Actual source code: bvtensor.c
slepc-3.13.4 2020-09-02
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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: Tensor BV that is represented in compact form as V = (I otimes U) S
12: */
14: #include <slepc/private/bvimpl.h>
15: #include <slepcblaslapack.h>
17: typedef struct {
18: BV U; /* first factor */
19: Mat S; /* second factor */
20: PetscScalar *qB; /* auxiliary matrix used in non-standard inner products */
21: PetscScalar *sw; /* work space */
22: PetscInt d; /* degree of the tensor BV */
23: PetscInt ld; /* leading dimension of a single block in S */
24: PetscInt puk; /* copy of the k value */
25: Vec u; /* auxiliary work vector */
26: } BV_TENSOR;
28: PetscErrorCode BVMultInPlace_Tensor(BV V,Mat Q,PetscInt s,PetscInt e)
29: {
31: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
32: PetscScalar *pS,*q;
33: PetscInt ldq,lds = ctx->ld*ctx->d;
36: MatGetSize(Q,&ldq,NULL);
37: MatDenseGetArray(ctx->S,&pS);
38: MatDenseGetArray(Q,&q);
39: BVMultInPlace_BLAS_Private(V,lds,V->k-V->l,ldq,s-V->l,e-V->l,pS+(V->nc+V->l)*lds,q+V->l*ldq+V->l,PETSC_FALSE);
40: MatDenseRestoreArray(Q,&q);
41: MatDenseRestoreArray(ctx->S,&pS);
42: return(0);
43: }
45: PetscErrorCode BVMultInPlaceTranspose_Tensor(BV V,Mat Q,PetscInt s,PetscInt e)
46: {
48: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
49: PetscScalar *pS,*q;
50: PetscInt ldq,lds = ctx->ld*ctx->d;
53: MatGetSize(Q,&ldq,NULL);
54: MatDenseGetArray(ctx->S,&pS);
55: MatDenseGetArray(Q,&q);
56: BVMultInPlace_BLAS_Private(V,lds,V->k-V->l,ldq,s-V->l,e-V->l,pS+(V->nc+V->l)*lds,q+V->l*ldq+V->l,PETSC_TRUE);
57: MatDenseRestoreArray(Q,&q);
58: MatDenseRestoreArray(ctx->S,&pS);
59: return(0);
60: }
62: PetscErrorCode BVDot_Tensor(BV X,BV Y,Mat M)
63: {
65: BV_TENSOR *x = (BV_TENSOR*)X->data,*y = (BV_TENSOR*)Y->data;
66: PetscScalar *m,*px,*py;
67: PetscInt ldm,lds = x->ld*x->d;
70: if (x->U!=y->U) SETERRQ(PetscObjectComm((PetscObject)X),PETSC_ERR_SUP,"BVDot() in BVTENSOR requires that both operands have the same U factor");
71: if (lds!=y->ld*y->d) SETERRQ2(PetscObjectComm((PetscObject)X),PETSC_ERR_ARG_SIZ,"Mismatching dimensions ld*d %D %D",lds,y->ld*y->d);
72: MatGetSize(M,&ldm,NULL);
73: MatDenseGetArray(x->S,&px);
74: MatDenseGetArray(y->S,&py);
75: MatDenseGetArray(M,&m);
76: BVDot_BLAS_Private(X,Y->k-Y->l,X->k-X->l,lds,ldm,py+(Y->nc+Y->l)*lds,px+(X->nc+X->l)*lds,m+X->l*ldm+Y->l,PETSC_FALSE);
77: MatDenseRestoreArray(M,&m);
78: MatDenseRestoreArray(x->S,&px);
79: MatDenseRestoreArray(y->S,&py);
80: return(0);
81: }
83: PetscErrorCode BVScale_Tensor(BV bv,PetscInt j,PetscScalar alpha)
84: {
86: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
87: PetscScalar *pS;
88: PetscInt lds = ctx->ld*ctx->d;
91: MatDenseGetArray(ctx->S,&pS);
92: if (j<0) {
93: BVScale_BLAS_Private(bv,(bv->k-bv->l)*lds,pS+(bv->nc+bv->l)*lds,alpha);
94: } else {
95: BVScale_BLAS_Private(bv,lds,pS+(bv->nc+j)*lds,alpha);
96: }
97: MatDenseRestoreArray(ctx->S,&pS);
98: return(0);
99: }
101: PetscErrorCode BVNorm_Tensor(BV bv,PetscInt j,NormType type,PetscReal *val)
102: {
104: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
105: PetscScalar *pS;
106: PetscInt lds = ctx->ld*ctx->d;
109: MatDenseGetArray(ctx->S,&pS);
110: if (j<0) {
111: BVNorm_LAPACK_Private(bv,lds,bv->k-bv->l,pS+(bv->nc+bv->l)*lds,type,val,PETSC_FALSE);
112: } else {
113: BVNorm_LAPACK_Private(bv,lds,1,pS+(bv->nc+j)*lds,type,val,PETSC_FALSE);
114: }
115: MatDenseRestoreArray(ctx->S,&pS);
116: return(0);
117: }
119: PetscErrorCode BVCopyColumn_Tensor(BV V,PetscInt j,PetscInt i)
120: {
122: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
123: PetscScalar *pS;
124: PetscInt lds = ctx->ld*ctx->d;
127: MatDenseGetArray(ctx->S,&pS);
128: PetscArraycpy(pS+(V->nc+i)*lds,pS+(V->nc+j)*lds,lds);
129: MatDenseRestoreArray(ctx->S,&pS);
130: return(0);
131: }
133: static PetscErrorCode BVTensorNormColumn(BV bv,PetscInt j,PetscReal *norm)
134: {
136: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
137: PetscBLASInt one=1,lds_;
138: PetscScalar sone=1.0,szero=0.0,*S,*x,dot;
139: PetscReal alpha=1.0,scale=0.0,aval;
140: PetscInt i,lds,ld=ctx->ld;
143: lds = ld*ctx->d;
144: MatDenseGetArray(ctx->S,&S);
145: PetscBLASIntCast(lds,&lds_);
146: if (ctx->qB) {
147: x = ctx->sw;
148: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,S+j*lds,&one,&szero,x,&one));
149: dot = PetscRealPart(BLASdot_(&lds_,S+j*lds,&one,x,&one));
150: BV_SafeSqrt(bv,dot,norm);
151: } else {
152: /* Compute *norm = BLASnrm2_(&lds_,S+j*lds,&one); */
153: if (lds==1) *norm = PetscAbsScalar(S[j*lds]);
154: else {
155: for (i=0;i<lds;i++) {
156: aval = PetscAbsScalar(S[i+j*lds]);
157: if (aval!=0.0) {
158: if (scale<aval) {
159: alpha = 1.0 + alpha*PetscSqr(scale/aval);
160: scale = aval;
161: } else alpha += PetscSqr(aval/scale);
162: }
163: }
164: *norm = scale*PetscSqrtReal(alpha);
165: }
166: }
167: return(0);
168: }
170: PetscErrorCode BVOrthogonalizeGS1_Tensor(BV bv,PetscInt k,Vec v,PetscBool *which,PetscScalar *h,PetscScalar *c,PetscReal *onorm,PetscReal *norm)
171: {
172: PetscErrorCode ierr;
173: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
174: PetscScalar *pS,*cc,*x,dot,sonem=-1.0,sone=1.0,szero=0.0;
175: PetscInt i,lds = ctx->ld*ctx->d;
176: PetscBLASInt lds_,k_,one=1;
177: const PetscScalar *omega;
180: if (v) SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Orthogonalization against an external vector is not allowed in BVTENSOR");
181: MatDenseGetArray(ctx->S,&pS);
182: if (!c) {
183: VecGetArray(bv->buffer,&cc);
184: } else cc = c;
185: PetscBLASIntCast(lds,&lds_);
186: PetscBLASIntCast(k,&k_);
188: if (onorm) { BVTensorNormColumn(bv,k,onorm); }
190: if (ctx->qB) x = ctx->sw;
191: else x = pS+k*lds;
193: if (bv->orthog_type==BV_ORTHOG_MGS) { /* modified Gram-Schmidt */
195: if (bv->indef) { /* signature */
196: VecGetArrayRead(bv->omega,&omega);
197: }
198: for (i=-bv->nc;i<k;i++) {
199: if (which && i>=0 && !which[i]) continue;
200: if (ctx->qB) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,pS+k*lds,&one,&szero,x,&one));
201: /* c_i = (s_k, s_i) */
202: dot = PetscRealPart(BLASdot_(&lds_,pS+i*lds,&one,x,&one));
203: if (bv->indef) dot /= PetscRealPart(omega[i]);
204: BV_SetValue(bv,i,0,cc,dot);
205: /* s_k = s_k - c_i s_i */
206: dot = -dot;
207: PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&lds_,&dot,pS+i*lds,&one,pS+k*lds,&one));
208: }
209: if (bv->indef) {
210: VecRestoreArrayRead(bv->omega,&omega);
211: }
213: } else { /* classical Gram-Schmidt */
214: if (ctx->qB) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,pS+k*lds,&one,&szero,x,&one));
216: /* cc = S_{0:k-1}^* s_k */
217: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&lds_,&k_,&sone,pS,&lds_,x,&one,&szero,cc,&one));
219: /* s_k = s_k - S_{0:k-1} cc */
220: if (bv->indef) { BV_ApplySignature(bv,k,cc,PETSC_TRUE); }
221: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&k_,&sonem,pS,&lds_,cc,&one,&sone,pS+k*lds,&one));
222: if (bv->indef) { BV_ApplySignature(bv,k,cc,PETSC_FALSE); }
223: }
225: if (norm) { BVTensorNormColumn(bv,k,norm); }
226: BV_AddCoefficients(bv,k,h,cc);
227: MatDenseRestoreArray(ctx->S,&pS);
228: VecRestoreArray(bv->buffer,&cc);
229: return(0);
230: }
232: PetscErrorCode BVView_Tensor(BV bv,PetscViewer viewer)
233: {
234: PetscErrorCode ierr;
235: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
236: PetscViewerFormat format;
237: PetscBool isascii;
238: const char *bvname,*uname,*sname;
241: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
242: if (isascii) {
243: PetscViewerGetFormat(viewer,&format);
244: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
245: PetscViewerASCIIPrintf(viewer,"number of tensor blocks (degree): %D\n",ctx->d);
246: PetscViewerASCIIPrintf(viewer,"number of columns of U factor: %D\n",ctx->ld);
247: return(0);
248: }
249: BVView(ctx->U,viewer);
250: MatView(ctx->S,viewer);
251: if (format == PETSC_VIEWER_ASCII_MATLAB) {
252: PetscObjectGetName((PetscObject)bv,&bvname);
253: PetscObjectGetName((PetscObject)ctx->U,&uname);
254: PetscObjectGetName((PetscObject)ctx->S,&sname);
255: PetscViewerASCIIPrintf(viewer,"%s=kron(eye(%D),%s)*%s(:,1:%D);\n",bvname,ctx->d,uname,sname,bv->k);
256: }
257: } else {
258: BVView(ctx->U,viewer);
259: MatView(ctx->S,viewer);
260: }
261: return(0);
262: }
264: static PetscErrorCode BVTensorUpdateMatrix(BV V,PetscInt ini,PetscInt end)
265: {
267: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
268: PetscInt i,j,r,c,l,k,ld=ctx->ld,lds=ctx->d*ctx->ld;
269: PetscScalar *qB,*sqB;
270: Vec u;
271: Mat A;
274: if (!V->matrix) return(0);
275: l = ctx->U->l; k = ctx->U->k;
276: /* update inner product matrix */
277: if (!ctx->qB) {
278: PetscCalloc2(lds*lds,&ctx->qB,lds,&ctx->sw);
279: VecDuplicate(ctx->U->t,&ctx->u);
280: }
281: ctx->U->l = 0;
282: for (r=0;r<ctx->d;r++) {
283: for (c=0;c<=r;c++) {
284: MatNestGetSubMat(V->matrix,r,c,&A);
285: if (A) {
286: qB = ctx->qB+c*ld*lds+r*ld;
287: for (i=ini;i<end;i++) {
288: BVGetColumn(ctx->U,i,&u);
289: MatMult(A,u,ctx->u);
290: ctx->U->k = i+1;
291: BVDotVec(ctx->U,ctx->u,qB+i*lds);
292: BVRestoreColumn(ctx->U,i,&u);
293: for (j=0;j<i;j++) qB[i+j*lds] = PetscConj(qB[j+i*lds]);
294: qB[i*lds+i] = PetscRealPart(qB[i+i*lds]);
295: }
296: if (c!=r) {
297: sqB = ctx->qB+r*ld*lds+c*ld;
298: for (i=ini;i<end;i++) for (j=0;j<=i;j++) {
299: sqB[i+j*lds] = PetscConj(qB[j+i*lds]);
300: sqB[j+i*lds] = qB[j+i*lds];
301: }
302: }
303: }
304: }
305: }
306: ctx->U->l = l; ctx->U->k = k;
307: return(0);
308: }
310: static PetscErrorCode BVTensorBuildFirstColumn_Tensor(BV V,PetscInt k)
311: {
313: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
314: PetscInt i,nq=0;
315: PetscScalar *pS,*omega;
316: PetscReal norm;
317: PetscBool breakdown=PETSC_FALSE;
320: MatDenseGetArray(ctx->S,&pS);
321: for (i=0;i<ctx->d;i++) {
322: if (i>=k) {
323: BVSetRandomColumn(ctx->U,nq);
324: } else {
325: BVCopyColumn(ctx->U,i,nq);
326: }
327: BVOrthogonalizeColumn(ctx->U,nq,pS+i*ctx->ld,&norm,&breakdown);
328: if (!breakdown) {
329: BVScaleColumn(ctx->U,nq,1.0/norm);
330: pS[nq+i*ctx->ld] = norm;
331: nq++;
332: }
333: }
334: MatDenseRestoreArray(ctx->S,&pS);
335: if (!nq) SETERRQ1(PetscObjectComm((PetscObject)V),1,"Cannot build first column of tensor BV; U should contain k=%D nonzero columns",k);
336: BVTensorUpdateMatrix(V,0,nq);
337: BVTensorNormColumn(V,0,&norm);
338: BVScale_Tensor(V,0,1.0/norm);
339: if (V->indef) {
340: BV_AllocateSignature(V);
341: VecGetArray(V->omega,&omega);
342: omega[0] = (norm<0.0)? -1.0: 1.0;
343: VecRestoreArray(V->omega,&omega);
344: }
345: /* set active columns */
346: ctx->U->l = 0;
347: ctx->U->k = nq;
348: return(0);
349: }
351: /*@
352: BVTensorBuildFirstColumn - Builds the first column of the tensor basis vectors
353: V from the data contained in the first k columns of U.
355: Collective on V
357: Input Parameters:
358: + V - the basis vectors context
359: - k - the number of columns of U with relevant information
361: Notes:
362: At most d columns are considered, where d is the degree of the tensor BV.
363: Given V = (I otimes U) S, this function computes the first column of V, that
364: is, it computes the coefficients of the first column of S by orthogonalizing
365: the first d columns of U. If k is less than d (or linearly dependent columns
366: are found) then additional random columns are used.
368: The computed column has unit norm.
370: Level: advanced
372: .seealso: BVCreateTensor()
373: @*/
374: PetscErrorCode BVTensorBuildFirstColumn(BV V,PetscInt k)
375: {
381: PetscUseMethod(V,"BVTensorBuildFirstColumn_C",(BV,PetscInt),(V,k));
382: return(0);
383: }
385: static PetscErrorCode BVTensorCompress_Tensor(BV V,PetscInt newc)
386: {
388: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
389: PetscInt nwu=0,nnc,nrow,lwa,r,c;
390: PetscInt i,j,k,n,lds=ctx->ld*ctx->d,deg=ctx->d,lock,cs1=V->k,rs1=ctx->U->k,rk=0,offu;
391: PetscScalar *S,*M,*Z,*pQ,*SS,*SS2,t,sone=1.0,zero=0.0,mone=-1.0,*p,*tau,*work,*qB,*sqB;
392: PetscReal *sg,tol,*rwork;
393: PetscBLASInt ld_,cs1_,rs1_,cs1tdeg,n_,info,lw_,newc_,newctdeg,nnc_,nrow_,nnctdeg,lds_,rk_;
394: Mat Q,A;
397: if (!cs1) return(0);
398: lwa = 6*ctx->ld*lds+2*cs1;
399: n = PetscMin(rs1,deg*cs1);
400: lock = ctx->U->l;
401: nnc = cs1-lock-newc;
402: nrow = rs1-lock;
403: PetscCalloc6(deg*newc*nnc,&SS,newc*nnc,&SS2,(rs1+lock+newc)*n,&pQ,deg*rs1,&tau,lwa,&work,6*n,&rwork);
404: offu = lock*(rs1+1);
405: M = work+nwu;
406: nwu += rs1*cs1*deg;
407: sg = rwork;
408: Z = work+nwu;
409: nwu += deg*cs1*n;
410: PetscBLASIntCast(n,&n_);
411: PetscBLASIntCast(nnc,&nnc_);
412: PetscBLASIntCast(cs1,&cs1_);
413: PetscBLASIntCast(rs1,&rs1_);
414: PetscBLASIntCast(newc,&newc_);
415: PetscBLASIntCast(newc*deg,&newctdeg);
416: PetscBLASIntCast(nnc*deg,&nnctdeg);
417: PetscBLASIntCast(cs1*deg,&cs1tdeg);
418: PetscBLASIntCast(lwa-nwu,&lw_);
419: PetscBLASIntCast(nrow,&nrow_);
420: PetscBLASIntCast(lds,&lds_);
421: MatDenseGetArray(ctx->S,&S);
423: if (newc>0) {
424: /* truncate columns associated with new converged eigenpairs */
425: for (j=0;j<deg;j++) {
426: for (i=lock;i<lock+newc;i++) {
427: PetscArraycpy(M+(i-lock+j*newc)*nrow,S+i*lds+j*ctx->ld+lock,nrow);
428: }
429: }
430: #if !defined (PETSC_USE_COMPLEX)
431: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&newctdeg,M,&nrow_,sg,pQ+offu,&rs1_,Z,&n_,work+nwu,&lw_,&info));
432: #else
433: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&newctdeg,M,&nrow_,sg,pQ+offu,&rs1_,Z,&n_,work+nwu,&lw_,rwork+n,&info));
434: #endif
435: SlepcCheckLapackInfo("gesvd",info);
436: /* SVD has rank min(newc,nrow) */
437: rk = PetscMin(newc,nrow);
438: for (i=0;i<rk;i++) {
439: t = sg[i];
440: PetscStackCallBLAS("BLASscal",BLASscal_(&newctdeg,&t,Z+i,&n_));
441: }
442: for (i=0;i<deg;i++) {
443: for (j=lock;j<lock+newc;j++) {
444: PetscArraycpy(S+j*lds+i*ctx->ld+lock,Z+(newc*i+j-lock)*n,rk);
445: PetscArrayzero(S+j*lds+i*ctx->ld+lock+rk,(ctx->ld-lock-rk));
446: }
447: }
448: /*
449: update columns associated with non-converged vectors, orthogonalize
450: against pQ so that next M has rank nnc+d-1 insted of nrow+d-1
451: */
452: for (i=0;i<deg;i++) {
453: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&newc_,&nnc_,&nrow_,&sone,pQ+offu,&rs1_,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_,&zero,SS+i*newc*nnc,&newc_));
454: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&nrow_,&nnc_,&newc_,&mone,pQ+offu,&rs1_,SS+i*newc*nnc,&newc_,&sone,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_));
455: /* repeat orthogonalization step */
456: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&newc_,&nnc_,&nrow_,&sone,pQ+offu,&rs1_,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_,&zero,SS2,&newc_));
457: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&nrow_,&nnc_,&newc_,&mone,pQ+offu,&rs1_,SS2,&newc_,&sone,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_));
458: for (j=0;j<newc*nnc;j++) *(SS+i*newc*nnc+j) += SS2[j];
459: }
460: }
462: /* truncate columns associated with non-converged eigenpairs */
463: for (j=0;j<deg;j++) {
464: for (i=lock+newc;i<cs1;i++) {
465: PetscArraycpy(M+(i-lock-newc+j*nnc)*nrow,S+i*lds+j*ctx->ld+lock,nrow);
466: }
467: }
468: #if !defined (PETSC_USE_COMPLEX)
469: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&nnctdeg,M,&nrow_,sg,pQ+offu+newc*rs1,&rs1_,Z,&n_,work+nwu,&lw_,&info));
470: #else
471: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&nnctdeg,M,&nrow_,sg,pQ+offu+newc*rs1,&rs1_,Z,&n_,work+nwu,&lw_,rwork+n,&info));
472: #endif
473: SlepcCheckLapackInfo("gesvd",info);
474: tol = PetscMax(rs1,deg*cs1)*PETSC_MACHINE_EPSILON*sg[0];
475: rk = 0;
476: for (i=0;i<PetscMin(nrow,nnctdeg);i++) if (sg[i]>tol) rk++;
477: rk = PetscMin(nnc+deg-1,rk);
478: /* the SVD has rank (at most) nnc+deg-1 */
479: for (i=0;i<rk;i++) {
480: t = sg[i];
481: PetscStackCallBLAS("BLASscal",BLASscal_(&nnctdeg,&t,Z+i,&n_));
482: }
483: /* update S */
484: PetscArrayzero(S+cs1*lds,(V->m-cs1)*lds);
485: k = ctx->ld-lock-newc-rk;
486: for (i=0;i<deg;i++) {
487: for (j=lock+newc;j<cs1;j++) {
488: PetscArraycpy(S+j*lds+i*ctx->ld+lock+newc,Z+(nnc*i+j-lock-newc)*n,rk);
489: PetscArrayzero(S+j*lds+i*ctx->ld+lock+newc+rk,k);
490: }
491: }
492: if (newc>0) {
493: for (i=0;i<deg;i++) {
494: p = SS+nnc*newc*i;
495: for (j=lock+newc;j<cs1;j++) {
496: for (k=0;k<newc;k++) S[j*lds+i*ctx->ld+lock+k] = *(p++);
497: }
498: }
499: }
501: /* orthogonalize pQ */
502: rk = rk+newc;
503: PetscBLASIntCast(rk,&rk_);
504: PetscBLASIntCast(cs1-lock,&nnc_);
505: PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&nrow_,&rk_,pQ+offu,&rs1_,tau,work+nwu,&lw_,&info));
506: SlepcCheckLapackInfo("geqrf",info);
507: for (i=0;i<deg;i++) {
508: PetscStackCallBLAS("BLAStrmm",BLAStrmm_("L","U","N","N",&rk_,&nnc_,&sone,pQ+offu,&rs1_,S+lock*lds+lock+i*ctx->ld,&lds_));
509: }
510: PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&nrow_,&rk_,&rk_,pQ+offu,&rs1_,tau,work+nwu,&lw_,&info));
511: SlepcCheckLapackInfo("orgqr",info);
513: /* update vectors U(:,idx) = U*Q(:,idx) */
514: rk = rk+lock;
515: for (i=0;i<lock;i++) pQ[i*(1+rs1)] = 1.0;
516: MatCreateSeqDense(PETSC_COMM_SELF,rs1,rk,pQ,&Q);
517: ctx->U->k = rs1;
518: BVMultInPlace(ctx->U,Q,lock,rk);
519: MatDestroy(&Q);
521: if (ctx->qB) {
522: /* update matrix qB */
523: PetscBLASIntCast(ctx->ld,&ld_);
524: PetscBLASIntCast(rk,&rk_);
525: for (r=0;r<ctx->d;r++) {
526: for (c=0;c<=r;c++) {
527: MatNestGetSubMat(V->matrix,r,c,&A);
528: if (A) {
529: qB = ctx->qB+r*ctx->ld+c*ctx->ld*lds;
530: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&rk_,&rs1_,&sone,qB,&lds_,pQ,&rs1_,&zero,work+nwu,&rs1_));
531: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&rk_,&rk_,&rs1_,&sone,pQ,&rs1_,work+nwu,&rs1_,&zero,qB,&lds_));
532: for (i=0;i<rk;i++) {
533: for (j=0;j<i;j++) qB[i+j*lds] = PetscConj(qB[j+i*lds]);
534: qB[i+i*lds] = PetscRealPart(qB[i+i*lds]);
535: }
536: for (i=rk;i<ctx->ld;i++) {
537: PetscArrayzero(qB+i*lds,ctx->ld);
538: }
539: for (i=0;i<rk;i++) {
540: PetscArrayzero(qB+i*lds+rk,(ctx->ld-rk));
541: }
542: if (c!=r) {
543: sqB = ctx->qB+r*ctx->ld*lds+c*ctx->ld;
544: for (i=0;i<ctx->ld;i++) for (j=0;j<ctx->ld;j++) sqB[i+j*lds] = PetscConj(qB[j+i*lds]);
545: }
546: }
547: }
548: }
549: }
551: /* free work space */
552: PetscFree6(SS,SS2,pQ,tau,work,rwork);
553: MatDenseRestoreArray(ctx->S,&S);
555: /* set active columns */
556: if (newc) ctx->U->l += newc;
557: ctx->U->k = rk;
558: return(0);
559: }
561: /*@
562: BVTensorCompress - Updates the U and S factors of the tensor basis vectors
563: object V by means of an SVD, removing redundant information.
565: Collective on V
567: Input Parameters:
568: + V - the tensor basis vectors context
569: - newc - additional columns to be locked
571: Notes:
572: This function is typically used when restarting Krylov solvers. Truncating a
573: tensor BV V = (I otimes U) S to its leading columns amounts to keeping the
574: leading columns of S. However, to effectively reduce the size of the
575: decomposition, it is necessary to compress it in a way that fewer columns of
576: U are employed. This can be achieved by means of an update that involves the
577: SVD of the low-rank matrix [S_0 S_1 ... S_{d-1}], where S_i are the pieces of S.
579: If newc is nonzero, then newc columns are added to the leading columns of V.
580: This means that the corresponding columns of the U and S factors will remain
581: invariant in subsequent operations.
583: Level: advanced
585: .seealso: BVCreateTensor(), BVSetActiveColumns()
586: @*/
587: PetscErrorCode BVTensorCompress(BV V,PetscInt newc)
588: {
594: PetscUseMethod(V,"BVTensorCompress_C",(BV,PetscInt),(V,newc));
595: return(0);
596: }
598: static PetscErrorCode BVTensorGetDegree_Tensor(BV bv,PetscInt *d)
599: {
600: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
603: *d = ctx->d;
604: return(0);
605: }
607: /*@
608: BVTensorGetDegree - Returns the number of blocks (degree) of the tensor BV.
610: Not collective
612: Input Parameter:
613: . bv - the basis vectors context
615: Output Parameter:
616: . d - the degree
618: Level: advanced
620: .seealso: BVCreateTensor()
621: @*/
622: PetscErrorCode BVTensorGetDegree(BV bv,PetscInt *d)
623: {
629: PetscUseMethod(bv,"BVTensorGetDegree_C",(BV,PetscInt*),(bv,d));
630: return(0);
631: }
633: static PetscErrorCode BVTensorGetFactors_Tensor(BV V,BV *U,Mat *S)
634: {
635: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
638: if (ctx->puk>-1) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_ORDER,"Previous call to BVTensonGetFactors without a BVTensorRestoreFactors call");
639: ctx->puk = ctx->U->k;
640: if (U) *U = ctx->U;
641: if (S) *S = ctx->S;
642: return(0);
643: }
645: /*@C
646: BVTensorGetFactors - Returns the two factors involved in the definition of the
647: tensor basis vectors object, V = (I otimes U) S.
649: Logically Collective on V
651: Input Parameter:
652: . V - the basis vectors context
654: Output Parameters:
655: + U - the BV factor
656: - S - the Mat factor
658: Notes:
659: The returned factors are references (not copies) of the internal factors,
660: so modifying them will change the tensor BV as well. Some operations of the
661: tensor BV assume that U has orthonormal columns, so if the user modifies U
662: this restriction must be taken into account.
664: The returned factors must not be destroyed. BVTensorRestoreFactors() must
665: be called when they are no longer needed.
667: Pass a NULL vector for any of the arguments that is not needed.
669: Level: advanced
671: .seealso: BVTensorRestoreFactors()
672: @*/
673: PetscErrorCode BVTensorGetFactors(BV V,BV *U,Mat *S)
674: {
679: PetscUseMethod(V,"BVTensorGetFactors_C",(BV,BV*,Mat*),(V,U,S));
680: return(0);
681: }
683: static PetscErrorCode BVTensorRestoreFactors_Tensor(BV V,BV *U,Mat *S)
684: {
686: BV_TENSOR *ctx = (BV_TENSOR*)V->data;
689: PetscObjectStateIncrease((PetscObject)V);
690: if (U) *U = NULL;
691: if (S) *S = NULL;
692: BVTensorUpdateMatrix(V,ctx->puk,ctx->U->k);
693: ctx->puk = -1;
694: return(0);
695: }
697: /*@C
698: BVTensorRestoreFactors - Restore the two factors that were obtained with
699: BVTensorGetFactors().
701: Logically Collective on V
703: Input Parameters:
704: + V - the basis vectors context
705: . U - the BV factor (or NULL)
706: - S - the Mat factor (or NULL)
708: Nots:
709: The arguments must match the corresponding call to BVTensorGetFactors().
711: Level: advanced
713: .seealso: BVTensorGetFactors()
714: @*/
715: PetscErrorCode BVTensorRestoreFactors(BV V,BV *U,Mat *S)
716: {
723: PetscUseMethod(V,"BVTensorRestoreFactors_C",(BV,BV*,Mat*),(V,U,S));
724: return(0);
725: }
727: PetscErrorCode BVDestroy_Tensor(BV bv)
728: {
730: BV_TENSOR *ctx = (BV_TENSOR*)bv->data;
733: BVDestroy(&ctx->U);
734: MatDestroy(&ctx->S);
735: if (ctx->u) {
736: PetscFree2(ctx->qB,ctx->sw);
737: VecDestroy(&ctx->u);
738: }
739: PetscFree(bv->data);
740: PetscObjectComposeFunction((PetscObject)bv,"BVTensorBuildFirstColumn_C",NULL);
741: PetscObjectComposeFunction((PetscObject)bv,"BVTensorCompress_C",NULL);
742: PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetDegree_C",NULL);
743: PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetFactors_C",NULL);
744: PetscObjectComposeFunction((PetscObject)bv,"BVTensorRestoreFactors_C",NULL);
745: return(0);
746: }
748: SLEPC_EXTERN PetscErrorCode BVCreate_Tensor(BV bv)
749: {
751: BV_TENSOR *ctx;
754: PetscNewLog(bv,&ctx);
755: bv->data = (void*)ctx;
756: ctx->puk = -1;
758: bv->ops->multinplace = BVMultInPlace_Tensor;
759: bv->ops->multinplacetrans = BVMultInPlaceTranspose_Tensor;
760: bv->ops->dot = BVDot_Tensor;
761: bv->ops->scale = BVScale_Tensor;
762: bv->ops->norm = BVNorm_Tensor;
763: bv->ops->copycolumn = BVCopyColumn_Tensor;
764: bv->ops->gramschmidt = BVOrthogonalizeGS1_Tensor;
765: bv->ops->destroy = BVDestroy_Tensor;
766: bv->ops->view = BVView_Tensor;
768: PetscObjectComposeFunction((PetscObject)bv,"BVTensorBuildFirstColumn_C",BVTensorBuildFirstColumn_Tensor);
769: PetscObjectComposeFunction((PetscObject)bv,"BVTensorCompress_C",BVTensorCompress_Tensor);
770: PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetDegree_C",BVTensorGetDegree_Tensor);
771: PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetFactors_C",BVTensorGetFactors_Tensor);
772: PetscObjectComposeFunction((PetscObject)bv,"BVTensorRestoreFactors_C",BVTensorRestoreFactors_Tensor);
773: return(0);
774: }
776: /*@
777: BVCreateTensor - Creates a tensor BV that is represented in compact form
778: as V = (I otimes U) S, where U has orthonormal columns.
780: Collective on U
782: Input Parameters:
783: + U - a basis vectors object
784: - d - the number of blocks (degree) of the tensor BV
786: Output Parameter:
787: . V - the new basis vectors context
789: Notes:
790: The new basis vectors object is V = (I otimes U) S, where otimes denotes
791: the Kronecker product, I is the identity matrix of order d, and S is a
792: sequential matrix allocated internally. This compact representation is
793: used e.g. to represent the Krylov basis generated with the linearization
794: of a matrix polynomial of degree d.
796: The size of V (number of rows) is equal to d times n, where n is the size
797: of U. The dimensions of S are d times m rows and m-d+1 columns, where m is
798: the number of columns of U, so m should be at least d.
800: The communicator of V will be the same as U.
802: On input, the content of U is irrelevant. Alternatively, it may contain
803: some nonzero columns that will be used by BVTensorBuildFirstColumn().
805: Level: advanced
807: .seealso: BVTensorGetDegree(), BVTensorGetFactors(), BVTensorBuildFirstColumn()
808: @*/
809: PetscErrorCode BVCreateTensor(BV U,PetscInt d,BV *V)
810: {
812: PetscBool match;
813: PetscInt n,N,m;
814: BV_TENSOR *ctx;
819: PetscObjectTypeCompare((PetscObject)U,BVTENSOR,&match);
820: if (match) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_SUP,"U cannot be of type tensor");
822: BVCreate(PetscObjectComm((PetscObject)U),V);
823: BVGetSizes(U,&n,&N,&m);
824: if (m<d) SETERRQ2(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_SIZ,"U has %D columns, it should have at least d=%D",m,d);
825: BVSetSizes(*V,d*n,d*N,m-d+1);
826: PetscObjectChangeTypeName((PetscObject)*V,BVTENSOR);
827: PetscLogEventBegin(BV_Create,*V,0,0,0);
828: BVCreate_Tensor(*V);
829: PetscLogEventEnd(BV_Create,*V,0,0,0);
831: ctx = (BV_TENSOR*)(*V)->data;
832: ctx->U = U;
833: ctx->d = d;
834: ctx->ld = m;
835: PetscObjectReference((PetscObject)U);
836: PetscLogObjectParent((PetscObject)*V,(PetscObject)U);
837: MatCreateSeqDense(PETSC_COMM_SELF,d*m,m-d+1,NULL,&ctx->S);
838: PetscLogObjectParent((PetscObject)*V,(PetscObject)ctx->S);
839: PetscObjectSetName((PetscObject)ctx->S,"S");
841: /* Copy user-provided attributes of U */
842: (*V)->orthog_type = U->orthog_type;
843: (*V)->orthog_ref = U->orthog_ref;
844: (*V)->orthog_eta = U->orthog_eta;
845: (*V)->orthog_block = U->orthog_block;
846: (*V)->vmm = U->vmm;
847: (*V)->rrandom = U->rrandom;
848: return(0);
849: }