GCC Code Coverage Report

Directory: ./
File: src/sys/classes/ds/impls/ghiep/dsghiep.c
Date: 2025-12-10 04:20:18
Exec Total Coverage
Lines: 706 783 90.2%
Functions: 17 17 100.0%
Branches: 1520 2769 54.9%
Line Branch Exec Source
1 /*
2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 SLEPc - Scalable Library for Eigenvalue Problem Computations
4 Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
6 This file is part of SLEPc.
7 SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 */
10
11 #include <slepc/private/dsimpl.h>
12 #include <slepcblaslapack.h>
13
14 579 static PetscErrorCode DSAllocate_GHIEP(DS ds,PetscInt ld)
15 {
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 579 PetscFunctionBegin;
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 579 PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
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 579 PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
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 579 PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
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 579 PetscCall(DSAllocateMat_Private(ds,DS_MAT_T));
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 579 PetscCall(DSAllocateMat_Private(ds,DS_MAT_D));
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 579 PetscCall(PetscFree(ds->perm));
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 579 PetscCall(PetscMalloc1(ld,&ds->perm));
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 121 PetscFunctionReturn(PETSC_SUCCESS);
25 }
26
27 10181 PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
28 {
29 10181 PetscReal *T,*S;
30 10181 PetscScalar *A,*B;
31 10181 PetscInt i,n,ld;
32
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 10181 PetscFunctionBegin;
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 10181 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
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 10181 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
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 10181 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
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 10181 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
38 10181 n = ds->n;
39 10181 ld = ds->ld;
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 10181 if (tocompact) { /* switch from dense (arrow) to compact storage */
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 60 PetscCall(PetscArrayzero(T,n));
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 60 PetscCall(PetscArrayzero(T+ld,n));
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 60 PetscCall(PetscArrayzero(T+2*ld,n));
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 60 PetscCall(PetscArrayzero(S,n));
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 600 for (i=0;i<n-1;i++) {
46 540 T[i] = PetscRealPart(A[i+i*ld]);
47 540 T[ld+i] = PetscRealPart(A[i+1+i*ld]);
48 540 S[i] = PetscRealPart(B[i+i*ld]);
49 }
50 60 T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
51 60 S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
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 60 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 */
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 339958 for (i=0;i<n;i++) {
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 329837 PetscCall(PetscArrayzero(A+i*ld,n));
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 401921 PetscCall(PetscArrayzero(B+i*ld,n));
57 }
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 329837 for (i=0;i<n-1;i++) {
59 319716 A[i+i*ld] = T[i];
60 319716 A[i+1+i*ld] = T[ld+i];
61 319716 A[i+(i+1)*ld] = T[ld+i];
62 319716 B[i+i*ld] = S[i];
63 }
64 10121 A[n-1+(n-1)*ld] = T[n-1];
65 10121 B[n-1+(n-1)*ld] = S[n-1];
66
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 219727 for (i=ds->l;i<ds->k;i++) {
67 209606 A[ds->k+i*ld] = T[2*ld+i];
68 209606 A[i+ds->k*ld] = T[2*ld+i];
69 }
70 }
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 10181 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
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 10181 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
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 10181 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
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 10181 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
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 2019 PetscFunctionReturn(PETSC_SUCCESS);
76 }
77
78 180 static PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
79 {
80 180 PetscViewerFormat format;
81 180 PetscInt i,j;
82 180 PetscReal *T,*S,value;
83 180 const char *methodname[] = {
84 "QR + Inverse Iteration",
85 "HZ method",
86 "QR"
87 };
88 180 const int nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);
89
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 180 PetscFunctionBegin;
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 180 PetscCall(PetscViewerGetFormat(viewer,&format));
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 180 if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
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 120 if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]));
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 120 PetscFunctionReturn(PETSC_SUCCESS);
95 }
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 60 if (ds->compact) {
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 60 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
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 60 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
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 60 PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
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 60 if (format == PETSC_VIEWER_ASCII_MATLAB) {
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n));
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",3*ds->n));
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = [\n"));
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 510 for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)T[i]));
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 450 for (i=0;i<ds->n-1;i++) {
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 390 if (T[i+ds->ld] !=0 && i!=ds->k-1) {
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 120 PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+2,i+1,(double)T[i+ds->ld]));
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 390 PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+2,(double)T[i+ds->ld]));
109 }
110 }
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 150 for (i = ds->l;i<ds->k;i++) {
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 90 if (T[i+2*ds->ld]) {
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 90 PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",ds->k+1,i+1,(double)T[i+2*ds->ld]));
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 90 PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,ds->k+1,(double)T[i+2*ds->ld]));
115 }
116 }
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]));
118
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n));
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"omega = zeros(%" PetscInt_FMT ",3);\n",3*ds->n));
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"omega = [\n"));
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 510 for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %18.16e\n",i+1,i+1,(double)S[i]));
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 60 PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]));
124
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
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 60 PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
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 60 PetscCall(PetscViewerFlush(viewer));
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 60 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
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 60 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
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 60 if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
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 12 PetscFunctionReturn(PETSC_SUCCESS);
157 }
158
159 17642 static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
160 {
161 17642 PetscReal b[4],M[4],*T,*S,d1,d2,s1,s2,e,scal1,scal2,wr1,wr2,wi,ep,norm;
162 17642 PetscScalar *X,Y[4],alpha,szero=0.0;
163 17642 const PetscScalar *A,*B,*Q;
164 17642 PetscInt k;
165 17642 PetscBLASInt two=2,n_,ld,one=1;
166 #if !defined(PETSC_USE_COMPLEX)
167 12519 PetscBLASInt four=4;
168 #endif
169
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 17642 PetscFunctionBegin;
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 17642 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
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 17642 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
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 17642 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
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 17642 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
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 17642 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
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 17642 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
177 17642 k = *idx;
178
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 17642 PetscCall(PetscBLASIntCast(ds->n,&n_));
179
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 17642 PetscCall(PetscBLASIntCast(ds->ld,&ld));
180
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 17642 if (k < ds->n-1) e = (ds->compact)?T[k+ld]:PetscRealPart(A[(k+1)+ld*k]);
181 else e = 0.0;
182
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 17642 if (e == 0.0) { /* Real */
183
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 16840 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
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 16840 if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
189 } else { /* 2x2 block */
190
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 802 if (ds->compact) {
191 802 s1 = S[k];
192 802 d1 = T[k];
193 802 s2 = S[k+1];
194 802 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 }
201 802 M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
202 802 b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
203 802 ep = LAPACKlamch_("S");
204 /* Compute eigenvalues of the block */
205
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 802 PetscCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
206
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 802 PetscCheck(wi!=0.0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Real block in DSVectors_GHIEP");
207 /* Complex eigenvalues */
208
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 802 PetscCheck(scal1>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
209 802 wr1 /= scal1;
210 802 wi /= scal1;
211 #if !defined(PETSC_USE_COMPLEX)
212
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 582 if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
213 84 Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
214 } else {
215 498 Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
216 }
217 582 norm = BLASnrm2_(&four,Y,&one);
218 582 norm = 1.0/norm;
219
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 582 if (ds->state >= DS_STATE_CONDENSED) {
220 455 alpha = norm;
221
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 455 PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,Q+k*ld,&ld,Y,&two,&szero,X+k*ld,&ld));
222
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 455 if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
223 } else {
224
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 127 PetscCall(PetscArrayzero(X+k*ld,2*ld));
225 127 X[k*ld+k] = Y[0]*norm;
226 127 X[k*ld+k+1] = Y[1]*norm;
227 127 X[(k+1)*ld+k] = Y[2]*norm;
228 127 X[(k+1)*ld+k+1] = Y[3]*norm;
229 }
230 #else
231
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 220 if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
232 22 Y[0] = PetscCMPLX(wr1-s2*d2,wi);
233 22 Y[1] = s2*e;
234 } else {
235 198 Y[0] = s1*e;
236 198 Y[1] = PetscCMPLX(wr1-s1*d1,wi);
237 }
238 220 norm = BLASnrm2_(&two,Y,&one);
239 220 norm = 1.0/norm;
240
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 220 if (ds->state >= DS_STATE_CONDENSED) {
241 153 alpha = norm;
242
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 153 PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,Q+k*ld,&ld,Y,&one,&szero,X+k*ld,&one));
243
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 153 if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
244 } else {
245
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 67 PetscCall(PetscArrayzero(X+k*ld,2*ld));
246 67 X[k*ld+k] = Y[0]*norm;
247 67 X[k*ld+k+1] = Y[1]*norm;
248 }
249 220 X[(k+1)*ld+k] = PetscConj(X[k*ld+k]);
250 220 X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
251 #endif
252 802 (*idx)++;
253 }
254
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 17642 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
255
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 17642 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
256
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 17642 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
257
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 17642 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
258
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 17642 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
259
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 17642 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
260
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 3883 PetscFunctionReturn(PETSC_SUCCESS);
261 }
262
263 17734 static PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
264 {
265 17734 PetscScalar *Z;
266 17734 const PetscScalar *A,*Q;
267 17734 PetscInt i;
268 17734 PetscReal e,*T,*S;
269
270
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 17734 PetscFunctionBegin;
271
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 17734 switch (mat) {
272 17734 case DS_MAT_X:
273 case DS_MAT_Y:
274
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 17734 if (k) PetscCall(DSVectors_GHIEP_Eigen_Some(ds,k,rnorm));
275 else {
276
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 286 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
277
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 286 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
278
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 286 PetscCall(MatDenseGetArray(ds->omat[mat],&Z));
279
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 286 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
280
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 4096 for (i=0; i<ds->n; i++) {
281
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 3810 e = (ds->compact)?T[i+ds->ld]:PetscRealPart(A[(i+1)+ds->ld*i]);
282
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 3810 if (e == 0.0) { /* real */
283
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 3616 if (ds->state >= DS_STATE_CONDENSED) PetscCall(PetscArraycpy(Z+i*ds->ld,Q+i*ds->ld,ds->ld));
284 else {
285
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 3616 PetscCall(PetscArrayzero(Z+i*ds->ld,ds->ld));
286 3616 Z[i+i*ds->ld] = 1.0;
287 }
288 } else {
289
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 194 PetscCall(DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm));
290
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 194 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
291 194 S[i]=S[i-1]=1.0;
292
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 3810 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
293 }
294 }
295
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 286 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
296
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 286 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
297
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 286 PetscCall(MatDenseRestoreArray(ds->omat[mat],&Z));
298
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 286 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
299 }
300 3903 break;
301 ✗ case DS_MAT_U:
302 case DS_MAT_V:
303 ✗ SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
304 ✗ default:
305 ✗ SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
306 }
307
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 3903 PetscFunctionReturn(PETSC_SUCCESS);
308 }
309
310 /*
311 Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
312 Only the index range n0..n1 is processed.
313 */
314 10560 PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
315 {
316 10560 PetscInt k,ld;
317 10560 PetscBLASInt two=2;
318 10560 const PetscScalar *A,*B;
319 10560 PetscReal *D,*T,b[4],M[4],d1,d2,s1,s2,e,scal1,scal2,ep,wr1,wr2,wi1;
320
321
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 10560 PetscFunctionBegin;
322 10560 ld = ds->ld;
323
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 10560 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
324
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 10560 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
325
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 10560 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
326
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 10560 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
327
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 22581 for (k=n0;k<n1;k++) {
328
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 12021 if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
329 else e = 0.0;
330
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 11048 if (e==0.0) { /* real eigenvalue */
331
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 11966 wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
332 #if !defined(PETSC_USE_COMPLEX)
333 6563 wi[k] = 0.0 ;
334 #endif
335 } else { /* diagonal block */
336
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 55 if (ds->compact) {
337 35 s1 = D[k];
338 35 d1 = T[k];
339 35 s2 = D[k+1];
340 35 d2 = T[k+1];
341 } else {
342 20 s1 = PetscRealPart(B[k*ld+k]);
343 20 d1 = PetscRealPart(A[k+k*ld]);
344 20 s2 = PetscRealPart(B[(k+1)*ld+k+1]);
345 20 d2 = PetscRealPart(A[k+1+(k+1)*ld]);
346 }
347 55 M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
348 55 b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
349 55 ep = LAPACKlamch_("S");
350 /* Compute eigenvalues of the block */
351
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 55 PetscCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
352
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 55 PetscCheck(scal1>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
353
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 55 if (wi1==0.0) { /* Real eigenvalues */
354 ✗ PetscCheck(scal2>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
355 ✗ wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
356 #if !defined(PETSC_USE_COMPLEX)
357 ✗ wi[k] = wi[k+1] = 0.0;
358 #endif
359 } else { /* Complex eigenvalues */
360 #if !defined(PETSC_USE_COMPLEX)
361 30 wr[k] = wr1/scal1;
362 30 wr[k+1] = wr[k];
363 30 wi[k] = wi1/scal1;
364 30 wi[k+1] = -wi[k];
365 #else
366 25 wr[k] = PetscCMPLX(wr1,wi1)/scal1;
367 25 wr[k+1] = PetscConj(wr[k]);
368 #endif
369 }
370 55 k++;
371 }
372 }
373 #if defined(PETSC_USE_COMPLEX)
374
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 1816 if (wi) {
375
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 7269 for (k=n0;k<n1;k++) wi[k] = 0.0;
376 }
377 #endif
378
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 10560 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
379
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 10560 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
380
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 10560 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
381
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 10560 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
382
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 2100 PetscFunctionReturn(PETSC_SUCCESS);
383 }
384
385 10560 static PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
386 {
387 10560 PetscInt n,i,*perm;
388 10560 PetscReal *d,*e,*s;
389
390
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 10560 PetscFunctionBegin;
391 #if !defined(PETSC_USE_COMPLEX)
392
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 8744 PetscAssertPointer(wi,3);
393 #endif
394 10560 n = ds->n;
395
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 10560 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
396 10560 e = d + ds->ld;
397
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 10560 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
398
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 10560 PetscCall(DSAllocateWork_Private(ds,ds->ld,ds->ld,0));
399 10560 perm = ds->perm;
400
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 10560 if (!rr) {
401 10560 rr = wr;
402 10560 ri = wi;
403 }
404
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 10560 PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE));
405
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 10560 if (!ds->compact) PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_TRUE));
406
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 10560 PetscCall(PetscArraycpy(ds->work,wr,n));
407
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 346556 for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
408 #if !defined(PETSC_USE_COMPLEX)
409
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 8744 PetscCall(PetscArraycpy(ds->work,wi,n));
410
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 296405 for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
411 #endif
412
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 10560 PetscCall(PetscArraycpy(ds->rwork,s,n));
413
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 346556 for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
414
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 10560 PetscCall(PetscArraycpy(ds->rwork,d,n));
415
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 346556 for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
416
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 10560 PetscCall(PetscArraycpy(ds->rwork,e,n-1));
417
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 10560 PetscCall(PetscArrayzero(e+ds->l,n-1-ds->l));
418
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 335996 for (i=ds->l;i<n-1;i++) {
419
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 325436 if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
420 }
421
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 10560 if (!ds->compact) PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
422
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 10560 PetscCall(DSPermuteColumns_Private(ds,ds->l,n,n,DS_MAT_Q,perm));
423
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 10560 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
424
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 10560 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
425
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 2100 PetscFunctionReturn(PETSC_SUCCESS);
426 }
427
428 10470 static PetscErrorCode DSUpdateExtraRow_GHIEP(DS ds)
429 {
430 10470 PetscInt i;
431 10470 PetscBLASInt n,ld,incx=1;
432 10470 PetscScalar *A,*x,*y,one=1.0,zero=0.0;
433 10470 const PetscScalar *Q;
434 10470 PetscReal *T,*b,*r,beta;
435
436
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 10470 PetscFunctionBegin;
437
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 10470 PetscCall(PetscBLASIntCast(ds->n,&n));
438
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 10470 PetscCall(PetscBLASIntCast(ds->ld,&ld));
439
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 10470 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
440
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 10470 if (ds->compact) {
441
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 10440 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
442 10440 b = T+ld;
443 10440 r = T+2*ld;
444 10440 beta = b[n-1]; /* in compact, we assume all entries are zero except the last one */
445
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 357182 for (i=0;i<n;i++) r[i] = PetscRealPart(beta*Q[n-1+i*ld]);
446 10440 ds->k = n;
447
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 10440 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
448 } else {
449
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 30 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
450
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 30 PetscCall(DSAllocateWork_Private(ds,2*ld,0,0));
451 30 x = ds->work;
452 30 y = ds->work+ld;
453
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 330 for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
454
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 30 PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
455
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 330 for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
456 30 ds->k = n;
457
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 30 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
458 }
459
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 10470 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
460
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 2082 PetscFunctionReturn(PETSC_SUCCESS);
461 }
462
463 /*
464 Get eigenvectors with inverse iteration.
465 The system matrix is in Hessenberg form.
466 */
467 10470 PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
468 {
469 10470 PetscInt i,off;
470 10470 PetscBLASInt *select,*infoC,ld,n1,mout,info;
471 10470 const PetscScalar *A,*B;
472 10470 PetscScalar *H,*X;
473 10470 PetscReal *s,*d,*e;
474 #if defined(PETSC_USE_COMPLEX)
475 1771 PetscInt j;
476 #endif
477
478
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 10470 PetscFunctionBegin;
479
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 10470 PetscCall(PetscBLASIntCast(ds->ld,&ld));
480
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 10470 PetscCall(PetscBLASIntCast(ds->n-ds->l,&n1));
481
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 10470 PetscCall(DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld));
482
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 10470 PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
483
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 10470 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
484
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 10470 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
485
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 10470 PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&H));
486
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 10470 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
487
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 10470 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
488 10470 e = d + ld;
489 10470 select = ds->iwork;
490 10470 infoC = ds->iwork + ld;
491 10470 off = ds->l+ds->l*ld;
492
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 10470 if (ds->compact) {
493 10450 H[off] = d[ds->l]*s[ds->l];
494 10450 H[off+ld] = e[ds->l]*s[ds->l];
495
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 324756 for (i=ds->l+1;i<ds->n-1;i++) {
496 314306 H[i+(i-1)*ld] = e[i-1]*s[i];
497 314306 H[i+i*ld] = d[i]*s[i];
498 314306 H[i+(i+1)*ld] = e[i]*s[i];
499 }
500 10450 H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
501 10450 H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
502 } else {
503 20 s[ds->l] = PetscRealPart(B[off]);
504 20 H[off] = A[off]*s[ds->l];
505 20 H[off+ld] = A[off+ld]*s[ds->l];
506
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 180 for (i=ds->l+1;i<ds->n-1;i++) {
507 160 s[i] = PetscRealPart(B[i+i*ld]);
508 160 H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
509 160 H[i+i*ld] = A[i+i*ld]*s[i];
510 160 H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
511 }
512 20 s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
513 20 H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
514 20 H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
515 }
516
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 10470 PetscCall(DSAllocateMat_Private(ds,DS_MAT_X));
517
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 10470 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
518
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 345876 for (i=0;i<n1;i++) select[i] = 1;
519 #if !defined(PETSC_USE_COMPLEX)
520
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 8699 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));
521 #else
522
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 1771 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));
523
524 /* Separate real and imaginary part of complex eigenvectors */
525
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 48652 for (j=ds->l;j<ds->n;j++) {
526
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 46881 if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
527
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 65916 for (i=ds->l;i<ds->n;i++) {
528 64757 X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
529 64757 X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
530 }
531 1159 j++;
532 }
533 }
534 #endif
535
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 10470 SlepcCheckLapackInfo("hsein",info);
536
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 10470 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
537
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 10470 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
538
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 10470 PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&H));
539
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 10470 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_X],&X));
540
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 10470 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
541
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 10470 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
542
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 10470 PetscCall(DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE));
543
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 2082 PetscFunctionReturn(PETSC_SUCCESS);
544 }
545
546 /*
547 Undo 2x2 blocks that have real eigenvalues.
548 */
549 30 PetscErrorCode DSGHIEPRealBlocks(DS ds)
550 {
551 30 PetscInt i;
552 30 PetscReal e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
553 30 PetscReal maxy,ep,scal1,scal2,snorm;
554 30 PetscReal *T,*D,b[4],M[4],wr1,wr2,wi;
555 30 PetscScalar *A,*B,*Q,Y[4],sone=1.0,szero=0.0;
556 30 PetscBLASInt m,two=2,ld;
557 30 PetscBool isreal;
558
559
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 30 PetscFunctionBegin;
560
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 30 PetscCall(PetscBLASIntCast(ds->ld,&ld));
561
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 30 PetscCall(PetscBLASIntCast(ds->n-ds->l,&m));
562
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 30 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
563
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 30 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
564
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 30 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
565
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 30 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
566
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 30 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
567
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 30 PetscCall(DSAllocateWork_Private(ds,2*m,0,0));
568
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 230 for (i=ds->l;i<ds->n-1;i++) {
569
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 200 e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
570
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 200 if (e != 0.0) { /* 2x2 block */
571
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 50 if (ds->compact) {
572 10 s1 = D[i];
573 10 d1 = T[i];
574 10 s2 = D[i+1];
575 10 d2 = T[i+1];
576 } else {
577 40 s1 = PetscRealPart(B[i*ld+i]);
578 40 d1 = PetscRealPart(A[i*ld+i]);
579 40 s2 = PetscRealPart(B[(i+1)*ld+i+1]);
580 40 d2 = PetscRealPart(A[(i+1)*ld+i+1]);
581 }
582 50 isreal = PETSC_FALSE;
583
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 50 if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
584 ✗ dd = d1-d2;
585 ✗ if (2*PetscAbsReal(e) <= dd) {
586 ✗ t = 2*e/dd;
587 ✗ t = t/(1 + PetscSqrtReal(1+t*t));
588 } else {
589 ✗ t = dd/(2*e);
590 ✗ ss = (t>=0)?1.0:-1.0;
591 ✗ t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
592 }
593 ✗ Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
594 ✗ Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
595 ✗ wr1 = d1+t*e; wr2 = d2-t*e;
596 ✗ ss1 = s1; ss2 = s2;
597 ✗ isreal = PETSC_TRUE;
598 } else {
599 50 ss1 = 1.0; ss2 = 1.0,
600 50 M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
601 50 b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
602 50 ep = LAPACKlamch_("S");
603
604 /* Compute eigenvalues of the block */
605
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 50 PetscCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
606
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 50 if (wi==0.0) { /* Real eigenvalues */
607 20 isreal = PETSC_TRUE;
608
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 20 PetscCheck(scal1>=ep && scal2>=ep,PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
609 20 wr1 /= scal1;
610 20 wr2 /= scal2;
611
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 20 if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
612 ✗ Y[0] = wr1-s2*d2;
613 ✗ Y[1] = s2*e;
614 } else {
615 20 Y[0] = s1*e;
616 20 Y[1] = wr1-s1*d1;
617 }
618 /* normalize with a signature*/
619
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 20 maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
620 20 scal1 = PetscRealPart(Y[0])/maxy;
621 20 scal2 = PetscRealPart(Y[1])/maxy;
622 20 snorm = scal1*scal1*s1 + scal2*scal2*s2;
623
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 20 if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
624 20 snorm = maxy*PetscSqrtReal(snorm);
625 20 Y[0] = Y[0]/snorm;
626 20 Y[1] = Y[1]/snorm;
627
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 20 if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
628 20 Y[2] = wr2-s2*d2;
629 20 Y[3] = s2*e;
630 } else {
631 ✗ Y[2] = s1*e;
632 ✗ Y[3] = wr2-s1*d1;
633 }
634
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 20 maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
635 20 scal1 = PetscRealPart(Y[2])/maxy;
636 20 scal2 = PetscRealPart(Y[3])/maxy;
637 20 snorm = scal1*scal1*s1 + scal2*scal2*s2;
638
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 20 if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
639 20 snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
640 }
641 50 wr1 *= ss1; wr2 *= ss2;
642 }
643
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 50 if (isreal) {
644
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 20 if (ds->compact) {
645 ✗ D[i] = ss1;
646 ✗ T[i] = wr1;
647 ✗ D[i+1] = ss2;
648 ✗ T[i+1] = wr2;
649 ✗ T[ld+i] = 0.0;
650 } else {
651 20 B[i*ld+i] = ss1;
652 20 A[i*ld+i] = wr1;
653 20 B[(i+1)*ld+i+1] = ss2;
654 20 A[(i+1)*ld+i+1] = wr2;
655 20 A[(i+1)+ld*i] = 0.0;
656 20 A[i+ld*(i+1)] = 0.0;
657 }
658
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 20 PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&two,&two,&sone,Q+ds->l+i*ld,&ld,Y,&two,&szero,ds->work,&m));
659
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 20 PetscCall(PetscArraycpy(Q+ds->l+i*ld,ds->work,m));
660
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 20 PetscCall(PetscArraycpy(Q+ds->l+(i+1)*ld,ds->work+m,m));
661 }
662 50 i++;
663 }
664 }
665
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 30 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
666
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 30 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
667
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 30 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
668
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 30 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
669
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 30 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
670
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 6 PetscFunctionReturn(PETSC_SUCCESS);
671 }
672
673 10480 static PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
674 {
675 10480 PetscInt i,off;
676 10480 PetscBLASInt n1,ld,one=1,info,lwork;
677 10480 const PetscScalar *A,*B;
678 10480 PetscScalar *H,*Q;
679 10480 PetscReal *d,*e,*s;
680 #if defined(PETSC_USE_COMPLEX)
681 1776 PetscInt j;
682 #endif
683
684
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 10480 PetscFunctionBegin;
685 #if !defined(PETSC_USE_COMPLEX)
686
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 8704 PetscAssertPointer(wi,3);
687 #endif
688
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 10480 PetscCall(PetscBLASIntCast(ds->n-ds->l,&n1));
689
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 10480 PetscCall(PetscBLASIntCast(ds->ld,&ld));
690 10480 off = ds->l + ds->l*ld;
691
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 10480 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
692
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 10480 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
693
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 10480 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
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 10480 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
695 10480 e = d + ld;
696 #if defined(PETSC_USE_DEBUG)
697 /* Check signature */
698
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 72320 for (i=0;i<ds->n;i++) {
699
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 70236 PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
700
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 70236 PetscCheck(de==1.0 || de==-1.0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal elements of the signature matrix must be 1 or -1");
701 }
702 #endif
703
704 /* Quick return if possible */
705
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 10480 if (n1 == 1) {
706
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 10 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
707
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 60 for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
708
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 10 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
709
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 10 PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
710
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 10 if (!ds->compact) {
711 ✗ d[ds->l] = PetscRealPart(A[off]);
712 ✗ s[ds->l] = PetscRealPart(B[off]);
713 }
714
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 10 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
715
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 10 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
716 10 wr[ds->l] = d[ds->l]/s[ds->l];
717
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 10 if (wi) wi[ds->l] = 0.0;
718
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 10 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
719
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 10 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
720
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 2 PetscFunctionReturn(PETSC_SUCCESS);
721 }
722
723
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 10470 PetscCall(DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2));
724 10470 lwork = ld*ld;
725
726 /* Reduce to pseudotriadiagonal form */
727
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 10470 PetscCall(DSIntermediate_GHIEP(ds));
728
729 /* Compute Eigenvalues (QR) */
730
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 10470 PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
731
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 10470 PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_W],&H));
732
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 10470 if (ds->compact) {
733 10450 H[off] = d[ds->l]*s[ds->l];
734 10450 H[off+ld] = e[ds->l]*s[ds->l];
735
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 324756 for (i=ds->l+1;i<ds->n-1;i++) {
736 314306 H[i+(i-1)*ld] = e[i-1]*s[i];
737 314306 H[i+i*ld] = d[i]*s[i];
738 314306 H[i+(i+1)*ld] = e[i]*s[i];
739 }
740 10450 H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
741 10450 H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
742 } else {
743 20 s[ds->l] = PetscRealPart(B[off]);
744 20 H[off] = A[off]*s[ds->l];
745 20 H[off+ld] = A[off+ld]*s[ds->l];
746
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 180 for (i=ds->l+1;i<ds->n-1;i++) {
747 160 s[i] = PetscRealPart(B[i+i*ld]);
748 160 H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
749 160 H[i+i*ld] = A[i+i*ld]*s[i];
750 160 H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
751 }
752 20 s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
753 20 H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
754 20 H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
755 }
756
757 #if !defined(PETSC_USE_COMPLEX)
758
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 8699 PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
759 #else
760
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 1771 PetscCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
761
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 49811 for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
762 /* Sort to have consecutive conjugate pairs */
763
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 48601 for (i=ds->l;i<ds->n;i++) {
764 46830 j=i+1;
765
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 1127556 while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
766
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 46830 if (j==ds->n) {
767
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 45620 PetscCheck(PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON,PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
768 45620 wr[i] = PetscRealPart(wr[i]);
769 } else { /* complex eigenvalue */
770 1210 wr[j] = wr[i+1];
771
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 1210 if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
772 1210 wr[i+1] = PetscConj(wr[i]);
773 1210 i++;
774 }
775 }
776 #endif
777
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 10470 SlepcCheckLapackInfo("hseqr",info);
778
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 10470 PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_W],&H));
779
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 10470 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
780
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 10470 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
781
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 10470 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
782
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 10470 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
783
784 /* Compute Eigenvectors with Inverse Iteration */
785
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 10470 PetscCall(DSGHIEPInverseIteration(ds,wr,wi));
786
787 /* Recover eigenvalues from diagonal */
788
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 10470 PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
789 #if defined(PETSC_USE_COMPLEX)
790
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 1771 if (wi) {
791
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 49811 for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
792 }
793 #endif
794
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 2082 PetscFunctionReturn(PETSC_SUCCESS);
795 }
796
797 40 static PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
798 {
799 40 PetscInt i,j,off,nwu=0,n,lw,lwr,nwru=0;
800 40 PetscBLASInt n_,ld,info,lwork,ilo,ihi;
801 40 const PetscScalar *A,*B;
802 40 PetscScalar *H,*Q,*X;
803 40 PetscReal *d,*s,*scale,nrm,*rcde,*rcdv;
804 #if defined(PETSC_USE_COMPLEX)
805 20 PetscInt k;
806 #endif
807
808
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 40 PetscFunctionBegin;
809 #if !defined(PETSC_USE_COMPLEX)
810
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 20 PetscAssertPointer(wi,3);
811 #endif
812 40 n = ds->n-ds->l;
813
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 40 PetscCall(PetscBLASIntCast(n,&n_));
814
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 40 PetscCall(PetscBLASIntCast(ds->ld,&ld));
815 40 off = ds->l + ds->l*ld;
816
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 40 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_A],&A));
817
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 40 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
818
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 40 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
819
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 40 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
820 #if defined(PETSC_USE_DEBUG)
821 /* Check signature */
822
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 78 for (i=0;i<ds->n;i++) {
823
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 70 PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
824
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 70 PetscCheck(de==1.0 || de==-1.0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal elements of the signature matrix must be 1 or -1");
825 }
826 #endif
827
828 /* Quick return if possible */
829
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 40 if (n_ == 1) {
830
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 10 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
831
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 60 for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
832
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 10 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
833
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 10 PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
834
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 10 if (!ds->compact) {
835 ✗ d[ds->l] = PetscRealPart(A[off]);
836 ✗ s[ds->l] = PetscRealPart(B[off]);
837 }
838
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 10 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
839
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 10 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
840 10 wr[ds->l] = d[ds->l]/s[ds->l];
841
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 10 if (wi) wi[ds->l] = 0.0;
842
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 10 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
843
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 10 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
844
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 2 PetscFunctionReturn(PETSC_SUCCESS);
845 }
846
847 30 lw = 14*ld+ld*ld;
848 30 lwr = 7*ld;
849
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 30 PetscCall(DSAllocateWork_Private(ds,lw,lwr,0));
850 30 scale = ds->rwork+nwru;
851 30 nwru += ld;
852 30 rcde = ds->rwork+nwru;
853 30 nwru += ld;
854 30 rcdv = ds->rwork+nwru;
855
856 /* Form pseudo-symmetric matrix */
857 30 H = ds->work+nwu;
858 30 nwu += n*n;
859
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 30 PetscCall(PetscArrayzero(H,n*n));
860
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 30 if (ds->compact) {
861
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 80 for (i=0;i<n-1;i++) {
862 70 H[i+i*n] = s[ds->l+i]*d[ds->l+i];
863 70 H[i+1+i*n] = s[ds->l+i+1]*d[ld+ds->l+i];
864 70 H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
865 }
866 10 H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
867
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 40 for (i=0;i<ds->k-ds->l;i++) {
868 30 H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
869 30 H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
870 }
871 } else {
872
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 220 for (j=0;j<n;j++) {
873
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 2200 for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
874 }
875 }
876
877 /* Compute eigenpairs */
878
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 30 PetscCall(PetscBLASIntCast(lw-nwu,&lwork));
879
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 30 PetscCall(DSAllocateMat_Private(ds,DS_MAT_X));
880
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 30 PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_X],&X));
881 #if !defined(PETSC_USE_COMPLEX)
882
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 15 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));
883 #else
884
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 15 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));
885
886 /* Sort to have consecutive conjugate pairs
887 Separate real and imaginary part of complex eigenvectors*/
888
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 140 for (i=ds->l;i<ds->n;i++) {
889 125 j=i+1;
890
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 480 while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
891
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 125 if (j==ds->n) {
892
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 110 PetscCheck(PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON,PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
893 110 wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
894
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 1150 for (k=ds->l;k<ds->n;k++) {
895 1040 X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
896 }
897 } else { /* complex eigenvalue */
898
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 15 if (j!=i+1) {
899 ✗ wr[j] = wr[i+1];
900 ✗ PetscCall(PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld));
901 }
902
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 15 if (PetscImaginaryPart(wr[i])<0) {
903 ✗ wr[i] = PetscConj(wr[i]);
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 } else {
909
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 155 for (k=ds->l;k<ds->n;k++) {
910 140 X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
911 140 X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
912 }
913 }
914 15 wr[i+1] = PetscConj(wr[i]);
915 15 i++;
916 }
917 }
918 #endif
919
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 30 SlepcCheckLapackInfo("geevx",info);
920
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 30 PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_X],&X));
921
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 30 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_A],&A));
922
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 30 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
923
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 30 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
924
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 30 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
925
926 /* Compute real s-orthonormal basis */
927
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 30 PetscCall(DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_FALSE));
928
929 /* Recover eigenvalues from diagonal */
930
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 30 PetscCall(DSGHIEPComplexEigs(ds,0,ds->l,wr,wi));
931 #if defined(PETSC_USE_COMPLEX)
932
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 15 if (wi) {
933
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 155 for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
934 }
935 #endif
936
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 6 PetscFunctionReturn(PETSC_SUCCESS);
937 }
938
939 9944 static PetscErrorCode DSGetTruncateSize_GHIEP(DS ds,PetscInt l,PetscInt n,PetscInt *k)
940 {
941 9944 PetscReal *T;
942
943
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 9944 PetscFunctionBegin;
944
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 9944 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
945
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 9944 if (T[l+(*k)-1+ds->ld] !=0.0) {
946
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 5965 if (l+(*k)<n-1) (*k)++;
947 ✗ else (*k)--;
948 }
949
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 9944 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
950
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 1972 PetscFunctionReturn(PETSC_SUCCESS);
951 }
952
953 10443 static PetscErrorCode DSTruncate_GHIEP(DS ds,PetscInt n,PetscBool trim)
954 {
955 10443 PetscInt i,ld=ds->ld,l=ds->l;
956 10443 PetscScalar *A;
957 10443 PetscReal *T,*b,*r,*omega;
958
959
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 10443 PetscFunctionBegin;
960
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 10443 if (ds->compact) {
961
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 10443 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
962
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 10443 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&omega));
963 #if defined(PETSC_USE_DEBUG)
964 /* make sure diagonal 2x2 block is not broken */
965
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 2077 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");
966 #endif
967 }
968
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 10443 if (trim) {
969
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 499 if (!ds->compact && ds->extrarow) { /* clean extra row */
970 ✗ PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
971 ✗ for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
972 ✗ PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
973 }
974 499 ds->l = 0;
975 499 ds->k = 0;
976 499 ds->n = n;
977 499 ds->t = ds->n; /* truncated length equal to the new dimension */
978 } else {
979
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 9944 if (!ds->compact && ds->extrarow && ds->k==ds->n) {
980 /* copy entries of extra row to the new position, then clean last row */
981 ✗ PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
982 ✗ for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
983 ✗ for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
984 ✗ PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
985 }
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 9944 if (ds->compact) {
987 9944 b = T+ld;
988 9944 r = T+2*ld;
989 9944 b[n-1] = r[n-1];
990 9944 b[n] = b[ds->n];
991 9944 omega[n] = omega[ds->n];
992 }
993
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 9944 ds->k = (ds->extrarow)? n: 0;
994 9944 ds->t = ds->n; /* truncated length equal to previous dimension */
995 9944 ds->n = n;
996 }
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 10443 if (ds->compact) {
998
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 10443 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
999
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 10443 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&omega));
1000 }
1001
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 2077 PetscFunctionReturn(PETSC_SUCCESS);
1002 }
1003
1004 #if !defined(PETSC_HAVE_MPIUNI)
1005 20 static PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
1006 {
1007 20 PetscScalar *A,*B,*Q;
1008 20 PetscReal *T,*D;
1009 20 PetscInt ld=ds->ld,l=ds->l,k=0,kr=0;
1010 20 PetscMPIInt n,rank,off=0,size,ldn,ld3,ld_;
1011
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 20 PetscFunctionBegin;
1013
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 20 if (ds->compact) kr = 4*ld;
1014 ✗ else k = 2*(ds->n-l)*ld;
1015
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 20 if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
1016
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 20 if (eigr) k += (ds->n-l);
1017
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 20 if (eigi) k += (ds->n-l);
1018
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 20 PetscCall(DSAllocateWork_Private(ds,k+kr,0,0));
1019
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 20 PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size));
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 20 PetscCall(PetscMPIIntCast(ds->n-l,&n));
1021
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 20 PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
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 20 PetscCall(PetscMPIIntCast(ld*3,&ld3));
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 20 PetscCall(PetscMPIIntCast(ld,&ld_));
1024
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 20 if (ds->compact) {
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 20 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
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 20 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
1027 } else {
1028 ✗ PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
1029 ✗ PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
1030 }
1031
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 20 if (ds->state>DS_STATE_RAW) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
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 20 PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
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 20 if (!rank) {
1034
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 10 if (ds->compact) {
1035
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 10 PetscCallMPI(MPI_Pack(T,ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1036
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 10 PetscCallMPI(MPI_Pack(D,ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1037 } else {
1038 ✗ PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1039 ✗ PetscCallMPI(MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1040 }
1041
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 10 if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
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 10 if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1043 #if !defined(PETSC_USE_COMPLEX)
1044
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 5 if (eigi) PetscCallMPI(MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
1045 #endif
1046 }
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 40 PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
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 20 if (rank) {
1049
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1050
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 10 PetscCallMPI(MPI_Unpack(ds->work,size,&off,T,ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
1051
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 10 PetscCallMPI(MPI_Unpack(ds->work,size,&off,D,ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
1052 } else {
1053 ✗ PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1054 ✗ PetscCallMPI(MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1055 }
1056
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 10 if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
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 10 if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1058 #if !defined(PETSC_USE_COMPLEX)
1059
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 5 if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
1060 #endif
1061 }
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 20 if (ds->compact) {
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 20 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
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 20 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
1065 } else {
1066 ✗ PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
1067 ✗ PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
1068 }
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 20 if (ds->state>DS_STATE_RAW) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
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 4 PetscFunctionReturn(PETSC_SUCCESS);
1071 }
1072 #endif
1073
1074 21789 static PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
1075 {
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 21789 PetscFunctionBegin;
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 21789 if ((m==DS_MAT_A && !ds->extrarow) || m==DS_MAT_B) *flg = PETSC_TRUE;
1078 21789 else *flg = PETSC_FALSE;
1079
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 21789 PetscFunctionReturn(PETSC_SUCCESS);
1080 }
1081
1082 /*MC
1083 DSGHIEP - Dense Generalized Hermitian Indefinite Eigenvalue Problem.
1084
1085 Notes:
1086 The problem is expressed as $AX = BX\Lambda$, where both $A$ and $B$ are
1087 real symmetric (or complex Hermitian) and possibly indefinite. $\Lambda$
1088 is a diagonal matrix whose diagonal elements are the arguments of `DSSolve()`.
1089 After solve, $A$ is overwritten with $\Lambda$. Note that in the case of real
1090 scalars, $A$ is overwritten with a real representation of $\Lambda$, i.e.,
1091 complex conjugate eigenvalue pairs are stored as a 2x2 block in the
1092 quasi-diagonal matrix.
1093
1094 In the intermediate state $A$ is reduced to tridiagonal form and $B$ is
1095 transformed into a signature matrix. In compact storage format, these
1096 matrices are stored in $T$ and $D$, respectively. Details of the implemented
1097 methods are presented in {cite:p}`Cam16c`.
1098
1099 Used DS matrices:
1100 + `DS_MAT_A` - first problem matrix
1101 . `DS_MAT_B` - second problem matrix
1102 . `DS_MAT_T` - symmetric tridiagonal matrix of the reduced pencil
1103 . `DS_MAT_D` - diagonal matrix (signature) of the reduced pencil
1104 - `DS_MAT_Q` - pseudo-orthogonal transformation that reduces $(A,B)$ to
1105 tridiagonal-diagonal form (intermediate step) or a real basis of eigenvectors
1106
1107 Implemented methods:
1108 + 0 - QR iteration plus inverse iteration for the eigenvectors
1109 . 1 - HZ iteration
1110 - 2 - QR iteration plus pseudo-orthogonalization for the eigenvectors
1111
1112 Level: beginner
1113
1114 .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`
1115 M*/
1116 476 SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
1117 {
1118
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 476 PetscFunctionBegin;
1119 476 ds->ops->allocate = DSAllocate_GHIEP;
1120 476 ds->ops->view = DSView_GHIEP;
1121 476 ds->ops->vectors = DSVectors_GHIEP;
1122 476 ds->ops->solve[0] = DSSolve_GHIEP_QR_II;
1123 476 ds->ops->solve[1] = DSSolve_GHIEP_HZ;
1124 476 ds->ops->solve[2] = DSSolve_GHIEP_QR;
1125 476 ds->ops->sort = DSSort_GHIEP;
1126 #if !defined(PETSC_HAVE_MPIUNI)
1127 476 ds->ops->synchronize = DSSynchronize_GHIEP;
1128 #endif
1129 476 ds->ops->gettruncatesize = DSGetTruncateSize_GHIEP;
1130 476 ds->ops->truncate = DSTruncate_GHIEP;
1131 476 ds->ops->update = DSUpdateExtraRow_GHIEP;
1132 476 ds->ops->hermitian = DSHermitian_GHIEP;
1133
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 476 PetscFunctionReturn(PETSC_SUCCESS);
1134 }
1135