Actual source code: dsghiep.c
slepc-3.21.1 2024-04-26
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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: static PetscErrorCode DSAllocate_GHIEP(DS ds,PetscInt ld)
15: {
16: PetscFunctionBegin;
17: PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
18: PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
19: PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
20: PetscCall(DSAllocateMat_Private(ds,DS_MAT_T));
21: PetscCall(DSAllocateMat_Private(ds,DS_MAT_D));
22: PetscCall(PetscFree(ds->perm));
23: PetscCall(PetscMalloc1(ld,&ds->perm));
24: PetscFunctionReturn(PETSC_SUCCESS);
25: }
27: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
28: {
29: PetscReal *T,*S;
30: PetscScalar *A,*B;
31: PetscInt i,n,ld;
33: PetscFunctionBegin;
34: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
35: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
36: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
37: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
38: n = ds->n;
39: ld = ds->ld;
40: if (tocompact) { /* switch from dense (arrow) to compact storage */
41: PetscCall(PetscArrayzero(T,n));
42: PetscCall(PetscArrayzero(T+ld,n));
43: PetscCall(PetscArrayzero(T+2*ld,n));
44: PetscCall(PetscArrayzero(S,n));
45: for (i=0;i<n-1;i++) {
46: T[i] = PetscRealPart(A[i+i*ld]);
47: T[ld+i] = PetscRealPart(A[i+1+i*ld]);
48: S[i] = PetscRealPart(B[i+i*ld]);
49: }
50: T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
51: S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
52: for (i=ds->l;i<ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
53: } else { /* switch from compact (arrow) to dense storage */
54: for (i=0;i<n;i++) {
55: PetscCall(PetscArrayzero(A+i*ld,n));
56: PetscCall(PetscArrayzero(B+i*ld,n));
57: }
58: for (i=0;i<n-1;i++) {
59: A[i+i*ld] = T[i];
60: A[i+1+i*ld] = T[ld+i];
61: A[i+(i+1)*ld] = T[ld+i];
62: B[i+i*ld] = S[i];
63: }
64: A[n-1+(n-1)*ld] = T[n-1];
65: B[n-1+(n-1)*ld] = S[n-1];
66: for (i=ds->l;i<ds->k;i++) {
67: A[ds->k+i*ld] = T[2*ld+i];
68: A[i+ds->k*ld] = T[2*ld+i];
69: }
70: }
71: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
72: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
73: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
74: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
75: PetscFunctionReturn(PETSC_SUCCESS);
76: }
78: static PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
79: {
80: PetscViewerFormat format;
81: PetscInt i,j;
82: PetscReal *T,*S,value;
83: const char *methodname[] = {
84: "QR + Inverse Iteration",
85: "HZ method",
86: "QR"
87: };
88: const int nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);
90: PetscFunctionBegin;
91: PetscCall(PetscViewerGetFormat(viewer,&format));
92: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
93: if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]));
94: PetscFunctionReturn(PETSC_SUCCESS);
95: }
96: if (ds->compact) {
97: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
98: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
99: PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
100: if (format == PETSC_VIEWER_ASCII_MATLAB) {
101: PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n));
102: PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",3*ds->n));
103: PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = [\n"));
104: for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)T[i]));
105: for (i=0;i<ds->n-1;i++) {
106: if (T[i+ds->ld] !=0 && i!=ds->k-1) {
107: PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+2,i+1,(double)T[i+ds->ld]));
108: PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+2,(double)T[i+ds->ld]));
109: }
110: }
111: for (i = ds->l;i<ds->k;i++) {
112: if (T[i+2*ds->ld]) {
113: PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",ds->k+1,i+1,(double)T[i+2*ds->ld]));
114: PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,ds->k+1,(double)T[i+2*ds->ld]));
115: }
116: }
117: PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]));
119: PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n));
120: PetscCall(PetscViewerASCIIPrintf(viewer,"omega = zeros(%" PetscInt_FMT ",3);\n",3*ds->n));
121: PetscCall(PetscViewerASCIIPrintf(viewer,"omega = [\n"));
122: for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)S[i]));
123: PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]));
125: } else {
126: PetscCall(PetscViewerASCIIPrintf(viewer,"T\n"));
127: for (i=0;i<ds->n;i++) {
128: for (j=0;j<ds->n;j++) {
129: if (i==j) value = T[i];
130: else if (i==j+1 || j==i+1) value = T[PetscMin(i,j)+ds->ld];
131: else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = T[PetscMin(i,j)+2*ds->ld];
132: else value = 0.0;
133: PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value));
134: }
135: PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
136: }
137: PetscCall(PetscViewerASCIIPrintf(viewer,"omega\n"));
138: for (i=0;i<ds->n;i++) {
139: for (j=0;j<ds->n;j++) {
140: if (i==j) value = S[i];
141: else value = 0.0;
142: PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value));
143: }
144: PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
145: }
146: }
147: PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
148: PetscCall(PetscViewerFlush(viewer));
149: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
150: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
151: } else {
152: PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
153: PetscCall(DSViewMat(ds,viewer,DS_MAT_B));
154: }
155: if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
156: PetscFunctionReturn(PETSC_SUCCESS);
157: }
159: static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
160: {
161: PetscReal b[4],M[4],*T,*S,d1,d2,s1,s2,e,scal1,scal2,wr1,wr2,wi,ep,norm;
162: PetscScalar *X,Y[4],alpha,szero=0.0;
163: const PetscScalar *A,*B,*Q;
164: PetscInt k;
165: PetscBLASInt two=2,n_,ld,one=1;
166: #if !defined(PETSC_USE_COMPLEX)
167: PetscBLASInt four=4;
168: #endif
170: PetscFunctionBegin;
171: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
172: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
173: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
174: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
175: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
176: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
177: k = *idx;
178: PetscCall(PetscBLASIntCast(ds->n,&n_));
179: PetscCall(PetscBLASIntCast(ds->ld,&ld));
180: if (k < ds->n-1) e = (ds->compact)?T[k+ld]:PetscRealPart(A[(k+1)+ld*k]);
181: else e = 0.0;
182: if (e == 0.0) { /* Real */
183: if (ds->state>=DS_STATE_CONDENSED) PetscCall(PetscArraycpy(X+k*ld,Q+k*ld,ld));
184: else {
185: PetscCall(PetscArrayzero(X+k*ds->ld,ds->ld));
186: X[k+k*ds->ld] = 1.0;
187: }
188: if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
189: } else { /* 2x2 block */
190: if (ds->compact) {
191: s1 = S[k];
192: d1 = T[k];
193: s2 = S[k+1];
194: d2 = T[k+1];
195: } else {
196: s1 = PetscRealPart(B[k*ld+k]);
197: d1 = PetscRealPart(A[k+k*ld]);
198: s2 = PetscRealPart(B[(k+1)*ld+k+1]);
199: d2 = PetscRealPart(A[k+1+(k+1)*ld]);
200: }
201: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
202: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
203: ep = LAPACKlamch_("S");
204: /* Compute eigenvalues of the block */
205: PetscCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
206: PetscCheck(wi!=0.0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Real block in DSVectors_GHIEP");
207: /* Complex eigenvalues */
208: PetscCheck(scal1>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
209: wr1 /= scal1;
210: wi /= scal1;
211: #if !defined(PETSC_USE_COMPLEX)
212: if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
213: Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
214: } else {
215: Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
216: }
217: norm = BLASnrm2_(&four,Y,&one);
218: norm = 1.0/norm;
219: if (ds->state >= DS_STATE_CONDENSED) {
220: alpha = norm;
221: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,Q+k*ld,&ld,Y,&two,&szero,X+k*ld,&ld));
222: if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
223: } else {
224: PetscCall(PetscArrayzero(X+k*ld,2*ld));
225: X[k*ld+k] = Y[0]*norm;
226: X[k*ld+k+1] = Y[1]*norm;
227: X[(k+1)*ld+k] = Y[2]*norm;
228: X[(k+1)*ld+k+1] = Y[3]*norm;
229: }
230: #else
231: if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
232: Y[0] = PetscCMPLX(wr1-s2*d2,wi);
233: Y[1] = s2*e;
234: } else {
235: Y[0] = s1*e;
236: Y[1] = PetscCMPLX(wr1-s1*d1,wi);
237: }
238: norm = BLASnrm2_(&two,Y,&one);
239: norm = 1.0/norm;
240: if (ds->state >= DS_STATE_CONDENSED) {
241: alpha = norm;
242: PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,Q+k*ld,&ld,Y,&one,&szero,X+k*ld,&one));
243: if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
244: } else {
245: PetscCall(PetscArrayzero(X+k*ld,2*ld));
246: X[k*ld+k] = Y[0]*norm;
247: X[k*ld+k+1] = Y[1]*norm;
248: }
249: X[(k+1)*ld+k] = PetscConj(X[k*ld+k]);
250: X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
251: #endif
252: (*idx)++;
253: }
254: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
255: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
256: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
257: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
258: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
259: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
260: PetscFunctionReturn(PETSC_SUCCESS);
261: }
263: static PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
264: {
265: PetscScalar *Z;
266: const PetscScalar *A,*Q;
267: PetscInt i;
268: PetscReal e,*T;
270: PetscFunctionBegin;
271: switch (mat) {
272: case DS_MAT_X:
273: case DS_MAT_Y:
274: if (k) PetscCall(DSVectors_GHIEP_Eigen_Some(ds,k,rnorm));
275: else {
276: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
277: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
278: PetscCall(MatDenseGetArray(ds->omat[mat],&Z));
279: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
280: for (i=0; i<ds->n; i++) {
281: e = (ds->compact)?T[i+ds->ld]:PetscRealPart(A[(i+1)+ds->ld*i]);
282: if (e == 0.0) { /* real */
283: if (ds->state >= DS_STATE_CONDENSED) PetscCall(PetscArraycpy(Z+i*ds->ld,Q+i*ds->ld,ds->ld));
284: else {
285: PetscCall(PetscArrayzero(Z+i*ds->ld,ds->ld));
286: Z[i+i*ds->ld] = 1.0;
287: }
288: } else PetscCall(DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm));
289: }
290: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
291: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
292: PetscCall(MatDenseRestoreArray(ds->omat[mat],&Z));
293: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
294: }
295: break;
296: case DS_MAT_U:
297: case DS_MAT_V:
298: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
299: default:
300: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
301: }
302: PetscFunctionReturn(PETSC_SUCCESS);
303: }
305: /*
306: Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
307: Only the index range n0..n1 is processed.
308: */
309: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
310: {
311: PetscInt k,ld;
312: PetscBLASInt two=2;
313: const PetscScalar *A,*B;
314: PetscReal *D,*T,b[4],M[4],d1,d2,s1,s2,e,scal1,scal2,ep,wr1,wr2,wi1;
316: PetscFunctionBegin;
317: ld = ds->ld;
318: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
319: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
320: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
321: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
322: for (k=n0;k<n1;k++) {
323: if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
324: else e = 0.0;
325: if (e==0.0) { /* real eigenvalue */
326: wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
327: #if !defined(PETSC_USE_COMPLEX)
328: wi[k] = 0.0 ;
329: #endif
330: } else { /* diagonal block */
331: if (ds->compact) {
332: s1 = D[k];
333: d1 = T[k];
334: s2 = D[k+1];
335: d2 = T[k+1];
336: } else {
337: s1 = PetscRealPart(B[k*ld+k]);
338: d1 = PetscRealPart(A[k+k*ld]);
339: s2 = PetscRealPart(B[(k+1)*ld+k+1]);
340: d2 = PetscRealPart(A[k+1+(k+1)*ld]);
341: }
342: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
343: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
344: ep = LAPACKlamch_("S");
345: /* Compute eigenvalues of the block */
346: PetscCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
347: PetscCheck(scal1>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
348: if (wi1==0.0) { /* Real eigenvalues */
349: PetscCheck(scal2>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
350: wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
351: #if !defined(PETSC_USE_COMPLEX)
352: wi[k] = wi[k+1] = 0.0;
353: #endif
354: } else { /* Complex eigenvalues */
355: #if !defined(PETSC_USE_COMPLEX)
356: wr[k] = wr1/scal1;
357: wr[k+1] = wr[k];
358: wi[k] = wi1/scal1;
359: wi[k+1] = -wi[k];
360: #else
361: wr[k] = PetscCMPLX(wr1,wi1)/scal1;
362: wr[k+1] = PetscConj(wr[k]);
363: #endif
364: }
365: k++;
366: }
367: }
368: #if defined(PETSC_USE_COMPLEX)
369: if (wi) {
370: for (k=n0;k<n1;k++) wi[k] = 0.0;
371: }
372: #endif
373: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
374: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
375: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
376: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
377: PetscFunctionReturn(PETSC_SUCCESS);
378: }
380: static PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
381: {
382: PetscInt n,i,*perm;
383: PetscReal *d,*e,*s;
385: PetscFunctionBegin;
386: #if !defined(PETSC_USE_COMPLEX)
387: PetscAssertPointer(wi,3);
388: #endif
389: n = ds->n;
390: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
391: e = d + ds->ld;
392: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
393: PetscCall(DSAllocateWork_Private(ds,ds->ld,ds->ld,0));
394: perm = ds->perm;
395: if (!rr) {
396: rr = wr;
397: ri = wi;
398: }
399: PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE));
400: if (!ds->compact) PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_TRUE));
401: PetscCall(PetscArraycpy(ds->work,wr,n));
402: for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
403: #if !defined(PETSC_USE_COMPLEX)
404: PetscCall(PetscArraycpy(ds->work,wi,n));
405: for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
406: #endif
407: PetscCall(PetscArraycpy(ds->rwork,s,n));
408: for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
409: PetscCall(PetscArraycpy(ds->rwork,d,n));
410: for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
411: PetscCall(PetscArraycpy(ds->rwork,e,n-1));
412: PetscCall(PetscArrayzero(e+ds->l,n-1-ds->l));
413: for (i=ds->l;i<n-1;i++) {
414: if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
415: }
416: if (!ds->compact) PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
417: PetscCall(DSPermuteColumns_Private(ds,ds->l,n,n,DS_MAT_Q,perm));
418: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
419: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
420: PetscFunctionReturn(PETSC_SUCCESS);
421: }
423: static PetscErrorCode DSUpdateExtraRow_GHIEP(DS ds)
424: {
425: PetscInt i;
426: PetscBLASInt n,ld,incx=1;
427: PetscScalar *A,*x,*y,one=1.0,zero=0.0;
428: const PetscScalar *Q;
429: PetscReal *T,*b,*r,beta;
431: PetscFunctionBegin;
432: PetscCall(PetscBLASIntCast(ds->n,&n));
433: PetscCall(PetscBLASIntCast(ds->ld,&ld));
434: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
435: if (ds->compact) {
436: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
437: b = T+ld;
438: r = T+2*ld;
439: beta = b[n-1]; /* in compact, we assume all entries are zero except the last one */
440: for (i=0;i<n;i++) r[i] = PetscRealPart(beta*Q[n-1+i*ld]);
441: ds->k = n;
442: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
443: } else {
444: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
445: PetscCall(DSAllocateWork_Private(ds,2*ld,0,0));
446: x = ds->work;
447: y = ds->work+ld;
448: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
449: PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
450: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
451: ds->k = n;
452: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
453: }
454: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
455: PetscFunctionReturn(PETSC_SUCCESS);
456: }
458: /*
459: Get eigenvectors with inverse iteration.
460: The system matrix is in Hessenberg form.
461: */
462: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
463: {
464: PetscInt i,off;
465: PetscBLASInt *select,*infoC,ld,n1,mout,info;
466: const PetscScalar *A,*B;
467: PetscScalar *H,*X;
468: PetscReal *s,*d,*e;
469: #if defined(PETSC_USE_COMPLEX)
470: PetscInt j;
471: #endif
473: PetscFunctionBegin;
474: PetscCall(PetscBLASIntCast(ds->ld,&ld));
475: PetscCall(PetscBLASIntCast(ds->n-ds->l,&n1));
476: PetscCall(DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld));
477: PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
478: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
479: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
480: PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&H));
481: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
482: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
483: e = d + ld;
484: select = ds->iwork;
485: infoC = ds->iwork + ld;
486: off = ds->l+ds->l*ld;
487: if (ds->compact) {
488: H[off] = d[ds->l]*s[ds->l];
489: H[off+ld] = e[ds->l]*s[ds->l];
490: for (i=ds->l+1;i<ds->n-1;i++) {
491: H[i+(i-1)*ld] = e[i-1]*s[i];
492: H[i+i*ld] = d[i]*s[i];
493: H[i+(i+1)*ld] = e[i]*s[i];
494: }
495: H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
496: H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
497: } else {
498: s[ds->l] = PetscRealPart(B[off]);
499: H[off] = A[off]*s[ds->l];
500: H[off+ld] = A[off+ld]*s[ds->l];
501: for (i=ds->l+1;i<ds->n-1;i++) {
502: s[i] = PetscRealPart(B[i+i*ld]);
503: H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
504: H[i+i*ld] = A[i+i*ld]*s[i];
505: H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
506: }
507: s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
508: H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
509: H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
510: }
511: PetscCall(DSAllocateMat_Private(ds,DS_MAT_X));
512: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
513: for (i=0;i<n1;i++) select[i] = 1;
514: #if !defined(PETSC_USE_COMPLEX)
515: PetscCallBLAS("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));
516: #else
517: PetscCallBLAS("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));
519: /* Separate real and imaginary part of complex eigenvectors */
520: for (j=ds->l;j<ds->n;j++) {
521: if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
522: for (i=ds->l;i<ds->n;i++) {
523: X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
524: X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
525: }
526: j++;
527: }
528: }
529: #endif
530: SlepcCheckLapackInfo("hsein",info);
531: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
532: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
533: PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&H));
534: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
535: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
536: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
537: PetscCall(DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE));
538: PetscFunctionReturn(PETSC_SUCCESS);
539: }
541: /*
542: Undo 2x2 blocks that have real eigenvalues.
543: */
544: PetscErrorCode DSGHIEPRealBlocks(DS ds)
545: {
546: PetscInt i;
547: PetscReal e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
548: PetscReal maxy,ep,scal1,scal2,snorm;
549: PetscReal *T,*D,b[4],M[4],wr1,wr2,wi;
550: PetscScalar *A,*B,*Q,Y[4],sone=1.0,szero=0.0;
551: PetscBLASInt m,two=2,ld;
552: PetscBool isreal;
554: PetscFunctionBegin;
555: PetscCall(PetscBLASIntCast(ds->ld,&ld));
556: PetscCall(PetscBLASIntCast(ds->n-ds->l,&m));
557: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
558: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
559: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
560: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
561: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
562: PetscCall(DSAllocateWork_Private(ds,2*m,0,0));
563: for (i=ds->l;i<ds->n-1;i++) {
564: e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
565: if (e != 0.0) { /* 2x2 block */
566: if (ds->compact) {
567: s1 = D[i];
568: d1 = T[i];
569: s2 = D[i+1];
570: d2 = T[i+1];
571: } else {
572: s1 = PetscRealPart(B[i*ld+i]);
573: d1 = PetscRealPart(A[i*ld+i]);
574: s2 = PetscRealPart(B[(i+1)*ld+i+1]);
575: d2 = PetscRealPart(A[(i+1)*ld+i+1]);
576: }
577: isreal = PETSC_FALSE;
578: if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
579: dd = d1-d2;
580: if (2*PetscAbsReal(e) <= dd) {
581: t = 2*e/dd;
582: t = t/(1 + PetscSqrtReal(1+t*t));
583: } else {
584: t = dd/(2*e);
585: ss = (t>=0)?1.0:-1.0;
586: t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
587: }
588: Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
589: Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
590: wr1 = d1+t*e; wr2 = d2-t*e;
591: ss1 = s1; ss2 = s2;
592: isreal = PETSC_TRUE;
593: } else {
594: ss1 = 1.0; ss2 = 1.0,
595: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
596: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
597: ep = LAPACKlamch_("S");
599: /* Compute eigenvalues of the block */
600: PetscCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
601: if (wi==0.0) { /* Real eigenvalues */
602: isreal = PETSC_TRUE;
603: PetscCheck(scal1>=ep && scal2>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
604: wr1 /= scal1;
605: wr2 /= scal2;
606: if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
607: Y[0] = wr1-s2*d2;
608: Y[1] = s2*e;
609: } else {
610: Y[0] = s1*e;
611: Y[1] = wr1-s1*d1;
612: }
613: /* normalize with a signature*/
614: maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
615: scal1 = PetscRealPart(Y[0])/maxy;
616: scal2 = PetscRealPart(Y[1])/maxy;
617: snorm = scal1*scal1*s1 + scal2*scal2*s2;
618: if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
619: snorm = maxy*PetscSqrtReal(snorm);
620: Y[0] = Y[0]/snorm;
621: Y[1] = Y[1]/snorm;
622: if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
623: Y[2] = wr2-s2*d2;
624: Y[3] = s2*e;
625: } else {
626: Y[2] = s1*e;
627: Y[3] = wr2-s1*d1;
628: }
629: maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
630: scal1 = PetscRealPart(Y[2])/maxy;
631: scal2 = PetscRealPart(Y[3])/maxy;
632: snorm = scal1*scal1*s1 + scal2*scal2*s2;
633: if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
634: snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
635: }
636: wr1 *= ss1; wr2 *= ss2;
637: }
638: if (isreal) {
639: if (ds->compact) {
640: D[i] = ss1;
641: T[i] = wr1;
642: D[i+1] = ss2;
643: T[i+1] = wr2;
644: T[ld+i] = 0.0;
645: } else {
646: B[i*ld+i] = ss1;
647: A[i*ld+i] = wr1;
648: B[(i+1)*ld+i+1] = ss2;
649: A[(i+1)*ld+i+1] = wr2;
650: A[(i+1)+ld*i] = 0.0;
651: A[i+ld*(i+1)] = 0.0;
652: }
653: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&two,&two,&sone,Q+ds->l+i*ld,&ld,Y,&two,&szero,ds->work,&m));
654: PetscCall(PetscArraycpy(Q+ds->l+i*ld,ds->work,m));
655: PetscCall(PetscArraycpy(Q+ds->l+(i+1)*ld,ds->work+m,m));
656: }
657: i++;
658: }
659: }
660: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
661: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
662: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
663: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
664: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
665: PetscFunctionReturn(PETSC_SUCCESS);
666: }
668: static PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
669: {
670: PetscInt i,off;
671: PetscBLASInt n1,ld,one=1,info,lwork;
672: const PetscScalar *A,*B;
673: PetscScalar *H,*Q;
674: PetscReal *d,*e,*s;
675: #if defined(PETSC_USE_COMPLEX)
676: PetscInt j;
677: #endif
679: PetscFunctionBegin;
680: #if !defined(PETSC_USE_COMPLEX)
681: PetscAssertPointer(wi,3);
682: #endif
683: PetscCall(PetscBLASIntCast(ds->n-ds->l,&n1));
684: PetscCall(PetscBLASIntCast(ds->ld,&ld));
685: off = ds->l + ds->l*ld;
686: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
687: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
688: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
689: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
690: e = d + ld;
691: #if defined(PETSC_USE_DEBUG)
692: /* Check signature */
693: for (i=0;i<ds->n;i++) {
694: PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
695: PetscCheck(de==1.0 || de==-1.0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal elements of the signature matrix must be 1 or -1");
696: }
697: #endif
699: /* Quick return if possible */
700: if (n1 == 1) {
701: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
702: for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
703: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
704: PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
705: if (!ds->compact) {
706: d[ds->l] = PetscRealPart(A[off]);
707: s[ds->l] = PetscRealPart(B[off]);
708: }
709: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
710: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
711: wr[ds->l] = d[ds->l]/s[ds->l];
712: if (wi) wi[ds->l] = 0.0;
713: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
714: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
715: PetscFunctionReturn(PETSC_SUCCESS);
716: }
718: PetscCall(DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2));
719: lwork = ld*ld;
721: /* Reduce to pseudotriadiagonal form */
722: PetscCall(DSIntermediate_GHIEP(ds));
724: /* Compute Eigenvalues (QR) */
725: PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
726: PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&H));
727: if (ds->compact) {
728: H[off] = d[ds->l]*s[ds->l];
729: H[off+ld] = e[ds->l]*s[ds->l];
730: for (i=ds->l+1;i<ds->n-1;i++) {
731: H[i+(i-1)*ld] = e[i-1]*s[i];
732: H[i+i*ld] = d[i]*s[i];
733: H[i+(i+1)*ld] = e[i]*s[i];
734: }
735: H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
736: H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
737: } else {
738: s[ds->l] = PetscRealPart(B[off]);
739: H[off] = A[off]*s[ds->l];
740: H[off+ld] = A[off+ld]*s[ds->l];
741: for (i=ds->l+1;i<ds->n-1;i++) {
742: s[i] = PetscRealPart(B[i+i*ld]);
743: H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
744: H[i+i*ld] = A[i+i*ld]*s[i];
745: H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
746: }
747: s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
748: H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
749: H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
750: }
752: #if !defined(PETSC_USE_COMPLEX)
753: PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
754: #else
755: PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
756: for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
757: /* Sort to have consecutive conjugate pairs */
758: for (i=ds->l;i<ds->n;i++) {
759: j=i+1;
760: while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
761: if (j==ds->n) {
762: PetscCheck(PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON,PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
763: wr[i] = PetscRealPart(wr[i]);
764: } else { /* complex eigenvalue */
765: wr[j] = wr[i+1];
766: if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
767: wr[i+1] = PetscConj(wr[i]);
768: i++;
769: }
770: }
771: #endif
772: SlepcCheckLapackInfo("hseqr",info);
773: PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&H));
774: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
775: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
776: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
777: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
779: /* Compute Eigenvectors with Inverse Iteration */
780: PetscCall(DSGHIEPInverseIteration(ds,wr,wi));
782: /* Recover eigenvalues from diagonal */
783: PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
784: #if defined(PETSC_USE_COMPLEX)
785: if (wi) {
786: for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
787: }
788: #endif
789: PetscFunctionReturn(PETSC_SUCCESS);
790: }
792: static PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
793: {
794: PetscInt i,j,off,nwu=0,n,lw,lwr,nwru=0;
795: PetscBLASInt n_,ld,info,lwork,ilo,ihi;
796: const PetscScalar *A,*B;
797: PetscScalar *H,*Q,*X;
798: PetscReal *d,*s,*scale,nrm,*rcde,*rcdv;
799: #if defined(PETSC_USE_COMPLEX)
800: PetscInt k;
801: #endif
803: PetscFunctionBegin;
804: #if !defined(PETSC_USE_COMPLEX)
805: PetscAssertPointer(wi,3);
806: #endif
807: n = ds->n-ds->l;
808: PetscCall(PetscBLASIntCast(n,&n_));
809: PetscCall(PetscBLASIntCast(ds->ld,&ld));
810: off = ds->l + ds->l*ld;
811: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
812: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
813: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
814: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
815: #if defined(PETSC_USE_DEBUG)
816: /* Check signature */
817: for (i=0;i<ds->n;i++) {
818: PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
819: PetscCheck(de==1.0 || de==-1.0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal elements of the signature matrix must be 1 or -1");
820: }
821: #endif
823: /* Quick return if possible */
824: if (n_ == 1) {
825: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
826: for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
827: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
828: PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
829: if (!ds->compact) {
830: d[ds->l] = PetscRealPart(A[off]);
831: s[ds->l] = PetscRealPart(B[off]);
832: }
833: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
834: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
835: wr[ds->l] = d[ds->l]/s[ds->l];
836: if (wi) wi[ds->l] = 0.0;
837: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
838: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
839: PetscFunctionReturn(PETSC_SUCCESS);
840: }
842: lw = 14*ld+ld*ld;
843: lwr = 7*ld;
844: PetscCall(DSAllocateWork_Private(ds,lw,lwr,0));
845: scale = ds->rwork+nwru;
846: nwru += ld;
847: rcde = ds->rwork+nwru;
848: nwru += ld;
849: rcdv = ds->rwork+nwru;
851: /* Form pseudo-symmetric matrix */
852: H = ds->work+nwu;
853: nwu += n*n;
854: PetscCall(PetscArrayzero(H,n*n));
855: if (ds->compact) {
856: for (i=0;i<n-1;i++) {
857: H[i+i*n] = s[ds->l+i]*d[ds->l+i];
858: H[i+1+i*n] = s[ds->l+i+1]*d[ld+ds->l+i];
859: H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
860: }
861: H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
862: for (i=0;i<ds->k-ds->l;i++) {
863: H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
864: H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
865: }
866: } else {
867: for (j=0;j<n;j++) {
868: for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
869: }
870: }
872: /* Compute eigenpairs */
873: PetscCall(PetscBLASIntCast(lw-nwu,&lwork));
874: PetscCall(DSAllocateMat_Private(ds,DS_MAT_X));
875: PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_X],&X));
876: #if !defined(PETSC_USE_COMPLEX)
877: PetscCallBLAS("LAPACKgeevx",LAPACKgeevx_("B","N","V","N",&n_,H,&n_,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&ilo,&ihi,scale,&nrm,rcde,rcdv,ds->work+nwu,&lwork,NULL,&info));
878: #else
879: PetscCallBLAS("LAPACKgeevx",LAPACKgeevx_("B","N","V","N",&n_,H,&n_,wr+ds->l,NULL,&ld,X+off,&ld,&ilo,&ihi,scale,&nrm,rcde,rcdv,ds->work+nwu,&lwork,ds->rwork+nwru,&info));
881: /* Sort to have consecutive conjugate pairs
882: Separate real and imaginary part of complex eigenvectors*/
883: for (i=ds->l;i<ds->n;i++) {
884: j=i+1;
885: while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
886: if (j==ds->n) {
887: PetscCheck(PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON,PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
888: wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
889: for (k=ds->l;k<ds->n;k++) {
890: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
891: }
892: } else { /* complex eigenvalue */
893: if (j!=i+1) {
894: wr[j] = wr[i+1];
895: PetscCall(PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld));
896: }
897: if (PetscImaginaryPart(wr[i])<0) {
898: wr[i] = PetscConj(wr[i]);
899: for (k=ds->l;k<ds->n;k++) {
900: X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
901: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
902: }
903: } else {
904: for (k=ds->l;k<ds->n;k++) {
905: X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
906: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
907: }
908: }
909: wr[i+1] = PetscConj(wr[i]);
910: i++;
911: }
912: }
913: #endif
914: SlepcCheckLapackInfo("geevx",info);
915: PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_X],&X));
916: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
917: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
918: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
919: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
921: /* Compute real s-orthonormal basis */
922: PetscCall(DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_FALSE));
924: /* Recover eigenvalues from diagonal */
925: PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
926: #if defined(PETSC_USE_COMPLEX)
927: if (wi) {
928: for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
929: }
930: #endif
931: PetscFunctionReturn(PETSC_SUCCESS);
932: }
934: static PetscErrorCode DSGetTruncateSize_GHIEP(DS ds,PetscInt l,PetscInt n,PetscInt *k)
935: {
936: PetscReal *T;
938: PetscFunctionBegin;
939: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
940: if (T[l+(*k)-1+ds->ld] !=0.0) {
941: if (l+(*k)<n-1) (*k)++;
942: else (*k)--;
943: }
944: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
945: PetscFunctionReturn(PETSC_SUCCESS);
946: }
948: static PetscErrorCode DSTruncate_GHIEP(DS ds,PetscInt n,PetscBool trim)
949: {
950: PetscInt i,ld=ds->ld,l=ds->l;
951: PetscScalar *A;
952: PetscReal *T,*b,*r,*omega;
954: PetscFunctionBegin;
955: if (ds->compact) {
956: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
957: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&omega));
958: #if defined(PETSC_USE_DEBUG)
959: /* make sure diagonal 2x2 block is not broken */
960: PetscCheck(ds->state<DS_STATE_CONDENSED || n==0 || n==ds->n || T[n-1+ld]==0.0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
961: #endif
962: }
963: if (trim) {
964: if (!ds->compact && ds->extrarow) { /* clean extra row */
965: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
966: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
967: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
968: }
969: ds->l = 0;
970: ds->k = 0;
971: ds->n = n;
972: ds->t = ds->n; /* truncated length equal to the new dimension */
973: } else {
974: if (!ds->compact && ds->extrarow && ds->k==ds->n) {
975: /* copy entries of extra row to the new position, then clean last row */
976: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
977: for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
978: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
979: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
980: }
981: if (ds->compact) {
982: b = T+ld;
983: r = T+2*ld;
984: b[n-1] = r[n-1];
985: b[n] = b[ds->n];
986: omega[n] = omega[ds->n];
987: }
988: ds->k = (ds->extrarow)? n: 0;
989: ds->t = ds->n; /* truncated length equal to previous dimension */
990: ds->n = n;
991: }
992: if (ds->compact) {
993: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
994: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&omega));
995: }
996: PetscFunctionReturn(PETSC_SUCCESS);
997: }
999: #if !defined(PETSC_HAVE_MPIUNI)
1000: static PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
1001: {
1002: PetscScalar *A,*B,*Q;
1003: PetscReal *T,*D;
1004: PetscInt ld=ds->ld,l=ds->l,k=0,kr=0;
1005: PetscMPIInt n,rank,off=0,size,ldn,ld3,ld_;
1007: PetscFunctionBegin;
1008: if (ds->compact) kr = 4*ld;
1009: else k = 2*(ds->n-l)*ld;
1010: if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
1011: if (eigr) k += (ds->n-l);
1012: if (eigi) k += (ds->n-l);
1013: PetscCall(DSAllocateWork_Private(ds,k+kr,0,0));
1014: PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size));
1015: PetscCall(PetscMPIIntCast(ds->n-l,&n));
1016: PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
1017: PetscCall(PetscMPIIntCast(ld*3,&ld3));
1018: PetscCall(PetscMPIIntCast(ld,&ld_));
1019: if (ds->compact) {
1020: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
1021: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
1022: } else {
1023: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
1024: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
1025: }
1026: if (ds->state>DS_STATE_RAW) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
1027: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
1028: if (!rank) {
1029: if (ds->compact) {
1030: PetscCallMPI(MPI_Pack(T,ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1031: PetscCallMPI(MPI_Pack(D,ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1032: } else {
1033: PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1034: PetscCallMPI(MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1035: }
1036: if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1037: if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1038: #if !defined(PETSC_USE_COMPLEX)
1039: if (eigi) PetscCallMPI(MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1040: #endif
1041: }
1042: PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
1043: if (rank) {
1044: if (ds->compact) {
1045: PetscCallMPI(MPI_Unpack(ds->work,size,&off,T,ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
1046: PetscCallMPI(MPI_Unpack(ds->work,size,&off,D,ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
1047: } else {
1048: PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1049: PetscCallMPI(MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1050: }
1051: if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1052: if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1053: #if !defined(PETSC_USE_COMPLEX)
1054: if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1055: #endif
1056: }
1057: if (ds->compact) {
1058: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
1059: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
1060: } else {
1061: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
1062: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
1063: }
1064: if (ds->state>DS_STATE_RAW) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
1065: PetscFunctionReturn(PETSC_SUCCESS);
1066: }
1067: #endif
1069: static PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
1070: {
1071: PetscFunctionBegin;
1072: if ((m==DS_MAT_A && !ds->extrarow) || m==DS_MAT_B) *flg = PETSC_TRUE;
1073: else *flg = PETSC_FALSE;
1074: PetscFunctionReturn(PETSC_SUCCESS);
1075: }
1077: /*MC
1078: DSGHIEP - Dense Generalized Hermitian Indefinite Eigenvalue Problem.
1080: Level: beginner
1082: Notes:
1083: The problem is expressed as A*X = B*X*Lambda, where both A and B are
1084: real symmetric (or complex Hermitian) and possibly indefinite. Lambda
1085: is a diagonal matrix whose diagonal elements are the arguments of DSSolve().
1086: After solve, A is overwritten with Lambda. Note that in the case of real
1087: scalars, A is overwritten with a real representation of Lambda, i.e.,
1088: complex conjugate eigenvalue pairs are stored as a 2x2 block in the
1089: quasi-diagonal matrix.
1091: In the intermediate state A is reduced to tridiagonal form and B is
1092: transformed into a signature matrix. In compact storage format, these
1093: matrices are stored in T and D, respectively.
1095: Used DS matrices:
1096: + DS_MAT_A - first problem matrix
1097: . DS_MAT_B - second problem matrix
1098: . DS_MAT_T - symmetric tridiagonal matrix of the reduced pencil
1099: . DS_MAT_D - diagonal matrix (signature) of the reduced pencil
1100: - DS_MAT_Q - pseudo-orthogonal transformation that reduces (A,B) to
1101: tridiagonal-diagonal form (intermediate step) or a real basis of eigenvectors
1103: Implemented methods:
1104: + 0 - QR iteration plus inverse iteration for the eigenvectors
1105: . 1 - HZ iteration
1106: - 2 - QR iteration plus pseudo-orthogonalization for the eigenvectors
1108: References:
1109: . 1. - C. Campos and J. E. Roman, "Restarted Q-Arnoldi-type methods exploiting
1110: symmetry in quadratic eigenvalue problems", BIT Numer. Math. 56(4):1213-1236, 2016.
1112: .seealso: DSCreate(), DSSetType(), DSType
1113: M*/
1114: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
1115: {
1116: PetscFunctionBegin;
1117: ds->ops->allocate = DSAllocate_GHIEP;
1118: ds->ops->view = DSView_GHIEP;
1119: ds->ops->vectors = DSVectors_GHIEP;
1120: ds->ops->solve[0] = DSSolve_GHIEP_QR_II;
1121: ds->ops->solve[1] = DSSolve_GHIEP_HZ;
1122: ds->ops->solve[2] = DSSolve_GHIEP_QR;
1123: ds->ops->sort = DSSort_GHIEP;
1124: #if !defined(PETSC_HAVE_MPIUNI)
1125: ds->ops->synchronize = DSSynchronize_GHIEP;
1126: #endif
1127: ds->ops->gettruncatesize = DSGetTruncateSize_GHIEP;
1128: ds->ops->truncate = DSTruncate_GHIEP;
1129: ds->ops->update = DSUpdateExtraRow_GHIEP;
1130: ds->ops->hermitian = DSHermitian_GHIEP;
1131: PetscFunctionReturn(PETSC_SUCCESS);
1132: }