Actual source code: dsgnhep.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>
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: PetscMalloc(ld*sizeof(PetscInt),&ds->perm);
57: PetscLogObjectMemory(ds,ld*sizeof(PetscInt));
58: return(0);
59: }
63: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
64: {
68: DSViewMat_Private(ds,viewer,DS_MAT_A);
69: DSViewMat_Private(ds,viewer,DS_MAT_B);
70: if (ds->state>DS_STATE_INTERMEDIATE) {
71: DSViewMat_Private(ds,viewer,DS_MAT_Z);
72: DSViewMat_Private(ds,viewer,DS_MAT_Q);
73: }
74: if (ds->mat[DS_MAT_X]) {
75: DSViewMat_Private(ds,viewer,DS_MAT_X);
76: }
77: if (ds->mat[DS_MAT_Y]) {
78: DSViewMat_Private(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: n = PetscBLASIntCast(ds->n);
100: ld = PetscBLASIntCast(ds->ld);
101: if (left) {
102: X = PETSC_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 = PETSC_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: 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: LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info);
131: #endif
132: if (info) SETERRQ1(((PetscObject)ds)->comm,PETSC_ERR_LIB,"Error in Lapack xTREVC %i",info);
133: if (select[(*k)] == 0 || mout != mm) SETERRQ(((PetscObject)ds)->comm,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: 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: n = PetscBLASIntCast(ds->n);
158: ld = PetscBLASIntCast(ds->ld);
159: if (left) {
160: X = PETSC_NULL;
161: Y = ds->mat[DS_MAT_Y];
162: side = "L";
163: } else {
164: X = ds->mat[DS_MAT_X];
165: Y = PETSC_NULL;
166: side = "R";
167: }
168: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
169: if (ds->state>=DS_STATE_CONDENSED) {
170: /* DSSolve() has been called, backtransform with matrix Q */
171: back = "B";
172: PetscMemcpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld*sizeof(PetscScalar));
173: } else {
174: back = "A";
175: DSSetState(ds,DS_STATE_CONDENSED);
176: }
177: #if defined(PETSC_USE_COMPLEX)
178: DSAllocateWork_Private(ds,2*ld,2*ld,0);
179: LAPACKtgevc_(side,back,PETSC_NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info);
180: #else
181: DSAllocateWork_Private(ds,6*ld,0,0);
182: LAPACKtgevc_(side,back,PETSC_NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info);
183: #endif
184: if (info) SETERRQ1(((PetscObject)ds)->comm,PETSC_ERR_LIB,"Error in Lapack xTREVC %i",info);
185: return(0);
186: #endif
187: }
191: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
192: {
196: if (rnorm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
197: switch (mat) {
198: case DS_MAT_X:
199: case DS_MAT_Y:
200: if (k) {
201: DSVectors_GNHEP_Eigen_Some(ds,k,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
202: } else {
203: DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
204: }
205: break;
206: default:
207: SETERRQ(((PetscObject)ds)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
208: }
209: return(0);
210: }
214: PetscErrorCode DSNormalize_GNHEP(DS ds,DSMatType mat,PetscInt col)
215: {
217: PetscInt i,i0,i1;
218: PetscBLASInt ld,n,one = 1;
219: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],norm,*x;
220: #if !defined(PETSC_USE_COMPLEX)
221: PetscScalar norm0;
222: #endif
225: switch (mat) {
226: case DS_MAT_X:
227: case DS_MAT_Y:
228: case DS_MAT_Q:
229: case DS_MAT_Z:
230: /* Supported matrices */
231: break;
232: case DS_MAT_U:
233: case DS_MAT_VT:
234: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
235: break;
236: default:
237: SETERRQ(((PetscObject)ds)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
238: }
240: n = PetscBLASIntCast(ds->n);
241: ld = PetscBLASIntCast(ds->ld);
242: DSGetArray(ds,mat,&x);
243: if (col < 0) {
244: i0 = 0; i1 = ds->n;
245: } else if(col>0 && (A[ds->ld*(col-1)+col] != 0.0 || (B && B[ds->ld*(col-1)+col] != 0.0))) {
246: i0 = col-1; i1 = col+1;
247: } else {
248: i0 = col; i1 = col+1;
249: }
250: for(i=i0; i<i1; i++) {
251: #if !defined(PETSC_USE_COMPLEX)
252: if(i<n-1 && (A[ds->ld*i+i+1] != 0.0 || (B && B[ds->ld*i+i+1] != 0.0))) {
253: norm = BLASnrm2_(&n,&x[ld*i],&one);
254: norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
255: norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
256: BLASscal_(&n,&norm,&x[ld*i],&one);
257: BLASscal_(&n,&norm,&x[ld*(i+1)],&one);
258: i++;
259: } else
260: #endif
261: {
262: norm = BLASnrm2_(&n,&x[ld*i],&one);
263: norm = 1.0/norm;
264: BLASscal_(&n,&norm,&x[ld*i],&one);
265: }
266: }
267: return(0);
268: }
272: PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
273: {
274: #if defined(SLEPC_MISSING_LAPACK_TGSEN)
276: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
277: #else
279: PetscInt i;
280: PetscBLASInt info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
281: 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;
284: if (!ds->comp_fun) return(0);
285: n = PetscBLASIntCast(ds->n);
286: ld = PetscBLASIntCast(ds->ld);
287: #if !defined(PETSC_USE_COMPLEX)
288: lwork = 4*n+16;
289: #else
290: lwork = 1;
291: #endif
292: liwork = 1;
293: DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
294: beta = ds->work;
295: work = ds->work + n;
296: lwork = ds->lwork - n;
297: selection = ds->iwork;
298: iwork = ds->iwork + n;
299: liwork = ds->liwork - n;
300: /* Compute the selected eigenvalue to be in the leading position */
301: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
302: PetscMemzero(selection,n*sizeof(PetscBLASInt));
303: for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
304: #if !defined(PETSC_USE_COMPLEX)
305: LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,wi,beta,Z,&ld,Q,&ld,&mout,PETSC_NULL,PETSC_NULL,PETSC_NULL,work,&lwork,iwork,&liwork,&info);
306: #else
307: LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,beta,Z,&ld,Q,&ld,&mout,PETSC_NULL,PETSC_NULL,PETSC_NULL,work,&lwork,iwork,&liwork,&info);
308: #endif
309: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTGSEN %d",info);
310: *k = mout;
311: for (i=0;i<n;i++) {
312: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
313: else wr[i] /= beta[i];
314: #if !defined(PETSC_USE_COMPLEX)
315: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
316: else wi[i] /= beta[i];
317: #endif
318: }
319: return(0);
320: #endif
321: }
325: PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
326: {
327: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
329: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
330: #else
332: PetscScalar re,im;
333: PetscInt i,j,pos,result;
334: PetscBLASInt ifst,ilst,info,n,ld,one=1;
335: 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];
336: #if !defined(PETSC_USE_COMPLEX)
337: PetscBLASInt lwork;
338: PetscScalar *work,a,safmin,scale1,scale2;
339: #endif
342: if (!ds->comp_fun) return(0);
343: n = PetscBLASIntCast(ds->n);
344: ld = PetscBLASIntCast(ds->ld);
345: #if !defined(PETSC_USE_COMPLEX)
346: lwork = -1;
347: LAPACKtgexc_(&one,&one,&ld,PETSC_NULL,&ld,PETSC_NULL,&ld,PETSC_NULL,&ld,PETSC_NULL,&ld,&one,&one,&a,&lwork,&info);
348: safmin = LAPACKlamch_("S");
349: lwork = a;
350: DSAllocateWork_Private(ds,lwork,0,0);
351: work = ds->work;
352: #endif
353: /* selection sort */
354: for (i=ds->l;i<n-1;i++) {
355: re = wr[i];
356: im = wi[i];
357: pos = 0;
358: j = i+1; /* j points to the next eigenvalue */
359: #if !defined(PETSC_USE_COMPLEX)
360: if (im != 0) j=i+2;
361: #endif
362: /* find minimum eigenvalue */
363: for (;j<n;j++) {
364: (*ds->comp_fun)(re,im,wr[j],wi[j],&result,ds->comp_ctx);
365: if (result > 0) {
366: re = wr[j];
367: im = wi[j];
368: pos = j;
369: }
370: #if !defined(PETSC_USE_COMPLEX)
371: if (wi[j] != 0) j++;
372: #endif
373: }
374: if (pos) {
375: /* interchange blocks */
376: ifst = PetscBLASIntCast(pos+1);
377: ilst = PetscBLASIntCast(i+1);
378: #if !defined(PETSC_USE_COMPLEX)
379: LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info);
380: #else
381: LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info);
382: #endif
383: if (info) SETERRQ1(((PetscObject)ds)->comm,PETSC_ERR_LIB,"Error in Lapack xTGEXC %i",info);
384: /* recover original eigenvalues from T and S matrices */
385: for (j=i;j<n;j++) {
386: #if !defined(PETSC_USE_COMPLEX)
387: if (j<n-1 && S[j*ld+j+1] != 0.0) {
388: /* complex conjugate eigenvalue */
389: LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im);
390: wr[j] = re / scale1;
391: wi[j] = im / scale1;
392: wr[j+1] = a / scale2;
393: wi[j+1] = -wi[j];
394: j++;
395: } else
396: #endif
397: {
398: if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
399: else wr[j] = S[j*ld+j] / T[j*ld+j];
400: wi[j] = 0.0;
401: }
402: }
403: }
404: #if !defined(PETSC_USE_COMPLEX)
405: if (wi[i] != 0.0) i++;
406: #endif
407: }
408: return(0);
409: #endif
410: }
414: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
415: {
419: if (!rr || wr == rr) {
420: DSSort_GNHEP_Total(ds,wr,wi);
421: } else {
422: DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
423: }
424: return(0);
425: }
429: /*
430: Write zeros from the column k to n in the lower triangular part of the
431: matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
432: make (S,T) a valid Schur decompositon.
433: */
434: 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)
435: {
436: #if defined(SLEPC_MISSING_LAPACK_LASV2)
438: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
439: #else
440: PetscInt i,j;
441: #if defined(PETSC_USE_COMPLEX)
442: PetscScalar s;
443: #else
444: PetscBLASInt ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
445: PetscScalar b11,b22,sr,cr,sl,cl;
446: #endif
449: if (!doProd && X) {
450: for (i=0;i<n;i++) for (j=0;j<n;j++) X[ldX*i+j] = 0.0;
451: for (i=0;i<n;i++) X[ldX*i+i] = 1.0;
452: }
453: if (!doProd && Y) {
454: for (i=0;i<n;i++) for (j=0;j<n;j++) Y[ldY*i+j] = 0.0;
455: for (i=0;i<n;i++) Y[ldX*i+i] = 1.0;
456: }
458: #if defined(PETSC_USE_COMPLEX)
459: for (i=k; i<n; i++) {
460: /* Some functions need the diagonal elements in T be real */
461: if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
462: s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
463: for(j=0;j<=i;j++) {
464: T[ldT*i+j] *= s;
465: S[ldS*i+j] *= s;
466: }
467: T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
468: if (X) for(j=0;j<n;j++) X[ldX*i+j] *= s;
469: }
470: j = i+1;
471: if (j<n) {
472: S[ldS*i+j] = 0.0;
473: if (T) T[ldT*i+j] = 0.0;
474: }
475: }
476: #else
477: ldS_ = PetscBLASIntCast(ldS);
478: ldT_ = PetscBLASIntCast(ldT);
479: n_ = PetscBLASIntCast(n);
480: for (i=k;i<n-1;i++) {
481: if (S[ldS*i+i+1] != 0.0) {
482: /* Check if T(i+1,i) and T(i,i+1) are zero */
483: if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
484: /* Check if T(i+1,i) and T(i,i+1) are negligible */
485: 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) {
486: T[ldT*i+i+1] = 0.0;
487: T[ldT*(i+1)+i] = 0.0;
489: } else {
490: /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
491: 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) {
492: LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr);
493: } 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) {
494: LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl);
495: } else {
496: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
497: }
498: n_i = PetscBLASIntCast(n-i);
499: n_i_2 = n_i - 2;
500: i_2 = PetscBLASIntCast(i+2);
501: i_ = PetscBLASIntCast(i);
502: if (b11 < 0.0) { cr=-cr; sr=-sr; b11=-b11; b22=-b22; }
503: BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl);
504: BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr);
505: BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl);
506: BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr);
507: if (X) BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr);
508: if (Y) BLASrot_(&n_,&Y[ldY*i],&one,&X[ldY*(i+1)],&one,&cl,&sl);
509: T[ldT*i+i] = b11;
510: T[ldT*i+i+1] = 0.0;
511: T[ldT*(i+1)+i] = 0.0;
512: T[ldT*(i+1)+i+1] = b22;
513: }
514: }
515: i++;
516: }
517: }
518: #endif
519: return(0);
520: #endif
521: }
525: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
526: {
527: #if defined(SLEPC_MISSING_LAPACK_GGES)
529: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
530: #else
532: PetscScalar *work,*beta,a;
533: PetscInt i;
534: PetscBLASInt lwork,info,n,ld,iaux;
535: 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];
539: n = PetscBLASIntCast(ds->n);
540: ld = PetscBLASIntCast(ds->ld);
541: lwork = -1;
542: #if !defined(PETSC_USE_COMPLEX)
543: LAPACKgges_("V","V","N",PETSC_NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,PETSC_NULL,Z,&ld,Q,&ld,&a,&lwork,PETSC_NULL,&info);
544: lwork = (PetscBLASInt)a;
545: DSAllocateWork_Private(ds,lwork+ld,0,0);
546: beta = ds->work;
547: work = beta+ds->n;
548: lwork = PetscBLASIntCast(ds->lwork-ds->n);
549: LAPACKgges_("V","V","N",PETSC_NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,PETSC_NULL,&info);
550: #else
551: LAPACKgges_("V","V","N",PETSC_NULL,&n,A,&ld,B,&ld,&iaux,wr,PETSC_NULL,Z,&ld,Q,&ld,&a,&lwork,PETSC_NULL,PETSC_NULL,&info);
552: lwork = (PetscBLASInt)PetscRealPart(a);
553: DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
554: beta = ds->work;
555: work = beta+ds->n;
556: lwork = PetscBLASIntCast(ds->lwork-ds->n);
557: LAPACKgges_("V","V","N",PETSC_NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,PETSC_NULL,&info);
558: #endif
559: if (info) SETERRQ1(((PetscObject)ds)->comm,PETSC_ERR_LIB,"Error in Lapack xGGES %i",info);
560: for (i=0;i<n;i++) {
561: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
562: else wr[i] /= beta[i];
563: #if !defined(PETSC_USE_COMPLEX)
564: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
565: else wi[i] /= beta[i];
566: #endif
567: }
568: return(0);
569: #endif
570: }
572: EXTERN_C_BEGIN
575: PetscErrorCode DSCreate_GNHEP(DS ds)
576: {
578: ds->ops->allocate = DSAllocate_GNHEP;
579: ds->ops->view = DSView_GNHEP;
580: ds->ops->vectors = DSVectors_GNHEP;
581: ds->ops->solve[0] = DSSolve_GNHEP;
582: ds->ops->sort = DSSort_GNHEP;
583: ds->ops->normalize = DSNormalize_GNHEP;
584: return(0);
585: }
586: EXTERN_C_END