,svd->nconv,k+l));
938: PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&VV));
940: /* copy the last vector to be the next initial vector */
941: if (svd->reason == SVD_CONVERGED_ITERATING && !breakdown) PetscCall(BVCopyColumn(U1,nv,k+l));
942: }
944: svd->nconv = k;
945: PetscCall(SVDLanczosBackTransform(svd,nv,svd->sigma,sigma,NULL));
946: PetscCall(SVDMonitor(svd,svd->its,svd->nconv,sigma,svd->errest,nv));
947: }
949: PetscCall(PetscFree2(w,sigma));
950: PetscFunctionReturn(PETSC_SUCCESS);
951: }
953: /* Move generalized left singular vectors (0..nconv) from U1 and U2 to its final destination svd->U (single variant) */
954: static inline PetscErrorCode SVDLeftSingularVectors_Single(SVD svd,BV U1,BV U2)
955: {
956: PetscInt i,k,m,p;
957: Vec u,u1,u2;
958: PetscScalar *ua,*u2a;
959: const PetscScalar *u1a;
960: PetscReal s;
962: PetscFunctionBegin;
963: PetscCall(MatGetLocalSize(svd->A,&m,NULL));
964: PetscCall(MatGetLocalSize(svd->B,&p,NULL));
965: for (i=0;i<svd->nconv;i++) {
966: PetscCall(BVGetColumn(U1,i,&u1));
967: PetscCall(BVGetColumn(U2,i,&u2));
968: PetscCall(BVGetColumn(svd->U,i,&u));
969: PetscCall(VecGetArrayRead(u1,&u1a));
970: PetscCall(VecGetArray(u,&ua));
971: PetscCall(VecGetArray(u2,&u2a));
972: /* Copy column from U1 to upper part of u */
973: for (k=0;k<m;k++) ua[k] = u1a[k];
974: /* Copy column from lower part of U to U2. Orthogonalize column in U2 and copy back to U */
975: for (k=0;k<p;k++) u2a[k] = ua[m+k];
976: PetscCall(VecRestoreArray(u2,&u2a));
977: PetscCall(BVRestoreColumn(U2,i,&u2));
978: PetscCall(BVOrthonormalizeColumn(U2,i,PETSC_FALSE,&s,NULL));
979: PetscCall(BVGetColumn(U2,i,&u2));
980: PetscCall(VecGetArray(u2,&u2a));
981: for (k=0;k<p;k++) ua[m+k] = u2a[k];
982: /* Update singular value */
983: svd->sigma[i] /= s;
984: PetscCall(VecRestoreArrayRead(u1,&u1a));
985: PetscCall(VecRestoreArray(u,&ua));
986: PetscCall(VecRestoreArray(u2,&u2a));
987: PetscCall(BVRestoreColumn(U1,i,&u1));
988: PetscCall(BVRestoreColumn(U2,i,&u2));
989: PetscCall(BVRestoreColumn(svd->U,i,&u));
990: }
991: PetscFunctionReturn(PETSC_SUCCESS);
992: }
994: static PetscErrorCode SVDLanczosGUpper(SVD svd,PetscReal *alpha,PetscReal *beta,PetscReal *alphah,PetscReal *betah,Mat Z,BV U1,BV U2,BV V,KSP ksp,PetscInt k,PetscInt *n,PetscBool *breakdown)
995: {
996: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
997: PetscInt i,j,m,p;
998: const PetscScalar *carr;
999: PetscScalar *arr,*u2arr;
1000: Vec u,v,ut=svd->workl[0],x=svd->workr[0],v1,u1,u2;
1001: PetscBool lindep=PETSC_FALSE,lindep1=PETSC_FALSE,lindep2=PETSC_FALSE;
1003: PetscFunctionBegin;
1004: PetscCall(MatCreateVecsEmpty(svd->A,NULL,&v1));
1005: PetscCall(MatGetLocalSize(svd->A,&m,NULL));
1006: PetscCall(MatGetLocalSize(svd->B,&p,NULL));
1008: for (i=k; i<*n; i++) {
1009: /* Compute vector i of BV U1 */
1010: PetscCall(BVGetColumn(V,i,&v));
1011: PetscCall(VecGetArrayRead(v,&carr));
1012: PetscCall(VecPlaceArray(v1,carr));
1013: PetscCall(BVInsertVec(U1,i,v1));
1014: PetscCall(VecResetArray(v1));
1015: if (!lanczos->oneside || i==k) PetscCall(BVOrthonormalizeColumn(U1,i,PETSC_FALSE,alpha+i,&lindep1));
1016: else { /* cheap computation of U1[i], if restart (i==k) do a full reorthogonalization */
1017: PetscCall(BVGetColumn(U1,i,&u2));
1018: if (i>0) {
1019: PetscCall(BVGetColumn(U1,i-1,&u1));
1020: PetscCall(VecAXPY(u2,-beta[i-1],u1));
1021: PetscCall(BVRestoreColumn(U1,i-1,&u1));
1022: }
1023: PetscCall(VecNorm(u2,NORM_2,&alpha[i]));
1024: if (alpha[i]==0.0) lindep = PETSC_TRUE;
1025: else PetscCall(VecScale(u2,1.0/alpha[i]));
1026: PetscCall(BVRestoreColumn(U1,i,&u2));
1027: }
1029: /* Compute vector i of BV U2 */
1030: PetscCall(BVGetColumn(U2,i,&u2));
1031: PetscCall(VecGetArray(u2,&u2arr));
1032: if (i%2) {
1033: for (j=0; j<p; j++) u2arr[j] = -carr[m+j];
1034: } else {
1035: for (j=0; j<p; j++) u2arr[j] = carr[m+j];
1036: }
1037: PetscCall(VecRestoreArray(u2,&u2arr));
1038: PetscCall(VecRestoreArrayRead(v,&carr));
1039: PetscCall(BVRestoreColumn(V,i,&v));
1040: if (lanczos->oneside && i>k) { /* cheap computation of U2[i], if restart (i==k) do a full reorthogonalization */
1041: if (i>0) {
1042: PetscCall(BVGetColumn(U2,i-1,&u1));
1043: PetscCall(VecAXPY(u2,(i%2)?betah[i-1]:-betah[i-1],u1));
1044: PetscCall(BVRestoreColumn(U2,i-1,&u1));
1045: }
1046: PetscCall(VecNorm(u2,NORM_2,&alphah[i]));
1047: if (alphah[i]==0.0) lindep = PETSC_TRUE;
1048: else PetscCall(VecScale(u2,1.0/alphah[i]));
1049: }
1050: PetscCall(BVRestoreColumn(U2,i,&u2));
1051: if (!lanczos->oneside || i==k) PetscCall(BVOrthonormalizeColumn(U2,i,PETSC_FALSE,alphah+i,&lindep2));
1052: if (i%2) alphah[i] = -alphah[i];
1053: if (PetscUnlikely(lindep1 || lindep2)) {
1054: lindep = PETSC_TRUE;
1055: *n = i;
1056: break;
1057: }
1059: /* Compute vector i+1 of BV V */
1060: PetscCall(BVGetColumn(V,i+1,&v));
1061: /* Form ut=[u;0] */
1062: PetscCall(BVGetColumn(U1,i,&u));
1063: PetscCall(VecZeroEntries(ut));
1064: PetscCall(VecGetArrayRead(u,&carr));
1065: PetscCall(VecGetArray(ut,&arr));
1066: for (j=0; j<m; j++) arr[j] = carr[j];
1067: PetscCall(VecRestoreArrayRead(u,&carr));
1068: PetscCall(VecRestoreArray(ut,&arr));
1069: /* Solve least squares problem */
1070: PetscCall(KSPSolve(ksp,ut,x));
1071: PetscCall(MatMult(Z,x,v));
1072: PetscCall(BVRestoreColumn(U1,i,&u));
1073: PetscCall(BVRestoreColumn(V,i+1,&v));
1074: PetscCall(BVOrthonormalizeColumn(V,i+1,PETSC_FALSE,beta+i,&lindep));
1075: betah[i] = -alpha[i]*beta[i]/alphah[i];
1076: if (PetscUnlikely(lindep)) {
1077: *n = i;
1078: break;
1079: }
1080: }
1081: if (breakdown) *breakdown = lindep;
1082: PetscCall(VecDestroy(&v1));
1083: PetscFunctionReturn(PETSC_SUCCESS);
1084: }
1086: /* generate random initial vector in column k for joint upper-upper bidiagonalization */
1087: static inline PetscErrorCode SVDInitialVectorGUpper(SVD svd,BV V,BV U1,PetscInt k,PetscBool *breakdown)
1088: {
1089: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1090: Vec u,v,ut=svd->workl[0],x=svd->workr[0];
1091: PetscInt m,j;
1092: PetscScalar *arr;
1093: const PetscScalar *carr;
1095: PetscFunctionBegin;
1096: /* Form ut=[u;0] where u is the k-th column of U1 */
1097: PetscCall(VecZeroEntries(ut));
1098: PetscCall(BVGetColumn(U1,k,&u));
1099: PetscCall(VecGetLocalSize(u,&m));
1100: PetscCall(VecGetArrayRead(u,&carr));
1101: PetscCall(VecGetArray(ut,&arr));
1102: for (j=0; j<m; j++) arr[j] = carr[j];
1103: PetscCall(VecRestoreArrayRead(u,&carr));
1104: PetscCall(VecRestoreArray(ut,&arr));
1105: PetscCall(BVRestoreColumn(U1,k,&u));
1106: /* Solve least squares problem Z*x=ut for x. Then set v=Z*x */
1107: PetscCall(KSPSolve(lanczos->ksp,ut,x));
1108: PetscCall(BVGetColumn(V,k,&v));
1109: PetscCall(MatMult(lanczos->Z,x,v));
1110: PetscCall(BVRestoreColumn(V,k,&v));
1111: if (breakdown) PetscCall(BVOrthonormalizeColumn(V,k,PETSC_FALSE,NULL,breakdown));
1112: else PetscCall(BVOrthonormalizeColumn(V,k,PETSC_TRUE,NULL,NULL));
1113: PetscFunctionReturn(PETSC_SUCCESS);
1114: }
1116: /* solve generalized problem with joint upper-upper bidiagonalization */
1117: PetscErrorCode SVDSolve_TRLanczosGUpper(SVD svd,BV U1,BV U2,BV V)
1118: {
1119: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1120: PetscReal *alpha,*beta,*alphah,*betah,normr,sigma0,*sigma;
1121: PetscScalar *w;
1122: PetscInt i,k,l,nv,ld;
1123: Mat U,Vmat,X;
1124: PetscBool breakdown=PETSC_FALSE;
1126: PetscFunctionBegin;
1127: PetscCall(DSGetLeadingDimension(svd->ds,&ld));
1128: PetscCall(PetscMalloc2(ld,&w,ld,&sigma));
1129: normr = (svd->conv==SVD_CONV_ABS)? PetscMax(svd->nrma,svd->nrmb*lanczos->scalef): 1.0;
1131: /* normalize start vector */
1132: if (!svd->ninil) PetscCall(BVSetRandomColumn(U1,0));
1133: PetscCall(SVDInitialVectorGUpper(svd,V,U1,0,NULL));
1135: l = 0;
1136: while (svd->reason == SVD_CONVERGED_ITERATING) {
1137: svd->its++;
1139: /* inner loop */
1140: nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
1141: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
1142: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_D,&alphah));
1143: beta = alpha + ld;
1144: betah = alpha + 2*ld;
1145: PetscCall(SVDLanczosGUpper(svd,alpha,beta,alphah,betah,lanczos->Z,U1,U2,V,lanczos->ksp,svd->nconv+l,&nv,&breakdown));
1146: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
1147: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_D,&alphah));
1148: PetscCall(BVSetActiveColumns(V,svd->nconv,nv));
1149: PetscCall(BVSetActiveColumns(U1,svd->nconv,nv));
1150: PetscCall(BVSetActiveColumns(U2,svd->nconv,nv));
1152: /* solve projected problem */
1153: PetscCall(DSSetDimensions(svd->ds,nv,svd->nconv,svd->nconv+l));
1154: PetscCall(DSGSVDSetDimensions(svd->ds,nv,nv));
1155: PetscCall(DSSetState(svd->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
1156: PetscCall(DSSolve(svd->ds,w,NULL));
1157: PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
1158: PetscCall(DSUpdateExtraRow(svd->ds));
1159: PetscCall(DSSynchronize(svd->ds,w,NULL));
1160: for (i=svd->nconv;i<nv;i++) svd->sigma[i] = PetscRealPart(w[i]);
1162: /* check convergence */
1163: PetscCall(SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,normr,&k));
1164: PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));
1166: sigma0 = svd->which==SVD_LARGEST? svd->sigma[0] : 1.0/svd->sigma[0];
1167: if (lanczos->scaleth!=0 && k==0 && sigma0>lanczos->scaleth) {
1169: /* Scale and start from scratch */
1170: lanczos->scalef *= svd->sigma[0];
1171: PetscCall(PetscInfo(svd,"Scaling by factor %g and starting from scratch\n",(double)lanczos->scalef));
1172: PetscCall(MatZUpdateScale(svd));
1173: if (svd->conv==SVD_CONV_ABS) normr = PetscMax(svd->nrma,svd->nrmb*lanczos->scalef);
1174: l = 0;
1175: if (!svd->ninil) PetscCall(BVSetRandomColumn(U1,0));
1176: PetscCall(SVDInitialVectorGUpper(svd,V,U1,0,NULL));
1178: } else {
1180: /* update l */
1181: if (svd->reason != SVD_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
1182: else l = PetscMax(1,(PetscInt)((nv-k)*lanczos->keep));
1183: if (!lanczos->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged triplets */
1184: if (l) PetscCall(PetscInfo(svd,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
1186: if (svd->reason == SVD_CONVERGED_ITERATING) {
1187: if (PetscUnlikely(breakdown || k==nv)) {
1188: /* Start a new bidiagonalization */
1189: PetscCall(PetscInfo(svd,"Breakdown in bidiagonalization (it=%" PetscInt_FMT ")\n",svd->its));
1190: if (k<svd->nsv) {
1191: PetscCall(BVSetRandomColumn(U1,k));
1192: PetscCall(SVDInitialVectorGUpper(svd,V,U1,k,&breakdown));
1193: if (breakdown) {
1194: svd->reason = SVD_DIVERGED_BREAKDOWN;
1195: PetscCall(PetscInfo(svd,"Unable to generate more start vectors\n"));
1196: }
1197: }
1198: } else PetscCall(DSTruncate(svd->ds,k+l,PETSC_FALSE));
1199: }
1200: /* compute converged singular vectors and restart vectors */
1201: PetscCall(DSGetMat(svd->ds,DS_MAT_X,&X));
1202: PetscCall(BVMultInPlace(V,X,svd->nconv,k+l));
1203: PetscCall(DSRestoreMat(svd->ds,DS_MAT_X,&X));
1204: PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
1205: PetscCall(BVMultInPlace(U1,U,svd->nconv,k+l));
1206: PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
1207: PetscCall(DSGetMat(svd->ds,DS_MAT_V,&Vmat));
1208: PetscCall(BVMultInPlace(U2,Vmat,svd->nconv,k+l));
1209: PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&Vmat));
1211: /* copy the last vector to be the next initial vector */
1212: if (svd->reason == SVD_CONVERGED_ITERATING && !breakdown) PetscCall(BVCopyColumn(V,nv,k+l));
1213: }
1215: svd->nconv = k;
1216: PetscCall(SVDLanczosBackTransform(svd,nv,svd->sigma,sigma,NULL));
1217: PetscCall(SVDMonitor(svd,svd->its,svd->nconv,sigma,svd->errest,nv));
1218: }
1220: PetscCall(PetscFree2(w,sigma));
1221: PetscFunctionReturn(PETSC_SUCCESS);
1222: }
1224: /* Move generalized left singular vectors (0..nconv) from U1 and U2 to its final destination svd->U (upper and lower variants) */
1225: static inline PetscErrorCode SVDLeftSingularVectors(SVD svd,BV U1,BV U2)
1226: {
1227: PetscInt i,k,m,p;
1228: Vec u,u1,u2;
1229: PetscScalar *ua;
1230: const PetscScalar *u1a,*u2a;
1232: PetscFunctionBegin;
1233: PetscCall(BVGetSizes(U1,&m,NULL,NULL));
1234: PetscCall(BVGetSizes(U2,&p,NULL,NULL));
1235: for (i=0;i<svd->nconv;i++) {
1236: PetscCall(BVGetColumn(U1,i,&u1));
1237: PetscCall(BVGetColumn(U2,i,&u2));
1238: PetscCall(BVGetColumn(svd->U,i,&u));
1239: PetscCall(VecGetArrayRead(u1,&u1a));
1240: PetscCall(VecGetArrayRead(u2,&u2a));
1241: PetscCall(VecGetArray(u,&ua));
1242: /* Copy column from u1 to upper part of u */
1243: for (k=0;k<m;k++) ua[k] = u1a[k];
1244: /* Copy column from u2 to lower part of u */
1245: for (k=0;k<p;k++) ua[m+k] = u2a[k];
1246: PetscCall(VecRestoreArrayRead(u1,&u1a));
1247: PetscCall(VecRestoreArrayRead(u2,&u2a));
1248: PetscCall(VecRestoreArray(u,&ua));
1249: PetscCall(BVRestoreColumn(U1,i,&u1));
1250: PetscCall(BVRestoreColumn(U2,i,&u2));
1251: PetscCall(BVRestoreColumn(svd->U,i,&u));
1252: }
1253: PetscFunctionReturn(PETSC_SUCCESS);
1254: }
1256: static PetscErrorCode SVDLanczosGLower(SVD svd,PetscReal *alpha,PetscReal *beta,PetscReal *alphah,PetscReal *betah,Mat Z,BV U1,BV U2,BV V,KSP ksp,PetscInt k,PetscInt *n,PetscBool *breakdown)
1257: {
1258: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1259: PetscInt i,j,m,p;
1260: const PetscScalar *carr;
1261: PetscScalar *arr,*u2arr;
1262: Vec u,v,ut=svd->workl[0],x=svd->workr[0],v1,u1,u2;
1263: PetscBool lindep=PETSC_FALSE;
1265: PetscFunctionBegin;
1266: PetscCall(MatCreateVecsEmpty(svd->A,NULL,&v1));
1267: PetscCall(MatGetLocalSize(svd->A,&m,NULL));
1268: PetscCall(MatGetLocalSize(svd->B,&p,NULL));
1270: for (i=k; i<*n; i++) {
1271: /* Compute vector i of BV U2 */
1272: PetscCall(BVGetColumn(V,i,&v));
1273: PetscCall(VecGetArrayRead(v,&carr));
1274: PetscCall(BVGetColumn(U2,i,&u2));
1275: PetscCall(VecGetArray(u2,&u2arr));
1276: if (i%2) {
1277: for (j=0; j<p; j++) u2arr[j] = -carr[m+j];
1278: } else {
1279: for (j=0; j<p; j++) u2arr[j] = carr[m+j];
1280: }
1281: PetscCall(VecRestoreArray(u2,&u2arr));
1282: if (lanczos->oneside && i>k) { /* cheap computation of U2[i], if restart (i==k) do a full reorthogonalization */
1283: if (i>0) {
1284: PetscCall(BVGetColumn(U2,i-1,&u1));
1285: PetscCall(VecAXPY(u2,(i%2)?betah[i-1]:-betah[i-1],u1));
1286: PetscCall(BVRestoreColumn(U2,i-1,&u1));
1287: }
1288: PetscCall(VecNorm(u2,NORM_2,&alphah[i]));
1289: if (alphah[i]==0.0) lindep = PETSC_TRUE;
1290: else PetscCall(VecScale(u2,1.0/alphah[i]));
1291: }
1292: PetscCall(BVRestoreColumn(U2,i,&u2));
1293: if (!lanczos->oneside || i==k) PetscCall(BVOrthonormalizeColumn(U2,i,PETSC_FALSE,alphah+i,&lindep));
1294: if (i%2) alphah[i] = -alphah[i];
1295: if (PetscUnlikely(lindep)) {
1296: PetscCall(BVRestoreColumn(V,i,&v));
1297: *n = i;
1298: break;
1299: }
1301: /* Compute vector i+1 of BV U1 */
1302: PetscCall(VecPlaceArray(v1,carr));
1303: PetscCall(BVInsertVec(U1,i+1,v1));
1304: PetscCall(VecResetArray(v1));
1305: PetscCall(BVOrthonormalizeColumn(U1,i+1,PETSC_FALSE,beta+i,&lindep));
1306: PetscCall(VecRestoreArrayRead(v,&carr));
1307: PetscCall(BVRestoreColumn(V,i,&v));
1308: if (PetscUnlikely(lindep)) {
1309: *n = i+1;
1310: break;
1311: }
1313: /* Compute vector i+1 of BV V */
1314: PetscCall(BVGetColumn(V,i+1,&v));
1315: /* Form ut=[u;0] where u is column i+1 of BV U1 */
1316: PetscCall(BVGetColumn(U1,i+1,&u));
1317: PetscCall(VecZeroEntries(ut));
1318: PetscCall(VecGetArrayRead(u,&carr));
1319: PetscCall(VecGetArray(ut,&arr));
1320: for (j=0; j<m; j++) arr[j] = carr[j];
1321: PetscCall(VecRestoreArrayRead(u,&carr));
1322: PetscCall(VecRestoreArray(ut,&arr));
1323: /* Solve least squares problem */
1324: PetscCall(KSPSolve(ksp,ut,x));
1325: PetscCall(MatMult(Z,x,v));
1326: PetscCall(BVRestoreColumn(U1,i+1,&u));
1327: PetscCall(BVRestoreColumn(V,i+1,&v));
1328: if (!lanczos->oneside || i==k) PetscCall(BVOrthonormalizeColumn(V,i+1,PETSC_FALSE,alpha+i+1,&lindep));
1329: else { /* cheap computation of V[i+1], if restart (i==k) do a full reorthogonalization */
1330: PetscCall(BVGetColumn(V,i+1,&u2));
1331: PetscCall(BVGetColumn(V,i,&u1));
1332: PetscCall(VecAXPY(u2,-beta[i],u1));
1333: PetscCall(BVRestoreColumn(V,i,&u1));
1334: PetscCall(VecNorm(u2,NORM_2,&alpha[i+1]));
1335: if (alpha[i+1]==0.0) lindep = PETSC_TRUE;
1336: else PetscCall(VecScale(u2,1.0/alpha[i+1]));
1337: PetscCall(BVRestoreColumn(V,i+1,&u2));
1338: }
1339: betah[i] = -alpha[i+1]*beta[i]/alphah[i];
1340: if (PetscUnlikely(lindep)) {
1341: *n = i+1;
1342: break;
1343: }
1344: }
1345: if (breakdown) *breakdown = lindep;
1346: PetscCall(VecDestroy(&v1));
1347: PetscFunctionReturn(PETSC_SUCCESS);
1348: }
1350: /* generate random initial vector in column k for joint lower-upper bidiagonalization */
1351: static inline PetscErrorCode SVDInitialVectorGLower(SVD svd,BV V,BV U1,BV U2,PetscInt k,PetscBool *breakdown)
1352: {
1353: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1354: const PetscScalar *carr;
1355: PetscScalar *arr;
1356: PetscReal *alpha;
1357: PetscInt j,m,p;
1358: Vec u,uh,v,ut=svd->workl[0],x=svd->workr[0];
1360: PetscFunctionBegin;
1361: PetscCall(MatGetLocalSize(svd->A,&m,NULL));
1362: PetscCall(MatGetLocalSize(svd->B,&p,NULL));
1363: /* Form ut=[0;uh], where uh is the k-th column of U2 */
1364: PetscCall(BVGetColumn(U2,k,&uh));
1365: PetscCall(VecZeroEntries(ut));
1366: PetscCall(VecGetArrayRead(uh,&carr));
1367: PetscCall(VecGetArray(ut,&arr));
1368: for (j=0; j<p; j++) arr[m+j] = carr[j];
1369: PetscCall(VecRestoreArrayRead(uh,&carr));
1370: PetscCall(VecRestoreArray(ut,&arr));
1371: PetscCall(BVRestoreColumn(U2,k,&uh));
1372: /* Solve least squares problem Z*x=ut for x. Then set ut=Z*x */
1373: PetscCall(KSPSolve(lanczos->ksp,ut,x));
1374: PetscCall(MatMult(lanczos->Z,x,ut));
1375: /* Form u, column k of BV U1, as the upper part of ut and orthonormalize */
1376: PetscCall(MatCreateVecsEmpty(svd->A,NULL,&u));
1377: PetscCall(VecGetArrayRead(ut,&carr));
1378: PetscCall(VecPlaceArray(u,carr));
1379: PetscCall(BVInsertVec(U1,k,u));
1380: PetscCall(VecResetArray(u));
1381: PetscCall(VecRestoreArrayRead(ut,&carr));
1382: PetscCall(VecDestroy(&u));
1383: if (breakdown) PetscCall(BVOrthonormalizeColumn(U1,k,PETSC_FALSE,NULL,breakdown));
1384: else PetscCall(BVOrthonormalizeColumn(U1,k,PETSC_TRUE,NULL,NULL));
1386: if (!breakdown || !*breakdown) {
1387: PetscCall(MatGetLocalSize(svd->A,&m,NULL));
1388: /* Compute k-th vector of BV V */
1389: PetscCall(BVGetColumn(V,k,&v));
1390: /* Form ut=[u;0] where u is the 1st column of U1 */
1391: PetscCall(BVGetColumn(U1,k,&u));
1392: PetscCall(VecZeroEntries(ut));
1393: PetscCall(VecGetArrayRead(u,&carr));
1394: PetscCall(VecGetArray(ut,&arr));
1395: for (j=0; j<m; j++) arr[j] = carr[j];
1396: PetscCall(VecRestoreArrayRead(u,&carr));
1397: PetscCall(VecRestoreArray(ut,&arr));
1398: /* Solve least squares problem */
1399: PetscCall(KSPSolve(lanczos->ksp,ut,x));
1400: PetscCall(MatMult(lanczos->Z,x,v));
1401: PetscCall(BVRestoreColumn(U1,k,&u));
1402: PetscCall(BVRestoreColumn(V,k,&v));
1403: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
1404: if (breakdown) PetscCall(BVOrthonormalizeColumn(V,k,PETSC_FALSE,alpha+k,breakdown));
1405: else PetscCall(BVOrthonormalizeColumn(V,k,PETSC_TRUE,alpha+k,NULL));
1406: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
1407: }
1408: PetscFunctionReturn(PETSC_SUCCESS);
1409: }
1411: /* solve generalized problem with joint lower-upper bidiagonalization */
1412: PetscErrorCode SVDSolve_TRLanczosGLower(SVD svd,BV U1,BV U2,BV V)
1413: {
1414: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1415: PetscReal *alpha,*beta,*alphah,*betah,normr,scalef,*sigma,sigma0;
1416: PetscScalar *w;
1417: PetscInt i,k,l,nv,ld;
1418: Mat U,Vmat,X;
1419: PetscBool breakdown=PETSC_FALSE,inverted;
1421: PetscFunctionBegin;
1422: PetscCall(DSGetLeadingDimension(svd->ds,&ld));
1423: PetscCall(PetscMalloc2(ld,&w,ld,&sigma));
1424: inverted = ((svd->which==SVD_LARGEST && svd->swapped) || (svd->which==SVD_SMALLEST && !svd->swapped))? PETSC_TRUE: PETSC_FALSE;
1425: scalef = svd->swapped? 1.0/lanczos->scalef : lanczos->scalef;
1426: normr = (svd->conv==SVD_CONV_ABS)? PetscMax(svd->nrma,svd->nrmb*scalef): 1.0;
1428: /* normalize start vector */
1429: if (!svd->ninil) PetscCall(BVSetRandomColumn(U2,0));
1430: PetscCall(SVDInitialVectorGLower(svd,V,U1,U2,0,NULL));
1432: l = 0;
1433: while (svd->reason == SVD_CONVERGED_ITERATING) {
1434: svd->its++;
1436: /* inner loop */
1437: nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
1438: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
1439: PetscCall(DSGetArrayReal(svd->ds,DS_MAT_D,&alphah));
1440: beta = alpha + ld;
1441: betah = alpha + 2*ld;
1442: PetscCall(SVDLanczosGLower(svd,alpha,beta,alphah,betah,lanczos->Z,U1,U2,V,lanczos->ksp,svd->nconv+l,&nv,&breakdown));
1443: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
1444: PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_D,&alphah));
1445: PetscCall(BVSetActiveColumns(V,svd->nconv,nv));
1446: PetscCall(BVSetActiveColumns(U1,svd->nconv,nv+1));
1447: PetscCall(BVSetActiveColumns(U2,svd->nconv,nv));
1449: /* solve projected problem */
1450: PetscCall(DSSetDimensions(svd->ds,nv+1,svd->nconv,svd->nconv+l));
1451: PetscCall(DSGSVDSetDimensions(svd->ds,nv,nv));
1452: PetscCall(DSSetState(svd->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE));
1453: PetscCall(DSSolve(svd->ds,w,NULL));
1454: PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
1455: PetscCall(DSUpdateExtraRow(svd->ds));
1456: PetscCall(DSSynchronize(svd->ds,w,NULL));
1457: for (i=svd->nconv;i<nv;i++) svd->sigma[i] = PetscRealPart(w[i]);
1459: /* check convergence */
1460: PetscCall(SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,normr,&k));
1461: PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));
1463: sigma0 = inverted? 1.0/svd->sigma[0] : svd->sigma[0];
1464: if (lanczos->scaleth!=0 && k==0 && sigma0>lanczos->scaleth) {
1466: /* Scale and start from scratch */
1467: lanczos->scalef *= svd->swapped? 1.0/svd->sigma[0] : svd->sigma[0];
1468: PetscCall(PetscInfo(svd,"Scaling by factor %g and starting from scratch\n",(double)lanczos->scalef));
1469: PetscCall(MatZUpdateScale(svd));
1470: scalef = svd->swapped? 1.0/lanczos->scalef : lanczos->scalef;
1471: if (svd->conv==SVD_CONV_ABS) normr = PetscMax(svd->nrma,svd->nrmb*scalef);
1472: l = 0;
1473: if (!svd->ninil) PetscCall(BVSetRandomColumn(U2,0));
1474: PetscCall(SVDInitialVectorGLower(svd,V,U1,U2,0,NULL));
1476: } else {
1478: /* update l */
1479: if (svd->reason != SVD_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
1480: else l = PetscMax(1,(PetscInt)((nv-k)*lanczos->keep));
1481: if (!lanczos->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged triplets */
1482: if (l) PetscCall(PetscInfo(svd,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
1484: if (svd->reason == SVD_CONVERGED_ITERATING) {
1485: if (PetscUnlikely(breakdown || k==nv)) {
1486: /* Start a new bidiagonalization */
1487: PetscCall(PetscInfo(svd,"Breakdown in bidiagonalization (it=%" PetscInt_FMT ")\n",svd->its));
1488: if (k<svd->nsv) {
1489: PetscCall(BVSetRandomColumn(U2,k));
1490: PetscCall(SVDInitialVectorGLower(svd,V,U1,U2,k,&breakdown));
1491: if (breakdown) {
1492: svd->reason = SVD_DIVERGED_BREAKDOWN;
1493: PetscCall(PetscInfo(svd,"Unable to generate more start vectors\n"));
1494: }
1495: }
1496: } else PetscCall(DSTruncate(svd->ds,k+l,PETSC_FALSE));
1497: }
1499: /* compute converged singular vectors and restart vectors */
1500: PetscCall(DSGetMat(svd->ds,DS_MAT_X,&X));
1501: PetscCall(BVMultInPlace(V,X,svd->nconv,k+l));
1502: PetscCall(DSRestoreMat(svd->ds,DS_MAT_X,&X));
1503: PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
1504: PetscCall(BVMultInPlace(U1,U,svd->nconv,k+l+1));
1505: PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
1506: PetscCall(DSGetMat(svd->ds,DS_MAT_V,&Vmat));
1507: PetscCall(BVMultInPlace(U2,Vmat,svd->nconv,k+l));
1508: PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&Vmat));
1510: /* copy the last vector to be the next initial vector */
1511: if (svd->reason == SVD_CONVERGED_ITERATING && !breakdown) PetscCall(BVCopyColumn(V,nv,k+l));
1512: }
1514: svd->nconv = k;
1515: PetscCall(SVDLanczosBackTransform(svd,nv,svd->sigma,sigma,NULL));
1516: PetscCall(SVDMonitor(svd,svd->its,svd->nconv,sigma,svd->errest,nv));
1517: }
1519: PetscCall(PetscFree2(w,sigma));
1520: PetscFunctionReturn(PETSC_SUCCESS);
1521: }
1523: PetscErrorCode SVDSolve_TRLanczos_GSVD(SVD svd)
1524: {
1525: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1526: PetscInt k,m,p;
1527: PetscBool convchg=PETSC_FALSE;
1528: BV U1,U2,UU;
1529: BVType type;
1530: Mat U,V;
1531: SlepcSC sc;
1533: PetscFunctionBegin;
1534: PetscCall(PetscCitationsRegister(citationg,&citedg));
1536: if (svd->swapped) {
1537: PetscCall(DSGetSlepcSC(svd->ds,&sc));
1538: if (svd->which==SVD_LARGEST) sc->comparison = SlepcCompareSmallestReal;
1539: else sc->comparison = SlepcCompareLargestReal;
1540: }
1541: if (svd->converged==SVDConvergedNorm) { /* override temporarily since computed residual is already relative to the norms */
1542: svd->converged = SVDConvergedAbsolute;
1543: convchg = PETSC_TRUE;
1544: }
1545: PetscCall(MatGetLocalSize(svd->A,&m,NULL));
1546: PetscCall(MatGetLocalSize(svd->B,&p,NULL));
1548: /* Create BV for U1 */
1549: PetscCall(BVCreate(PetscObjectComm((PetscObject)svd),&U1));
1550: PetscCall(BVGetType(svd->U,&type));
1551: PetscCall(BVSetType(U1,type));
1552: PetscCall(BVGetSizes(svd->U,NULL,NULL,&k));
1553: PetscCall(BVSetSizes(U1,m,PETSC_DECIDE,k));
1555: /* Create BV for U2 */
1556: PetscCall(BVCreate(PetscObjectComm((PetscObject)svd),&U2));
1557: PetscCall(BVSetType(U2,type));
1558: PetscCall(BVSetSizes(U2,p,PETSC_DECIDE,k));
1560: /* Copy initial vectors from svd->U to U1 and U2 */
1561: if (svd->ninil) {
1562: Vec u, uh, nest, aux[2];
1563: PetscCall(BVGetColumn(U1,0,&u));
1564: PetscCall(BVGetColumn(U2,0,&uh));
1565: aux[0] = u;
1566: aux[1] = uh;
1567: PetscCall(VecCreateNest(PetscObjectComm((PetscObject)svd),2,NULL,aux,&nest));
1568: PetscCall(BVCopyVec(svd->U,0,nest));
1569: PetscCall(BVRestoreColumn(U1,0,&u));
1570: PetscCall(BVRestoreColumn(U2,0,&uh));
1571: PetscCall(VecDestroy(&nest));
1572: }
1574: switch (lanczos->bidiag) {
1575: case SVD_TRLANCZOS_GBIDIAG_SINGLE:
1576: PetscCall(SVDSolve_TRLanczosGSingle(svd,U1,svd->U));
1577: break;
1578: case SVD_TRLANCZOS_GBIDIAG_UPPER:
1579: PetscCall(SVDSolve_TRLanczosGUpper(svd,U1,U2,svd->U));
1580: break;
1581: case SVD_TRLANCZOS_GBIDIAG_LOWER:
1582: PetscCall(SVDSolve_TRLanczosGLower(svd,U1,U2,svd->U));
1583: break;
1584: }
1586: /* Compute converged right singular vectors */
1587: PetscCall(BVSetActiveColumns(svd->U,0,svd->nconv));
1588: PetscCall(BVSetActiveColumns(svd->V,0,svd->nconv));
1589: PetscCall(BVGetMat(svd->U,&U));
1590: PetscCall(BVGetMat(svd->V,&V));
1591: PetscCall(KSPMatSolve(lanczos->ksp,U,V));
1592: PetscCall(BVRestoreMat(svd->U,&U));
1593: PetscCall(BVRestoreMat(svd->V,&V));
1595: /* Finish computing left singular vectors and move them to its place */
1596: if (svd->swapped) SWAP(U1,U2,UU);
1597: switch (lanczos->bidiag) {
1598: case SVD_TRLANCZOS_GBIDIAG_SINGLE:
1599: PetscCall(SVDLeftSingularVectors_Single(svd,U1,U2));
1600: break;
1601: case SVD_TRLANCZOS_GBIDIAG_UPPER:
1602: case SVD_TRLANCZOS_GBIDIAG_LOWER:
1603: PetscCall(SVDLeftSingularVectors(svd,U1,U2));
1604: break;
1605: }
1607: /* undo scaling and compute the reciprocals of sigma if matrices were swapped */
1608: PetscCall(SVDLanczosBackTransform(svd,svd->nconv,svd->sigma,NULL,svd->V));
1610: PetscCall(BVDestroy(&U1));
1611: PetscCall(BVDestroy(&U2));
1612: PetscCall(DSTruncate(svd->ds,svd->nconv,PETSC_TRUE));
1613: if (convchg) svd->converged = SVDConvergedNorm;
1614: PetscFunctionReturn(PETSC_SUCCESS);
1615: }
1617: PetscErrorCode SVDSetFromOptions_TRLanczos(SVD svd,PetscOptionItems *PetscOptionsObject)
1618: {
1619: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1620: PetscBool flg,val,lock;
1621: PetscReal keep,scale;
1622: SVDTRLanczosGBidiag bidiag;
1624: PetscFunctionBegin;
1625: PetscOptionsHeadBegin(PetscOptionsObject,"SVD TRLanczos Options");
1627: PetscCall(PetscOptionsBool("-svd_trlanczos_oneside","Use one-side reorthogonalization","SVDTRLanczosSetOneSide",lanczos->oneside,&val,&flg));
1628: if (flg) PetscCall(SVDTRLanczosSetOneSide(svd,val));
1630: PetscCall(PetscOptionsReal("-svd_trlanczos_restart","Proportion of vectors kept after restart","SVDTRLanczosSetRestart",0.5,&keep,&flg));
1631: if (flg) PetscCall(SVDTRLanczosSetRestart(svd,keep));
1633: PetscCall(PetscOptionsBool("-svd_trlanczos_locking","Choose between locking and non-locking variants","SVDTRLanczosSetLocking",PETSC_TRUE,&lock,&flg));
1634: if (flg) PetscCall(SVDTRLanczosSetLocking(svd,lock));
1636: PetscCall(PetscOptionsEnum("-svd_trlanczos_gbidiag","Bidiagonalization choice for Generalized Problem","SVDTRLanczosSetGBidiag",SVDTRLanczosGBidiags,(PetscEnum)lanczos->bidiag,(PetscEnum*)&bidiag,&flg));
1637: if (flg) PetscCall(SVDTRLanczosSetGBidiag(svd,bidiag));
1639: PetscCall(PetscOptionsBool("-svd_trlanczos_explicitmatrix","Build explicit matrix for KSP solver","SVDTRLanczosSetExplicitMatrix",lanczos->explicitmatrix,&val,&flg));
1640: if (flg) PetscCall(SVDTRLanczosSetExplicitMatrix(svd,val));
1642: PetscCall(SVDTRLanczosGetScale(svd,&scale));
1643: PetscCall(PetscOptionsReal("-svd_trlanczos_scale","Scale parameter for matrix B","SVDTRLanczosSetScale",scale,&scale,&flg));
1644: if (flg) PetscCall(SVDTRLanczosSetScale(svd,scale));
1646: PetscOptionsHeadEnd();
1648: if (svd->OPb) {
1649: if (!lanczos->ksp) PetscCall(SVDTRLanczosGetKSP(svd,&lanczos->ksp));
1650: PetscCall(KSPSetFromOptions(lanczos->ksp));
1651: }
1652: PetscFunctionReturn(PETSC_SUCCESS);
1653: }
1655: static PetscErrorCode SVDTRLanczosSetOneSide_TRLanczos(SVD svd,PetscBool oneside)
1656: {
1657: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1659: PetscFunctionBegin;
1660: if (lanczos->oneside != oneside) {
1661: lanczos->oneside = oneside;
1662: svd->state = SVD_STATE_INITIAL;
1663: }
1664: PetscFunctionReturn(PETSC_SUCCESS);
1665: }
1667: /*@
1668: SVDTRLanczosSetOneSide - Indicate if the variant of the Lanczos method
1669: to be used is one-sided or two-sided.
1671: Logically Collective
1673: Input Parameters:
1674: + svd - singular value solver
1675: - oneside - boolean flag indicating if the method is one-sided or not
1677: Options Database Key:
1678: . -svd_trlanczos_oneside <boolean> - Indicates the boolean flag
1680: Notes:
1681: By default, a two-sided variant is selected, which is sometimes slightly
1682: more robust. However, the one-sided variant is faster because it avoids
1683: the orthogonalization associated to left singular vectors.
1685: One-sided orthogonalization is also available for the GSVD, in which case
1686: two orthogonalizations out of three are avoided.
1688: Level: advanced
1690: .seealso: SVDLanczosSetOneSide()
1691: @*/
1692: PetscErrorCode SVDTRLanczosSetOneSide(SVD svd,PetscBool oneside)
1693: {
1694: PetscFunctionBegin;
1697: PetscTryMethod(svd,"SVDTRLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
1698: PetscFunctionReturn(PETSC_SUCCESS);
1699: }
1701: static PetscErrorCode SVDTRLanczosGetOneSide_TRLanczos(SVD svd,PetscBool *oneside)
1702: {
1703: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1705: PetscFunctionBegin;
1706: *oneside = lanczos->oneside;
1707: PetscFunctionReturn(PETSC_SUCCESS);
1708: }
1710: /*@
1711: SVDTRLanczosGetOneSide - Gets if the variant of the Lanczos method
1712: to be used is one-sided or two-sided.
1714: Not Collective
1716: Input Parameters:
1717: . svd - singular value solver
1719: Output Parameters:
1720: . oneside - boolean flag indicating if the method is one-sided or not
1722: Level: advanced
1724: .seealso: SVDTRLanczosSetOneSide()
1725: @*/
1726: PetscErrorCode SVDTRLanczosGetOneSide(SVD svd,PetscBool *oneside)
1727: {
1728: PetscFunctionBegin;
1731: PetscUseMethod(svd,"SVDTRLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
1732: PetscFunctionReturn(PETSC_SUCCESS);
1733: }
1735: static PetscErrorCode SVDTRLanczosSetGBidiag_TRLanczos(SVD svd,SVDTRLanczosGBidiag bidiag)
1736: {
1737: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1739: PetscFunctionBegin;
1740: switch (bidiag) {
1741: case SVD_TRLANCZOS_GBIDIAG_SINGLE:
1742: case SVD_TRLANCZOS_GBIDIAG_UPPER:
1743: case SVD_TRLANCZOS_GBIDIAG_LOWER:
1744: if (lanczos->bidiag != bidiag) {
1745: lanczos->bidiag = bidiag;
1746: svd->state = SVD_STATE_INITIAL;
1747: }
1748: break;
1749: default:
1750: SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"Invalid bidiagonalization choice");
1751: }
1752: PetscFunctionReturn(PETSC_SUCCESS);
1753: }
1755: /*@
1756: SVDTRLanczosSetGBidiag - Sets the bidiagonalization choice to use in
1757: the GSVD TRLanczos solver.
1759: Logically Collective
1761: Input Parameters:
1762: + svd - the singular value solver
1763: - bidiag - the bidiagonalization choice
1765: Options Database Key:
1766: . -svd_trlanczos_gbidiag - Sets the bidiagonalization choice (either 's' or 'juu'
1767: or 'jlu')
1769: Level: advanced
1771: .seealso: SVDTRLanczosGetGBidiag(), SVDTRLanczosGBidiag
1772: @*/
1773: PetscErrorCode SVDTRLanczosSetGBidiag(SVD svd,SVDTRLanczosGBidiag bidiag)
1774: {
1775: PetscFunctionBegin;
1778: PetscTryMethod(svd,"SVDTRLanczosSetGBidiag_C",(SVD,SVDTRLanczosGBidiag),(svd,bidiag));
1779: PetscFunctionReturn(PETSC_SUCCESS);
1780: }
1782: static PetscErrorCode SVDTRLanczosGetGBidiag_TRLanczos(SVD svd,SVDTRLanczosGBidiag *bidiag)
1783: {
1784: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
1786: PetscFunctionBegin;
1787: *bidiag = lanczos->bidiag;
1788: PetscFunctionReturn(PETSC_SUCCESS);
1789: }
1791: /*@
1792: SVDTRLanczosGetGBidiag - Gets the bidiagonalization choice used in the GSVD
1793: TRLanczos solver.
1795: Not Collective
1797: Input Parameter:
1798: . svd - the singular value solver
1800: Output Parameter:
1801: . bidiag - the bidiagonalization choice
1803: Level: advanced
1805: .seealso: SVDTRLanczosSetGBidiag(), SVDTRLanczosGBidiag
1806: @*/
1807: PetscErrorCode SVDTRLanczosGetGBidiag(SVD svd,SVDTRLanczosGBidiag *bidiag)
1808: {
1809: PetscFunctionBegin;
1812: PetscUseMethod(svd,"SVDTRLanczosGetGBidiag_C",(SVD,SVDTRLanczosGBidiag*),(svd,bidiag));
1813: PetscFunctionReturn(PETSC_SUCCESS);
1814: }
1816: static PetscErrorCode SVDTRLanczosSetKSP_TRLanczos(SVD svd,KSP ksp)
1817: {
1818: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
1820: PetscFunctionBegin;
1821: PetscCall(PetscObjectReference((PetscObject)ksp));
1822: PetscCall(KSPDestroy(&ctx->ksp));
1823: ctx->ksp = ksp;
1824: svd->state = SVD_STATE_INITIAL;
1825: PetscFunctionReturn(PETSC_SUCCESS);
1826: }
1828: /*@
1829: SVDTRLanczosSetKSP - Associate a linear solver object (KSP) to the SVD solver.
1831: Collective
1833: Input Parameters:
1834: + svd - SVD solver
1835: - ksp - the linear solver object
1837: Note:
1838: Only used for the GSVD problem.
1840: Level: advanced
1842: .seealso: SVDTRLanczosGetKSP()
1843: @*/
1844: PetscErrorCode SVDTRLanczosSetKSP(SVD svd,KSP ksp)
1845: {
1846: PetscFunctionBegin;
1849: PetscCheckSameComm(svd,1,ksp,2);
1850: PetscTryMethod(svd,"SVDTRLanczosSetKSP_C",(SVD,KSP),(svd,ksp));
1851: PetscFunctionReturn(PETSC_SUCCESS);
1852: }
1854: static PetscErrorCode SVDTRLanczosGetKSP_TRLanczos(SVD svd,KSP *ksp)
1855: {
1856: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
1857: PC pc;
1859: PetscFunctionBegin;
1860: if (!ctx->ksp) {
1861: /* Create linear solver */
1862: PetscCall(KSPCreate(PetscObjectComm((PetscObject)svd),&ctx->ksp));
1863: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)svd,1));
1864: PetscCall(KSPSetOptionsPrefix(ctx->ksp,((PetscObject)svd)->prefix));
1865: PetscCall(KSPAppendOptionsPrefix(ctx->ksp,"svd_trlanczos_"));
1866: PetscCall(PetscObjectSetOptions((PetscObject)ctx->ksp,((PetscObject)svd)->options));
1867: PetscCall(KSPSetType(ctx->ksp,KSPLSQR));
1868: PetscCall(KSPGetPC(ctx->ksp,&pc));
1869: PetscCall(PCSetType(pc,PCNONE));
1870: PetscCall(KSPSetErrorIfNotConverged(ctx->ksp,PETSC_TRUE));
1871: PetscCall(KSPSetTolerances(ctx->ksp,SlepcDefaultTol(svd->tol)/10.0,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT));
1872: }
1873: *ksp = ctx->ksp;
1874: PetscFunctionReturn(PETSC_SUCCESS);
1875: }
1877: /*@
1878: SVDTRLanczosGetKSP - Retrieve the linear solver object (KSP) associated with
1879: the SVD solver.
1881: Collective
1883: Input Parameter:
1884: . svd - SVD solver
1886: Output Parameter:
1887: . ksp - the linear solver object
1889: Level: advanced
1891: .seealso: SVDTRLanczosSetKSP()
1892: @*/
1893: PetscErrorCode SVDTRLanczosGetKSP(SVD svd,KSP *ksp)
1894: {
1895: PetscFunctionBegin;
1898: PetscUseMethod(svd,"SVDTRLanczosGetKSP_C",(SVD,KSP*),(svd,ksp));
1899: PetscFunctionReturn(PETSC_SUCCESS);
1900: }
1902: static PetscErrorCode SVDTRLanczosSetRestart_TRLanczos(SVD svd,PetscReal keep)
1903: {
1904: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
1906: PetscFunctionBegin;
1907: if (keep==(PetscReal)PETSC_DEFAULT) ctx->keep = 0.5;
1908: else {
1909: PetscCheck(keep>=0.1 && keep<=0.9,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument %g must be in the range [0.1,0.9]",(double)keep);
1910: ctx->keep = keep;
1911: }
1912: PetscFunctionReturn(PETSC_SUCCESS);
1913: }
1915: /*@
1916: SVDTRLanczosSetRestart - Sets the restart parameter for the thick-restart
1917: Lanczos method, in particular the proportion of basis vectors that must be
1918: kept after restart.
1920: Logically Collective
1922: Input Parameters:
1923: + svd - the singular value solver
1924: - keep - the number of vectors to be kept at restart
1926: Options Database Key:
1927: . -svd_trlanczos_restart - Sets the restart parameter
1929: Notes:
1930: Allowed values are in the range [0.1,0.9]. The default is 0.5.
1932: Level: advanced
1934: .seealso: SVDTRLanczosGetRestart()
1935: @*/
1936: PetscErrorCode SVDTRLanczosSetRestart(SVD svd,PetscReal keep)
1937: {
1938: PetscFunctionBegin;
1941: PetscTryMethod(svd,"SVDTRLanczosSetRestart_C",(SVD,PetscReal),(svd,keep));
1942: PetscFunctionReturn(PETSC_SUCCESS);
1943: }
1945: static PetscErrorCode SVDTRLanczosGetRestart_TRLanczos(SVD svd,PetscReal *keep)
1946: {
1947: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
1949: PetscFunctionBegin;
1950: *keep = ctx->keep;
1951: PetscFunctionReturn(PETSC_SUCCESS);
1952: }
1954: /*@
1955: SVDTRLanczosGetRestart - Gets the restart parameter used in the thick-restart
1956: Lanczos method.
1958: Not Collective
1960: Input Parameter:
1961: . svd - the singular value solver
1963: Output Parameter:
1964: . keep - the restart parameter
1966: Level: advanced
1968: .seealso: SVDTRLanczosSetRestart()
1969: @*/
1970: PetscErrorCode SVDTRLanczosGetRestart(SVD svd,PetscReal *keep)
1971: {
1972: PetscFunctionBegin;
1975: PetscUseMethod(svd,"SVDTRLanczosGetRestart_C",(SVD,PetscReal*),(svd,keep));
1976: PetscFunctionReturn(PETSC_SUCCESS);
1977: }
1979: static PetscErrorCode SVDTRLanczosSetLocking_TRLanczos(SVD svd,PetscBool lock)
1980: {
1981: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
1983: PetscFunctionBegin;
1984: ctx->lock = lock;
1985: PetscFunctionReturn(PETSC_SUCCESS);
1986: }
1988: /*@
1989: SVDTRLanczosSetLocking - Choose between locking and non-locking variants of
1990: the thick-restart Lanczos method.
1992: Logically Collective
1994: Input Parameters:
1995: + svd - the singular value solver
1996: - lock - true if the locking variant must be selected
1998: Options Database Key:
1999: . -svd_trlanczos_locking - Sets the locking flag
2001: Notes:
2002: The default is to lock converged singular triplets when the method restarts.
2003: This behaviour can be changed so that all directions are kept in the
2004: working subspace even if already converged to working accuracy (the
2005: non-locking variant).
2007: Level: advanced
2009: .seealso: SVDTRLanczosGetLocking()
2010: @*/
2011: PetscErrorCode SVDTRLanczosSetLocking(SVD svd,PetscBool lock)
2012: {
2013: PetscFunctionBegin;
2016: PetscTryMethod(svd,"SVDTRLanczosSetLocking_C",(SVD,PetscBool),(svd,lock));
2017: PetscFunctionReturn(PETSC_SUCCESS);
2018: }
2020: static PetscErrorCode SVDTRLanczosGetLocking_TRLanczos(SVD svd,PetscBool *lock)
2021: {
2022: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
2024: PetscFunctionBegin;
2025: *lock = ctx->lock;
2026: PetscFunctionReturn(PETSC_SUCCESS);
2027: }
2029: /*@
2030: SVDTRLanczosGetLocking - Gets the locking flag used in the thick-restart
2031: Lanczos method.
2033: Not Collective
2035: Input Parameter:
2036: . svd - the singular value solver
2038: Output Parameter:
2039: . lock - the locking flag
2041: Level: advanced
2043: .seealso: SVDTRLanczosSetLocking()
2044: @*/
2045: PetscErrorCode SVDTRLanczosGetLocking(SVD svd,PetscBool *lock)
2046: {
2047: PetscFunctionBegin;
2050: PetscUseMethod(svd,"SVDTRLanczosGetLocking_C",(SVD,PetscBool*),(svd,lock));
2051: PetscFunctionReturn(PETSC_SUCCESS);
2052: }
2054: static PetscErrorCode SVDTRLanczosSetExplicitMatrix_TRLanczos(SVD svd,PetscBool explicitmat)
2055: {
2056: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
2058: PetscFunctionBegin;
2059: if (lanczos->explicitmatrix != explicitmat) {
2060: lanczos->explicitmatrix = explicitmat;
2061: svd->state = SVD_STATE_INITIAL;
2062: }
2063: PetscFunctionReturn(PETSC_SUCCESS);
2064: }
2066: /*@
2067: SVDTRLanczosSetExplicitMatrix - Indicate if the matrix Z=[A;B] must
2068: be built explicitly.
2070: Logically Collective
2072: Input Parameters:
2073: + svd - singular value solver
2074: - explicitmat - Boolean flag indicating if Z=[A;B] is built explicitly
2076: Options Database Key:
2077: . -svd_trlanczos_explicitmatrix <boolean> - Indicates the boolean flag
2079: Notes:
2080: This option is relevant for the GSVD case only.
2081: Z is the coefficient matrix of the KSP solver used internally.
2083: Level: advanced
2085: .seealso: SVDTRLanczosGetExplicitMatrix()
2086: @*/
2087: PetscErrorCode SVDTRLanczosSetExplicitMatrix(SVD svd,PetscBool explicitmat)
2088: {
2089: PetscFunctionBegin;
2092: PetscTryMethod(svd,"SVDTRLanczosSetExplicitMatrix_C",(SVD,PetscBool),(svd,explicitmat));
2093: PetscFunctionReturn(PETSC_SUCCESS);
2094: }
2096: static PetscErrorCode SVDTRLanczosGetExplicitMatrix_TRLanczos(SVD svd,PetscBool *explicitmat)
2097: {
2098: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
2100: PetscFunctionBegin;
2101: *explicitmat = lanczos->explicitmatrix;
2102: PetscFunctionReturn(PETSC_SUCCESS);
2103: }
2105: /*@
2106: SVDTRLanczosGetExplicitMatrix - Returns the flag indicating if Z=[A;B] is built explicitly.
2108: Not Collective
2110: Input Parameter:
2111: . svd - singular value solver
2113: Output Parameter:
2114: . explicitmat - the mode flag
2116: Level: advanced
2118: .seealso: SVDTRLanczosSetExplicitMatrix()
2119: @*/
2120: PetscErrorCode SVDTRLanczosGetExplicitMatrix(SVD svd,PetscBool *explicitmat)
2121: {
2122: PetscFunctionBegin;
2125: PetscUseMethod(svd,"SVDTRLanczosGetExplicitMatrix_C",(SVD,PetscBool*),(svd,explicitmat));
2126: PetscFunctionReturn(PETSC_SUCCESS);
2127: }
2129: static PetscErrorCode SVDTRLanczosSetScale_TRLanczos(SVD svd,PetscReal scale)
2130: {
2131: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
2133: PetscFunctionBegin;
2134: if (scale<0) {
2135: ctx->scalef = 1.0;
2136: ctx->scaleth = -scale;
2137: } else {
2138: ctx->scalef = scale;
2139: ctx->scaleth = 0.0;
2140: }
2141: PetscFunctionReturn(PETSC_SUCCESS);
2142: }
2144: /*@
2145: SVDTRLanczosSetScale - Sets the scale parameter for the GSVD.
2147: Logically Collective
2149: Input Parameters:
2150: + svd - singular value solver
2151: - scale - scale parameter
2153: Options Database Key:
2154: . -svd_trlanczos_scale <real> - scale factor/threshold
2156: Notes:
2157: This parameter is relevant for the GSVD case only. If the parameter is
2158: positive, it indicates the scale factor for B in matrix Z=[A;B]. If
2159: negative, its absolute value is the threshold for automatic scaling.
2160: In automatic scaling, whenever the largest approximate generalized singular
2161: value (or the inverse of the smallest value, if SVD_SMALLEST is used)
2162: exceeds the threshold, the computation is restarted with matrix B
2163: scaled by that value.
2165: Level: advanced
2167: .seealso: SVDTRLanczosGetScale()
2168: @*/
2169: PetscErrorCode SVDTRLanczosSetScale(SVD svd,PetscReal scale)
2170: {
2171: PetscFunctionBegin;
2174: PetscTryMethod(svd,"SVDTRLanczosSetScale_C",(SVD,PetscReal),(svd,scale));
2175: PetscFunctionReturn(PETSC_SUCCESS);
2176: }
2178: static PetscErrorCode SVDTRLanczosGetScale_TRLanczos(SVD svd,PetscReal *scale)
2179: {
2180: SVD_TRLANCZOS *ctx = (SVD_TRLANCZOS*)svd->data;
2182: PetscFunctionBegin;
2183: if (ctx->scaleth==0) *scale = ctx->scalef;
2184: else *scale = -ctx->scaleth;
2185: PetscFunctionReturn(PETSC_SUCCESS);
2186: }
2188: /*@
2189: SVDTRLanczosGetScale - Gets the scale parameter for the GSVD.
2191: Not Collective
2193: Input Parameter:
2194: . svd - the singular value solver
2196: Output Parameter:
2197: . scale - the scale parameter
2199: Notes:
2200: This parameter is relevant for the GSVD case only. If the parameter is
2201: positive, it indicates the scale factor for B in matrix Z=[A;B]. If
2202: negative, its absolute value is the threshold for automatic scaling.
2204: Level: advanced
2206: .seealso: SVDTRLanczosSetScale()
2207: @*/
2208: PetscErrorCode SVDTRLanczosGetScale(SVD svd,PetscReal *scale)
2209: {
2210: PetscFunctionBegin;
2213: PetscUseMethod(svd,"SVDTRLanczosGetScale_C",(SVD,PetscReal*),(svd,scale));
2214: PetscFunctionReturn(PETSC_SUCCESS);
2215: }
2217: PetscErrorCode SVDReset_TRLanczos(SVD svd)
2218: {
2219: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
2221: PetscFunctionBegin;
2222: if (svd->isgeneralized || (!svd->problem_type && svd->OPb)) {
2223: PetscCall(KSPReset(lanczos->ksp));
2224: PetscCall(MatDestroy(&lanczos->Z));
2225: }
2226: PetscFunctionReturn(PETSC_SUCCESS);
2227: }
2229: PetscErrorCode SVDDestroy_TRLanczos(SVD svd)
2230: {
2231: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
2233: PetscFunctionBegin;
2234: if (svd->isgeneralized || (!svd->problem_type && svd->OPb)) PetscCall(KSPDestroy(&lanczos->ksp));
2235: PetscCall(PetscFree(svd->data));
2236: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetOneSide_C",NULL));
2237: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetOneSide_C",NULL));
2238: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetGBidiag_C",NULL));
2239: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetGBidiag_C",NULL));
2240: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetKSP_C",NULL));
2241: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetKSP_C",NULL));
2242: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetRestart_C",NULL));
2243: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetRestart_C",NULL));
2244: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetLocking_C",NULL));
2245: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetLocking_C",NULL));
2246: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetExplicitMatrix_C",NULL));
2247: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetExplicitMatrix_C",NULL));
2248: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetScale_C",NULL));
2249: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetScale_C",NULL));
2250: PetscFunctionReturn(PETSC_SUCCESS);
2251: }
2253: PetscErrorCode SVDView_TRLanczos(SVD svd,PetscViewer viewer)
2254: {
2255: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
2256: PetscBool isascii;
2258: PetscFunctionBegin;
2259: PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
2260: if (isascii) {
2261: PetscCall(PetscViewerASCIIPrintf(viewer," %d%% of basis vectors kept after restart\n",(int)(100*lanczos->keep)));
2262: PetscCall(PetscViewerASCIIPrintf(viewer," using the %slocking variant\n",lanczos->lock?"":"non-"));
2263: if (svd->isgeneralized) {
2264: const char *bidiag="";
2266: switch (lanczos->bidiag) {
2267: case SVD_TRLANCZOS_GBIDIAG_SINGLE: bidiag = "single"; break;
2268: case SVD_TRLANCZOS_GBIDIAG_UPPER: bidiag = "joint upper-upper"; break;
2269: case SVD_TRLANCZOS_GBIDIAG_LOWER: bidiag = "joint lower-upper"; break;
2270: }
2271: PetscCall(PetscViewerASCIIPrintf(viewer," bidiagonalization choice: %s\n",bidiag));
2272: PetscCall(PetscViewerASCIIPrintf(viewer," %s matrix\n",lanczos->explicitmatrix?"explicit":"implicit"));
2273: if (lanczos->scaleth==0) PetscCall(PetscViewerASCIIPrintf(viewer," scale factor for matrix B: %g\n",(double)lanczos->scalef));
2274: else PetscCall(PetscViewerASCIIPrintf(viewer," automatic scaling for matrix B with threshold: %g\n",(double)lanczos->scaleth));
2275: if (!lanczos->ksp) PetscCall(SVDTRLanczosGetKSP(svd,&lanczos->ksp));
2276: PetscCall(PetscViewerASCIIPushTab(viewer));
2277: PetscCall(KSPView(lanczos->ksp,viewer));
2278: PetscCall(PetscViewerASCIIPopTab(viewer));
2279: } else PetscCall(PetscViewerASCIIPrintf(viewer," %s-sided reorthogonalization\n",lanczos->oneside? "one": "two"));
2280: }
2281: PetscFunctionReturn(PETSC_SUCCESS);
2282: }
2284: PetscErrorCode SVDSetDSType_TRLanczos(SVD svd)
2285: {
2286: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
2287: DSType dstype;
2289: PetscFunctionBegin;
2290: dstype = svd->ishyperbolic? DSHSVD: DSSVD;
2291: if (svd->OPb && (lanczos->bidiag==SVD_TRLANCZOS_GBIDIAG_UPPER || lanczos->bidiag==SVD_TRLANCZOS_GBIDIAG_LOWER)) dstype = DSGSVD;
2292: PetscCall(DSSetType(svd->ds,dstype));
2293: PetscFunctionReturn(PETSC_SUCCESS);
2294: }
2296: SLEPC_EXTERN PetscErrorCode SVDCreate_TRLanczos(SVD svd)
2297: {
2298: SVD_TRLANCZOS *ctx;
2300: PetscFunctionBegin;
2301: PetscCall(PetscNew(&ctx));
2302: svd->data = (void*)ctx;
2304: ctx->lock = PETSC_TRUE;
2305: ctx->bidiag = SVD_TRLANCZOS_GBIDIAG_LOWER;
2306: ctx->scalef = 1.0;
2307: ctx->scaleth = 0.0;
2309: svd->ops->setup = SVDSetUp_TRLanczos;
2310: svd->ops->solve = SVDSolve_TRLanczos;
2311: svd->ops->solveg = SVDSolve_TRLanczos_GSVD;
2312: svd->ops->solveh = SVDSolve_TRLanczos_HSVD;
2313: svd->ops->destroy = SVDDestroy_TRLanczos;
2314: svd->ops->reset = SVDReset_TRLanczos;
2315: svd->ops->setfromoptions = SVDSetFromOptions_TRLanczos;
2316: svd->ops->view = SVDView_TRLanczos;
2317: svd->ops->setdstype = SVDSetDSType_TRLanczos;
2318: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetOneSide_C",SVDTRLanczosSetOneSide_TRLanczos));
2319: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetOneSide_C",SVDTRLanczosGetOneSide_TRLanczos));
2320: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetGBidiag_C",SVDTRLanczosSetGBidiag_TRLanczos));
2321: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetGBidiag_C",SVDTRLanczosGetGBidiag_TRLanczos));
2322: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetKSP_C",SVDTRLanczosSetKSP_TRLanczos));
2323: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetKSP_C",SVDTRLanczosGetKSP_TRLanczos));
2324: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetRestart_C",SVDTRLanczosSetRestart_TRLanczos));
2325: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetRestart_C",SVDTRLanczosGetRestart_TRLanczos));
2326: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetLocking_C",SVDTRLanczosSetLocking_TRLanczos));
2327: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetLocking_C",SVDTRLanczosGetLocking_TRLanczos));
2328: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetExplicitMatrix_C",SVDTRLanczosSetExplicitMatrix_TRLanczos));
2329: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetExplicitMatrix_C",SVDTRLanczosGetExplicitMatrix_TRLanczos));
2330: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetScale_C",SVDTRLanczosSetScale_TRLanczos));
2331: PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetScale_C",SVDTRLanczosGetScale_TRLanczos));
2332: PetscFunctionReturn(PETSC_SUCCESS);
2333: }