Actual source code: dsgnhep.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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: /*
15: 1) Patterns of A and B
16: DS_STATE_RAW: DS_STATE_INTERM/CONDENSED
17: 0 n-1 0 n-1
18: ------------- -------------
19: 0 |* * * * * *| 0 |* * * * * *|
20: |* * * * * *| | * * * * *|
21: |* * * * * *| | * * * *|
22: |* * * * * *| | * * * *|
23: |* * * * * *| | * *|
24: n-1 |* * * * * *| n-1 | *|
25: ------------- -------------
27: 2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
28: */
31: 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);
33: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
34: {
38: DSAllocateMat_Private(ds,DS_MAT_A);
39: DSAllocateMat_Private(ds,DS_MAT_B);
40: DSAllocateMat_Private(ds,DS_MAT_Z);
41: DSAllocateMat_Private(ds,DS_MAT_Q);
42: PetscFree(ds->perm);
43: PetscMalloc1(ld,&ds->perm);
44: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
45: return(0);
46: }
48: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
49: {
50: PetscErrorCode ierr;
51: PetscViewerFormat format;
54: PetscViewerGetFormat(viewer,&format);
55: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
56: DSViewMat(ds,viewer,DS_MAT_A);
57: DSViewMat(ds,viewer,DS_MAT_B);
58: if (ds->state>DS_STATE_INTERMEDIATE) {
59: DSViewMat(ds,viewer,DS_MAT_Z);
60: DSViewMat(ds,viewer,DS_MAT_Q);
61: }
62: if (ds->mat[DS_MAT_X]) {
63: DSViewMat(ds,viewer,DS_MAT_X);
64: }
65: if (ds->mat[DS_MAT_Y]) {
66: DSViewMat(ds,viewer,DS_MAT_Y);
67: }
68: return(0);
69: }
71: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
72: {
73: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
75: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
76: #else
78: PetscInt i;
79: PetscBLASInt n,ld,mout,info,*select,mm,inc = 1;
80: PetscScalar *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp,fone=1.0,fzero=0.0;
81: PetscReal norm;
82: PetscBool iscomplex = PETSC_FALSE;
83: const char *side;
86: PetscBLASIntCast(ds->n,&n);
87: PetscBLASIntCast(ds->ld,&ld);
88: if (left) {
89: X = NULL;
90: Y = &ds->mat[DS_MAT_Y][ld*(*k)];
91: side = "L";
92: } else {
93: X = &ds->mat[DS_MAT_X][ld*(*k)];
94: Y = NULL;
95: side = "R";
96: }
97: Z = left? Y: X;
98: DSAllocateWork_Private(ds,0,0,ld);
99: select = ds->iwork;
100: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
101: if (ds->state <= DS_STATE_INTERMEDIATE) {
102: DSSetIdentity(ds,DS_MAT_Q);
103: DSSetIdentity(ds,DS_MAT_Z);
104: }
105: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
106: if (ds->state < DS_STATE_CONDENSED) {
107: DSSetState(ds,DS_STATE_CONDENSED);
108: }
110: /* compute k-th eigenvector */
111: select[*k] = (PetscBLASInt)PETSC_TRUE;
112: #if defined(PETSC_USE_COMPLEX)
113: mm = 1;
114: DSAllocateWork_Private(ds,2*ld,2*ld,0);
115: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
116: #else
117: if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
118: mm = iscomplex? 2: 1;
119: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
120: DSAllocateWork_Private(ds,6*ld,0,0);
121: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
122: #endif
123: SlepcCheckLapackInfo("tgevc",info);
124: if (!select[*k] || mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");
126: /* accumulate and normalize eigenvectors */
127: PetscMemcpy(ds->work,Z,mm*ld*sizeof(PetscScalar));
128: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,ds->mat[left?DS_MAT_Z:DS_MAT_Q],&ld,ds->work,&ld,&fzero,Z,&ld));
129: norm = BLASnrm2_(&n,Z,&inc);
130: #if !defined(PETSC_USE_COMPLEX)
131: if (iscomplex) {
132: tmp = BLASnrm2_(&n,Z+ld,&inc);
133: norm = SlepcAbsEigenvalue(norm,tmp);
134: }
135: #endif
136: tmp = 1.0 / norm;
137: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z,&inc));
138: #if !defined(PETSC_USE_COMPLEX)
139: if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+ld,&inc));
140: #endif
142: /* set output arguments */
143: if (iscomplex) (*k)++;
144: if (rnorm) {
145: if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
146: else *rnorm = PetscAbsScalar(Z[n-1]);
147: }
148: return(0);
149: #endif
150: }
152: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
153: {
154: #if defined(SLEPC_MISSING_LAPACK_TGEVC)
156: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEVC - Lapack routine is unavailable");
157: #else
159: PetscInt i;
160: PetscBLASInt n,ld,mout,info,inc = 1;
161: PetscBool iscomplex;
162: PetscScalar *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp;
163: PetscReal norm;
164: const char *side,*back;
167: PetscBLASIntCast(ds->n,&n);
168: PetscBLASIntCast(ds->ld,&ld);
169: if (left) {
170: X = NULL;
171: Y = ds->mat[DS_MAT_Y];
172: side = "L";
173: } else {
174: X = ds->mat[DS_MAT_X];
175: Y = NULL;
176: side = "R";
177: }
178: Z = left? Y: X;
179: if (ds->state <= DS_STATE_INTERMEDIATE) {
180: DSSetIdentity(ds,DS_MAT_Q);
181: DSSetIdentity(ds,DS_MAT_Z);
182: }
183: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld,PETSC_TRUE);
184: if (ds->state>=DS_STATE_CONDENSED) {
185: /* DSSolve() has been called, backtransform with matrix Q */
186: back = "B";
187: PetscMemcpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld*sizeof(PetscScalar));
188: } else {
189: back = "A";
190: DSSetState(ds,DS_STATE_CONDENSED);
191: }
192: #if defined(PETSC_USE_COMPLEX)
193: DSAllocateWork_Private(ds,2*ld,2*ld,0);
194: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
195: #else
196: DSAllocateWork_Private(ds,6*ld,0,0);
197: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
198: #endif
199: SlepcCheckLapackInfo("tgevc",info);
201: /* normalize eigenvectors */
202: for (i=0;i<n;i++) {
203: iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
204: norm = BLASnrm2_(&n,Z+i*ld,&inc);
205: #if !defined(PETSC_USE_COMPLEX)
206: if (iscomplex) {
207: tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
208: norm = SlepcAbsEigenvalue(norm,tmp);
209: }
210: #endif
211: tmp = 1.0 / norm;
212: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
213: #if !defined(PETSC_USE_COMPLEX)
214: if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
215: #endif
216: if (iscomplex) i++;
217: }
218: return(0);
219: #endif
220: }
222: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
223: {
227: switch (mat) {
228: case DS_MAT_X:
229: case DS_MAT_Y:
230: if (k) {
231: DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
232: } else {
233: DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
234: }
235: break;
236: default:
237: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
238: }
239: return(0);
240: }
242: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
243: {
244: #if defined(PETSC_MISSING_LAPACK_TGSEN)
246: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGSEN - Lapack routine is unavailable");
247: #else
249: PetscInt i;
250: PetscBLASInt info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
251: 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;
254: if (!ds->sc) return(0);
255: PetscBLASIntCast(ds->n,&n);
256: PetscBLASIntCast(ds->ld,&ld);
257: #if !defined(PETSC_USE_COMPLEX)
258: lwork = 4*n+16;
259: #else
260: lwork = 1;
261: #endif
262: liwork = 1;
263: DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
264: beta = ds->work;
265: work = ds->work + n;
266: lwork = ds->lwork - n;
267: selection = ds->iwork;
268: iwork = ds->iwork + n;
269: liwork = ds->liwork - n;
270: /* Compute the selected eigenvalue to be in the leading position */
271: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
272: PetscMemzero(selection,n*sizeof(PetscBLASInt));
273: for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
274: #if !defined(PETSC_USE_COMPLEX)
275: 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));
276: #else
277: 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));
278: #endif
279: SlepcCheckLapackInfo("tgsen",info);
280: *k = mout;
281: for (i=0;i<n;i++) {
282: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
283: else wr[i] /= beta[i];
284: #if !defined(PETSC_USE_COMPLEX)
285: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
286: else wi[i] /= beta[i];
287: #endif
288: }
289: return(0);
290: #endif
291: }
293: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
294: {
295: #if defined(SLEPC_MISSING_LAPACK_TGEXC) || !defined(PETSC_USE_COMPLEX) && (defined(SLEPC_MISSING_LAPACK_LAMCH) || defined(SLEPC_MISSING_LAPACK_LAG2))
297: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"TGEXC/LAMCH/LAG2 - Lapack routines are unavailable");
298: #else
300: PetscScalar re;
301: PetscInt i,j,pos,result;
302: PetscBLASInt ifst,ilst,info,n,ld,one=1;
303: 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];
304: #if !defined(PETSC_USE_COMPLEX)
305: PetscBLASInt lwork;
306: PetscScalar *work,a,safmin,scale1,scale2,im;
307: #endif
310: if (!ds->sc) return(0);
311: PetscBLASIntCast(ds->n,&n);
312: PetscBLASIntCast(ds->ld,&ld);
313: #if !defined(PETSC_USE_COMPLEX)
314: lwork = -1;
315: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
316: SlepcCheckLapackInfo("tgexc",info);
317: safmin = LAPACKlamch_("S");
318: PetscBLASIntCast((PetscInt)a,&lwork);
319: DSAllocateWork_Private(ds,lwork,0,0);
320: work = ds->work;
321: #endif
322: /* selection sort */
323: for (i=ds->l;i<n-1;i++) {
324: re = wr[i];
325: #if !defined(PETSC_USE_COMPLEX)
326: im = wi[i];
327: #endif
328: pos = 0;
329: j = i+1; /* j points to the next eigenvalue */
330: #if !defined(PETSC_USE_COMPLEX)
331: if (im != 0) j=i+2;
332: #endif
333: /* find minimum eigenvalue */
334: for (;j<n;j++) {
335: #if !defined(PETSC_USE_COMPLEX)
336: SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
337: #else
338: SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
339: #endif
340: if (result > 0) {
341: re = wr[j];
342: #if !defined(PETSC_USE_COMPLEX)
343: im = wi[j];
344: #endif
345: pos = j;
346: }
347: #if !defined(PETSC_USE_COMPLEX)
348: if (wi[j] != 0) j++;
349: #endif
350: }
351: if (pos) {
352: /* interchange blocks */
353: PetscBLASIntCast(pos+1,&ifst);
354: PetscBLASIntCast(i+1,&ilst);
355: #if !defined(PETSC_USE_COMPLEX)
356: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
357: #else
358: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
359: #endif
360: SlepcCheckLapackInfo("tgexc",info);
361: /* recover original eigenvalues from T and S matrices */
362: for (j=i;j<n;j++) {
363: #if !defined(PETSC_USE_COMPLEX)
364: if (j<n-1 && S[j*ld+j+1] != 0.0) {
365: /* complex conjugate eigenvalue */
366: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
367: wr[j] = re / scale1;
368: wi[j] = im / scale1;
369: wr[j+1] = a / scale2;
370: wi[j+1] = -wi[j];
371: j++;
372: } else
373: #endif
374: {
375: if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
376: else wr[j] = S[j*ld+j] / T[j*ld+j];
377: #if !defined(PETSC_USE_COMPLEX)
378: wi[j] = 0.0;
379: #endif
380: }
381: }
382: }
383: #if !defined(PETSC_USE_COMPLEX)
384: if (wi[i] != 0.0) i++;
385: #endif
386: }
387: return(0);
388: #endif
389: }
391: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
392: {
396: if (!rr || wr == rr) {
397: DSSort_GNHEP_Total(ds,wr,wi);
398: } else {
399: DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
400: }
401: return(0);
402: }
404: /*
405: Write zeros from the column k to n in the lower triangular part of the
406: matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
407: make (S,T) a valid Schur decompositon.
408: */
409: 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)
410: {
411: #if defined(SLEPC_MISSING_LAPACK_LASV2)
413: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LASV2 - Lapack routine is unavailable");
414: #else
415: PetscInt i,j;
416: #if defined(PETSC_USE_COMPLEX)
417: PetscScalar s;
418: #else
420: PetscBLASInt ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
421: PetscScalar b11,b22,sr,cr,sl,cl;
422: #endif
425: if (!doProd && X) {
426: for (i=0;i<n;i++) for (j=0;j<n;j++) X[ldX*i+j] = 0.0;
427: for (i=0;i<n;i++) X[ldX*i+i] = 1.0;
428: }
429: if (!doProd && Y) {
430: for (i=0;i<n;i++) for (j=0;j<n;j++) Y[ldY*i+j] = 0.0;
431: for (i=0;i<n;i++) Y[ldX*i+i] = 1.0;
432: }
434: #if defined(PETSC_USE_COMPLEX)
435: for (i=k; i<n; i++) {
436: /* Some functions need the diagonal elements in T be real */
437: if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
438: s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
439: for (j=0;j<=i;j++) {
440: T[ldT*i+j] *= s;
441: S[ldS*i+j] *= s;
442: }
443: T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
444: if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
445: }
446: j = i+1;
447: if (j<n) {
448: S[ldS*i+j] = 0.0;
449: if (T) T[ldT*i+j] = 0.0;
450: }
451: }
452: #else
453: PetscBLASIntCast(ldS,&ldS_);
454: PetscBLASIntCast(ldT,&ldT_);
455: PetscBLASIntCast(n,&n_);
456: for (i=k;i<n-1;i++) {
457: if (S[ldS*i+i+1] != 0.0) {
458: /* Check if T(i+1,i) and T(i,i+1) are zero */
459: if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
460: /* Check if T(i+1,i) and T(i,i+1) are negligible */
461: 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) {
462: T[ldT*i+i+1] = 0.0;
463: T[ldT*(i+1)+i] = 0.0;
465: } else {
466: /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
467: 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) {
468: PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
469: } 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) {
470: PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
471: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
472: PetscBLASIntCast(n-i,&n_i);
473: n_i_2 = n_i - 2;
474: PetscBLASIntCast(i+2,&i_2);
475: PetscBLASIntCast(i,&i_);
476: if (b11 < 0.0) {
477: cr = -cr;
478: sr = -sr;
479: b11 = -b11;
480: b22 = -b22;
481: }
482: PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
483: PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
484: PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
485: PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
486: if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
487: if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
488: T[ldT*i+i] = b11;
489: T[ldT*i+i+1] = 0.0;
490: T[ldT*(i+1)+i] = 0.0;
491: T[ldT*(i+1)+i+1] = b22;
492: }
493: }
494: i++;
495: }
496: }
497: #endif
498: return(0);
499: #endif
500: }
502: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
503: {
504: #if defined(PETSC_MISSING_LAPACK_GGES)
506: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGES - Lapack routines are unavailable");
507: #else
509: PetscScalar *work,*beta,a;
510: PetscInt i;
511: PetscBLASInt lwork,info,n,ld,iaux;
512: 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];
515: #if !defined(PETSC_USE_COMPLEX)
517: #endif
518: PetscBLASIntCast(ds->n,&n);
519: PetscBLASIntCast(ds->ld,&ld);
520: lwork = -1;
521: #if !defined(PETSC_USE_COMPLEX)
522: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
523: PetscBLASIntCast((PetscInt)a,&lwork);
524: DSAllocateWork_Private(ds,lwork+ld,0,0);
525: beta = ds->work;
526: work = beta+ds->n;
527: PetscBLASIntCast(ds->lwork-ds->n,&lwork);
528: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
529: #else
530: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
531: PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
532: DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
533: beta = ds->work;
534: work = beta+ds->n;
535: PetscBLASIntCast(ds->lwork-ds->n,&lwork);
536: 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));
537: #endif
538: SlepcCheckLapackInfo("gges",info);
539: for (i=0;i<n;i++) {
540: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
541: else wr[i] /= beta[i];
542: #if !defined(PETSC_USE_COMPLEX)
543: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
544: else wi[i] /= beta[i];
545: #else
546: if (wi) wi[i] = 0.0;
547: #endif
548: }
549: return(0);
550: #endif
551: }
553: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
554: {
556: PetscInt ld=ds->ld,l=ds->l,k;
557: PetscMPIInt n,rank,off=0,size,ldn;
560: k = 2*(ds->n-l)*ld;
561: if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
562: if (eigr) k += (ds->n-l);
563: if (eigi) k += (ds->n-l);
564: DSAllocateWork_Private(ds,k,0,0);
565: PetscMPIIntCast(k*sizeof(PetscScalar),&size);
566: PetscMPIIntCast(ds->n-l,&n);
567: PetscMPIIntCast(ld*(ds->n-l),&ldn);
568: MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
569: if (!rank) {
570: MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
571: MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
572: if (ds->state>DS_STATE_RAW) {
573: MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
574: MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
575: }
576: if (eigr) {
577: MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
578: }
579: if (eigi) {
580: MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
581: }
582: }
583: MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
584: if (rank) {
585: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
586: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
587: if (ds->state>DS_STATE_RAW) {
588: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
589: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
590: }
591: if (eigr) {
592: MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
593: }
594: if (eigi) {
595: MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
596: }
597: }
598: return(0);
599: }
601: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
602: {
604: ds->ops->allocate = DSAllocate_GNHEP;
605: ds->ops->view = DSView_GNHEP;
606: ds->ops->vectors = DSVectors_GNHEP;
607: ds->ops->solve[0] = DSSolve_GNHEP;
608: ds->ops->sort = DSSort_GNHEP;
609: ds->ops->synchronize = DSSynchronize_GNHEP;
610: return(0);
611: }