Actual source code: dsghiep.c
slepc-3.17.2 2022-08-09
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: PetscErrorCode DSAllocate_GHIEP(DS ds,PetscInt ld)
15: {
16: DSAllocateMat_Private(ds,DS_MAT_A);
17: DSAllocateMat_Private(ds,DS_MAT_B);
18: DSAllocateMat_Private(ds,DS_MAT_Q);
19: DSAllocateMatReal_Private(ds,DS_MAT_T);
20: DSAllocateMatReal_Private(ds,DS_MAT_D);
21: PetscFree(ds->perm);
22: PetscMalloc1(ld,&ds->perm);
23: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
24: PetscFunctionReturn(0);
25: }
27: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
28: {
29: PetscReal *T,*S;
30: PetscScalar *A,*B;
31: PetscInt i,n,ld;
33: A = ds->mat[DS_MAT_A];
34: B = ds->mat[DS_MAT_B];
35: T = ds->rmat[DS_MAT_T];
36: S = ds->rmat[DS_MAT_D];
37: n = ds->n;
38: ld = ds->ld;
39: if (tocompact) { /* switch from dense (arrow) to compact storage */
40: PetscArrayzero(T,n);
41: PetscArrayzero(T+ld,n);
42: PetscArrayzero(T+2*ld,n);
43: PetscArrayzero(S,n);
44: for (i=0;i<n-1;i++) {
45: T[i] = PetscRealPart(A[i+i*ld]);
46: T[ld+i] = PetscRealPart(A[i+1+i*ld]);
47: S[i] = PetscRealPart(B[i+i*ld]);
48: }
49: T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
50: S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
51: for (i=ds->l;i<ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
52: } else { /* switch from compact (arrow) to dense storage */
53: for (i=0;i<n;i++) {
54: PetscArrayzero(A+i*ld,n);
55: PetscArrayzero(B+i*ld,n);
56: }
57: for (i=0;i<n-1;i++) {
58: A[i+i*ld] = T[i];
59: A[i+1+i*ld] = T[ld+i];
60: A[i+(i+1)*ld] = T[ld+i];
61: B[i+i*ld] = S[i];
62: }
63: A[n-1+(n-1)*ld] = T[n-1];
64: B[n-1+(n-1)*ld] = S[n-1];
65: for (i=ds->l;i<ds->k;i++) {
66: A[ds->k+i*ld] = T[2*ld+i];
67: A[i+ds->k*ld] = T[2*ld+i];
68: }
69: }
70: PetscFunctionReturn(0);
71: }
73: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
74: {
75: PetscViewerFormat format;
76: PetscInt i,j;
77: PetscReal value;
78: const char *methodname[] = {
79: "QR + Inverse Iteration",
80: "HZ method",
81: "QR"
82: };
83: const int nmeth=sizeof(methodname)/sizeof(methodname[0]);
85: PetscViewerGetFormat(viewer,&format);
86: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
87: if (ds->method<nmeth) PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
88: PetscFunctionReturn(0);
89: }
90: if (ds->compact) {
91: PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
92: if (format == PETSC_VIEWER_ASCII_MATLAB) {
93: PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n);
94: PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",3*ds->n);
95: PetscViewerASCIIPrintf(viewer,"zzz = [\n");
96: for (i=0;i<ds->n;i++) PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
97: for (i=0;i<ds->n-1;i++) {
98: if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
99: PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+2,i+1,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
100: PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+2,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
101: }
102: }
103: for (i = ds->l;i<ds->k;i++) {
104: if (*(ds->rmat[DS_MAT_T]+2*ds->ld+i)) {
105: PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",ds->k+1,i+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
106: PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,ds->k+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
107: }
108: }
109: PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);
111: PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n);
112: PetscViewerASCIIPrintf(viewer,"omega = zeros(%" PetscInt_FMT ",3);\n",3*ds->n);
113: PetscViewerASCIIPrintf(viewer,"omega = [\n");
114: for (i=0;i<ds->n;i++) PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_D]+i));
115: PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);
117: } else {
118: PetscViewerASCIIPrintf(viewer,"T\n");
119: for (i=0;i<ds->n;i++) {
120: for (j=0;j<ds->n;j++) {
121: if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
122: else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
123: 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));
124: else value = 0.0;
125: PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
126: }
127: PetscViewerASCIIPrintf(viewer,"\n");
128: }
129: PetscViewerASCIIPrintf(viewer,"omega\n");
130: for (i=0;i<ds->n;i++) {
131: for (j=0;j<ds->n;j++) {
132: if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
133: else value = 0.0;
134: PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
135: }
136: PetscViewerASCIIPrintf(viewer,"\n");
137: }
138: }
139: PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
140: PetscViewerFlush(viewer);
141: } else {
142: DSViewMat(ds,viewer,DS_MAT_A);
143: DSViewMat(ds,viewer,DS_MAT_B);
144: }
145: if (ds->state>DS_STATE_INTERMEDIATE) DSViewMat(ds,viewer,DS_MAT_Q);
146: PetscFunctionReturn(0);
147: }
149: static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
150: {
151: PetscReal b[4],M[4],d1,d2,s1,s2,e;
152: PetscReal scal1,scal2,wr1,wr2,wi,ep,norm;
153: PetscScalar *Q,*X,Y[4],alpha,zeroS = 0.0;
154: PetscInt k;
155: PetscBLASInt two = 2,n_,ld,one=1;
156: #if !defined(PETSC_USE_COMPLEX)
157: PetscBLASInt four=4;
158: #endif
160: X = ds->mat[DS_MAT_X];
161: Q = ds->mat[DS_MAT_Q];
162: k = *idx;
163: PetscBLASIntCast(ds->n,&n_);
164: PetscBLASIntCast(ds->ld,&ld);
165: if (k < ds->n-1) e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ld+k):PetscRealPart(*(ds->mat[DS_MAT_A]+(k+1)+ld*k));
166: else e = 0.0;
167: if (e == 0.0) { /* Real */
168: if (ds->state>=DS_STATE_CONDENSED) PetscArraycpy(X+k*ld,Q+k*ld,ld);
169: else {
170: PetscArrayzero(X+k*ds->ld,ds->ld);
171: X[k+k*ds->ld] = 1.0;
172: }
173: if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
174: } else { /* 2x2 block */
175: if (ds->compact) {
176: s1 = *(ds->rmat[DS_MAT_D]+k);
177: d1 = *(ds->rmat[DS_MAT_T]+k);
178: s2 = *(ds->rmat[DS_MAT_D]+k+1);
179: d2 = *(ds->rmat[DS_MAT_T]+k+1);
180: } else {
181: s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
182: d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
183: s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
184: d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
185: }
186: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
187: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
188: ep = LAPACKlamch_("S");
189: /* Compute eigenvalues of the block */
190: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
192: /* Complex eigenvalues */
194: wr1 /= scal1;
195: wi /= scal1;
196: #if !defined(PETSC_USE_COMPLEX)
197: if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
198: Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
199: } else {
200: Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
201: }
202: norm = BLASnrm2_(&four,Y,&one);
203: norm = 1.0/norm;
204: if (ds->state >= DS_STATE_CONDENSED) {
205: alpha = norm;
206: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
207: if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
208: } else {
209: PetscArrayzero(X+k*ld,2*ld);
210: X[k*ld+k] = Y[0]*norm;
211: X[k*ld+k+1] = Y[1]*norm;
212: X[(k+1)*ld+k] = Y[2]*norm;
213: X[(k+1)*ld+k+1] = Y[3]*norm;
214: }
215: #else
216: if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
217: Y[0] = PetscCMPLX(wr1-s2*d2,wi);
218: Y[1] = s2*e;
219: } else {
220: Y[0] = s1*e;
221: Y[1] = PetscCMPLX(wr1-s1*d1,wi);
222: }
223: norm = BLASnrm2_(&two,Y,&one);
224: norm = 1.0/norm;
225: if (ds->state >= DS_STATE_CONDENSED) {
226: alpha = norm;
227: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
228: if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
229: } else {
230: PetscArrayzero(X+k*ld,2*ld);
231: X[k*ld+k] = Y[0]*norm;
232: X[k*ld+k+1] = Y[1]*norm;
233: }
234: X[(k+1)*ld+k] = PetscConj(X[k*ld+k]);
235: X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
236: #endif
237: (*idx)++;
238: }
239: PetscFunctionReturn(0);
240: }
242: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
243: {
244: PetscInt i;
245: PetscReal e;
247: switch (mat) {
248: case DS_MAT_X:
249: case DS_MAT_Y:
250: if (k) DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
251: else {
252: for (i=0; i<ds->n; i++) {
253: e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
254: if (e == 0.0) { /* real */
255: if (ds->state >= DS_STATE_CONDENSED) PetscArraycpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld);
256: else {
257: PetscArrayzero(ds->mat[mat]+i*ds->ld,ds->ld);
258: *(ds->mat[mat]+i+i*ds->ld) = 1.0;
259: }
260: } else DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
261: }
262: }
263: break;
264: case DS_MAT_U:
265: case DS_MAT_V:
266: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
267: default:
268: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
269: }
270: PetscFunctionReturn(0);
271: }
273: /*
274: Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
275: Only the index range n0..n1 is processed.
276: */
277: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
278: {
279: PetscInt k,ld;
280: PetscBLASInt two=2;
281: PetscScalar *A,*B;
282: PetscReal *D,*T;
283: PetscReal b[4],M[4],d1,d2,s1,s2,e;
284: PetscReal scal1,scal2,ep,wr1,wr2,wi1;
286: ld = ds->ld;
287: A = ds->mat[DS_MAT_A];
288: B = ds->mat[DS_MAT_B];
289: D = ds->rmat[DS_MAT_D];
290: T = ds->rmat[DS_MAT_T];
291: for (k=n0;k<n1;k++) {
292: if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
293: else e = 0.0;
294: if (e==0.0) { /* real eigenvalue */
295: wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
296: #if !defined(PETSC_USE_COMPLEX)
297: wi[k] = 0.0 ;
298: #endif
299: } else { /* diagonal block */
300: if (ds->compact) {
301: s1 = D[k];
302: d1 = T[k];
303: s2 = D[k+1];
304: d2 = T[k+1];
305: } else {
306: s1 = PetscRealPart(B[k*ld+k]);
307: d1 = PetscRealPart(A[k+k*ld]);
308: s2 = PetscRealPart(B[(k+1)*ld+k+1]);
309: d2 = PetscRealPart(A[k+1+(k+1)*ld]);
310: }
311: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
312: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
313: ep = LAPACKlamch_("S");
314: /* Compute eigenvalues of the block */
315: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
317: if (wi1==0.0) { /* Real eigenvalues */
319: wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
320: #if !defined(PETSC_USE_COMPLEX)
321: wi[k] = wi[k+1] = 0.0;
322: #endif
323: } else { /* Complex eigenvalues */
324: #if !defined(PETSC_USE_COMPLEX)
325: wr[k] = wr1/scal1;
326: wr[k+1] = wr[k];
327: wi[k] = wi1/scal1;
328: wi[k+1] = -wi[k];
329: #else
330: wr[k] = PetscCMPLX(wr1,wi1)/scal1;
331: wr[k+1] = PetscConj(wr[k]);
332: #endif
333: }
334: k++;
335: }
336: }
337: #if defined(PETSC_USE_COMPLEX)
338: if (wi) {
339: for (k=n0;k<n1;k++) wi[k] = 0.0;
340: }
341: #endif
342: PetscFunctionReturn(0);
343: }
345: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
346: {
347: PetscInt n,i,*perm;
348: PetscReal *d,*e,*s;
350: #if !defined(PETSC_USE_COMPLEX)
352: #endif
353: n = ds->n;
354: d = ds->rmat[DS_MAT_T];
355: e = d + ds->ld;
356: s = ds->rmat[DS_MAT_D];
357: DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
358: perm = ds->perm;
359: if (!rr) {
360: rr = wr;
361: ri = wi;
362: }
363: DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
364: if (!ds->compact) DSSwitchFormat_GHIEP(ds,PETSC_TRUE);
365: PetscArraycpy(ds->work,wr,n);
366: for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
367: #if !defined(PETSC_USE_COMPLEX)
368: PetscArraycpy(ds->work,wi,n);
369: for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
370: #endif
371: PetscArraycpy(ds->rwork,s,n);
372: for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
373: PetscArraycpy(ds->rwork,d,n);
374: for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
375: PetscArraycpy(ds->rwork,e,n-1);
376: PetscArrayzero(e+ds->l,n-1-ds->l);
377: for (i=ds->l;i<n-1;i++) {
378: if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
379: }
380: if (!ds->compact) DSSwitchFormat_GHIEP(ds,PETSC_FALSE);
381: DSPermuteColumns_Private(ds,ds->l,n,n,DS_MAT_Q,perm);
382: PetscFunctionReturn(0);
383: }
385: PetscErrorCode DSUpdateExtraRow_GHIEP(DS ds)
386: {
387: PetscInt i;
388: PetscBLASInt n,ld,incx=1;
389: PetscScalar *A,*Q,*x,*y,one=1.0,zero=0.0;
390: PetscReal *b,*r,beta;
392: PetscBLASIntCast(ds->n,&n);
393: PetscBLASIntCast(ds->ld,&ld);
394: A = ds->mat[DS_MAT_A];
395: Q = ds->mat[DS_MAT_Q];
396: b = ds->rmat[DS_MAT_T]+ld;
397: r = ds->rmat[DS_MAT_T]+2*ld;
399: if (ds->compact) {
400: beta = b[n-1]; /* in compact, we assume all entries are zero except the last one */
401: for (i=0;i<n;i++) r[i] = PetscRealPart(beta*Q[n-1+i*ld]);
402: ds->k = n;
403: } else {
404: DSAllocateWork_Private(ds,2*ld,0,0);
405: x = ds->work;
406: y = ds->work+ld;
407: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
408: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
409: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
410: ds->k = n;
411: }
412: PetscFunctionReturn(0);
413: }
415: /*
416: Get eigenvectors with inverse iteration.
417: The system matrix is in Hessenberg form.
418: */
419: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
420: {
421: PetscInt i,off;
422: PetscBLASInt *select,*infoC,ld,n1,mout,info;
423: PetscScalar *A,*B,*H,*X;
424: PetscReal *s,*d,*e;
425: #if defined(PETSC_USE_COMPLEX)
426: PetscInt j;
427: #endif
429: PetscBLASIntCast(ds->ld,&ld);
430: PetscBLASIntCast(ds->n-ds->l,&n1);
431: DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
432: DSAllocateMat_Private(ds,DS_MAT_W);
433: A = ds->mat[DS_MAT_A];
434: B = ds->mat[DS_MAT_B];
435: H = ds->mat[DS_MAT_W];
436: s = ds->rmat[DS_MAT_D];
437: d = ds->rmat[DS_MAT_T];
438: e = d + ld;
439: select = ds->iwork;
440: infoC = ds->iwork + ld;
441: off = ds->l+ds->l*ld;
442: if (ds->compact) {
443: H[off] = d[ds->l]*s[ds->l];
444: H[off+ld] = e[ds->l]*s[ds->l];
445: for (i=ds->l+1;i<ds->n-1;i++) {
446: H[i+(i-1)*ld] = e[i-1]*s[i];
447: H[i+i*ld] = d[i]*s[i];
448: H[i+(i+1)*ld] = e[i]*s[i];
449: }
450: H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
451: H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
452: } else {
453: s[ds->l] = PetscRealPart(B[off]);
454: H[off] = A[off]*s[ds->l];
455: H[off+ld] = A[off+ld]*s[ds->l];
456: for (i=ds->l+1;i<ds->n-1;i++) {
457: s[i] = PetscRealPart(B[i+i*ld]);
458: H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
459: H[i+i*ld] = A[i+i*ld]*s[i];
460: H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
461: }
462: s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
463: H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
464: H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
465: }
466: DSAllocateMat_Private(ds,DS_MAT_X);
467: X = ds->mat[DS_MAT_X];
468: for (i=0;i<n1;i++) select[i] = 1;
469: #if !defined(PETSC_USE_COMPLEX)
470: 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));
471: #else
472: 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));
474: /* Separate real and imaginary part of complex eigenvectors */
475: for (j=ds->l;j<ds->n;j++) {
476: if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
477: for (i=ds->l;i<ds->n;i++) {
478: X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
479: X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
480: }
481: j++;
482: }
483: }
484: #endif
485: SlepcCheckLapackInfo("hsein",info);
486: DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
487: PetscFunctionReturn(0);
488: }
490: /*
491: Undo 2x2 blocks that have real eigenvalues.
492: */
493: PetscErrorCode DSGHIEPRealBlocks(DS ds)
494: {
495: PetscInt i;
496: PetscReal e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
497: PetscReal maxy,ep,scal1,scal2,snorm;
498: PetscReal *T,*D,b[4],M[4],wr1,wr2,wi;
499: PetscScalar *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
500: PetscBLASInt m,two=2,ld;
501: PetscBool isreal;
503: PetscBLASIntCast(ds->ld,&ld);
504: PetscBLASIntCast(ds->n-ds->l,&m);
505: A = ds->mat[DS_MAT_A];
506: B = ds->mat[DS_MAT_B];
507: T = ds->rmat[DS_MAT_T];
508: D = ds->rmat[DS_MAT_D];
509: DSAllocateWork_Private(ds,2*m,0,0);
510: for (i=ds->l;i<ds->n-1;i++) {
511: e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
512: if (e != 0.0) { /* 2x2 block */
513: if (ds->compact) {
514: s1 = D[i];
515: d1 = T[i];
516: s2 = D[i+1];
517: d2 = T[i+1];
518: } else {
519: s1 = PetscRealPart(B[i*ld+i]);
520: d1 = PetscRealPart(A[i*ld+i]);
521: s2 = PetscRealPart(B[(i+1)*ld+i+1]);
522: d2 = PetscRealPart(A[(i+1)*ld+i+1]);
523: }
524: isreal = PETSC_FALSE;
525: if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
526: dd = d1-d2;
527: if (2*PetscAbsReal(e) <= dd) {
528: t = 2*e/dd;
529: t = t/(1 + PetscSqrtReal(1+t*t));
530: } else {
531: t = dd/(2*e);
532: ss = (t>=0)?1.0:-1.0;
533: t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
534: }
535: Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
536: Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
537: wr1 = d1+t*e; wr2 = d2-t*e;
538: ss1 = s1; ss2 = s2;
539: isreal = PETSC_TRUE;
540: } else {
541: ss1 = 1.0; ss2 = 1.0,
542: M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
543: b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
544: ep = LAPACKlamch_("S");
546: /* Compute eigenvalues of the block */
547: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
548: if (wi==0.0) { /* Real eigenvalues */
549: isreal = PETSC_TRUE;
551: wr1 /= scal1;
552: wr2 /= scal2;
553: if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
554: Y[0] = wr1-s2*d2;
555: Y[1] = s2*e;
556: } else {
557: Y[0] = s1*e;
558: Y[1] = wr1-s1*d1;
559: }
560: /* normalize with a signature*/
561: maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
562: scal1 = PetscRealPart(Y[0])/maxy;
563: scal2 = PetscRealPart(Y[1])/maxy;
564: snorm = scal1*scal1*s1 + scal2*scal2*s2;
565: if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
566: snorm = maxy*PetscSqrtReal(snorm);
567: Y[0] = Y[0]/snorm;
568: Y[1] = Y[1]/snorm;
569: if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
570: Y[2] = wr2-s2*d2;
571: Y[3] = s2*e;
572: } else {
573: Y[2] = s1*e;
574: Y[3] = wr2-s1*d1;
575: }
576: maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
577: scal1 = PetscRealPart(Y[2])/maxy;
578: scal2 = PetscRealPart(Y[3])/maxy;
579: snorm = scal1*scal1*s1 + scal2*scal2*s2;
580: if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
581: snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
582: }
583: wr1 *= ss1; wr2 *= ss2;
584: }
585: if (isreal) {
586: if (ds->compact) {
587: D[i] = ss1;
588: T[i] = wr1;
589: D[i+1] = ss2;
590: T[i+1] = wr2;
591: T[ld+i] = 0.0;
592: } else {
593: B[i*ld+i] = ss1;
594: A[i*ld+i] = wr1;
595: B[(i+1)*ld+i+1] = ss2;
596: A[(i+1)*ld+i+1] = wr2;
597: A[(i+1)+ld*i] = 0.0;
598: A[i+ld*(i+1)] = 0.0;
599: }
600: 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));
601: PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m);
602: PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m);
603: }
604: i++;
605: }
606: }
607: PetscFunctionReturn(0);
608: }
610: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
611: {
612: PetscInt i,off;
613: PetscBLASInt n1,ld,one,info,lwork;
614: PetscScalar *H,*A,*B,*Q;
615: PetscReal *d,*e,*s;
616: #if defined(PETSC_USE_COMPLEX)
617: PetscInt j;
618: #endif
620: #if !defined(PETSC_USE_COMPLEX)
622: #endif
623: one = 1;
624: PetscBLASIntCast(ds->n-ds->l,&n1);
625: PetscBLASIntCast(ds->ld,&ld);
626: off = ds->l + ds->l*ld;
627: A = ds->mat[DS_MAT_A];
628: B = ds->mat[DS_MAT_B];
629: Q = ds->mat[DS_MAT_Q];
630: d = ds->rmat[DS_MAT_T];
631: e = ds->rmat[DS_MAT_T] + ld;
632: s = ds->rmat[DS_MAT_D];
633: #if defined(PETSC_USE_DEBUG)
634: /* Check signature */
635: for (i=0;i<ds->n;i++) {
636: PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
638: }
639: #endif
640: DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
641: lwork = ld*ld;
643: /* Quick return if possible */
644: if (n1 == 1) {
645: for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
646: DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
647: if (!ds->compact) {
648: d[ds->l] = PetscRealPart(A[off]);
649: s[ds->l] = PetscRealPart(B[off]);
650: }
651: wr[ds->l] = d[ds->l]/s[ds->l];
652: if (wi) wi[ds->l] = 0.0;
653: PetscFunctionReturn(0);
654: }
655: /* Reduce to pseudotriadiagonal form */
656: DSIntermediate_GHIEP(ds);
658: /* Compute Eigenvalues (QR) */
659: DSAllocateMat_Private(ds,DS_MAT_W);
660: H = ds->mat[DS_MAT_W];
661: if (ds->compact) {
662: H[off] = d[ds->l]*s[ds->l];
663: H[off+ld] = e[ds->l]*s[ds->l];
664: for (i=ds->l+1;i<ds->n-1;i++) {
665: H[i+(i-1)*ld] = e[i-1]*s[i];
666: H[i+i*ld] = d[i]*s[i];
667: H[i+(i+1)*ld] = e[i]*s[i];
668: }
669: H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
670: H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
671: } else {
672: s[ds->l] = PetscRealPart(B[off]);
673: H[off] = A[off]*s[ds->l];
674: H[off+ld] = A[off+ld]*s[ds->l];
675: for (i=ds->l+1;i<ds->n-1;i++) {
676: s[i] = PetscRealPart(B[i+i*ld]);
677: H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
678: H[i+i*ld] = A[i+i*ld]*s[i];
679: H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
680: }
681: s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
682: H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
683: H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
684: }
686: #if !defined(PETSC_USE_COMPLEX)
687: PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
688: #else
689: PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
690: for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
691: /* Sort to have consecutive conjugate pairs */
692: for (i=ds->l;i<ds->n;i++) {
693: j=i+1;
694: while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
695: if (j==ds->n) {
697: wr[i]=PetscRealPart(wr[i]);
698: } else { /* complex eigenvalue */
699: wr[j] = wr[i+1];
700: if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
701: wr[i+1] = PetscConj(wr[i]);
702: i++;
703: }
704: }
705: #endif
706: SlepcCheckLapackInfo("hseqr",info);
707: /* Compute Eigenvectors with Inverse Iteration */
708: DSGHIEPInverseIteration(ds,wr,wi);
710: /* Recover eigenvalues from diagonal */
711: DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
712: #if defined(PETSC_USE_COMPLEX)
713: if (wi) {
714: for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
715: }
716: #endif
717: PetscFunctionReturn(0);
718: }
720: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
721: {
722: PetscInt i,j,off,nwu=0,n,lw,lwr,nwru=0;
723: PetscBLASInt n_,ld,info,lwork,ilo,ihi;
724: PetscScalar *H,*A,*B,*Q,*X;
725: PetscReal *d,*s,*scale,nrm,*rcde,*rcdv;
726: #if defined(PETSC_USE_COMPLEX)
727: PetscInt k;
728: #endif
730: #if !defined(PETSC_USE_COMPLEX)
732: #endif
733: n = ds->n-ds->l;
734: PetscBLASIntCast(n,&n_);
735: PetscBLASIntCast(ds->ld,&ld);
736: off = ds->l + ds->l*ld;
737: A = ds->mat[DS_MAT_A];
738: B = ds->mat[DS_MAT_B];
739: Q = ds->mat[DS_MAT_Q];
740: d = ds->rmat[DS_MAT_T];
741: s = ds->rmat[DS_MAT_D];
742: #if defined(PETSC_USE_DEBUG)
743: /* Check signature */
744: for (i=0;i<ds->n;i++) {
745: PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
747: }
748: #endif
749: lw = 14*ld+ld*ld;
750: lwr = 7*ld;
751: DSAllocateWork_Private(ds,lw,lwr,0);
752: scale = ds->rwork+nwru;
753: nwru += ld;
754: rcde = ds->rwork+nwru;
755: nwru += ld;
756: rcdv = ds->rwork+nwru;
757: /* Quick return if possible */
758: if (n_ == 1) {
759: for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
760: DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
761: if (!ds->compact) {
762: d[ds->l] = PetscRealPart(A[off]);
763: s[ds->l] = PetscRealPart(B[off]);
764: }
765: wr[ds->l] = d[ds->l]/s[ds->l];
766: if (wi) wi[ds->l] = 0.0;
767: PetscFunctionReturn(0);
768: }
770: /* Form pseudo-symmetric matrix */
771: H = ds->work+nwu;
772: nwu += n*n;
773: PetscArrayzero(H,n*n);
774: if (ds->compact) {
775: for (i=0;i<n-1;i++) {
776: H[i+i*n] = s[ds->l+i]*d[ds->l+i];
777: H[i+1+i*n] = s[ds->l+i+1]*d[ld+ds->l+i];
778: H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
779: }
780: H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
781: for (i=0;i<ds->k-ds->l;i++) {
782: H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
783: H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
784: }
785: } else {
786: for (j=0;j<n;j++) {
787: for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
788: }
789: }
791: /* Compute eigenpairs */
792: PetscBLASIntCast(lw-nwu,&lwork);
793: DSAllocateMat_Private(ds,DS_MAT_X);
794: X = ds->mat[DS_MAT_X];
795: #if !defined(PETSC_USE_COMPLEX)
796: PetscStackCallBLAS("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));
797: #else
798: PetscStackCallBLAS("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));
800: /* Sort to have consecutive conjugate pairs
801: Separate real and imaginary part of complex eigenvectors*/
802: for (i=ds->l;i<ds->n;i++) {
803: j=i+1;
804: while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
805: if (j==ds->n) {
807: wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
808: for (k=ds->l;k<ds->n;k++) {
809: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
810: }
811: } else { /* complex eigenvalue */
812: if (j!=i+1) {
813: wr[j] = wr[i+1];
814: PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld);
815: }
816: if (PetscImaginaryPart(wr[i])<0) {
817: wr[i] = PetscConj(wr[i]);
818: for (k=ds->l;k<ds->n;k++) {
819: X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
820: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
821: }
822: } else {
823: for (k=ds->l;k<ds->n;k++) {
824: X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
825: X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
826: }
827: }
828: wr[i+1] = PetscConj(wr[i]);
829: i++;
830: }
831: }
832: #endif
833: SlepcCheckLapackInfo("geevx",info);
835: /* Compute real s-orthonormal basis */
836: DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_FALSE);
838: /* Recover eigenvalues from diagonal */
839: DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
840: #if defined(PETSC_USE_COMPLEX)
841: if (wi) {
842: for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
843: }
844: #endif
845: PetscFunctionReturn(0);
846: }
848: PetscErrorCode DSGetTruncateSize_GHIEP(DS ds,PetscInt l,PetscInt n,PetscInt *k)
849: {
850: PetscReal *T = ds->rmat[DS_MAT_T];
852: if (T[l+(*k)-1+ds->ld] !=0.0) {
853: if (l+(*k)<n-1) (*k)++;
854: else (*k)--;
855: }
856: PetscFunctionReturn(0);
857: }
859: PetscErrorCode DSTruncate_GHIEP(DS ds,PetscInt n,PetscBool trim)
860: {
861: PetscInt i,ld=ds->ld,l=ds->l;
862: PetscScalar *A = ds->mat[DS_MAT_A];
863: PetscReal *T = ds->rmat[DS_MAT_T],*b,*r,*omega;
865: #if defined(PETSC_USE_DEBUG)
866: /* make sure diagonal 2x2 block is not broken */
868: #endif
869: if (trim) {
870: if (!ds->compact && ds->extrarow) { /* clean extra row */
871: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
872: }
873: ds->l = 0;
874: ds->k = 0;
875: ds->n = n;
876: ds->t = ds->n; /* truncated length equal to the new dimension */
877: } else {
878: if (!ds->compact && ds->extrarow && ds->k==ds->n) {
879: /* copy entries of extra row to the new position, then clean last row */
880: for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
881: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
882: }
883: if (ds->compact) {
884: b = T+ld;
885: r = T+2*ld;
886: omega = ds->rmat[DS_MAT_D];
887: b[n-1] = r[n-1];
888: b[n] = b[ds->n];
889: omega[n] = omega[ds->n];
890: }
891: ds->k = (ds->extrarow)? n: 0;
892: ds->t = ds->n; /* truncated length equal to previous dimension */
893: ds->n = n;
894: }
895: PetscFunctionReturn(0);
896: }
898: PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
899: {
900: PetscInt ld=ds->ld,l=ds->l,k=0,kr=0;
901: PetscMPIInt n,rank,off=0,size,ldn,ld3,ld_;
903: if (ds->compact) kr = 4*ld;
904: else k = 2*(ds->n-l)*ld;
905: if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
906: if (eigr) k += (ds->n-l);
907: if (eigi) k += (ds->n-l);
908: DSAllocateWork_Private(ds,k+kr,0,0);
909: PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
910: PetscMPIIntCast(ds->n-l,&n);
911: PetscMPIIntCast(ld*(ds->n-l),&ldn);
912: PetscMPIIntCast(ld*3,&ld3);
913: PetscMPIIntCast(ld,&ld_);
914: MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
915: if (!rank) {
916: if (ds->compact) {
917: MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
918: MPI_Pack(ds->rmat[DS_MAT_D],ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
919: } else {
920: MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
921: MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
922: }
923: if (ds->state>DS_STATE_RAW) MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
924: if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
925: #if !defined(PETSC_USE_COMPLEX)
926: if (eigi) MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
927: #endif
928: }
929: MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
930: if (rank) {
931: if (ds->compact) {
932: MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
933: MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_D],ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds));
934: } else {
935: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
936: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
937: }
938: if (ds->state>DS_STATE_RAW) MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
939: if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
940: #if !defined(PETSC_USE_COMPLEX)
941: if (eigi) MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
942: #endif
943: }
944: PetscFunctionReturn(0);
945: }
947: PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
948: {
949: if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
950: else *flg = PETSC_FALSE;
951: PetscFunctionReturn(0);
952: }
954: /*MC
955: DSGHIEP - Dense Generalized Hermitian Indefinite Eigenvalue Problem.
957: Level: beginner
959: Notes:
960: The problem is expressed as A*X = B*X*Lambda, where both A and B are
961: real symmetric (or complex Hermitian) and possibly indefinite. Lambda
962: is a diagonal matrix whose diagonal elements are the arguments of DSSolve().
963: After solve, A is overwritten with Lambda. Note that in the case of real
964: scalars, A is overwritten with a real representation of Lambda, i.e.,
965: complex conjugate eigenvalue pairs are stored as a 2x2 block in the
966: quasi-diagonal matrix.
968: In the intermediate state A is reduced to tridiagonal form and B is
969: transformed into a signature matrix. In compact storage format, these
970: matrices are stored in T and D, respectively.
972: Used DS matrices:
973: + DS_MAT_A - first problem matrix
974: . DS_MAT_B - second problem matrix
975: . DS_MAT_T - symmetric tridiagonal matrix of the reduced pencil
976: . DS_MAT_D - diagonal matrix (signature) of the reduced pencil
977: - DS_MAT_Q - pseudo-orthogonal transformation that reduces (A,B) to
978: tridiagonal-diagonal form (intermediate step) or a real basis of eigenvectors
980: Implemented methods:
981: + 0 - QR iteration plus inverse iteration for the eigenvectors
982: . 1 - HZ iteration
983: - 2 - QR iteration plus pseudo-orthogonalization for the eigenvectors
985: References:
986: . 1. - C. Campos and J. E. Roman, "Restarted Q-Arnoldi-type methods exploiting
987: symmetry in quadratic eigenvalue problems", BIT Numer. Math. 56(4):1213-1236, 2016.
989: .seealso: DSCreate(), DSSetType(), DSType
990: M*/
991: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
992: {
993: ds->ops->allocate = DSAllocate_GHIEP;
994: ds->ops->view = DSView_GHIEP;
995: ds->ops->vectors = DSVectors_GHIEP;
996: ds->ops->solve[0] = DSSolve_GHIEP_QR_II;
997: ds->ops->solve[1] = DSSolve_GHIEP_HZ;
998: ds->ops->solve[2] = DSSolve_GHIEP_QR;
999: ds->ops->sort = DSSort_GHIEP;
1000: ds->ops->synchronize = DSSynchronize_GHIEP;
1001: ds->ops->gettruncatesize = DSGetTruncateSize_GHIEP;
1002: ds->ops->truncate = DSTruncate_GHIEP;
1003: ds->ops->update = DSUpdateExtraRow_GHIEP;
1004: ds->ops->hermitian = DSHermitian_GHIEP;
1005: PetscFunctionReturn(0);
1006: }