Actual source code: dshsvd.c

slepc-main 2024-11-09
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  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: */

 11: #include <slepc/private/dsimpl.h>
 12: #include <slepcblaslapack.h>

 14: typedef struct {
 15:   PetscInt  m;             /* number of columns */
 16:   PetscInt  t;             /* number of rows of V after truncating */
 17:   PetscBool reorth;        /* reorthogonalize left vectors */
 18: } DS_HSVD;

 20: static PetscErrorCode DSAllocate_HSVD(DS ds,PetscInt ld)
 21: {
 22:   PetscFunctionBegin;
 23:   if (!ds->compact) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
 24:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_U));
 25:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_V));
 26:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_T));
 27:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_D));
 28:   PetscCall(PetscFree(ds->perm));
 29:   PetscCall(PetscMalloc1(ld,&ds->perm));
 30:   PetscFunctionReturn(PETSC_SUCCESS);
 31: }

 33: /*   0       l           k                 m-1
 34:     -----------------------------------------
 35:     |*       .           .                  |
 36:     |  *     .           .                  |
 37:     |    *   .           .                  |
 38:     |      * .           .                  |
 39:     |        o           o                  |
 40:     |          o         o                  |
 41:     |            o       o                  |
 42:     |              o     o                  |
 43:     |                o   o                  |
 44:     |                  o o                  |
 45:     |                    o x                |
 46:     |                      x x              |
 47:     |                        x x            |
 48:     |                          x x          |
 49:     |                            x x        |
 50:     |                              x x      |
 51:     |                                x x    |
 52:     |                                  x x  |
 53:     |                                    x x|
 54: n-1 |                                      x|
 55:     -----------------------------------------
 56: */

 58: static PetscErrorCode DSView_HSVD(DS ds,PetscViewer viewer)
 59: {
 60:   DS_HSVD           *ctx = (DS_HSVD*)ds->data;
 61:   PetscViewerFormat format;
 62:   PetscInt          i,j,r,c,m=ctx->m,rows,cols;
 63:   PetscReal         *T,*S,value;
 64:   const char        *methodname[] = {
 65:                      "Cross product A'*Omega*A"
 66:   };
 67:   const int         nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);

 69:   PetscFunctionBegin;
 70:   PetscCall(PetscViewerGetFormat(viewer,&format));
 71:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
 72:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscCall(PetscViewerASCIIPrintf(viewer,"number of columns: %" PetscInt_FMT "\n",m));
 73:     if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]));
 74:     if (ctx->reorth) PetscCall(PetscViewerASCIIPrintf(viewer,"reorthogonalizing left vectors\n"));
 75:     PetscFunctionReturn(PETSC_SUCCESS);
 76:   }
 77:   PetscCheck(m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
 78:   if (ds->compact) {
 79:     PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
 80:     PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
 81:     PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
 82:     rows = ds->n;
 83:     cols = ds->extrarow? m+1: m;
 84:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
 85:       PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",rows,cols));
 86:       PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",2*ds->n));
 87:       PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = [\n"));
 88:       for (i=0;i<PetscMin(ds->n,m);i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,i+1,(double)T[i]));
 89:       for (i=0;i<cols-1;i++) {
 90:         c = PetscMax(i+2,ds->k+1);
 91:         r = i+1;
 92:         value = i<ds->l? 0.0: T[i+ds->ld];
 93:         PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",r,c,(double)value));
 94:       }
 95:       PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]));
 96:       PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n));
 97:       PetscCall(PetscViewerASCIIPrintf(viewer,"omega = zeros(%" PetscInt_FMT ",3);\n",3*ds->n));
 98:       PetscCall(PetscViewerASCIIPrintf(viewer,"omega = [\n"));
 99:       for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,i+1,(double)S[i]));
100:       PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_D]));
101:     } else {
102:       PetscCall(PetscViewerASCIIPrintf(viewer,"T\n"));
103:       for (i=0;i<rows;i++) {
104:         for (j=0;j<cols;j++) {
105:           if (i==j) value = T[i];
106:           else if (i<ds->l) value = 0.0;
107:           else if (i<ds->k && j==ds->k) value = T[PetscMin(i,j)+ds->ld];
108:           else if (i+1==j && i>=ds->k) value = T[i+ds->ld];
109:           else value = 0.0;
110:           PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value));
111:         }
112:         PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
113:       }
114:       PetscCall(PetscViewerASCIIPrintf(viewer,"omega\n"));
115:       for (i=0;i<ds->n;i++) {
116:         for (j=0;j<ds->n;j++) {
117:           if (i==j) value = S[i];
118:           else value = 0.0;
119:           PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value));
120:         }
121:         PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
122:       }
123:     }
124:     PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
125:     PetscCall(PetscViewerFlush(viewer));
126:     PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
127:     PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
128:   } else {
129:     PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
130:     PetscCall(DSViewMat(ds,viewer,DS_MAT_D));
131:   }
132:   if (ds->state>DS_STATE_INTERMEDIATE) {
133:     PetscCall(DSViewMat(ds,viewer,DS_MAT_U));
134:     PetscCall(DSViewMat(ds,viewer,DS_MAT_V));
135:   }
136:   PetscFunctionReturn(PETSC_SUCCESS);
137: }

139: static PetscErrorCode DSVectors_HSVD(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
140: {
141:   PetscFunctionBegin;
142:   switch (mat) {
143:     case DS_MAT_U:
144:     case DS_MAT_V:
145:       if (rnorm) *rnorm = 0.0;
146:       break;
147:     default:
148:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
149:   }
150:   PetscFunctionReturn(PETSC_SUCCESS);
151: }

153: static PetscErrorCode DSSort_HSVD(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
154: {
155:   DS_HSVD        *ctx = (DS_HSVD*)ds->data;
156:   PetscInt       n,l,i,*perm,ld=ds->ld;
157:   PetscScalar    *A;
158:   PetscReal      *d,*s;

160:   PetscFunctionBegin;
161:   if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
162:   PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
163:   l = ds->l;
164:   n = PetscMin(ds->n,ctx->m);
165:   PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
166:   PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
167:   PetscCall(DSAllocateWork_Private(ds,0,ds->ld,0));
168:   perm = ds->perm;
169:   if (!rr) PetscCall(DSSortEigenvaluesReal_Private(ds,d,perm));
170:   else PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE));
171:   PetscCall(PetscArraycpy(ds->rwork,s,n));
172:   for (i=l;i<n;i++) s[i]  = ds->rwork[perm[i]];
173:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
174:   PetscCall(DSPermuteBoth_Private(ds,l,n,ds->n,ctx->m,DS_MAT_U,DS_MAT_V,perm));
175:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
176:   if (!ds->compact) {
177:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
178:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
179:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
180:   }
181:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
182:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
183:   PetscFunctionReturn(PETSC_SUCCESS);
184: }

186: static PetscErrorCode DSUpdateExtraRow_HSVD(DS ds)
187: {
188:   DS_HSVD           *ctx = (DS_HSVD*)ds->data;
189:   PetscInt          i;
190:   PetscBLASInt      n=0,m=0,ld,l;
191:   const PetscScalar *U;
192:   PetscReal         *T,*e,*Omega,beta;

194:   PetscFunctionBegin;
195:   PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
196:   PetscCall(PetscBLASIntCast(ds->n,&n));
197:   PetscCall(PetscBLASIntCast(ctx->m,&m));
198:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
199:   PetscCall(PetscBLASIntCast(ds->l,&l));
200:   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_U],&U));
201:   PetscCall(DSGetArrayReal(ds,DS_MAT_D,&Omega));
202:   PetscCheck(ds->compact,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for non-compact storage");
203:   PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
204:   e = T+ld;
205:   beta = PetscAbs(e[m-1]);   /* in compact, we assume all entries are zero except the last one */
206:   for (i=0;i<n;i++) e[i] = PetscRealPart(beta*U[n-1+i*ld]*Omega[i]);
207:   ds->k = m;
208:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
209:   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_U],&U));
210:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&Omega));
211:   PetscFunctionReturn(PETSC_SUCCESS);
212: }

214: static PetscErrorCode DSTruncate_HSVD(DS ds,PetscInt n,PetscBool trim)
215: {
216:   PetscInt    i,ld=ds->ld,l=ds->l;
217:   PetscScalar *A;
218:   DS_HSVD     *ctx = (DS_HSVD*)ds->data;

220:   PetscFunctionBegin;
221:   if (!ds->compact && ds->extrarow) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
222:   if (trim) {
223:     if (!ds->compact && ds->extrarow) {   /* clean extra column */
224:       for (i=l;i<ds->n;i++) A[i+ctx->m*ld] = 0.0;
225:     }
226:     ds->l  = 0;
227:     ds->k  = 0;
228:     ds->n  = n;
229:     ctx->m = n;
230:     ds->t  = ds->n;   /* truncated length equal to the new dimension */
231:     ctx->t = ctx->m;  /* must also keep the previous dimension of V */
232:   } else {
233:     if (!ds->compact && ds->extrarow && ds->k==ds->n) {
234:       /* copy entries of extra column to the new position, then clean last row */
235:       for (i=l;i<n;i++) A[i+n*ld] = A[i+ctx->m*ld];
236:       for (i=l;i<ds->n;i++) A[i+ctx->m*ld] = 0.0;
237:     }
238:     ds->k  = (ds->extrarow)? n: 0;
239:     ds->t  = ds->n;   /* truncated length equal to previous dimension */
240:     ctx->t = ctx->m;  /* must also keep the previous dimension of V */
241:     ds->n  = n;
242:     ctx->m = n;
243:   }
244:   if (!ds->compact && ds->extrarow) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
245:   PetscFunctionReturn(PETSC_SUCCESS);
246: }

248: static PetscErrorCode DSSolve_HSVD_CROSS(DS ds,PetscScalar *wr,PetscScalar *wi)
249: {
250:   DS_HSVD        *ctx = (DS_HSVD*)ds->data;
251:   PetscInt       i,j,k=ds->k,rwu=0,iwu=0,swu=0,nv;
252:   PetscBLASInt   n1,n2,info,l=0,n=0,m=0,ld,off,one=1,*perm,*cmplx,incx=1,lwork;
253:   PetscScalar    *A,*U,*V,scal,*R,sone=1.0,szero=0.0;
254:   PetscReal      *d,*e,*dd,*ee,*Omega;

256:   PetscFunctionBegin;
257:   PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
258:   PetscCall(PetscBLASIntCast(ds->n,&n));
259:   PetscCall(PetscBLASIntCast(ctx->m,&m));
260:   PetscCheck(!ds->compact || n==m,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for non-square matrices in compact storage");
261:   PetscCheck(ds->compact || n>=m,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for the case of more columns than rows");
262:   PetscCall(PetscBLASIntCast(ds->l,&l));
263:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
264:   PetscCall(PetscBLASIntCast(PetscMax(0,ds->k-ds->l+1),&n2));
265:   n1 = n-l;     /* n1 = size of leading block, excl. locked + size of trailing block */
266:   off = l+l*ld;
267:   if (!ds->compact) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
268:   PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_U],&U));
269:   PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_V],&V));
270:   PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
271:   e = d+ld;
272:   PetscCall(DSGetArrayReal(ds,DS_MAT_D,&Omega));
273:   PetscCall(PetscArrayzero(U,ld*ld));
274:   for (i=0;i<l;i++) U[i+i*ld] = 1.0;
275:   PetscCall(PetscArrayzero(V,ld*ld));
276:   for (i=0;i<n;i++) V[i+i*ld] = 1.0;
277:   for (i=0;i<l;i++) wr[i] = d[i];
278:   if (wi) for (i=0;i<l;i++) wi[i] = 0.0;

280:   if (ds->compact) {
281:     /* Form the arrow tridiagonal cross product T=A'*Omega*A, where A is the arrow
282:        bidiagonal matrix formed by d, e. T is stored in dd, ee */
283:     PetscCall(DSAllocateWork_Private(ds,(n+6)*ld,4*ld,2*ld));
284:     R = ds->work+swu;
285:     swu += n*ld;
286:     perm = ds->iwork+iwu;
287:     iwu += n;
288:     cmplx = ds->iwork+iwu;
289:     dd = ds->rwork+rwu;
290:     rwu += ld;
291:     ee = ds->rwork+rwu;
292:     rwu += ld;
293:     for (i=0;i<l;i++) {dd[i] = d[i]*d[i]*Omega[i]; ee[i] = 0.0;}
294:     for (i=l;i<=ds->k;i++) {
295:       dd[i] = Omega[i]*d[i]*d[i];
296:       ee[i] = Omega[i]*d[i]*e[i];
297:     }
298:     for (i=l;i<k;i++) dd[k] += Omega[i]*e[i]*e[i];
299:     for (i=k+1;i<n;i++) {
300:       dd[i] = Omega[i]*d[i]*d[i]+Omega[i-1]*e[i-1]*e[i-1];
301:       ee[i] = Omega[i]*d[i]*e[i];
302:     }

304:     /* Reduce T to tridiagonal form */
305:     PetscCall(DSArrowTridiag(n2,dd+l,ee+l,V+off,ld));

307:     /* Solve the tridiagonal eigenproblem corresponding to T */
308:     PetscCallBLAS("LAPACKsteqr",LAPACKsteqr_("V",&n1,dd+l,ee+l,V+off,&ld,ds->rwork+rwu,&info));
309:     SlepcCheckLapackInfo("steqr",info);
310:     for (i=l;i<n;i++) wr[i] = PetscSqrtScalar(PetscAbs(dd[i]));

312:     /* Build left singular vectors: U=A*V*Sigma^-1 */
313:     PetscCall(PetscArrayzero(U+l*ld,n1*ld));
314:     for (i=l;i<n-1;i++) {
315:       scal = d[i];
316:       PetscCallBLAS("BLASaxpy",BLASaxpy_(&n1,&scal,V+l*ld+i,&ld,U+l*ld+i,&ld));
317:       j = (i<k)?k:i+1;
318:       scal = e[i];
319:       PetscCallBLAS("BLASaxpy",BLASaxpy_(&n1,&scal,V+l*ld+j,&ld,U+l*ld+i,&ld));
320:     }
321:     scal = d[n-1];
322:     PetscCallBLAS("BLASaxpy",BLASaxpy_(&n1,&scal,V+off+(n1-1),&ld,U+off+(n1-1),&ld));
323:     /* Multiply by Sigma^-1 */
324:     for (i=l;i<n;i++) {scal = 1.0/wr[i]; PetscCallBLAS("BLASscal",BLASscal_(&n1,&scal,U+i*ld+l,&one));}

326:   } else { /* non-compact */

328:     PetscCall(DSAllocateWork_Private(ds,(n+6)*ld,PetscDefined(USE_COMPLEX)?4*ld:ld,2*ld));
329:     R = ds->work+swu;
330:     swu += n*ld;
331:     perm = ds->iwork+iwu;
332:     iwu += n;
333:     cmplx = ds->iwork+iwu;
334:     dd = ds->rwork+rwu;
335:     for (j=l;j<m;j++) {
336:       for (i=0;i<n;i++) ds->work[i] = Omega[i]*A[i+j*ld];
337:       PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&m,&sone,A,&ld,ds->work,&incx,&szero,V+j*ld,&incx));
338:     }

340:     /* compute eigenvalues */
341:     lwork = (n+6)*ld;
342: #if defined(PETSC_USE_COMPLEX)
343:     rwu += ld;
344:     PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&m,V,&ld,dd,ds->work,&lwork,ds->rwork+rwu,&info));
345: #else
346:     PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&m,V,&ld,dd,ds->work,&lwork,&info));
347: #endif
348:     SlepcCheckLapackInfo("syev",info);
349:     for (i=l;i<PetscMin(n,m);i++) d[i] = PetscSqrtReal(PetscAbsReal(dd[i]));

351:     /* Build left singular vectors: U=A*V*Sigma^-1 */
352:     for (j=l;j<PetscMin(n,m);j++) {
353:       scal = 1.0/d[j];
354:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&m,&scal,A,&ld,V+j*ld,&incx,&szero,U+j*ld,&incx));
355:     }
356:   }

358:   if (ctx->reorth) { /* Reinforce orthogonality */
359:     nv = n1;
360:     for (i=0;i<n;i++) cmplx[i] = 0;
361:     PetscCall(DSPseudoOrthog_HR(&nv,U+off,ld,Omega+l,R,ld,perm,cmplx,NULL,ds->work+swu));
362:   } else { /* Update Omega */
363:     for (i=l;i<PetscMin(n,m);i++) Omega[i] = PetscSign(dd[i]);
364:   }

366:   /* Update projected problem */
367:   if (ds->compact) {
368:     for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
369:     PetscCall(PetscArrayzero(e,n-1));
370:   } else {
371:     for (i=l;i<m;i++) PetscCall(PetscArrayzero(A+l+i*ld,n-l));
372:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
373:   }
374:   for (i=l;i<PetscMin(n,m);i++) wr[i] = d[i];
375:   if (wi) for (i=l;i<PetscMin(n,m);i++) wi[i] = 0.0;

377:   if (ctx->reorth) { /* Update vectors V with R */
378:     scal = -1.0;
379:     for (i=0;i<nv;i++) {
380:       if (PetscRealPart(R[i+i*ld]) < 0.0) PetscCallBLAS("BLASscal",BLASscal_(&n1,&scal,V+(i+l)*ld+l,&one));
381:     }
382:   }

384:   if (!ds->compact) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
385:   PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_U],&U));
386:   PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_V],&V));
387:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
388:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&Omega));
389:   PetscFunctionReturn(PETSC_SUCCESS);
390: }

392: #if !defined(PETSC_HAVE_MPIUNI)
393: static PetscErrorCode DSSynchronize_HSVD(DS ds,PetscScalar eigr[],PetscScalar eigi[])
394: {
395:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
396:   PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;
397:   PetscScalar    *A,*U,*V;
398:   PetscReal      *T,*D;

400:   PetscFunctionBegin;
401:   if (ds->compact) kr = 3*ld;
402:   else k = (ds->n-l)*ld;
403:   kr += ld;
404:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
405:   if (eigr) k += ds->n-l;
406:   PetscCall(DSAllocateWork_Private(ds,k+kr,0,0));
407:   PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size));
408:   PetscCall(PetscMPIIntCast(ds->n-l,&n));
409:   PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
410:   PetscCall(PetscMPIIntCast(3*ld,&ld3));
411:   PetscCall(PetscMPIIntCast(ld,&ld_));
412:   if (ds->compact) PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
413:   else PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
414:   PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
415:   if (ds->state>DS_STATE_RAW) {
416:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_U],&U));
417:     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_V],&V));
418:   }
419:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
420:   if (!rank) {
421:     if (ds->compact) PetscCallMPI(MPI_Pack(T,ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
422:     else PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
423:     PetscCallMPI(MPI_Pack(D,ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
424:     if (ds->state>DS_STATE_RAW) {
425:       PetscCallMPI(MPI_Pack(U+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
426:       PetscCallMPI(MPI_Pack(V+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
427:     }
428:     if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
429:   }
430:   PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
431:   if (rank) {
432:     if (ds->compact) PetscCallMPI(MPI_Unpack(ds->work,size,&off,T,ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
433:     else PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
434:     PetscCallMPI(MPI_Unpack(ds->work,size,&off,D,ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
435:     if (ds->state>DS_STATE_RAW) {
436:       PetscCallMPI(MPI_Unpack(ds->work,size,&off,U+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
437:       PetscCallMPI(MPI_Unpack(ds->work,size,&off,V+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
438:     }
439:     if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
440:   }
441:   if (ds->compact) PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
442:   else PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
443:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
444:   if (ds->state>DS_STATE_RAW) {
445:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_U],&U));
446:     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_V],&V));
447:   }
448:   PetscFunctionReturn(PETSC_SUCCESS);
449: }
450: #endif

452: static PetscErrorCode DSMatGetSize_HSVD(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
453: {
454:   DS_HSVD *ctx = (DS_HSVD*)ds->data;

456:   PetscFunctionBegin;
457:   PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
458:   switch (t) {
459:     case DS_MAT_A:
460:       *rows = ds->n;
461:       *cols = ds->extrarow? ctx->m+1: ctx->m;
462:       break;
463:     case DS_MAT_T:
464:       *rows = ds->n;
465:       *cols = PetscDefined(USE_COMPLEX)? 2: 3;
466:       break;
467:     case DS_MAT_D:
468:       *rows = ds->n;
469:       *cols = 1;
470:       break;
471:     case DS_MAT_U:
472:       *rows = ds->state==DS_STATE_TRUNCATED? ds->t: ds->n;
473:       *cols = ds->n;
474:       break;
475:     case DS_MAT_V:
476:       *rows = ds->state==DS_STATE_TRUNCATED? ctx->t: ctx->m;
477:       *cols = ctx->m;
478:       break;
479:     default:
480:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid t parameter");
481:   }
482:   PetscFunctionReturn(PETSC_SUCCESS);
483: }

485: static PetscErrorCode DSHSVDSetDimensions_HSVD(DS ds,PetscInt m)
486: {
487:   DS_HSVD *ctx = (DS_HSVD*)ds->data;

489:   PetscFunctionBegin;
490:   DSCheckAlloc(ds,1);
491:   if (m==PETSC_DECIDE || m==PETSC_DEFAULT) {
492:     ctx->m = ds->ld;
493:   } else {
494:     PetscCheck(m>0 && m<=ds->ld,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of m. Must be between 1 and ld");
495:     ctx->m = m;
496:   }
497:   PetscFunctionReturn(PETSC_SUCCESS);
498: }

500: /*@
501:    DSHSVDSetDimensions - Sets the number of columns for a DSHSVD.

503:    Logically Collective

505:    Input Parameters:
506: +  ds - the direct solver context
507: -  m  - the number of columns

509:    Notes:
510:    This call is complementary to DSSetDimensions(), to provide a dimension
511:    that is specific to this DS type.

513:    Level: intermediate

515: .seealso: DSHSVDGetDimensions(), DSSetDimensions()
516: @*/
517: PetscErrorCode DSHSVDSetDimensions(DS ds,PetscInt m)
518: {
519:   PetscFunctionBegin;
522:   PetscTryMethod(ds,"DSHSVDSetDimensions_C",(DS,PetscInt),(ds,m));
523:   PetscFunctionReturn(PETSC_SUCCESS);
524: }

526: static PetscErrorCode DSHSVDGetDimensions_HSVD(DS ds,PetscInt *m)
527: {
528:   DS_HSVD *ctx = (DS_HSVD*)ds->data;

530:   PetscFunctionBegin;
531:   *m = ctx->m;
532:   PetscFunctionReturn(PETSC_SUCCESS);
533: }

535: /*@
536:    DSHSVDGetDimensions - Returns the number of columns for a DSHSVD.

538:    Not Collective

540:    Input Parameter:
541: .  ds - the direct solver context

543:    Output Parameters:
544: .  m - the number of columns

546:    Level: intermediate

548: .seealso: DSHSVDSetDimensions()
549: @*/
550: PetscErrorCode DSHSVDGetDimensions(DS ds,PetscInt *m)
551: {
552:   PetscFunctionBegin;
554:   PetscAssertPointer(m,2);
555:   PetscUseMethod(ds,"DSHSVDGetDimensions_C",(DS,PetscInt*),(ds,m));
556:   PetscFunctionReturn(PETSC_SUCCESS);
557: }

559: static PetscErrorCode DSHSVDSetReorthogonalize_HSVD(DS ds,PetscBool reorth)
560: {
561:   DS_HSVD *ctx = (DS_HSVD*)ds->data;

563:   PetscFunctionBegin;
564:   ctx->reorth = reorth;
565:   PetscFunctionReturn(PETSC_SUCCESS);
566: }

568: /*@
569:    DSHSVDSetReorthogonalize - Sets the reorthogonalization of the left vectors in a DSHSVD.

571:    Logically Collective

573:    Input Parameters:
574: +  ds     - the direct solver context
575: -  reorth - the reorthogonalization flag

577:    Options Database Key:
578: .  -ds_hsvd_reorthog <bool> - sets the reorthogonalization flag

580:    Note:
581:    The computed left vectors (U) should be orthogonal with respect to the signature (D).
582:    But it may be necessary to enforce this with a final reorthogonalization step (omitted
583:    by default).

585:    Level: intermediate

587: .seealso: DSHSVDGetReorthogonalize()
588: @*/
589: PetscErrorCode DSHSVDSetReorthogonalize(DS ds,PetscBool reorth)
590: {
591:   PetscFunctionBegin;
594:   PetscTryMethod(ds,"DSHSVDSetReorthogonalize_C",(DS,PetscBool),(ds,reorth));
595:   PetscFunctionReturn(PETSC_SUCCESS);
596: }

598: static PetscErrorCode DSHSVDGetReorthogonalize_HSVD(DS ds,PetscBool *reorth)
599: {
600:   DS_HSVD *ctx = (DS_HSVD*)ds->data;

602:   PetscFunctionBegin;
603:   *reorth = ctx->reorth;
604:   PetscFunctionReturn(PETSC_SUCCESS);
605: }

607: /*@
608:    DSHSVDGetReorthogonalize - Returns the reorthogonalization flag of a DSHSVD.

610:    Not Collective

612:    Input Parameter:
613: .  ds - the direct solver context

615:    Output Parameters:
616: .  reorth - the reorthogonalization flag

618:    Level: intermediate

620: .seealso: DSHSVDSetReorthogonalize()
621: @*/
622: PetscErrorCode DSHSVDGetReorthogonalize(DS ds,PetscBool *reorth)
623: {
624:   PetscFunctionBegin;
626:   PetscAssertPointer(reorth,2);
627:   PetscUseMethod(ds,"DSHSVDGetReorthogonalize_C",(DS,PetscBool*),(ds,reorth));
628:   PetscFunctionReturn(PETSC_SUCCESS);
629: }

631: static PetscErrorCode DSSetFromOptions_HSVD(DS ds,PetscOptionItems *PetscOptionsObject)
632: {
633:   PetscBool      flg,reorth;

635:   PetscFunctionBegin;
636:   PetscOptionsHeadBegin(PetscOptionsObject,"DS HSVD Options");

638:     PetscCall(PetscOptionsBool("-ds_hsvd_reorthog","Reorthogonalize U vectors","DSHSVDSetReorthogonalize",PETSC_FALSE,&reorth,&flg));
639:     if (flg) PetscCall(DSHSVDSetReorthogonalize(ds,reorth));

641:   PetscOptionsHeadEnd();
642:   PetscFunctionReturn(PETSC_SUCCESS);
643: }

645: static PetscErrorCode DSDestroy_HSVD(DS ds)
646: {
647:   PetscFunctionBegin;
648:   PetscCall(PetscFree(ds->data));
649:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetDimensions_C",NULL));
650:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetDimensions_C",NULL));
651:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetReorthogonalize_C",NULL));
652:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetReorthogonalize_C",NULL));
653:   PetscFunctionReturn(PETSC_SUCCESS);
654: }

656: static PetscErrorCode DSSetCompact_HSVD(DS ds,PetscBool comp)
657: {
658:   PetscFunctionBegin;
659:   if (!comp) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
660:   PetscFunctionReturn(PETSC_SUCCESS);
661: }

663: /*MC
664:    DSHSVD - Dense Hyperbolic Singular Value Decomposition.

666:    Level: beginner

668:    Notes:
669:    The problem is expressed as A = U*Sigma*V', where A is rectangular in
670:    general, with n rows and m columns. U is orthogonal with respect to a
671:    signature matrix, stored in D. V is orthogonal. Sigma is a diagonal
672:    matrix whose diagonal elements are the arguments of DSSolve(). After
673:    solve, A is overwritten with Sigma, D is overwritten with the new signature.

675:    The matrices of left and right singular vectors, U and V, have size n and m,
676:    respectively. The number of columns m must be specified via DSHSVDSetDimensions().

678:    If the DS object is in the intermediate state, A is assumed to be in upper
679:    bidiagonal form (possibly with an arrow) and is stored in compact format
680:    on matrix T. The compact storage is implemented for the square case
681:    only, m=n. The extra row should be interpreted in this case as an extra column.

683:    Used DS matrices:
684: +  DS_MAT_A - problem matrix (used only if compact=false)
685: .  DS_MAT_T - upper bidiagonal matrix
686: .  DS_MAT_D - diagonal matrix (signature)
687: .  DS_MAT_U - left singular vectors
688: -  DS_MAT_V - right singular vectors

690:    Implemented methods:
691: .  0 - Cross product A'*Omega*A

693: .seealso: DSCreate(), DSSetType(), DSType, DSHSVDSetDimensions()
694: M*/
695: SLEPC_EXTERN PetscErrorCode DSCreate_HSVD(DS ds)
696: {
697:   DS_HSVD         *ctx;

699:   PetscFunctionBegin;
700:   PetscCall(PetscNew(&ctx));
701:   ds->data = (void*)ctx;

703:   ds->ops->allocate       = DSAllocate_HSVD;
704:   ds->ops->setfromoptions = DSSetFromOptions_HSVD;
705:   ds->ops->view           = DSView_HSVD;
706:   ds->ops->vectors        = DSVectors_HSVD;
707:   ds->ops->solve[0]       = DSSolve_HSVD_CROSS;
708:   ds->ops->sort           = DSSort_HSVD;
709:   ds->ops->truncate       = DSTruncate_HSVD;
710:   ds->ops->update         = DSUpdateExtraRow_HSVD;
711:   ds->ops->destroy        = DSDestroy_HSVD;
712:   ds->ops->matgetsize     = DSMatGetSize_HSVD;
713: #if !defined(PETSC_HAVE_MPIUNI)
714:   ds->ops->synchronize    = DSSynchronize_HSVD;
715: #endif
716:   ds->ops->setcompact     = DSSetCompact_HSVD;
717:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetDimensions_C",DSHSVDSetDimensions_HSVD));
718:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetDimensions_C",DSHSVDGetDimensions_HSVD));
719:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetReorthogonalize_C",DSHSVDSetReorthogonalize_HSVD));
720:   PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetReorthogonalize_C",DSHSVDGetReorthogonalize_HSVD));
721:   PetscFunctionReturn(PETSC_SUCCESS);
722: }