Actual source code: dsnhep.c
slepc-3.9.0 2018-04-12
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2018, 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: {
32: DSViewMat(ds,viewer,DS_MAT_A);
33: if (ds->state>DS_STATE_INTERMEDIATE) {
34: DSViewMat(ds,viewer,DS_MAT_Q);
35: }
36: if (ds->mat[DS_MAT_X]) {
37: DSViewMat(ds,viewer,DS_MAT_X);
38: }
39: if (ds->mat[DS_MAT_Y]) {
40: DSViewMat(ds,viewer,DS_MAT_Y);
41: }
42: return(0);
43: }
45: static PetscErrorCode DSVectors_NHEP_Refined_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
46: {
47: #if defined(PETSC_MISSING_LAPACK_GESVD)
49: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
50: #else
52: PetscInt i,j;
53: PetscBLASInt info,ld,n,n1,lwork,inc=1;
54: PetscScalar sdummy,done=1.0,zero=0.0;
55: PetscReal *sigma;
56: PetscBool iscomplex = PETSC_FALSE;
57: PetscScalar *A = ds->mat[DS_MAT_A];
58: PetscScalar *Q = ds->mat[DS_MAT_Q];
59: PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
60: PetscScalar *W;
63: if (left) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for left vectors");
64: PetscBLASIntCast(ds->n,&n);
65: PetscBLASIntCast(ds->ld,&ld);
66: n1 = n+1;
67: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
68: if (iscomplex) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complex eigenvalues yet");
69: DSAllocateWork_Private(ds,5*ld,6*ld,0);
70: DSAllocateMat_Private(ds,DS_MAT_W);
71: W = ds->mat[DS_MAT_W];
72: lwork = 5*ld;
73: sigma = ds->rwork+5*ld;
75: /* build A-w*I in W */
76: for (j=0;j<n;j++)
77: for (i=0;i<=n;i++)
78: W[i+j*ld] = A[i+j*ld];
79: for (i=0;i<n;i++)
80: W[i+i*ld] -= A[(*k)+(*k)*ld];
82: /* compute SVD of W */
83: #if !defined(PETSC_USE_COMPLEX)
84: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,&info));
85: #else
86: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&n1,&n,W,&ld,sigma,&sdummy,&ld,&sdummy,&ld,ds->work,&lwork,ds->rwork,&info));
87: #endif
88: SlepcCheckLapackInfo("gesvd",info);
90: /* the smallest singular value is the new error estimate */
91: if (rnorm) *rnorm = sigma[n-1];
93: /* update vector with right singular vector associated to smallest singular value,
94: accumulating the transformation matrix Q */
95: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,W+n-1,&ld,&zero,X+(*k)*ld,&inc));
96: return(0);
97: #endif
98: }
100: static PetscErrorCode DSVectors_NHEP_Refined_All(DS ds,PetscBool left)
101: {
103: PetscInt i;
106: for (i=0;i<ds->n;i++) {
107: DSVectors_NHEP_Refined_Some(ds,&i,NULL,left);
108: }
109: return(0);
110: }
112: static PetscErrorCode DSVectors_NHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
113: {
114: #if defined(SLEPC_MISSING_LAPACK_TREVC)
116: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
117: #else
119: PetscInt i;
120: PetscBLASInt mm=1,mout,info,ld,n,*select,inc = 1;
121: PetscScalar tmp,done=1.0,zero=0.0;
122: PetscReal norm;
123: PetscBool iscomplex = PETSC_FALSE;
124: PetscScalar *A = ds->mat[DS_MAT_A];
125: PetscScalar *Q = ds->mat[DS_MAT_Q];
126: PetscScalar *X = ds->mat[left?DS_MAT_Y:DS_MAT_X];
127: PetscScalar *Y;
130: PetscBLASIntCast(ds->n,&n);
131: PetscBLASIntCast(ds->ld,&ld);
132: DSAllocateWork_Private(ds,0,0,ld);
133: select = ds->iwork;
134: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
136: /* compute k-th eigenvector Y of A */
137: Y = X+(*k)*ld;
138: select[*k] = (PetscBLASInt)PETSC_TRUE;
139: #if !defined(PETSC_USE_COMPLEX)
140: if ((*k)<n-1 && A[(*k)+1+(*k)*ld]!=0.0) iscomplex = PETSC_TRUE;
141: mm = iscomplex? 2: 1;
142: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
143: DSAllocateWork_Private(ds,3*ld,0,0);
144: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,&info));
145: #else
146: DSAllocateWork_Private(ds,2*ld,ld,0);
147: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(left?"L":"R","S",select,&n,A,&ld,Y,&ld,Y,&ld,&mm,&mout,ds->work,ds->rwork,&info));
148: #endif
149: SlepcCheckLapackInfo("trevc",info);
150: if (mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Inconsistent arguments");
152: /* accumulate and normalize eigenvectors */
153: if (ds->state>=DS_STATE_CONDENSED) {
154: PetscMemcpy(ds->work,Y,mout*ld*sizeof(PetscScalar));
155: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work,&inc,&zero,Y,&inc));
156: #if !defined(PETSC_USE_COMPLEX)
157: if (iscomplex) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&done,Q,&ld,ds->work+ld,&inc,&zero,Y+ld,&inc));
158: #endif
159: norm = BLASnrm2_(&n,Y,&inc);
160: #if !defined(PETSC_USE_COMPLEX)
161: if (iscomplex) {
162: tmp = BLASnrm2_(&n,Y+ld,&inc);
163: norm = SlepcAbsEigenvalue(norm,tmp);
164: }
165: #endif
166: tmp = 1.0 / norm;
167: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y,&inc));
168: #if !defined(PETSC_USE_COMPLEX)
169: if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Y+ld,&inc));
170: #endif
171: }
173: /* set output arguments */
174: if (iscomplex) (*k)++;
175: if (rnorm) {
176: if (iscomplex) *rnorm = SlepcAbsEigenvalue(Y[n-1],Y[n-1+ld]);
177: else *rnorm = PetscAbsScalar(Y[n-1]);
178: }
179: return(0);
180: #endif
181: }
183: static PetscErrorCode DSVectors_NHEP_Eigen_All(DS ds,PetscBool left)
184: {
185: #if defined(SLEPC_MISSING_LAPACK_TREVC)
187: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREVC - Lapack routine is unavailable");
188: #else
190: PetscInt i;
191: PetscBLASInt n,ld,mout,info,inc = 1;
192: PetscBool iscomplex;
193: PetscScalar *X,*Y,*Z,*A = ds->mat[DS_MAT_A],tmp;
194: PetscReal norm;
195: const char *side,*back;
198: PetscBLASIntCast(ds->n,&n);
199: PetscBLASIntCast(ds->ld,&ld);
200: if (left) {
201: X = NULL;
202: Y = ds->mat[DS_MAT_Y];
203: side = "L";
204: } else {
205: X = ds->mat[DS_MAT_X];
206: Y = NULL;
207: side = "R";
208: }
209: Z = left? Y: X;
210: if (ds->state>=DS_STATE_CONDENSED) {
211: /* DSSolve() has been called, backtransform with matrix Q */
212: back = "B";
213: PetscMemcpy(Z,ds->mat[DS_MAT_Q],ld*ld*sizeof(PetscScalar));
214: } else back = "A";
215: #if !defined(PETSC_USE_COMPLEX)
216: DSAllocateWork_Private(ds,3*ld,0,0);
217: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
218: #else
219: DSAllocateWork_Private(ds,2*ld,ld,0);
220: PetscStackCallBLAS("LAPACKtrevc",LAPACKtrevc_(side,back,NULL,&n,A,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
221: #endif
222: SlepcCheckLapackInfo("trevc",info);
224: /* normalize eigenvectors */
225: for (i=0;i<n;i++) {
226: iscomplex = (i<n-1 && A[i+1+i*ld]!=0.0)? PETSC_TRUE: PETSC_FALSE;
227: norm = BLASnrm2_(&n,Z+i*ld,&inc);
228: #if !defined(PETSC_USE_COMPLEX)
229: if (iscomplex) {
230: tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
231: norm = SlepcAbsEigenvalue(norm,tmp);
232: }
233: #endif
234: tmp = 1.0 / norm;
235: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
236: #if !defined(PETSC_USE_COMPLEX)
237: if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
238: #endif
239: if (iscomplex) i++;
240: }
241: return(0);
242: #endif
243: }
245: PetscErrorCode DSVectors_NHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
246: {
250: switch (mat) {
251: case DS_MAT_X:
252: if (ds->refined) {
253: if (!ds->extrarow) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Refined vectors require activating the extra row");
254: if (j) {
255: DSVectors_NHEP_Refined_Some(ds,j,rnorm,PETSC_FALSE);
256: } else {
257: DSVectors_NHEP_Refined_All(ds,PETSC_FALSE);
258: }
259: } else {
260: if (j) {
261: DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_FALSE);
262: } else {
263: DSVectors_NHEP_Eigen_All(ds,PETSC_FALSE);
264: }
265: }
266: break;
267: case DS_MAT_Y:
268: if (ds->refined) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
269: if (j) {
270: DSVectors_NHEP_Eigen_Some(ds,j,rnorm,PETSC_TRUE);
271: } else {
272: DSVectors_NHEP_Eigen_All(ds,PETSC_TRUE);
273: }
274: break;
275: case DS_MAT_U:
276: case DS_MAT_VT:
277: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
278: break;
279: default:
280: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
281: }
282: if (ds->state < DS_STATE_CONDENSED) {
283: DSSetState(ds,DS_STATE_CONDENSED);
284: }
285: return(0);
286: }
288: static PetscErrorCode DSSort_NHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
289: {
290: #if defined(PETSC_MISSING_LAPACK_TRSEN)
292: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TRSEN - Lapack routine is unavailable");
293: #else
295: PetscInt i;
296: PetscBLASInt info,n,ld,mout,lwork,*selection;
297: PetscScalar *T = ds->mat[DS_MAT_A],*Q = ds->mat[DS_MAT_Q],*work;
298: #if !defined(PETSC_USE_COMPLEX)
299: PetscBLASInt *iwork,liwork;
300: #endif
303: if (!k) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"Must supply argument k");
304: PetscBLASIntCast(ds->n,&n);
305: PetscBLASIntCast(ds->ld,&ld);
306: #if !defined(PETSC_USE_COMPLEX)
307: lwork = n;
308: liwork = 1;
309: DSAllocateWork_Private(ds,lwork,0,liwork+n);
310: work = ds->work;
311: lwork = ds->lwork;
312: selection = ds->iwork;
313: iwork = ds->iwork + n;
314: liwork = ds->liwork - n;
315: #else
316: lwork = 1;
317: DSAllocateWork_Private(ds,lwork,0,n);
318: work = ds->work;
319: selection = ds->iwork;
320: #endif
321: /* Compute the selected eigenvalue to be in the leading position */
322: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
323: PetscMemzero(selection,n*sizeof(PetscBLASInt));
324: for (i=0;i<*k;i++) selection[ds->perm[i]] = 1;
325: #if !defined(PETSC_USE_COMPLEX)
326: PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,wi,&mout,NULL,NULL,work,&lwork,iwork,&liwork,&info));
327: #else
328: PetscStackCallBLAS("LAPACKtrsen",LAPACKtrsen_("N","V",selection,&n,T,&ld,Q,&ld,wr,&mout,NULL,NULL,work,&lwork,&info));
329: #endif
330: SlepcCheckLapackInfo("trsen",info);
331: *k = mout;
332: return(0);
333: #endif
334: }
336: static PetscErrorCode DSSort_NHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
337: {
338: #if defined(SLEPC_MISSING_LAPACK_TREXC)
340: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TREXC - Lapack routine is unavailable");
341: #else
343: PetscScalar re;
344: PetscInt i,j,pos,result;
345: PetscBLASInt ifst,ilst,info,n,ld;
346: PetscScalar *T = ds->mat[DS_MAT_A];
347: PetscScalar *Q = ds->mat[DS_MAT_Q];
348: #if !defined(PETSC_USE_COMPLEX)
349: PetscScalar *work,im;
350: #endif
353: PetscBLASIntCast(ds->n,&n);
354: PetscBLASIntCast(ds->ld,&ld);
355: #if !defined(PETSC_USE_COMPLEX)
356: DSAllocateWork_Private(ds,ld,0,0);
357: work = ds->work;
358: #endif
359: /* selection sort */
360: for (i=ds->l;i<n-1;i++) {
361: re = wr[i];
362: #if !defined(PETSC_USE_COMPLEX)
363: im = wi[i];
364: #endif
365: pos = 0;
366: j=i+1; /* j points to the next eigenvalue */
367: #if !defined(PETSC_USE_COMPLEX)
368: if (im != 0) j=i+2;
369: #endif
370: /* find minimum eigenvalue */
371: for (;j<n;j++) {
372: #if !defined(PETSC_USE_COMPLEX)
373: SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
374: #else
375: SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
376: #endif
377: if (result > 0) {
378: re = wr[j];
379: #if !defined(PETSC_USE_COMPLEX)
380: im = wi[j];
381: #endif
382: pos = j;
383: }
384: #if !defined(PETSC_USE_COMPLEX)
385: if (wi[j] != 0) j++;
386: #endif
387: }
388: if (pos) {
389: /* interchange blocks */
390: PetscBLASIntCast(pos+1,&ifst);
391: PetscBLASIntCast(i+1,&ilst);
392: #if !defined(PETSC_USE_COMPLEX)
393: PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,work,&info));
394: #else
395: PetscStackCallBLAS("LAPACKtrexc",LAPACKtrexc_("V",&n,T,&ld,Q,&ld,&ifst,&ilst,&info));
396: #endif
397: SlepcCheckLapackInfo("trexc",info);
398: /* recover original eigenvalues from T matrix */
399: for (j=i;j<n;j++) {
400: wr[j] = T[j+j*ld];
401: #if !defined(PETSC_USE_COMPLEX)
402: if (j<n-1 && T[j+1+j*ld] != 0.0) {
403: /* complex conjugate eigenvalue */
404: wi[j] = PetscSqrtReal(PetscAbsReal(T[j+1+j*ld])) *
405: PetscSqrtReal(PetscAbsReal(T[j+(j+1)*ld]));
406: wr[j+1] = wr[j];
407: wi[j+1] = -wi[j];
408: j++;
409: } else {
410: wi[j] = 0.0;
411: }
412: #endif
413: }
414: }
415: #if !defined(PETSC_USE_COMPLEX)
416: if (wi[i] != 0) i++;
417: #endif
418: }
419: return(0);
420: #endif
421: }
423: PetscErrorCode DSSort_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
424: {
428: if (!rr || wr == rr) {
429: DSSort_NHEP_Total(ds,wr,wi);
430: } else {
431: DSSort_NHEP_Arbitrary(ds,wr,wi,rr,ri,k);
432: }
433: return(0);
434: }
436: PetscErrorCode DSUpdateExtraRow_NHEP(DS ds)
437: {
439: PetscInt i;
440: PetscBLASInt n,ld,incx=1;
441: PetscScalar *A,*Q,*x,*y,one=1.0,zero=0.0;
444: PetscBLASIntCast(ds->n,&n);
445: PetscBLASIntCast(ds->ld,&ld);
446: A = ds->mat[DS_MAT_A];
447: Q = ds->mat[DS_MAT_Q];
448: DSAllocateWork_Private(ds,2*ld,0,0);
449: x = ds->work;
450: y = ds->work+ld;
451: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
452: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
453: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
454: ds->k = n;
455: return(0);
456: }
458: /*
459: Reduce a matrix A to upper Hessenberg form Q'*A*Q, where Q is an orthogonal matrix.
460: The result overwrites A. Matrix A has the form
462: [ S | * ]
463: A = [-------]
464: [ R | H ]
466: where S is an upper (quasi-)triangular matrix of order k, H is an upper Hessenberg
467: matrix of order n-k, and R is all zeros except the first row (the arrow).
468: The algorithm uses elementary reflectors to annihilate entries in the arrow, and
469: then proceeds upwards.
470: If ilo>1, then it is assumed that the first ilo-1 entries of the arrow are zero, and
471: hence the first ilo-1 rows and columns of Q are set to the identity matrix.
473: Required workspace is 2*n.
474: */
475: static PetscErrorCode ArrowHessenberg(PetscBLASInt n,PetscBLASInt k,PetscBLASInt ilo,PetscScalar *A,PetscBLASInt lda,PetscScalar *Q,PetscBLASInt ldq,PetscScalar *work)
476: {
477: #if defined(SLEPC_MISSING_LAPACK_LARFG) || defined(SLEPC_MISSING_LAPACK_LARF)
479: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LARFG/LARF - Lapack routines are unavailable");
480: #else
481: PetscBLASInt i,j,n0,m,inc=1,incn=-1;
482: PetscScalar t,*v=work,*w=work+n,tau,tauc;
485: m = n-ilo+1;
486: for (i=k;i>ilo;i--) {
487: for (j=0;j<=i-ilo;j++) v[j] = A[i+(i-j-1)*lda]; /* _larfg does not allow negative inc, so use buffer */
488: n0 = i-ilo+1;
489: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0,v,v+1,&inc,&tau));
490: for (j=1;j<=i-ilo;j++) v[j] = PetscConj(v[j]);
491: tauc = PetscConj(tau);
492: A[i+(i-1)*lda] = v[0];
493: v[0] = 1.0;
494: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&i,&n0,v,&incn,&tauc,A+(ilo-1)*lda,&lda,w));
495: for (j=1;j<=i-ilo;j++) A[i+(i-j-1)*lda] = 0.0;
496: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0,&m,v,&incn,&tau,A+ilo-1+(ilo-1)*lda,&lda,w));
497: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0,&m,v,&incn,&tau,Q+ilo-1+(ilo-1)*ldq,&ldq,w));
498: }
499: /* trivial in-place transposition of Q */
500: for (j=ilo-1;j<k;j++) {
501: for (i=j;i<k;i++) {
502: t = Q[i+j*ldq];
503: if (i!=j) Q[i+j*ldq] = PetscConj(Q[j+i*ldq]);
504: Q[j+i*ldq] = PetscConj(t);
505: }
506: }
507: return(0);
508: #endif
509: }
511: PetscErrorCode DSSolve_NHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
512: {
513: #if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
515: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable");
516: #else
518: PetscScalar *work,*tau;
519: PetscInt i,j;
520: PetscBLASInt ilo,lwork,info,n,k,ld;
521: PetscScalar *A = ds->mat[DS_MAT_A];
522: PetscScalar *Q = ds->mat[DS_MAT_Q];
525: #if !defined(PETSC_USE_COMPLEX)
527: #endif
528: PetscBLASIntCast(ds->n,&n);
529: PetscBLASIntCast(ds->ld,&ld);
530: PetscBLASIntCast(ds->l+1,&ilo);
531: PetscBLASIntCast(ds->k,&k);
532: DSAllocateWork_Private(ds,ld+6*ld,0,0);
533: tau = ds->work;
534: work = ds->work+ld;
535: lwork = 6*ld;
537: /* initialize orthogonal matrix */
538: PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
539: for (i=0;i<n;i++) Q[i+i*ld] = 1.0;
540: if (n==1) { /* quick return */
541: wr[0] = A[0];
542: wi[0] = 0.0;
543: return(0);
544: }
546: /* reduce to upper Hessenberg form */
547: if (ds->state<DS_STATE_INTERMEDIATE) {
548: if (PETSC_FALSE && k>0) {
549: ArrowHessenberg(n,k,ilo,A,ld,Q,ld,work);
550: } else {
551: PetscStackCallBLAS("LAPACKgehrd",LAPACKgehrd_(&n,&ilo,&n,A,&ld,tau,work,&lwork,&info));
552: SlepcCheckLapackInfo("gehrd",info);
553: for (j=0;j<n-1;j++) {
554: for (i=j+2;i<n;i++) {
555: Q[i+j*ld] = A[i+j*ld];
556: A[i+j*ld] = 0.0;
557: }
558: }
559: PetscStackCallBLAS("LAPACKorghr",LAPACKorghr_(&n,&ilo,&n,Q,&ld,tau,work,&lwork,&info));
560: SlepcCheckLapackInfo("orghr",info);
561: }
562: }
564: /* compute the (real) Schur form */
565: #if !defined(PETSC_USE_COMPLEX)
566: PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,wi,Q,&ld,work,&lwork,&info));
567: for (j=0;j<ds->l;j++) {
568: if (j==n-1 || A[j+1+j*ld] == 0.0) {
569: /* real eigenvalue */
570: wr[j] = A[j+j*ld];
571: wi[j] = 0.0;
572: } else {
573: /* complex eigenvalue */
574: wr[j] = A[j+j*ld];
575: wr[j+1] = A[j+j*ld];
576: wi[j] = PetscSqrtReal(PetscAbsReal(A[j+1+j*ld])) *
577: PetscSqrtReal(PetscAbsReal(A[j+(j+1)*ld]));
578: wi[j+1] = -wi[j];
579: j++;
580: }
581: }
582: #else
583: PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("S","V",&n,&ilo,&n,A,&ld,wr,Q,&ld,work,&lwork,&info));
584: if (wi) for (i=ds->l;i<n;i++) wi[i] = 0.0;
585: #endif
586: SlepcCheckLapackInfo("hseqr",info);
587: return(0);
588: #endif
589: }
591: PetscErrorCode DSSynchronize_NHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
592: {
594: PetscInt ld=ds->ld,l=ds->l,k;
595: PetscMPIInt n,rank,off=0,size,ldn;
598: k = (ds->n-l)*ld;
599: if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
600: if (eigr) k += ds->n-l;
601: if (eigi) k += ds->n-l;
602: DSAllocateWork_Private(ds,k,0,0);
603: PetscMPIIntCast(k*sizeof(PetscScalar),&size);
604: PetscMPIIntCast(ds->n-l,&n);
605: PetscMPIIntCast(ld*(ds->n-l),&ldn);
606: MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
607: if (!rank) {
608: MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
609: if (ds->state>DS_STATE_RAW) {
610: MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
611: }
612: if (eigr) {
613: MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
614: }
615: if (eigi) {
616: MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
617: }
618: }
619: MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
620: if (rank) {
621: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
622: if (ds->state>DS_STATE_RAW) {
623: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
624: }
625: if (eigr) {
626: MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
627: }
628: if (eigi) {
629: MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
630: }
631: }
632: return(0);
633: }
635: PetscErrorCode DSTruncate_NHEP(DS ds,PetscInt n)
636: {
637: PetscInt i,newn,ld=ds->ld,l=ds->l;
638: PetscScalar *A;
641: if (ds->state==DS_STATE_CONDENSED) ds->t = ds->n;
642: A = ds->mat[DS_MAT_A];
643: /* be careful not to break a diagonal 2x2 block */
644: if (A[n+(n-1)*ld]==0.0) newn = n;
645: else {
646: if (n<ds->n-1) newn = n+1;
647: else newn = n-1;
648: }
649: if (ds->extrarow && ds->k==ds->n) {
650: /* copy entries of extra row to the new position, then clean last row */
651: for (i=l;i<newn;i++) A[newn+i*ld] = A[ds->n+i*ld];
652: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
653: }
654: ds->k = 0;
655: ds->n = newn;
656: return(0);
657: }
659: PetscErrorCode DSCond_NHEP(DS ds,PetscReal *cond)
660: {
661: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRI) || defined(SLEPC_MISSING_LAPACK_LANGE) || defined(SLEPC_MISSING_LAPACK_LANHS)
663: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRI/LANGE/LANHS - Lapack routines are unavailable");
664: #else
666: PetscScalar *work;
667: PetscReal *rwork;
668: PetscBLASInt *ipiv;
669: PetscBLASInt lwork,info,n,ld;
670: PetscReal hn,hin;
671: PetscScalar *A;
674: PetscBLASIntCast(ds->n,&n);
675: PetscBLASIntCast(ds->ld,&ld);
676: lwork = 8*ld;
677: DSAllocateWork_Private(ds,lwork,ld,ld);
678: work = ds->work;
679: rwork = ds->rwork;
680: ipiv = ds->iwork;
682: /* use workspace matrix W to avoid overwriting A */
683: DSAllocateMat_Private(ds,DS_MAT_W);
684: A = ds->mat[DS_MAT_W];
685: PetscMemcpy(A,ds->mat[DS_MAT_A],sizeof(PetscScalar)*ds->ld*ds->ld);
687: /* norm of A */
688: if (ds->state<DS_STATE_INTERMEDIATE) hn = LAPACKlange_("I",&n,&n,A,&ld,rwork);
689: else hn = LAPACKlanhs_("I",&n,A,&ld,rwork);
691: /* norm of inv(A) */
692: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,A,&ld,ipiv,&info));
693: SlepcCheckLapackInfo("getrf",info);
694: PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,A,&ld,ipiv,work,&lwork,&info));
695: SlepcCheckLapackInfo("getri",info);
696: hin = LAPACKlange_("I",&n,&n,A,&ld,rwork);
698: *cond = hn*hin;
699: return(0);
700: #endif
701: }
703: PetscErrorCode DSTranslateHarmonic_NHEP(DS ds,PetscScalar tau,PetscReal beta,PetscBool recover,PetscScalar *gin,PetscReal *gamma)
704: {
705: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRS)
707: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRS - Lapack routines are unavailable");
708: #else
710: PetscInt i,j;
711: PetscBLASInt *ipiv,info,n,ld,one=1,ncol;
712: PetscScalar *A,*B,*Q,*g=gin,*ghat;
713: PetscScalar done=1.0,dmone=-1.0,dzero=0.0;
714: PetscReal gnorm;
717: PetscBLASIntCast(ds->n,&n);
718: PetscBLASIntCast(ds->ld,&ld);
719: A = ds->mat[DS_MAT_A];
721: if (!recover) {
723: DSAllocateWork_Private(ds,0,0,ld);
724: ipiv = ds->iwork;
725: if (!g) {
726: DSAllocateWork_Private(ds,ld,0,0);
727: g = ds->work;
728: }
729: /* use workspace matrix W to factor A-tau*eye(n) */
730: DSAllocateMat_Private(ds,DS_MAT_W);
731: B = ds->mat[DS_MAT_W];
732: PetscMemcpy(B,A,sizeof(PetscScalar)*ld*ld);
734: /* Vector g initialy stores b = beta*e_n^T */
735: PetscMemzero(g,n*sizeof(PetscScalar));
736: g[n-1] = beta;
738: /* g = (A-tau*eye(n))'\b */
739: for (i=0;i<n;i++) B[i+i*ld] -= tau;
740: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n,&n,B,&ld,ipiv,&info));
741: SlepcCheckLapackInfo("getrf",info);
742: PetscLogFlops(2.0*n*n*n/3.0);
743: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n,&one,B,&ld,ipiv,g,&ld,&info));
744: SlepcCheckLapackInfo("getrs",info);
745: PetscLogFlops(2.0*n*n-n);
747: /* A = A + g*b' */
748: for (i=0;i<n;i++) A[i+(n-1)*ld] += g[i]*beta;
750: } else { /* recover */
753: DSAllocateWork_Private(ds,ld,0,0);
754: ghat = ds->work;
755: Q = ds->mat[DS_MAT_Q];
757: /* g^ = -Q(:,idx)'*g */
758: PetscBLASIntCast(ds->l+ds->k,&ncol);
759: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&ncol,&dmone,Q,&ld,g,&one,&dzero,ghat,&one));
761: /* A = A + g^*b' */
762: for (i=0;i<ds->l+ds->k;i++)
763: for (j=ds->l;j<ds->l+ds->k;j++)
764: A[i+j*ld] += ghat[i]*Q[n-1+j*ld]*beta;
766: /* g~ = (I-Q(:,idx)*Q(:,idx)')*g = g+Q(:,idx)*g^ */
767: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&ncol,&done,Q,&ld,ghat,&one,&done,g,&one));
768: }
770: /* Compute gamma factor */
771: if (gamma) {
772: gnorm = 0.0;
773: for (i=0;i<n;i++) gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));
774: *gamma = PetscSqrtReal(1.0+gnorm);
775: }
776: return(0);
777: #endif
778: }
780: PETSC_EXTERN PetscErrorCode DSCreate_NHEP(DS ds)
781: {
783: ds->ops->allocate = DSAllocate_NHEP;
784: ds->ops->view = DSView_NHEP;
785: ds->ops->vectors = DSVectors_NHEP;
786: ds->ops->solve[0] = DSSolve_NHEP;
787: ds->ops->sort = DSSort_NHEP;
788: ds->ops->synchronize = DSSynchronize_NHEP;
789: ds->ops->truncate = DSTruncate_NHEP;
790: ds->ops->update = DSUpdateExtraRow_NHEP;
791: ds->ops->cond = DSCond_NHEP;
792: ds->ops->transharm = DSTranslateHarmonic_NHEP;
793: return(0);
794: }