Actual source code: dsgnhep.c
slepc-3.6.1 2015-09-03
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
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>
23: #include <slepcblaslapack.h>
25: /*
26: 1) Patterns of A and B
27: DS_STATE_RAW: DS_STATE_INTERM/CONDENSED
28: 0 n-1 0 n-1
29: ------------- -------------
30: 0 |* * * * * *| 0 |* * * * * *|
31: |* * * * * *| | * * * * *|
32: |* * * * * *| | * * * *|
33: |* * * * * *| | * * * *|
34: |* * * * * *| | * *|
35: n-1 |* * * * * *| n-1 | *|
36: ------------- -------------
38: 2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
39: */
42: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY,PetscBool doProd);
46: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
47: {
51: DSAllocateMat_Private(ds,DS_MAT_A);
52: DSAllocateMat_Private(ds,DS_MAT_B);
53: DSAllocateMat_Private(ds,DS_MAT_Z);
54: DSAllocateMat_Private(ds,DS_MAT_Q);
55: PetscFree(ds->perm);
56: PetscMalloc1(ld,&ds->perm);
57: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
58: return(0);
59: }
63: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
64: {
68: DSViewMat(ds,viewer,DS_MAT_A);
69: DSViewMat(ds,viewer,DS_MAT_B);
70: if (ds->state>DS_STATE_INTERMEDIATE) {
71: DSViewMat(ds,viewer,DS_MAT_Z);
72: DSViewMat(ds,viewer,DS_MAT_Q);
73: }
74: if (ds->mat[DS_MAT_X]) {
75: DSViewMat(ds,viewer,DS_MAT_X);
76: }
77: if (ds->mat[DS_MAT_Y]) {
78: DSViewMat(ds,viewer,DS_MAT_Y);
79: }
80: return(0);
81: }
85: PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscBool left)
86: {
87: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
89: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
90: #else
92: PetscInt i;
93: PetscBLASInt n,ld,mout,info,*select,mm;
94: PetscScalar *X,*Y,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],fone=1.0,fzero=0.0;
95: PetscBool iscomplex = PETSC_FALSE;
96: const char *side;
99: PetscBLASIntCast(ds->n,&n);
100: PetscBLASIntCast(ds->ld,&ld);
101: if (left) {
102: X = NULL;
103: Y = &ds->mat[DS_MAT_Y][ld*(*k)];
104: side = "L";
105: } else {
106: X = &ds->mat[DS_MAT_X][ld*(*k)];
107: Y = NULL;
108: side = "R";
109: }
110: DSAllocateWork_Private(ds,0,0,ld);
111: select = ds->iwork;
112: for (i=0;i<n;i++) select[i] = 0;
113: select[*k] = 1;
114: if (ds->state <= DS_STATE_INTERMEDIATE) {
115: DSSetIdentity(ds,DS_MAT_Q);
116: DSSetIdentity(ds,DS_MAT_Z);
117: }
118: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
119: if (ds->state < DS_STATE_CONDENSED) {
120: DSSetState(ds,DS_STATE_CONDENSED);
121: }
122: #if defined(PETSC_USE_COMPLEX)
123: mm = 1;
124: DSAllocateWork_Private(ds,2*ld,2*ld,0);
125: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
126: #else
127: if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
128: mm = iscomplex ? 2 : 1;
129: DSAllocateWork_Private(ds,6*ld,0,0);
130: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
131: #endif
132: if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEVC %i",info);
133: if (select[(*k)] == 0 || mout != mm) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Unsupported the computation of the second vector in a complex pair");
134: /* Backtransform: (X/Y) <- (Q/Z) * (X/Y) */
135: PetscMemcpy(ds->work,left?Y:X,mm*ld*sizeof(PetscScalar));
136: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,ds->mat[left?DS_MAT_Z:DS_MAT_Q],&ld,ds->work,&ld,&fzero,left?Y:X,&ld));
137: /* Update k to the last vector index in the conjugate pair */
138: if (iscomplex) (*k)++;
139: return(0);
140: #endif
141: }
145: PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
146: {
147: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
149: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
150: #else
152: PetscBLASInt n,ld,mout,info;
153: PetscScalar *X,*Y,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];
154: const char *side,*back;
157: PetscBLASIntCast(ds->n,&n);
158: PetscBLASIntCast(ds->ld,&ld);
159: if (left) {
160: X = NULL;
161: Y = ds->mat[DS_MAT_Y];
162: side = "L";
163: } else {
164: X = ds->mat[DS_MAT_X];
165: Y = NULL;
166: side = "R";
167: }
168: if (ds->state <= DS_STATE_INTERMEDIATE) {
169: DSSetIdentity(ds,DS_MAT_Q);
170: DSSetIdentity(ds,DS_MAT_Z);
171: }
172: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
173: if (ds->state>=DS_STATE_CONDENSED) {
174: /* DSSolve() has been called, backtransform with matrix Q */
175: back = "B";
176: PetscMemcpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld*sizeof(PetscScalar));
177: } else {
178: back = "A";
179: DSSetState(ds,DS_STATE_CONDENSED);
180: }
181: #if defined(PETSC_USE_COMPLEX)
182: DSAllocateWork_Private(ds,2*ld,2*ld,0);
183: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
184: #else
185: DSAllocateWork_Private(ds,6*ld,0,0);
186: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
187: #endif
188: if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEVC %i",info);
189: return(0);
190: #endif
191: }
195: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
196: {
200: if (rnorm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
201: switch (mat) {
202: case DS_MAT_X:
203: case DS_MAT_Y:
204: if (k) {
205: DSVectors_GNHEP_Eigen_Some(ds,k,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
206: } else {
207: DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
208: }
209: break;
210: default:
211: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
212: }
213: return(0);
214: }
218: PetscErrorCode DSNormalize_GNHEP(DS ds,DSMatType mat,PetscInt col)
219: {
221: PetscInt i,i0,i1;
222: PetscBLASInt ld,n,one = 1;
223: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],norm,*x;
224: #if !defined(PETSC_USE_COMPLEX)
225: PetscScalar norm0;
226: #endif
229: switch (mat) {
230: case DS_MAT_X:
231: case DS_MAT_Y:
232: case DS_MAT_Q:
233: case DS_MAT_Z:
234: /* Supported matrices */
235: break;
236: case DS_MAT_U:
237: case DS_MAT_VT:
238: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
239: break;
240: default:
241: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
242: }
244: PetscBLASIntCast(ds->n,&n);
245: PetscBLASIntCast(ds->ld,&ld);
246: DSGetArray(ds,mat,&x);
247: if (col < 0) {
248: i0 = 0; i1 = ds->n;
249: } else if (col>0 && (A[ds->ld*(col-1)+col] != 0.0 || (B && B[ds->ld*(col-1)+col] != 0.0))) {
250: i0 = col-1; i1 = col+1;
251: } else {
252: i0 = col; i1 = col+1;
253: }
254: for (i=i0;i<i1;i++) {
255: #if !defined(PETSC_USE_COMPLEX)
256: if (i<n-1 && (A[ds->ld*i+i+1] != 0.0 || (B && B[ds->ld*i+i+1] != 0.0))) {
257: norm = BLASnrm2_(&n,&x[ld*i],&one);
258: norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
259: norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
260: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
261: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
262: i++;
263: } else
264: #endif
265: {
266: norm = BLASnrm2_(&n,&x[ld*i],&one);
267: norm = 1.0/norm;
268: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
269: }
270: }
271: return(0);
272: }
276: PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
277: {
278: #if defined(SLEPC_MISSING_LAPACK_TGSEN)
280: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
281: #else
283: PetscInt i;
284: PetscBLASInt info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
285: PetscScalar *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Q = ds->mat[DS_MAT_Q],*Z = ds->mat[DS_MAT_Z],*work,*beta;
288: if (!ds->sc) return(0);
289: PetscBLASIntCast(ds->n,&n);
290: PetscBLASIntCast(ds->ld,&ld);
291: #if !defined(PETSC_USE_COMPLEX)
292: lwork = 4*n+16;
293: #else
294: lwork = 1;
295: #endif
296: liwork = 1;
297: DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
298: beta = ds->work;
299: work = ds->work + n;
300: lwork = ds->lwork - n;
301: selection = ds->iwork;
302: iwork = ds->iwork + n;
303: liwork = ds->liwork - n;
304: /* Compute the selected eigenvalue to be in the leading position */
305: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
306: PetscMemzero(selection,n*sizeof(PetscBLASInt));
307: for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
308: #if !defined(PETSC_USE_COMPLEX)
309: PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,wi,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
310: #else
311: PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
312: #endif
313: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTGSEN %d",info);
314: *k = mout;
315: for (i=0;i<n;i++) {
316: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
317: else wr[i] /= beta[i];
318: #if !defined(PETSC_USE_COMPLEX)
319: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
320: else wi[i] /= beta[i];
321: #endif
322: }
323: return(0);
324: #endif
325: }
329: PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
330: {
331: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
333: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
334: #else
336: PetscScalar re;
337: PetscInt i,j,pos,result;
338: PetscBLASInt ifst,ilst,info,n,ld,one=1;
339: PetscScalar *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];
340: #if !defined(PETSC_USE_COMPLEX)
341: PetscBLASInt lwork;
342: PetscScalar *work,a,safmin,scale1,scale2,im;
343: #endif
346: if (!ds->sc) return(0);
347: PetscBLASIntCast(ds->n,&n);
348: PetscBLASIntCast(ds->ld,&ld);
349: #if !defined(PETSC_USE_COMPLEX)
350: lwork = -1;
351: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
352: safmin = LAPACKlamch_("S");
353: PetscBLASIntCast((PetscInt)a,&lwork);
354: DSAllocateWork_Private(ds,lwork,0,0);
355: work = ds->work;
356: #endif
357: /* selection sort */
358: for (i=ds->l;i<n-1;i++) {
359: re = wr[i];
360: #if !defined(PETSC_USE_COMPLEX)
361: im = wi[i];
362: #endif
363: pos = 0;
364: j = i+1; /* j points to the next eigenvalue */
365: #if !defined(PETSC_USE_COMPLEX)
366: if (im != 0) j=i+2;
367: #endif
368: /* find minimum eigenvalue */
369: for (;j<n;j++) {
370: #if !defined(PETSC_USE_COMPLEX)
371: SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
372: #else
373: SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
374: #endif
375: if (result > 0) {
376: re = wr[j];
377: #if !defined(PETSC_USE_COMPLEX)
378: im = wi[j];
379: #endif
380: pos = j;
381: }
382: #if !defined(PETSC_USE_COMPLEX)
383: if (wi[j] != 0) j++;
384: #endif
385: }
386: if (pos) {
387: /* interchange blocks */
388: PetscBLASIntCast(pos+1,&ifst);
389: PetscBLASIntCast(i+1,&ilst);
390: #if !defined(PETSC_USE_COMPLEX)
391: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
392: #else
393: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
394: #endif
395: if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xTGEXC %i",info);
396: /* recover original eigenvalues from T and S matrices */
397: for (j=i;j<n;j++) {
398: #if !defined(PETSC_USE_COMPLEX)
399: if (j<n-1 && S[j*ld+j+1] != 0.0) {
400: /* complex conjugate eigenvalue */
401: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
402: wr[j] = re / scale1;
403: wi[j] = im / scale1;
404: wr[j+1] = a / scale2;
405: wi[j+1] = -wi[j];
406: j++;
407: } else
408: #endif
409: {
410: if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
411: else wr[j] = S[j*ld+j] / T[j*ld+j];
412: #if !defined(PETSC_USE_COMPLEX)
413: wi[j] = 0.0;
414: #endif
415: }
416: }
417: }
418: #if !defined(PETSC_USE_COMPLEX)
419: if (wi[i] != 0.0) i++;
420: #endif
421: }
422: return(0);
423: #endif
424: }
428: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
429: {
433: if (!rr || wr == rr) {
434: DSSort_GNHEP_Total(ds,wr,wi);
435: } else {
436: DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
437: }
438: return(0);
439: }
443: /*
444: Write zeros from the column k to n in the lower triangular part of the
445: matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
446: make (S,T) a valid Schur decompositon.
447: */
448: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY,PetscBool doProd)
449: {
450: #if defined(SLEPC_MISSING_LAPACK_LASV2)
452: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
453: #else
454: PetscInt i,j;
455: #if defined(PETSC_USE_COMPLEX)
456: PetscScalar s;
457: #else
459: PetscBLASInt ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
460: PetscScalar b11,b22,sr,cr,sl,cl;
461: #endif
464: if (!doProd && X) {
465: for (i=0;i<n;i++) for (j=0;j<n;j++) X[ldX*i+j] = 0.0;
466: for (i=0;i<n;i++) X[ldX*i+i] = 1.0;
467: }
468: if (!doProd && Y) {
469: for (i=0;i<n;i++) for (j=0;j<n;j++) Y[ldY*i+j] = 0.0;
470: for (i=0;i<n;i++) Y[ldX*i+i] = 1.0;
471: }
473: #if defined(PETSC_USE_COMPLEX)
474: for (i=k; i<n; i++) {
475: /* Some functions need the diagonal elements in T be real */
476: if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
477: s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
478: for (j=0;j<=i;j++) {
479: T[ldT*i+j] *= s;
480: S[ldS*i+j] *= s;
481: }
482: T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
483: if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
484: }
485: j = i+1;
486: if (j<n) {
487: S[ldS*i+j] = 0.0;
488: if (T) T[ldT*i+j] = 0.0;
489: }
490: }
491: #else
492: PetscBLASIntCast(ldS,&ldS_);
493: PetscBLASIntCast(ldT,&ldT_);
494: PetscBLASIntCast(n,&n_);
495: for (i=k;i<n-1;i++) {
496: if (S[ldS*i+i+1] != 0.0) {
497: /* Check if T(i+1,i) and T(i,i+1) are zero */
498: if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
499: /* Check if T(i+1,i) and T(i,i+1) are negligible */
500: if (PetscAbs(T[ldT*(i+1)+i])+PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1]))*PETSC_MACHINE_EPSILON) {
501: T[ldT*i+i+1] = 0.0;
502: T[ldT*(i+1)+i] = 0.0;
504: } else {
505: /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
506: if (PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*(i+1)+i]))*PETSC_MACHINE_EPSILON) {
507: PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
508: } else if (PetscAbs(T[ldT*(i+1)+i]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*i+i+1]))*PETSC_MACHINE_EPSILON) {
509: PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
510: } else {
511: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
512: }
513: PetscBLASIntCast(n-i,&n_i);
514: n_i_2 = n_i - 2;
515: PetscBLASIntCast(i+2,&i_2);
516: PetscBLASIntCast(i,&i_);
517: if (b11 < 0.0) {
518: cr = -cr;
519: sr = -sr;
520: b11 = -b11;
521: b22 = -b22;
522: }
523: PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
524: PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
525: PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
526: PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
527: if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
528: if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
529: T[ldT*i+i] = b11;
530: T[ldT*i+i+1] = 0.0;
531: T[ldT*(i+1)+i] = 0.0;
532: T[ldT*(i+1)+i+1] = b22;
533: }
534: }
535: i++;
536: }
537: }
538: #endif
539: return(0);
540: #endif
541: }
545: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
546: {
547: #if defined(PETSC_MISSING_LAPACK_GGES)
549: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
550: #else
552: PetscScalar *work,*beta,a;
553: PetscInt i;
554: PetscBLASInt lwork,info,n,ld,iaux;
555: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];
558: #if !defined(PETSC_USE_COMPLEX)
560: #endif
561: PetscBLASIntCast(ds->n,&n);
562: PetscBLASIntCast(ds->ld,&ld);
563: lwork = -1;
564: #if !defined(PETSC_USE_COMPLEX)
565: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
566: PetscBLASIntCast((PetscInt)a,&lwork);
567: DSAllocateWork_Private(ds,lwork+ld,0,0);
568: beta = ds->work;
569: work = beta+ds->n;
570: PetscBLASIntCast(ds->lwork-ds->n,&lwork);
571: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
572: #else
573: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
574: PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
575: DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
576: beta = ds->work;
577: work = beta+ds->n;
578: PetscBLASIntCast(ds->lwork-ds->n,&lwork);
579: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
580: #endif
581: if (info) SETERRQ1(PetscObjectComm((PetscObject)ds),PETSC_ERR_LIB,"Error in Lapack xGGES %i",info);
582: for (i=0;i<n;i++) {
583: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
584: else wr[i] /= beta[i];
585: #if !defined(PETSC_USE_COMPLEX)
586: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
587: else wi[i] /= beta[i];
588: #else
589: if (wi) wi[i] = 0.0;
590: #endif
591: }
592: return(0);
593: #endif
594: }
598: PETSC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
599: {
601: ds->ops->allocate = DSAllocate_GNHEP;
602: ds->ops->view = DSView_GNHEP;
603: ds->ops->vectors = DSVectors_GNHEP;
604: ds->ops->solve[0] = DSSolve_GNHEP;
605: ds->ops->sort = DSSort_GNHEP;
606: ds->ops->normalize = DSNormalize_GNHEP;
607: return(0);
608: }