Actual source code: dsghiep.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: */
21: #include <slepc/private/dsimpl.h>
22: #include <slepcblaslapack.h>
26: PetscErrorCode DSAllocate_GHIEP(DS ds,PetscInt ld)
27: {
31: DSAllocateMat_Private(ds,DS_MAT_A);
32: DSAllocateMat_Private(ds,DS_MAT_B);
33: DSAllocateMat_Private(ds,DS_MAT_Q);
34: DSAllocateMatReal_Private(ds,DS_MAT_T);
35: DSAllocateMatReal_Private(ds,DS_MAT_D);
36: PetscFree(ds->perm);
37: PetscMalloc1(ld,&ds->perm);
38: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
39: return(0);
40: }
44: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
45: {
47: PetscReal *T,*S;
48: PetscScalar *A,*B;
49: PetscInt i,n,ld;
52: A = ds->mat[DS_MAT_A];
53: B = ds->mat[DS_MAT_B];
54: T = ds->rmat[DS_MAT_T];
55: S = ds->rmat[DS_MAT_D];
56: n = ds->n;
57: ld = ds->ld;
58: if (tocompact) { /* switch from dense (arrow) to compact storage */
59: PetscMemzero(T,3*ld*sizeof(PetscReal));
60: PetscMemzero(S,ld*sizeof(PetscReal));
61: for (i=0;i<n-1;i++) {
62: T[i] = PetscRealPart(A[i+i*ld]);
63: T[ld+i] = PetscRealPart(A[i+1+i*ld]);
64: S[i] = PetscRealPart(B[i+i*ld]);
65: }
66: T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
67: S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
68: for (i=ds->l;i< ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
69: } else { /* switch from compact (arrow) to dense storage */
70: PetscMemzero(A,ld*ld*sizeof(PetscScalar));
71: PetscMemzero(B,ld*ld*sizeof(PetscScalar));
72: for (i=0;i<n-1;i++) {
73: A[i+i*ld] = T[i];
74: A[i+1+i*ld] = T[ld+i];
75: A[i+(i+1)*ld] = T[ld+i];
76: B[i+i*ld] = S[i];
77: }
78: A[n-1+(n-1)*ld] = T[n-1];
79: B[n-1+(n-1)*ld] = S[n-1];
80: for (i=ds->l;i<ds->k;i++) {
81: A[ds->k+i*ld] = T[2*ld+i];
82: A[i+ds->k*ld] = T[2*ld+i];
83: }
84: }
85: return(0);
86: }
90: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
91: {
92: PetscErrorCode ierr;
93: PetscViewerFormat format;
94: PetscInt i,j;
95: PetscReal value;
96: const char *methodname[] = {
97: "HR method",
98: "QR + Inverse Iteration",
99: "QR",
100: "DQDS + Inverse Iteration "
101: };
102: const int nmeth=sizeof(methodname)/sizeof(methodname[0]);
105: PetscViewerGetFormat(viewer,&format);
106: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
107: if (ds->method>=nmeth) {
108: PetscViewerASCIIPrintf(viewer,"solving the problem with: INVALID METHOD\n");
109: } else {
110: PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
111: }
112: return(0);
113: }
114: if (ds->compact) {
115: PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
116: if (format == PETSC_VIEWER_ASCII_MATLAB) {
117: PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
118: PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
119: PetscViewerASCIIPrintf(viewer,"zzz = [\n");
120: for (i=0;i<ds->n;i++) {
121: PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_T]+i));
122: }
123: for (i=0;i<ds->n-1;i++) {
124: if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
125: PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+2,i+1,*(ds->rmat[DS_MAT_T]+ds->ld+i));
126: PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+1,i+2,*(ds->rmat[DS_MAT_T]+ds->ld+i));
127: }
128: }
129: for (i = ds->l;i<ds->k;i++) {
130: if (*(ds->rmat[DS_MAT_T]+2*ds->ld+i)) {
131: PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",ds->k+1,i+1,*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
132: PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+1,ds->k+1,*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
133: }
134: }
135: PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);
137: PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
138: PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ds->n);
139: PetscViewerASCIIPrintf(viewer,"omega = [\n");
140: for (i=0;i<ds->n;i++) {
141: PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_D]+i));
142: }
143: PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);
145: } else {
146: PetscViewerASCIIPrintf(viewer,"T\n");
147: for (i=0;i<ds->n;i++) {
148: for (j=0;j<ds->n;j++) {
149: if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
150: else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
151: else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = *(ds->rmat[DS_MAT_T]+2*ds->ld+PetscMin(i,j));
152: else value = 0.0;
153: PetscViewerASCIIPrintf(viewer," %18.16e ",value);
154: }
155: PetscViewerASCIIPrintf(viewer,"\n");
156: }
157: PetscViewerASCIIPrintf(viewer,"omega\n");
158: for (i=0;i<ds->n;i++) {
159: for (j=0;j<ds->n;j++) {
160: if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
161: else value = 0.0;
162: PetscViewerASCIIPrintf(viewer," %18.16e ",value);
163: }
164: PetscViewerASCIIPrintf(viewer,"\n");
165: }
166: }
167: PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
168: PetscViewerFlush(viewer);
169: } else {
170: DSViewMat(ds,viewer,DS_MAT_A);
171: DSViewMat(ds,viewer,DS_MAT_B);
172: }
173: if (ds->state>DS_STATE_INTERMEDIATE) {
174: DSViewMat(ds,viewer,DS_MAT_Q);
175: }
176: return(0);
177: }
181: PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
182: {
184: PetscReal b[4],M[4],d1,d2,s1,s2,e;
185: PetscReal scal1,scal2,wr1,wr2,wi,ep,norm;
186: PetscScalar *Q,*X,Y[4],alpha,zeroS = 0.0;
187: PetscInt k;
188: PetscBLASInt two = 2,n_,ld,one=1;
189: #if !defined(PETSC_USE_COMPLEX)
190: PetscBLASInt four=4;
191: #endif
194: X = ds->mat[DS_MAT_X];
195: Q = ds->mat[DS_MAT_Q];
196: k = *idx;
197: PetscBLASIntCast(ds->n,&n_);
198: PetscBLASIntCast(ds->ld,&ld);
199: if (k < ds->n-1) {
200: e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ld+k):PetscRealPart(*(ds->mat[DS_MAT_A]+(k+1)+ld*k));
201: } else e = 0.0;
202: if (e == 0.0) {/* Real */
203: if (ds->state>=DS_STATE_CONDENSED) {
204: PetscMemcpy(X+k*ld,Q+k*ld,ld*sizeof(PetscScalar));
205: } else {
206: PetscMemzero(X+k*ds->ld,ds->ld*sizeof(PetscScalar));
207: X[k+k*ds->ld] = 1.0;
208: }
209: if (rnorm) {
210: *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
211: }
212: } else { /* 2x2 block */
213: if (ds->compact) {
214: s1 = *(ds->rmat[DS_MAT_D]+k);
215: d1 = *(ds->rmat[DS_MAT_T]+k);
216: s2 = *(ds->rmat[DS_MAT_D]+k+1);
217: d2 = *(ds->rmat[DS_MAT_T]+k+1);
218: } else {
219: s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
220: d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
221: s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
222: d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
223: }
224: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
225: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
226: ep = LAPACKlamch_("S");
227: /* Compute eigenvalues of the block */
228: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
229: if (wi==0.0) /* Real eigenvalues */
230: SETERRQ(PETSC_COMM_SELF,1,"Real block in DSVectors_GHIEP");
231: else { /* Complex eigenvalues */
232: if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
233: wr1 /= scal1; wi /= scal1;
234: #if !defined(PETSC_USE_COMPLEX)
235: if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
236: Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
237: } else {
238: Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
239: }
240: norm = BLASnrm2_(&four,Y,&one);
241: norm = 1/norm;
242: if (ds->state >= DS_STATE_CONDENSED) {
243: alpha = norm;
244: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
245: if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
246: } else {
247: PetscMemzero(X+k*ld,2*ld*sizeof(PetscScalar));
248: X[k*ld+k] = Y[0]*norm; X[k*ld+k+1] = Y[1]*norm;
249: X[(k+1)*ld+k] = Y[2]*norm; X[(k+1)*ld+k+1] = Y[3]*norm;
250: }
251: #else
252: if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
253: Y[0] = wr1-s2*d2+PETSC_i*wi; Y[1] = s2*e;
254: } else {
255: Y[0] = s1*e; Y[1] = wr1-s1*d1+PETSC_i*wi;
256: }
257: norm = BLASnrm2_(&two,Y,&one);
258: norm = 1/norm;
259: if (ds->state >= DS_STATE_CONDENSED) {
260: alpha = norm;
261: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
262: if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
263: } else {
264: PetscMemzero(X+k*ld,2*ld*sizeof(PetscScalar));
265: X[k*ld+k] = Y[0]*norm; X[k*ld+k+1] = Y[1]*norm;
266: }
267: X[(k+1)*ld+k] = PetscConj(X[k*ld+k]); X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
268: #endif
269: (*idx)++;
270: }
271: }
272: return(0);
273: }
277: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
278: {
279: PetscInt i;
280: PetscReal e;
284: switch (mat) {
285: case DS_MAT_X:
286: case DS_MAT_Y:
287: if (k) {
288: DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
289: } else {
290: for (i=0; i<ds->n; i++) {
291: e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
292: if (e == 0.0) {/* real */
293: if (ds->state >= DS_STATE_CONDENSED) {
294: PetscMemcpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld*sizeof(PetscScalar));
295: } else {
296: PetscMemzero(ds->mat[mat]+i*ds->ld,ds->ld*sizeof(PetscScalar));
297: *(ds->mat[mat]+i+i*ds->ld) = 1.0;
298: }
299: } else {
300: DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
301: }
302: }
303: }
304: break;
305: case DS_MAT_U:
306: case DS_MAT_VT:
307: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
308: break;
309: default:
310: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
311: }
312: return(0);
313: }
317: /*
318: Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
319: Only the index range n0..n1 is processed.
320: */
321: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
322: {
323: PetscInt k,ld;
324: PetscBLASInt two=2;
325: PetscScalar *A,*B;
326: PetscReal *D,*T;
327: PetscReal b[4],M[4],d1,d2,s1,s2,e;
328: PetscReal scal1,scal2,ep,wr1,wr2,wi1;
331: ld = ds->ld;
332: A = ds->mat[DS_MAT_A];
333: B = ds->mat[DS_MAT_B];
334: D = ds->rmat[DS_MAT_D];
335: T = ds->rmat[DS_MAT_T];
336: for (k=n0;k<n1;k++) {
337: if (k < n1-1) {
338: e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
339: } else {
340: e = 0.0;
341: }
342: if (e==0.0) {
343: /* real eigenvalue */
344: wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
345: #if !defined(PETSC_USE_COMPLEX)
346: wi[k] = 0.0 ;
347: #endif
348: } else {
349: /* diagonal block */
350: if (ds->compact) {
351: s1 = D[k];
352: d1 = T[k];
353: s2 = D[k+1];
354: d2 = T[k+1];
355: } else {
356: s1 = PetscRealPart(B[k*ld+k]);
357: d1 = PetscRealPart(A[k+k*ld]);
358: s2 = PetscRealPart(B[(k+1)*ld+k+1]);
359: d2 = PetscRealPart(A[k+1+(k+1)*ld]);
360: }
361: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
362: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
363: ep = LAPACKlamch_("S");
364: /* Compute eigenvalues of the block */
365: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
366: if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
367: wr[k] = wr1/scal1;
368: if (wi1==0.0) { /* Real eigenvalues */
369: if (scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
370: wr[k+1] = wr2/scal2;
371: #if !defined(PETSC_USE_COMPLEX)
372: wi[k] = 0.0;
373: wi[k+1] = 0.0;
374: #endif
375: } else { /* Complex eigenvalues */
376: #if !defined(PETSC_USE_COMPLEX)
377: wr[k+1] = wr[k];
378: wi[k] = wi1/scal1;
379: wi[k+1] = -wi[k];
380: #else
381: wr[k] += PETSC_i*wi1/scal1;
382: wr[k+1] = PetscConj(wr[k]);
383: #endif
384: }
385: k++;
386: }
387: }
388: #if defined(PETSC_USE_COMPLEX)
389: if (wi) {
390: for (k=n0;k<n1;k++) wi[k] = 0.0;
391: }
392: #endif
393: return(0);
394: }
398: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
399: {
401: PetscInt n,i,*perm;
402: PetscReal *d,*e,*s;
405: #if !defined(PETSC_USE_COMPLEX)
407: #endif
408: n = ds->n;
409: d = ds->rmat[DS_MAT_T];
410: e = d + ds->ld;
411: s = ds->rmat[DS_MAT_D];
412: DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
413: perm = ds->perm;
414: if (!rr) {
415: rr = wr;
416: ri = wi;
417: }
418: DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
419: if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_TRUE); }
420: PetscMemcpy(ds->work,wr,n*sizeof(PetscScalar));
421: for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
422: #if !defined(PETSC_USE_COMPLEX)
423: PetscMemcpy(ds->work,wi,n*sizeof(PetscScalar));
424: for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
425: #endif
426: PetscMemcpy(ds->rwork,s,n*sizeof(PetscReal));
427: for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
428: PetscMemcpy(ds->rwork,d,n*sizeof(PetscReal));
429: for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
430: PetscMemcpy(ds->rwork,e,(n-1)*sizeof(PetscReal));
431: PetscMemzero(e+ds->l,(n-1-ds->l)*sizeof(PetscScalar));
432: for (i=ds->l;i<n-1;i++) {
433: if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
434: }
435: if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
436: DSPermuteColumns_Private(ds,ds->l,n,DS_MAT_Q,perm);
437: return(0);
438: }
443: /*
444: Get eigenvectors with inverse iteration.
445: The system matrix is in Hessenberg form.
446: */
447: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
448: {
449: #if defined(PETSC_MISSING_LAPACK_HSEIN)
451: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEIN - Lapack routine is unavailable");
452: #else
454: PetscInt i,off;
455: PetscBLASInt *select,*infoC,ld,n1,mout,info;
456: PetscScalar *A,*B,*H,*X;
457: PetscReal *s,*d,*e;
458: #if defined(PETSC_USE_COMPLEX)
459: PetscInt j;
460: #endif
463: PetscBLASIntCast(ds->ld,&ld);
464: PetscBLASIntCast(ds->n-ds->l,&n1);
465: DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
466: DSAllocateMat_Private(ds,DS_MAT_W);
467: A = ds->mat[DS_MAT_A];
468: B = ds->mat[DS_MAT_B];
469: H = ds->mat[DS_MAT_W];
470: s = ds->rmat[DS_MAT_D];
471: d = ds->rmat[DS_MAT_T];
472: e = d + ld;
473: select = ds->iwork;
474: infoC = ds->iwork + ld;
475: off = ds->l+ds->l*ld;
476: if (ds->compact) {
477: H[off] = d[ds->l]*s[ds->l];
478: H[off+ld] = e[ds->l]*s[ds->l];
479: for (i=ds->l+1;i<ds->n-1;i++) {
480: H[i+(i-1)*ld] = e[i-1]*s[i];
481: H[i+i*ld] = d[i]*s[i];
482: H[i+(i+1)*ld] = e[i]*s[i];
483: }
484: H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
485: H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
486: } else {
487: s[ds->l] = PetscRealPart(B[off]);
488: H[off] = A[off]*s[ds->l];
489: H[off+ld] = A[off+ld]*s[ds->l];
490: for (i=ds->l+1;i<ds->n-1;i++) {
491: s[i] = PetscRealPart(B[i+i*ld]);
492: H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
493: H[i+i*ld] = A[i+i*ld]*s[i];
494: H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
495: }
496: s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
497: H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
498: H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
499: }
500: DSAllocateMat_Private(ds,DS_MAT_X);
501: X = ds->mat[DS_MAT_X];
502: for (i=0;i<n1;i++) select[i] = 1;
503: #if !defined(PETSC_USE_COMPLEX)
504: PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,NULL,infoC,&info));
505: #else
506: PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,ds->rwork,NULL,infoC,&info));
508: /* Separate real and imaginary part of complex eigenvectors */
509: for (j=ds->l;j<ds->n;j++) {
510: if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
511: for (i=ds->l;i<ds->n;i++) {
512: X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
513: X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
514: }
515: j++;
516: }
517: }
518: #endif
519: if (info<0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in hsein routine %d",-i);
520: if (info>0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Convergence error in hsein routine %d",i);
521: DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
522: return(0);
523: #endif
524: }
529: /*
530: Undo 2x2 blocks that have real eigenvalues.
531: */
532: PetscErrorCode DSGHIEPRealBlocks(DS ds)
533: {
535: PetscInt i;
536: PetscReal e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
537: PetscReal maxy,ep,scal1,scal2,snorm;
538: PetscReal *T,*D,b[4],M[4],wr1,wr2,wi;
539: PetscScalar *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
540: PetscBLASInt m,two=2,ld;
541: PetscBool isreal;
544: PetscBLASIntCast(ds->ld,&ld);
545: PetscBLASIntCast(ds->n-ds->l,&m);
546: A = ds->mat[DS_MAT_A];
547: B = ds->mat[DS_MAT_B];
548: T = ds->rmat[DS_MAT_T];
549: D = ds->rmat[DS_MAT_D];
550: DSAllocateWork_Private(ds,2*m,0,0);
551: for (i=ds->l;i<ds->n-1;i++) {
552: e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
553: if (e != 0.0) { /* 2x2 block */
554: if (ds->compact) {
555: s1 = D[i];
556: d1 = T[i];
557: s2 = D[i+1];
558: d2 = T[i+1];
559: } else {
560: s1 = PetscRealPart(B[i*ld+i]);
561: d1 = PetscRealPart(A[i*ld+i]);
562: s2 = PetscRealPart(B[(i+1)*ld+i+1]);
563: d2 = PetscRealPart(A[(i+1)*ld+i+1]);
564: }
565: isreal = PETSC_FALSE;
566: if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
567: dd = d1-d2;
568: if (2*PetscAbsReal(e) <= dd) {
569: t = 2*e/dd;
570: t = t/(1 + PetscSqrtReal(1+t*t));
571: } else {
572: t = dd/(2*e);
573: ss = (t>=0)?1.0:-1.0;
574: t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
575: }
576: Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
577: Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
578: wr1 = d1+t*e;
579: wr2 = d2-t*e;
580: ss1 = s1; ss2 = s2;
581: isreal = PETSC_TRUE;
582: } else {
583: ss1 = 1.0; ss2 = 1.0,
584: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
585: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
586: ep = LAPACKlamch_("S");
588: /* Compute eigenvalues of the block */
589: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
590: if (wi==0.0) { /* Real eigenvalues */
591: isreal = PETSC_TRUE;
592: if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
593: wr1 /= scal1; wr2 /= scal2;
594: if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
595: Y[0] = wr1-s2*d2;
596: Y[1] = s2*e;
597: } else {
598: Y[0] = s1*e;
599: Y[1] = wr1-s1*d1;
600: }
601: /* normalize with a signature*/
602: maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
603: scal1 = PetscRealPart(Y[0])/maxy; scal2 = PetscRealPart(Y[1])/maxy;
604: snorm = scal1*scal1*s1 + scal2*scal2*s2;
605: if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
606: snorm = maxy*PetscSqrtReal(snorm); Y[0] = Y[0]/snorm; Y[1] = Y[1]/snorm;
607: if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
608: Y[2] = wr2-s2*d2;
609: Y[3] = s2*e;
610: } else {
611: Y[2] = s1*e;
612: Y[3] = wr2-s1*d1;
613: }
614: maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
615: scal1 = PetscRealPart(Y[2])/maxy; scal2 = PetscRealPart(Y[3])/maxy;
616: snorm = scal1*scal1*s1 + scal2*scal2*s2;
617: if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
618: snorm = maxy*PetscSqrtReal(snorm);Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
619: }
620: wr1 *= ss1; wr2 *= ss2;
621: }
622: if (isreal) {
623: if (ds->compact) {
624: D[i] = ss1;
625: T[i] = wr1;
626: D[i+1] = ss2;
627: T[i+1] = wr2;
628: T[ld+i] = 0.0;
629: } else {
630: B[i*ld+i] = ss1;
631: A[i*ld+i] = wr1;
632: B[(i+1)*ld+i+1] = ss2;
633: A[(i+1)*ld+i+1] = wr2;
634: A[(i+1)+ld*i] = 0.0;
635: A[i+ld*(i+1)] = 0.0;
636: }
637: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&two,&two,&oneS,ds->mat[DS_MAT_Q]+ds->l+i*ld,&ld,Y,&two,&zeroS,ds->work,&m));
638: PetscMemcpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m*sizeof(PetscScalar));
639: PetscMemcpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m*sizeof(PetscScalar));
640: }
641: i++;
642: }
643: }
644: return(0);
645: }
649: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
650: {
651: #if defined(PETSC_MISSING_LAPACK_HSEQR)
653: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable");
654: #else
656: PetscInt i,off;
657: PetscBLASInt n1,ld,one,info,lwork;
658: PetscScalar *H,*A,*B,*Q;
659: PetscReal *d,*e,*s;
660: #if defined(PETSC_USE_COMPLEX)
661: PetscInt j;
662: #endif
665: #if !defined(PETSC_USE_COMPLEX)
667: #endif
668: one = 1;
669: PetscBLASIntCast(ds->n-ds->l,&n1);
670: PetscBLASIntCast(ds->ld,&ld);
671: off = ds->l + ds->l*ld;
672: A = ds->mat[DS_MAT_A];
673: B = ds->mat[DS_MAT_B];
674: Q = ds->mat[DS_MAT_Q];
675: d = ds->rmat[DS_MAT_T];
676: e = ds->rmat[DS_MAT_T] + ld;
677: s = ds->rmat[DS_MAT_D];
678: DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
679: lwork = ld*ld;
681: /* Quick return if possible */
682: if (n1 == 1) {
683: *(Q+off) = 1;
684: if (!ds->compact) {
685: d[ds->l] = PetscRealPart(A[off]);
686: s[ds->l] = PetscRealPart(B[off]);
687: }
688: wr[ds->l] = d[ds->l]/s[ds->l];
689: if (wi) wi[ds->l] = 0.0;
690: return(0);
691: }
692: /* Reduce to pseudotriadiagonal form */
693: DSIntermediate_GHIEP(ds);
695: /* Compute Eigenvalues (QR)*/
696: DSAllocateMat_Private(ds,DS_MAT_W);
697: H = ds->mat[DS_MAT_W];
698: if (ds->compact) {
699: H[off] = d[ds->l]*s[ds->l];
700: H[off+ld] = e[ds->l]*s[ds->l];
701: for (i=ds->l+1;i<ds->n-1;i++) {
702: H[i+(i-1)*ld] = e[i-1]*s[i];
703: H[i+i*ld] = d[i]*s[i];
704: H[i+(i+1)*ld] = e[i]*s[i];
705: }
706: H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
707: H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
708: } else {
709: s[ds->l] = PetscRealPart(B[off]);
710: H[off] = A[off]*s[ds->l];
711: H[off+ld] = A[off+ld]*s[ds->l];
712: for (i=ds->l+1;i<ds->n-1;i++) {
713: s[i] = PetscRealPart(B[i+i*ld]);
714: H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
715: H[i+i*ld] = A[i+i*ld]*s[i];
716: H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
717: }
718: s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
719: H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
720: H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
721: }
723: #if !defined(PETSC_USE_COMPLEX)
724: PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
725: #else
726: PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
728: /* Sort to have consecutive conjugate pairs */
729: for (i=ds->l;i<ds->n;i++) {
730: j=i+1;
731: while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
732: if (j==ds->n) {
733: if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) wr[i]=PetscRealPart(wr[i]);
734: else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"In QR_II complex without conjugate pair");
735: } else { /* complex eigenvalue */
736: wr[j] = wr[i+1];
737: if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
738: wr[i+1] = PetscConj(wr[i]);
739: i++;
740: }
741: }
742: #endif
743: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);
744: /* Compute Eigenvectors with Inverse Iteration */
745: DSGHIEPInverseIteration(ds,wr,wi);
747: /* Recover eigenvalues from diagonal */
748: DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
749: #if defined(PETSC_USE_COMPLEX)
750: if (wi) {
751: for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
752: }
753: #endif
754: return(0);
755: #endif
756: }
760: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
761: {
762: #if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
764: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable");
765: #else
767: PetscInt i,off,nwu=0,n,lw;
768: PetscBLASInt n_,ld,info,lwork;
769: PetscScalar *H,*A,*B,*Q,*X;
770: PetscReal *d,*s;
771: #if defined(PETSC_USE_COMPLEX)
772: PetscInt j,k;
773: #endif
776: #if !defined(PETSC_USE_COMPLEX)
778: #endif
779: n = ds->n-ds->l;
780: PetscBLASIntCast(n,&n_);
781: PetscBLASIntCast(ds->ld,&ld);
782: off = ds->l + ds->l*ld;
783: A = ds->mat[DS_MAT_A];
784: B = ds->mat[DS_MAT_B];
785: Q = ds->mat[DS_MAT_Q];
786: d = ds->rmat[DS_MAT_T];
787: s = ds->rmat[DS_MAT_D];
788: lw = 14*ld+ld*ld;
789: DSAllocateWork_Private(ds,lw,2*ld,0);
791: /* Quick return if possible */
792: if (n_ == 1) {
793: *(Q+off) = 1;
794: if (!ds->compact) {
795: d[ds->l] = PetscRealPart(A[off]);
796: s[ds->l] = PetscRealPart(B[off]);
797: }
798: wr[ds->l] = d[ds->l]/s[ds->l];
799: if (wi) wi[ds->l] = 0.0;
800: return(0);
801: }
803: /* Form pseudo-symmetric matrix */
804: H = ds->work+nwu;
805: nwu += n*n;
806: PetscMemzero(H,n*n*sizeof(PetscScalar));
807: if (ds->compact) {
808: for (i=0;i<n-1;i++) {
809: H[i+i*n] = s[ds->l+i]*d[ds->l+i];
810: H[i+1+i*n] = s[ds->l+i+1]*d[ld+ds->l+i];
811: H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
812: }
813: H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
814: for (i=0;i<ds->k-ds->l;i++) {
815: H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
816: H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
817: }
818: } else {
819: for (i=0;i<n-1;i++) {
820: H[i+i*n] = B[off+i+i*ld]*A[off+i+i*ld];
821: H[i+1+i*n] = B[off+i+1+(i+1)*ld]*A[off+i+1+i*ld];
822: H[i+(i+1)*n] = B[off+i+i*ld]*A[off+i+(i+1)*ld];
823: }
824: H[n-1+(n-1)*n] = B[off+n-1+(n-1)*ld]*A[off+n-1+(n-1)*n];
825: for (i=0;i<ds->k-ds->l;i++) {
826: H[ds->k-ds->l+i*n] = B[ds->k*(1+ld)]*A[off+ds->k-ds->l+i*ld];
827: H[i+(ds->k-ds->l)*n] = B[(i+ds->l)*(1+ld)]*A[off+i+(ds->k-ds->l)*ld];
828: }
829: }
830:
831: /* Compute eigenpairs */
832: PetscBLASIntCast(lw-nwu,&lwork);
833: DSAllocateMat_Private(ds,DS_MAT_X);
834: X = ds->mat[DS_MAT_X];
835: #if !defined(PETSC_USE_COMPLEX)
836: PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&n_,H,&n_,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,ds->work+nwu,&lwork,&info));
837: #else
838: PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&n_,H,&n_,wr+ds->l,NULL,&ld,X+off,&ld,ds->work+nwu,&lwork,ds->rwork,&info));
840: /* Sort to have consecutive conjugate pairs
841: Separate real and imaginary part of complex eigenvectors*/
842: for (i=ds->l;i<ds->n;i++) {
843: j=i+1;
844: while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
845: if (j==ds->n) {
846: if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) {
847: wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
848: for (k=ds->l;k<ds->n;k++) {
849: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
850: }
851: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"In QR_II complex without conjugate pair");
852: } else { /* complex eigenvalue */
853: if (j!=i+1) {
854: wr[j] = wr[i+1];
855: PetscMemcpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld*sizeof(PetscScalar));
856: }
857: if (PetscImaginaryPart(wr[i])<0) {
858: wr[i] = PetscConj(wr[i]);
859: for (k=ds->l;k<ds->n;k++) {
860: X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
861: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
862: }
863: } else {
864: for (k=ds->l;k<ds->n;k++) {
865: X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
866: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
867: }
868: }
869: wr[i+1] = PetscConj(wr[i]);
870: i++;
871: }
872: }
873: #endif
874: if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);
876: /* Compute real s-orthonormal basis */
877: DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_FALSE);
879: /* Recover eigenvalues from diagonal */
880: DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
881: #if defined(PETSC_USE_COMPLEX)
882: if (wi) {
883: for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
884: }
885: #endif
886: return(0);
887: #endif
888: }
892: PetscErrorCode DSNormalize_GHIEP(DS ds,DSMatType mat,PetscInt col)
893: {
895: PetscInt i,i0,i1;
896: PetscBLASInt ld,n,one = 1;
897: PetscScalar *A = ds->mat[DS_MAT_A],norm,*x;
898: #if !defined(PETSC_USE_COMPLEX)
899: PetscScalar norm0;
900: #endif
903: switch (mat) {
904: case DS_MAT_X:
905: case DS_MAT_Y:
906: case DS_MAT_Q:
907: /* Supported matrices */
908: break;
909: case DS_MAT_U:
910: case DS_MAT_VT:
911: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
912: break;
913: default:
914: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
915: }
917: PetscBLASIntCast(ds->n,&n);
918: PetscBLASIntCast(ds->ld,&ld);
919: DSGetArray(ds,mat,&x);
920: if (col < 0) {
921: i0 = 0; i1 = ds->n;
922: } else if (col>0 && A[ds->ld*(col-1)+col] != 0.0) {
923: i0 = col-1; i1 = col+1;
924: } else {
925: i0 = col; i1 = col+1;
926: }
927: for (i=i0; i<i1; i++) {
928: #if !defined(PETSC_USE_COMPLEX)
929: if (i<n-1 && A[ds->ld*i+i+1] != 0.0) {
930: norm = BLASnrm2_(&n,&x[ld*i],&one);
931: norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
932: norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
933: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
934: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
935: i++;
936: } else
937: #endif
938: {
939: norm = BLASnrm2_(&n,&x[ld*i],&one);
940: norm = 1.0/norm;
941: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
942: }
943: }
944: return(0);
945: }
949: PETSC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
950: {
952: ds->ops->allocate = DSAllocate_GHIEP;
953: ds->ops->view = DSView_GHIEP;
954: ds->ops->vectors = DSVectors_GHIEP;
955: ds->ops->solve[0] = DSSolve_GHIEP_HZ;
956: ds->ops->solve[1] = DSSolve_GHIEP_QR_II;
957: ds->ops->solve[2] = DSSolve_GHIEP_QR;
958: ds->ops->solve[3] = DSSolve_GHIEP_DQDS_II;
959: ds->ops->sort = DSSort_GHIEP;
960: ds->ops->normalize = DSNormalize_GHIEP;
961: return(0);
962: }