Actual source code: dsnhep.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2012, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7:
8: SLEPc is free software: you can redistribute it and/or modify it under the
9: terms of version 3 of the GNU Lesser General Public License as published by
10: the Free Software Foundation.
12: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
13: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15: more details.
17: You should have received a copy of the GNU Lesser General Public License
18: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
19: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: */
22: #include <slepc-private/dsimpl.h> /*I "slepcds.h" I*/
23: #include <slepcblaslapack.h>
27: PetscErrorCode DSAllocate_NHEP(DS ds,PetscInt ld)
28: {
32: DSAllocateMat_Private(ds,DS_MAT_A);
33: DSAllocateMat_Private(ds,DS_MAT_Q);
34: PetscFree(ds->perm);
35: PetscMalloc(ld*sizeof(PetscInt),&ds->perm);
36: PetscLogObjectMemory(ds,ld*sizeof(PetscInt));
37: return(0);
38: }
42: PetscErrorCode DSView_NHEP(DS ds,PetscViewer viewer)
43: {
47: DSViewMat_Private(ds,viewer,DS_MAT_A);
48: if (ds->state>DS_STATE_INTERMEDIATE) {
49: DSViewMat_Private(ds,viewer,DS_MAT_Q);
50: }
51: if (ds->mat[DS_MAT_X]) {
52: DSViewMat_Private(ds,viewer,DS_MAT_X);
53: }
54: if (ds->mat[DS_MAT_Y]) {
55: DSViewMat_Private(ds,viewer,DS_MAT_Y);
56: }
57: return(0);
58: }
62: PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
63: {
64: #if defined(SLEPC_MISSING_LAPACK_GESVD)
66: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
67: #else
69: PetscInt i,j;
70: PetscBLASInt info,ld,n,n1,lwork,inc=1;
71: PetscScalar sdummy,done=1.0,zero=0.0;
72: PetscReal *sigma;
73: PetscBool iscomplex = PETSC_FALSE;
74: PetscScalar *A = ds->mat[DS_MAT_A];
75: PetscScalar *Q = ds->mat[DS_MAT_Q];
76: PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
77: PetscScalar *W;
80: if (left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for left vectors");
81: n = PetscBLASIntCast(ds->n);
82: ld = PetscBLASIntCast(ds->ld);
83: n1 = n+1;
84: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
85: if (iscomplex) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complex eigenvalues yet");
86: DSAllocateWork_Private(ds,5*ld,6*ld,0);
87: DSAllocateMat_Private(ds,DS_MAT_W);
88: W = ds->mat[DS_MAT_W];
89: lwork = 5*ld;
90: sigma = ds->rwork+5*ld;
92: /* build A-w*I in W */
93: for (j=0;j<n;j++)
94: for (i=0;i<=n;i++)
95: W[i+j*ld] = A[i+j*ld];
96: for (i=0;i<n;i++)
97: W[i+i*ld] -= A[(*k)+(*k)*ld];
99: /* compute SVD of W */
100: #if !defined(PETSC_USE_COMPLEX)
101: LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,&info);
102: #else
103: LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,ds->rwork,&info);
104: #endif
105: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESVD %d",info);
107: /* the smallest singular value is the new error estimate */
108: if (rnorm) *rnorm = sigma[n-1];
110: /* update vector with right singular vector associated to smallest singular value,
111: accumulating the transformation matrix Q */
112: BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc);
113: return(0);
114: #endif
115: }
119: PetscErrorCode DSVectors_NHEP_Refined_All(DS ds,PetscBool left)
120: {
122: PetscInt i;
125: for (i=0;i<ds->n;i++) {
126: DSVectors_NHEP_Refined_Some(ds,&i,PETSC_NULL,left);
127: }
128: return(0);
129: }
133: PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
134: {
135: #if defined(SLEPC_MISSING_LAPACK_TREVC)
137: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
138: #else
140: PetscInt i;
141: PetscBLASInt mm=1,mout,info,ld,n,inc = 1;
142: PetscScalar tmp,done=1.0,zero=0.0;
143: PetscReal norm;
144: PetscBool iscomplex = PETSC_FALSE;
145: PetscBLASInt *select;
146: PetscScalar *A = ds->mat[DS_MAT_A];
147: PetscScalar *Q = ds->mat[DS_MAT_Q];
148: PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
149: PetscScalar *Y;
152: n = PetscBLASIntCast(ds->n);
153: ld = PetscBLASIntCast(ds->ld);
154: DSAllocateWork_Private(ds,0,0,ld);
155: select = ds->iwork;
156: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
158: /* Compute k-th eigenvector Y of A */
159: Y = X+(*k)*ld;
160: select[*k] = (PetscBLASInt)PETSC_TRUE;
161: #if !defined(PETSC_USE_COMPLEX)
162: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
163: mm = iscomplex? 2: 1;
164: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
165: DSAllocateWork_Private(ds,3*ld,0,0);
166: LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info);
167: #else
168: DSAllocateWork_Private(ds,2*ld,ld,0);
169: LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info);
170: #endif
171: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREVC %d",info);
172: if (mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");
174: /* accumulate and normalize eigenvectors */
175: if (ds->state>=DS_STATE_CONDENSED) {
176: PetscMemcpy(ds->work,Y,mout*ld*sizeof(PetscScalar));
177: BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work,&inc,&zero,Y,&inc);
178: #if !defined(PETSC_USE_COMPLEX)
179: if (iscomplex) BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work+ld,&inc,&zero,Y+ld,&inc);
180: #endif
181: norm = BLASnrm2_(&n,Y,&inc);
182: #if !defined(PETSC_USE_COMPLEX)
183: if (iscomplex) {
184: tmp = BLASnrm2_(&n,Y+ld,&inc);
185: norm = SlepcAbsEigenvalue(norm,tmp);
186: }
187: #endif
188: tmp = 1.0 / norm;
189: BLASscal_(&n,&tmp,Y,&inc);
190: #if !defined(PETSC_USE_COMPLEX)
191: if (iscomplex) BLASscal_(&n,&tmp,Y+ld,&inc);
192: #endif
193: }
195: /* set output arguments */
196: if (iscomplex) (*k)++;
197: if (rnorm) {
198: if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
199: else *rnorm = PetscAbsScalar(Y[n-1]);
200: }
201: return(0);
202: #endif
203: }
207: PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
208: {
209: #if defined(SLEPC_MISSING_LAPACK_TREVC)
211: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
212: #else
214: PetscBLASInt n,ld,mout,info;
215: PetscScalar *X,*Y,*A = ds->mat[DS_MAT_A];
216: const char *side,*back;
219: n = PetscBLASIntCast(ds->n);
220: ld = PetscBLASIntCast(ds->ld);
221: if (left) {
222: X = PETSC_NULL;
223: Y = ds->mat[DS_MAT_Y];
224: side = "L";
225: } else {
226: X = ds->mat[DS_MAT_X];
227: Y = PETSC_NULL;
228: side = "R";
229: }
230: if (ds->state>=DS_STATE_CONDENSED) {
231: /* DSSolve() has been called, backtransform with matrix Q */
232: back = "B";
233: PetscMemcpy(left?Y:X,ds->mat[DS_MAT_Q],ld*ld*sizeof(PetscScalar));
234: } else back = "A";
235: #if !defined(PETSC_USE_COMPLEX)
236: DSAllocateWork_Private(ds,3*ld,0,0);
237: LAPACKtrevc_(side,back,PETSC_NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info);
238: #else
239: DSAllocateWork_Private(ds,2*ld,ld,0);
240: LAPACKtrevc_(side,back,PETSC_NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info);
241: #endif
242: if (info) SETERRQ1(((PetscObject)ds)->comm,PETSC_ERR_LIB,"Error in Lapack xTREVC %i",info);
243: return(0);
244: #endif
245: }
249: PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
250: {
254: switch (mat) {
255: case DS_MAT_X:
256: if (ds->refined) {
257: if (!ds->extrarow) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Refined vectors require activating the extra row");
258: if (j) {
259: DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE);
260: } else {
261: DSVectors_NHEP_Refined_All(ds,PETSC_FALSE);
262: }
263: } else {
264: if (j) {
265: DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
266: } else {
267: DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE);
268: }
269: }
270: break;
271: case DS_MAT_Y:
272: if (ds->refined) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
273: if (j) {
274: DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
275: } else {
276: DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE);
277: }
278: break;
279: case DS_MAT_U:
280: case DS_MAT_VT:
281: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
282: break;
283: default:
284: SETERRQ(((PetscObject)ds)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
285: }
286: return(0);
287: }
291: PetscErrorCode DSNormalize_NHEP(DS ds,DSMatType mat,PetscInt col)
292: {
294: PetscInt i,i0,i1;
295: PetscBLASInt ld,n,one = 1;
296: PetscScalar *A = ds->mat[DS_MAT_A],norm,*x;
297: #if !defined(PETSC_USE_COMPLEX)
298: PetscScalar norm0;
299: #endif
302: switch (mat) {
303: case DS_MAT_X:
304: case DS_MAT_Y:
305: case DS_MAT_Q:
306: /* Supported matrices */
307: break;
308: case DS_MAT_U:
309: case DS_MAT_VT:
310: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
311: break;
312: default:
313: SETERRQ(((PetscObject)ds)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
314: }
316: n = PetscBLASIntCast(ds->n);
317: ld = PetscBLASIntCast(ds->ld);
318: DSGetArray(ds,mat,&x);
319: if (col < 0) {
320: i0 = 0; i1 = ds->n;
321: } else if(col>0 && A[ds->ld*(col-1)+col] != 0.0) {
322: i0 = col-1; i1 = col+1;
323: } else {
324: i0 = col; i1 = col+1;
325: }
326: for(i=i0; i<i1; i++) {
327: #if !defined(PETSC_USE_COMPLEX)
328: if(i<n-1 && A[ds->ld*i+i+1] != 0.0) {
329: norm = BLASnrm2_(&n,&x[ld*i],&one);
330: norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
331: norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
332: BLASscal_(&n,&norm,&x[ld*i],&one);
333: BLASscal_(&n,&norm,&x[ld*(i+1)],&one);
334: i++;
335: } else
336: #endif
337: {
338: norm = BLASnrm2_(&n,&x[ld*i],&one);
339: norm = 1.0/norm;
340: BLASscal_(&n,&norm,&x[ld*i],&one);
341: }
342: }
343: return(0);
344: }
348: PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
349: {
350: #if defined(SLEPC_MISSING_LAPACK_TRSEN)
352: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable");
353: #else
355: PetscInt i;
356: PetscBLASInt info,n,ld,mout,lwork,*selection;
357: PetscScalar *T = ds->mat[DS_MAT_A],*Q = ds->mat[DS_MAT_Q],*work;
358: #if !defined(PETSC_USE_COMPLEX)
359: PetscBLASInt *iwork,liwork;
360: #endif
363: if (!k) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must supply argument k");
364: n = PetscBLASIntCast(ds->n);
365: ld = PetscBLASIntCast(ds->ld);
366: #if !defined(PETSC_USE_COMPLEX)
367: lwork = n;
368: liwork = 1;
369: DSAllocateWork_Private(ds,lwork,0,liwork+n);
370: work = ds->work;
371: lwork = ds->lwork;
372: selection = ds->iwork;
373: iwork = ds->iwork + n;
374: liwork = ds->liwork - n;
375: #else
376: lwork = 1;
377: DSAllocateWork_Private(ds,lwork,0,n);
378: work = ds->work;
379: selection = ds->iwork;
380: #endif
381: /* Compute the selected eigenvalue to be in the leading position */
382: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
383: PetscMemzero(selection,n*sizeof(PetscBLASInt));
384: for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
385: #if !defined(PETSC_USE_COMPLEX)
386: LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,PETSC_NULL,PETSC_NULL,work,&lwork,iwork,&liwork,&info);
387: #else
388: LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,PETSC_NULL,PETSC_NULL,work,&lwork,&info);
389: #endif
390: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTRSEN %d",info);
391: *k = mout;
392: return(0);
393: #endif
394: }
398: PetscErrorCode DSSort_NHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
399: {
400: #if defined(SLEPC_MISSING_LAPACK_TREXC)
402: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREXC - Lapack routine is unavailable");
403: #else
405: PetscScalar re;
406: PetscInt i,j,pos,result;
407: PetscBLASInt ifst,ilst,info,n,ld;
408: PetscScalar *T = ds->mat[DS_MAT_A];
409: PetscScalar *Q = ds->mat[DS_MAT_Q];
410: #if !defined(PETSC_USE_COMPLEX)
411: PetscScalar *work,im;
412: #endif
415: n = PetscBLASIntCast(ds->n);
416: ld = PetscBLASIntCast(ds->ld);
417: #if !defined(PETSC_USE_COMPLEX)
418: DSAllocateWork_Private(ds,ld,0,0);
419: work = ds->work;
420: #endif
421: /* selection sort */
422: for (i=ds->l;i<n-1;i++) {
423: re = wr[i];
424: #if !defined(PETSC_USE_COMPLEX)
425: im = wi[i];
426: #endif
427: pos = 0;
428: j=i+1; /* j points to the next eigenvalue */
429: #if !defined(PETSC_USE_COMPLEX)
430: if (im != 0) j=i+2;
431: #endif
432: /* find minimum eigenvalue */
433: for (;j<n;j++) {
434: #if !defined(PETSC_USE_COMPLEX)
435: (*ds->comp_fun)(re,im,wr[j],wi[j],&result,ds->comp_ctx);
436: #else
437: (*ds->comp_fun)(re,0.0,wr[j],0.0,&result,ds->comp_ctx);
438: #endif
439: if (result > 0) {
440: re = wr[j];
441: #if !defined(PETSC_USE_COMPLEX)
442: im = wi[j];
443: #endif
444: pos = j;
445: }
446: #if !defined(PETSC_USE_COMPLEX)
447: if (wi[j] != 0) j++;
448: #endif
449: }
450: if (pos) {
451: /* interchange blocks */
452: ifst = PetscBLASIntCast(pos+1);
453: ilst = PetscBLASIntCast(i+1);
454: #if !defined(PETSC_USE_COMPLEX)
455: LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info);
456: #else
457: LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info);
458: #endif
459: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREXC %d",info);
460: /* recover original eigenvalues from T matrix */
461: for (j=i;j<n;j++) {
462: wr[j] = T[j+j*ld];
463: #if !defined(PETSC_USE_COMPLEX)
464: if (j<n-1 && T[j+1+j*ld] != 0.0) {
465: /* complex conjugate eigenvalue */
466: wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld])) *
467: PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld]));
468: wr[j+1] = wr[j];
469: wi[j+1] = -wi[j];
470: j++;
471: } else {
472: wi[j] = 0.0;
473: }
474: #endif
475: }
476: }
477: #if !defined(PETSC_USE_COMPLEX)
478: if (wi[i] != 0) i++;
479: #endif
480: }
481: return(0);
482: #endif
483: }
487: PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
488: {
492: if (!rr || wr == rr) {
493: DSSort_NHEP_Total(ds,wr,wi);
494: } else {
495: DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k);
496: }
497: return(0);
498: }
502: PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
503: {
505: PetscInt i;
506: PetscBLASInt n,ld,incx=1;
507: PetscScalar *A,*Q,*x,*y,one=1.0,zero=0.0;
510: n = PetscBLASIntCast(ds->n);
511: ld = PetscBLASIntCast(ds->ld);
512: A = ds->mat[DS_MAT_A];
513: Q = ds->mat[DS_MAT_Q];
514: DSAllocateWork_Private(ds,2*ld,0,0);
515: x = ds->work;
516: y = ds->work+ld;
517: for (i=0;i<n;i++) x[i] = A[n+i*ld];
518: BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx);
519: for (i=0;i<n;i++) A[n+i*ld] = y[i];
520: ds->k = n;
521: return(0);
522: }
526: PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
527: {
528: #if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
530: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable");
531: #else
533: PetscScalar *work,*tau;
534: PetscInt i,j;
535: PetscBLASInt ilo,lwork,info,n,ld;
536: PetscScalar *A = ds->mat[DS_MAT_A];
537: PetscScalar *Q = ds->mat[DS_MAT_Q];
540: #if !defined(PETSC_USE_COMPLEX)
542: #endif
543: n = PetscBLASIntCast(ds->n);
544: ld = PetscBLASIntCast(ds->ld);
545: ilo = PetscBLASIntCast(ds->l+1);
546: DSAllocateWork_Private(ds,ld+ld*ld,0,0);
547: tau = ds->work;
548: work = ds->work+ld;
549: lwork = ld*ld;
551: /* initialize orthogonal matrix */
552: PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
553: for (i=0;i<n;i++)
554: Q[i+i*ld] = 1.0;
555: if (n==1) return(0);
557: /* reduce to upper Hessenberg form */
558: if (ds->state<DS_STATE_INTERMEDIATE) {
559: LAPACKgehrd_(&n,&ilo,&n,A,&ld,tau,work,&lwork,&info);
560: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEHRD %d",info);
561: for (j=0;j<n-1;j++) {
562: for (i=j+2;i<n;i++) {
563: Q[i+j*ld] = A[i+j*ld];
564: A[i+j*ld] = 0.0;
565: }
566: }
567: LAPACKorghr_(&n,&ilo,&n,Q,&ld,tau,work,&lwork,&info);
568: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGHR %d",info);
569: }
571: /* compute the (real) Schur form */
572: #if !defined(PETSC_USE_COMPLEX)
573: LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,wi,Q,&ld,work,&lwork,&info);
574: for (j=0;j<ds->l;j++) {
575: if (j==n-1 || A[j+1+j*ld] == 0.0) {
576: /* real eigenvalue */
577: wr[j] = A[j+j*ld];
578: wi[j] = 0.0;
579: } else {
580: /* complex eigenvalue */
581: wr[j] = A[j+j*ld];
582: wr[j+1] = A[j+j*ld];
583: wi[j] = PetscSqrtReal(PetscAbsReal(A[j+1+j*ld])) *
584: PetscSqrtReal(PetscAbsReal(A[j+(j+1)*ld]));
585: wi[j+1] = -wi[j];
586: j++;
587: }
588: }
589: #else
590: LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,Q,&ld,work,&lwork,&info);
591: if (wi) for (i=ds->l;i<n;i++) wi[i] = 0.0;
592: #endif
593: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",info);
594: return(0);
595: #endif
596: }
600: PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n)
601: {
602: PetscInt i,newn,ld=ds->ld,l=ds->l;
603: PetscScalar *A;
606: if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
607: A = ds->mat[DS_MAT_A];
608: /* be careful not to break a diagonal 2x2 block */
609: if (A[n+(n-1)*ld]==0.0) newn = n;
610: else {
611: if (n<ds->n-1) newn = n+1;
612: else newn = n-1;
613: }
614: if (ds->extrarow && ds->k==ds->n) {
615: /* copy entries of extra row to the new position, then clean last row */
616: for (i=l;i<newn;i++) A[newn+i*ld] = A[ds->n+i*ld];
617: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
618: }
619: ds->k = 0;
620: ds->n = newn;
621: return(0);
622: }
626: PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
627: {
628: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(SLEPC_MISSING_LAPACK_GETRI) || defined(SLEPC_MISSING_LAPACK_LANGE) || defined(SLEPC_MISSING_LAPACK_LANHS)
630: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRI/LANGE/LANHS - Lapack routines are unavailable");
631: #else
633: PetscScalar *work;
634: PetscReal *rwork;
635: PetscBLASInt *ipiv;
636: PetscBLASInt lwork,info,n,ld;
637: PetscReal hn,hin;
638: PetscScalar *A;
641: n = PetscBLASIntCast(ds->n);
642: ld = PetscBLASIntCast(ds->ld);
643: lwork = 8*ld;
644: DSAllocateWork_Private(ds,lwork,ld,ld);
645: work = ds->work;
646: rwork = ds->rwork;
647: ipiv = ds->iwork;
649: /* use workspace matrix W to avoid overwriting A */
650: DSAllocateMat_Private(ds,DS_MAT_W);
651: A = ds->mat[DS_MAT_W];
652: PetscMemcpy(A,ds->mat[DS_MAT_A],sizeof(PetscScalar)*ds->ld*ds->ld);
654: /* norm of A */
655: if (ds->state<DS_STATE_INTERMEDIATE) hn = LAPACKlange_("I",&n,&n,A,&ld,rwork);
656: else hn = LAPACKlanhs_("I",&n,A,&ld,rwork);
658: /* norm of inv(A) */
659: LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info);
660: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGETRF %d",info);
661: LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info);
662: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGETRI %d",info);
663: hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);
665: *cond = hn*hin;
666: return(0);
667: #endif
668: }
672: PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gamma)
673: {
674: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRS)
676: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRS - Lapack routines are unavailable");
677: #else
679: PetscInt i,j;
680: PetscBLASInt *ipiv,info,n,ld,one=1,ncol;
681: PetscScalar *A,*B,*Q,*g=gin,*ghat;
682: PetscScalar done=1.0,dmone=-1.0,dzero=0.0;
683: PetscReal gnorm;
686: n = PetscBLASIntCast(ds->n);
687: ld = PetscBLASIntCast(ds->ld);
688: A = ds->mat[DS_MAT_A];
690: if (!recover) {
692: DSAllocateWork_Private(ds,0,0,ld);
693: ipiv = ds->iwork;
694: if (!g) {
695: DSAllocateWork_Private(ds,ld,0,0);
696: g = ds->work;
697: }
698: /* use workspace matrix W to factor A-tau*eye(n) */
699: DSAllocateMat_Private(ds,DS_MAT_W);
700: B = ds->mat[DS_MAT_W];
701: PetscMemcpy(B,A,sizeof(PetscScalar)*ld*ld);
703: /* Vector g initialy stores b = beta*e_n^T */
704: PetscMemzero(g,n*sizeof(PetscScalar));
705: g[n-1] = beta;
706:
707: /* g = (A-tau*eye(n))'\b */
708: for (i=0;i<n;i++)
709: B[i+i*ld] -= tau;
710: LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info);
711: if (info<0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to LU factorization");
712: if (info>0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Bad LU factorization");
713: PetscLogFlops(2.0*n*n*n/3.0);
714: LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info);
715: if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"GETRS - Bad solve");
716: PetscLogFlops(2.0*n*n-n);
718: /* A = A + g*b' */
719: for (i=0;i<n;i++)
720: A[i+(n-1)*ld] += g[i]*beta;
722: } else { /* recover */
725: DSAllocateWork_Private(ds,ld,0,0);
726: ghat = ds->work;
727: Q = ds->mat[DS_MAT_Q];
729: /* g^ = -Q(:,idx)'*g */
730: ncol = PetscBLASIntCast(ds->l+ds->k);
731: BLASgemv_("C",&n,&ncol,&dmone,Q,&ld,g,&one,&dzero,ghat,&one);
733: /* A = A + g^*b' */
734: for (i=0;i<ds->l+ds->k;i++)
735: for (j=ds->l;j<ds->l+ds->k;j++)
736: A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;
738: /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
739: BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one);
740: }
742: /* Compute gamma factor */
743: if (gamma) {
744: gnorm = 0.0;
745: for (i=0;i<n;i++)
746: gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));
747: *gamma = PetscSqrtReal(1.0+gnorm);
748: }
749: return(0);
750: #endif
751: }
753: EXTERN_C_BEGIN
756: PetscErrorCode DSCreate_NHEP(DS ds)
757: {
759: ds->ops->allocate = DSAllocate_NHEP;
760: ds->ops->view = DSView_NHEP;
761: ds->ops->vectors = DSVectors_NHEP;
762: ds->ops->solve[0] = DSSolve_NHEP;
763: ds->ops->sort = DSSort_NHEP;
764: ds->ops->truncate = DSTruncate_NHEP;
765: ds->ops->update = DSUpdateExtraRow_NHEP;
766: ds->ops->cond = DSCond_NHEP;
767: ds->ops->transharm = DSTranslateHarmonic_NHEP;
768: ds->ops->normalize = DSNormalize_NHEP;
769: return(0);
770: }
771: EXTERN_C_END