Actual source code: dsnhep.c
slepc-3.16.1 2021-11-17
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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: PetscErrorCode DSAllocate_NHEP(DS ds,PetscInt ld)
15: {
19: DSAllocateMat_Private(ds,DS_MAT_A);
20: DSAllocateMat_Private(ds,DS_MAT_Q);
21: PetscFree(ds->perm);
22: PetscMalloc1(ld,&ds->perm);
23: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
24: return(0);
25: }
27: PetscErrorCode DSView_NHEP(DS ds,PetscViewer viewer)
28: {
29: PetscErrorCode ierr;
30: PetscViewerFormat format;
33: PetscViewerGetFormat(viewer,&format);
34: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
35: DSViewMat(ds,viewer,DS_MAT_A);
36: if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_Q); }
37: if (ds->mat[DS_MAT_X]) { DSViewMat(ds,viewer,DS_MAT_X); }
38: if (ds->mat[DS_MAT_Y]) { DSViewMat(ds,viewer,DS_MAT_Y); }
39: return(0);
40: }
42: static PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
43: {
45: PetscInt i,j;
46: PetscBLASInt info,ld,n,n1,lwork,inc=1;
47: PetscScalar sdummy,done=1.0,zero=0.0;
48: PetscReal *sigma;
49: PetscBool iscomplex = PETSC_FALSE;
50: PetscScalar *A = ds->mat[DS_MAT_A];
51: PetscScalar *Q = ds->mat[DS_MAT_Q];
52: PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
53: PetscScalar *W;
56: if (left) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for left vectors");
57: PetscBLASIntCast(ds->n,&n);
58: PetscBLASIntCast(ds->ld,&ld);
59: n1 = n+1;
60: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
61: if (iscomplex) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complex eigenvalues yet");
62: DSAllocateWork_Private(ds,5*ld,6*ld,0);
63: DSAllocateMat_Private(ds,DS_MAT_W);
64: W = ds->mat[DS_MAT_W];
65: lwork = 5*ld;
66: sigma = ds->rwork+5*ld;
68: /* build A-w*I in W */
69: for (j=0;j<n;j++)
70: for (i=0;i<=n;i++)
71: W[i+j*ld] = A[i+j*ld];
72: for (i=0;i<n;i++)
73: W[i+i*ld] -= A[(*k)+(*k)*ld];
75: /* compute SVD of W */
76: #if !defined(PETSC_USE_COMPLEX)
77: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,&info));
78: #else
79: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,ds->rwork,&info));
80: #endif
81: SlepcCheckLapackInfo("gesvd",info);
83: /* the smallest singular value is the new error estimate */
84: if (rnorm) *rnorm = sigma[n-1];
86: /* update vector with right singular vector associated to smallest singular value,
87: accumulating the transformation matrix Q */
88: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc));
89: return(0);
90: }
92: static PetscErrorCode DSVectors_NHEP_Refined_All(DS ds,PetscBool left)
93: {
95: PetscInt i;
98: for (i=0;i<ds->n;i++) {
99: DSVectors_NHEP_Refined_Some(ds,&i,NULL,left);
100: }
101: return(0);
102: }
104: static PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
105: {
107: PetscInt i;
108: PetscBLASInt mm=1,mout,info,ld,n,*select,inc=1,cols=1,zero=0;
109: PetscScalar sone=1.0,szero=0.0;
110: PetscReal norm,done=1.0;
111: PetscBool iscomplex = PETSC_FALSE;
112: PetscScalar *A = ds->mat[DS_MAT_A];
113: PetscScalar *Q = ds->mat[DS_MAT_Q];
114: PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
115: PetscScalar *Y;
118: PetscBLASIntCast(ds->n,&n);
119: PetscBLASIntCast(ds->ld,&ld);
120: DSAllocateWork_Private(ds,0,0,ld);
121: select = ds->iwork;
122: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
124: /* compute k-th eigenvector Y of A */
125: Y = X+(*k)*ld;
126: select[*k] = (PetscBLASInt)PETSC_TRUE;
127: #if !defined(PETSC_USE_COMPLEX)
128: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
129: mm = iscomplex? 2: 1;
130: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
131: DSAllocateWork_Private(ds,3*ld,0,0);
132: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
133: #else
134: DSAllocateWork_Private(ds,2*ld,ld,0);
135: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
136: #endif
137: SlepcCheckLapackInfo("trevc",info);
138: if (mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");
140: /* accumulate and normalize eigenvectors */
141: if (ds->state>=DS_STATE_CONDENSED) {
142: PetscArraycpy(ds->work,Y,mout*ld);
143: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work,&inc,&szero,Y,&inc));
144: #if !defined(PETSC_USE_COMPLEX)
145: if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,Q,&ld,ds->work+ld,&inc,&szero,Y+ld,&inc));
146: #endif
147: cols = 1;
148: norm = BLASnrm2_(&n,Y,&inc);
149: #if !defined(PETSC_USE_COMPLEX)
150: if (iscomplex) {
151: norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Y+ld,&inc));
152: cols = 2;
153: }
154: #endif
155: PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Y,&ld,&info));
156: SlepcCheckLapackInfo("lascl",info);
157: }
159: /* set output arguments */
160: if (iscomplex) (*k)++;
161: if (rnorm) {
162: if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
163: else *rnorm = PetscAbsScalar(Y[n-1]);
164: }
165: return(0);
166: }
168: static PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
169: {
171: PetscInt i;
172: PetscBLASInt n,ld,mout,info,inc=1,cols,zero=0;
173: PetscBool iscomplex;
174: PetscScalar *X,*Y,*Z,*A = ds->mat[DS_MAT_A];
175: PetscReal norm,done=1.0;
176: const char *side,*back;
179: PetscBLASIntCast(ds->n,&n);
180: PetscBLASIntCast(ds->ld,&ld);
181: if (left) {
182: X = NULL;
183: Y = ds->mat[DS_MAT_Y];
184: side = "L";
185: } else {
186: X = ds->mat[DS_MAT_X];
187: Y = NULL;
188: side = "R";
189: }
190: Z = left? Y: X;
191: if (ds->state>=DS_STATE_CONDENSED) {
192: /* DSSolve() has been called, backtransform with matrix Q */
193: back = "B";
194: PetscArraycpy(Z,ds->mat[DS_MAT_Q],ld*ld);
195: } else back = "A";
196: #if !defined(PETSC_USE_COMPLEX)
197: DSAllocateWork_Private(ds,3*ld,0,0);
198: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
199: #else
200: DSAllocateWork_Private(ds,2*ld,ld,0);
201: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
202: #endif
203: SlepcCheckLapackInfo("trevc",info);
205: /* normalize eigenvectors */
206: for (i=0;i<n;i++) {
207: iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
208: cols = 1;
209: norm = BLASnrm2_(&n,Z+i*ld,&inc);
210: #if !defined(PETSC_USE_COMPLEX)
211: if (iscomplex) {
212: norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Z+(i+1)*ld,&inc));
213: cols = 2;
214: }
215: #endif
216: PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Z+i*ld,&ld,&info));
217: SlepcCheckLapackInfo("lascl",info);
218: if (iscomplex) i++;
219: }
220: return(0);
221: }
223: PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
224: {
228: switch (mat) {
229: case DS_MAT_X:
230: if (ds->refined) {
231: if (!ds->extrarow) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Refined vectors require activating the extra row");
232: if (j) {
233: DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE);
234: } else {
235: DSVectors_NHEP_Refined_All(ds,PETSC_FALSE);
236: }
237: } else {
238: if (j) {
239: DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
240: } else {
241: DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE);
242: }
243: }
244: break;
245: case DS_MAT_Y:
246: if (ds->refined) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
247: if (j) {
248: DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
249: } else {
250: DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE);
251: }
252: break;
253: case DS_MAT_U:
254: case DS_MAT_V:
255: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
256: default:
257: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
258: }
259: return(0);
260: }
262: static PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
263: {
265: PetscInt i;
266: PetscBLASInt info,n,ld,mout,lwork,*selection;
267: PetscScalar *T = ds->mat[DS_MAT_A],*Q = ds->mat[DS_MAT_Q],*work;
268: PetscReal dummy;
269: #if !defined(PETSC_USE_COMPLEX)
270: PetscBLASInt *iwork,liwork;
271: #endif
274: if (!k) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Must supply argument k");
275: PetscBLASIntCast(ds->n,&n);
276: PetscBLASIntCast(ds->ld,&ld);
277: #if !defined(PETSC_USE_COMPLEX)
278: lwork = n;
279: liwork = 1;
280: DSAllocateWork_Private(ds,lwork,0,liwork+n);
281: work = ds->work;
282: lwork = ds->lwork;
283: selection = ds->iwork;
284: iwork = ds->iwork + n;
285: liwork = ds->liwork - n;
286: #else
287: lwork = 1;
288: DSAllocateWork_Private(ds,lwork,0,n);
289: work = ds->work;
290: selection = ds->iwork;
291: #endif
292: /* Compute the selected eigenvalue to be in the leading position */
293: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
294: PetscArrayzero(selection,n);
295: for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
296: #if !defined(PETSC_USE_COMPLEX)
297: PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,&dummy,&dummy,work,&lwork,iwork,&liwork,&info));
298: #else
299: PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,&dummy,&dummy,work,&lwork,&info));
300: #endif
301: SlepcCheckLapackInfo("trsen",info);
302: *k = mout;
303: return(0);
304: }
306: PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
307: {
311: if (!rr || wr == rr) {
312: DSSort_NHEP_Total(ds,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
313: } else {
314: DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k);
315: }
316: return(0);
317: }
319: static PetscErrorCode DSSortWithPermutation_NHEP(DS ds,PetscInt *perm,PetscScalar *wr,PetscScalar *wi)
320: {
324: DSSortWithPermutation_NHEP_Private(ds,perm,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
325: return(0);
326: }
328: PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
329: {
331: PetscInt i;
332: PetscBLASInt n,ld,incx=1;
333: PetscScalar *A,*Q,*x,*y,one=1.0,zero=0.0;
336: PetscBLASIntCast(ds->n,&n);
337: PetscBLASIntCast(ds->ld,&ld);
338: A = ds->mat[DS_MAT_A];
339: Q = ds->mat[DS_MAT_Q];
340: DSAllocateWork_Private(ds,2*ld,0,0);
341: x = ds->work;
342: y = ds->work+ld;
343: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
344: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
345: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
346: ds->k = n;
347: return(0);
348: }
350: PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
351: {
355: #if !defined(PETSC_USE_COMPLEX)
357: #endif
358: DSSolve_NHEP_Private(ds,ds->mat[DS_MAT_A],ds->mat[DS_MAT_Q],wr,wi);
359: return(0);
360: }
362: PetscErrorCode DSSynchronize_NHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
363: {
365: PetscInt ld=ds->ld,l=ds->l,k;
366: PetscMPIInt n,rank,off=0,size,ldn;
369: k = (ds->n-l)*ld;
370: if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
371: if (eigr) k += ds->n-l;
372: if (eigi) k += ds->n-l;
373: DSAllocateWork_Private(ds,k,0,0);
374: PetscMPIIntCast(k*sizeof(PetscScalar),&size);
375: PetscMPIIntCast(ds->n-l,&n);
376: PetscMPIIntCast(ld*(ds->n-l),&ldn);
377: MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
378: if (!rank) {
379: MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
380: if (ds->state>DS_STATE_RAW) {
381: MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
382: }
383: if (eigr) {
384: MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
385: }
386: #if !defined(PETSC_USE_COMPLEX)
387: if (eigi) {
388: MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
389: }
390: #endif
391: }
392: MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
393: if (rank) {
394: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
395: if (ds->state>DS_STATE_RAW) {
396: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
397: }
398: if (eigr) {
399: MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
400: }
401: #if !defined(PETSC_USE_COMPLEX)
402: if (eigi) {
403: MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
404: }
405: #endif
406: }
407: return(0);
408: }
410: PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n,PetscBool trim)
411: {
412: PetscInt i,ld=ds->ld,l=ds->l;
413: PetscScalar *A = ds->mat[DS_MAT_A];
416: #if defined(PETSC_USE_DEBUG)
417: /* make sure diagonal 2x2 block is not broken */
418: if (ds->state>=DS_STATE_CONDENSED && n>0 && n<ds->n && A[n+(n-1)*ld]!=0.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
419: #endif
420: if (trim) {
421: if (ds->extrarow) { /* clean extra row */
422: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
423: }
424: ds->l = 0;
425: ds->k = 0;
426: ds->n = n;
427: ds->t = ds->n; /* truncated length equal to the new dimension */
428: } else {
429: if (ds->extrarow && ds->k==ds->n) {
430: /* copy entries of extra row to the new position, then clean last row */
431: for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
432: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
433: }
434: ds->k = (ds->extrarow)? n: 0;
435: ds->t = ds->n; /* truncated length equal to previous dimension */
436: ds->n = n;
437: }
438: return(0);
439: }
441: PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
442: {
444: PetscScalar *work;
445: PetscReal *rwork;
446: PetscBLASInt *ipiv;
447: PetscBLASInt lwork,info,n,ld;
448: PetscReal hn,hin;
449: PetscScalar *A;
452: PetscBLASIntCast(ds->n,&n);
453: PetscBLASIntCast(ds->ld,&ld);
454: lwork = 8*ld;
455: DSAllocateWork_Private(ds,lwork,ld,ld);
456: work = ds->work;
457: rwork = ds->rwork;
458: ipiv = ds->iwork;
460: /* use workspace matrix W to avoid overwriting A */
461: DSAllocateMat_Private(ds,DS_MAT_W);
462: A = ds->mat[DS_MAT_W];
463: PetscArraycpy(A,ds->mat[DS_MAT_A],ds->ld*ds->ld);
465: /* norm of A */
466: if (ds->state<DS_STATE_INTERMEDIATE) hn = LAPACKlange_("I",&n,&n,A,&ld,rwork);
467: else hn = LAPACKlanhs_("I",&n,A,&ld,rwork);
469: /* norm of inv(A) */
470: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
471: SlepcCheckLapackInfo("getrf",info);
472: PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
473: SlepcCheckLapackInfo("getri",info);
474: hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);
476: *cond = hn*hin;
477: return(0);
478: }
480: PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gammaout)
481: {
483: PetscInt i,j;
484: PetscBLASInt *ipiv,info,n,ld,one=1,ncol;
485: PetscScalar *A,*B,*Q,*g=gin,*ghat;
486: PetscScalar done=1.0,dmone=-1.0,dzero=0.0;
487: PetscReal gamma=1.0;
490: PetscBLASIntCast(ds->n,&n);
491: PetscBLASIntCast(ds->ld,&ld);
492: A = ds->mat[DS_MAT_A];
494: if (!recover) {
496: DSAllocateWork_Private(ds,0,0,ld);
497: ipiv = ds->iwork;
498: if (!g) {
499: DSAllocateWork_Private(ds,ld,0,0);
500: g = ds->work;
501: }
502: /* use workspace matrix W to factor A-tau*eye(n) */
503: DSAllocateMat_Private(ds,DS_MAT_W);
504: B = ds->mat[DS_MAT_W];
505: PetscArraycpy(B,A,ld*ld);
507: /* Vector g initially stores b = beta*e_n^T */
508: PetscArrayzero(g,n);
509: g[n-1] = beta;
511: /* g = (A-tau*eye(n))'\b */
512: for (i=0;i<n;i++) B[i+i*ld] -= tau;
513: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info));
514: SlepcCheckLapackInfo("getrf",info);
515: PetscLogFlops(2.0*n*n*n/3.0);
516: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info));
517: SlepcCheckLapackInfo("getrs",info);
518: PetscLogFlops(2.0*n*n-n);
520: /* A = A + g*b' */
521: for (i=0;i<n;i++) A[i+(n-1)*ld] += g[i]*beta;
523: } else { /* recover */
525: DSAllocateWork_Private(ds,ld,0,0);
526: ghat = ds->work;
527: Q = ds->mat[DS_MAT_Q];
529: /* g^ = -Q(:,idx)'*g */
530: PetscBLASIntCast(ds->l+ds->k,&ncol);
531: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&ncol,&dmone,Q,&ld,g,&one,&dzero,ghat,&one));
533: /* A = A + g^*b' */
534: for (i=0;i<ds->l+ds->k;i++)
535: for (j=ds->l;j<ds->l+ds->k;j++)
536: A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;
538: /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
539: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one));
540: }
542: /* Compute gamma factor */
543: if (gammaout || (recover && ds->extrarow)) gamma = SlepcAbs(1.0,BLASnrm2_(&n,g,&one));
544: if (gammaout) *gammaout = gamma;
545: if (recover && ds->extrarow) {
546: for (j=ds->l;j<ds->l+ds->k;j++) A[ds->n+j*ld] *= gamma;
547: }
548: return(0);
549: }
551: /*MC
552: DSNHEP - Dense Non-Hermitian Eigenvalue Problem.
554: Level: beginner
556: Notes:
557: The problem is expressed as A*X = X*Lambda, where A is the input matrix.
558: Lambda is a diagonal matrix whose diagonal elements are the arguments of
559: DSSolve(). After solve, A is overwritten with the upper quasi-triangular
560: matrix T of the (real) Schur form, A*Q = Q*T.
562: In the intermediate state A is reduced to upper Hessenberg form.
564: Computation of left eigenvectors is supported, but two-sided Krylov solvers
565: usually rely on the related DSNHEPTS.
567: Used DS matrices:
568: + DS_MAT_A - problem matrix
569: - DS_MAT_Q - orthogonal/unitary transformation that reduces to Hessenberg form
570: (intermediate step) or matrix of orthogonal Schur vectors
572: Implemented methods:
573: . 0 - Implicit QR (_hseqr)
575: .seealso: DSCreate(), DSSetType(), DSType
576: M*/
577: SLEPC_EXTERN PetscErrorCode DSCreate_NHEP(DS ds)
578: {
580: ds->ops->allocate = DSAllocate_NHEP;
581: ds->ops->view = DSView_NHEP;
582: ds->ops->vectors = DSVectors_NHEP;
583: ds->ops->solve[0] = DSSolve_NHEP;
584: ds->ops->sort = DSSort_NHEP;
585: ds->ops->sortperm = DSSortWithPermutation_NHEP;
586: ds->ops->synchronize = DSSynchronize_NHEP;
587: ds->ops->gettruncatesize = DSGetTruncateSize_Default;
588: ds->ops->truncate = DSTruncate_NHEP;
589: ds->ops->update = DSUpdateExtraRow_NHEP;
590: ds->ops->cond = DSCond_NHEP;
591: ds->ops->transharm = DSTranslateHarmonic_NHEP;
592: return(0);
593: }