GCC Code Coverage Report

Directory: ./
File: src/sys/classes/ds/impls/ghiep/invit.c
Date: 2025-10-03 04:28:47
Exec Total Coverage
Lines: 444 487 91.2%
Functions: 8 8 100.0%
Branches: 889 1504 59.1%
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 struct HRtr
15 {
16 PetscScalar *data;
17 PetscInt m;
18 PetscInt idx[2];
19 PetscInt n[2];
20 PetscScalar tau[2];
21 PetscReal alpha;
22 PetscReal cs;
23 PetscReal sn;
24 PetscInt type;
25 };
26
27 /*
28 Generates a hyperbolic rotation
29 if x1*x1 - x2*x2 != 0
30 r = sqrt(|x1*x1 - x2*x2|)
31 c = x1/r s = x2/r
32
33 | c -s||x1| |d*r|
34 |-s c||x2| = | 0 |
35 where d = 1 for type==1 and -1 for type==2
36 Returns the condition number of the reduction
37 */
38 219908 static PetscErrorCode HRGen(PetscReal x1,PetscReal x2,PetscInt *type,PetscReal *c,PetscReal *s,PetscReal *r,PetscReal *cond)
39 {
40 219908 PetscReal t,n2,xa,xb;
41 219908 PetscInt type_;
42
43
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 219908 PetscFunctionBegin;
44
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 219908 if (x2==0.0) {
45 ✗ *r = PetscAbsReal(x1); *c = (x1>=0.0)?1.0:-1.0; *s = 0.0;
46 ✗ if (type) *type = 1;
47 ✗ PetscFunctionReturn(PETSC_SUCCESS);
48 }
49
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 219908 if (PetscAbsReal(x1) == PetscAbsReal(x2)) {
50 /* hyperbolic rotation doesn't exist */
51 ✗ *c = *s = *r = 0.0;
52 ✗ if (type) *type = 0;
53 ✗ *cond = PETSC_MAX_REAL;
54 ✗ PetscFunctionReturn(PETSC_SUCCESS);
55 }
56
57
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 219908 if (PetscAbsReal(x1)>PetscAbsReal(x2)) {
58 xa = x1; xb = x2; type_ = 1;
59 } else {
60 39317 xa = x2; xb = x1; type_ = 2;
61 }
62 219908 t = xb/xa;
63 219908 n2 = PetscAbsReal(1 - t*t);
64 219908 *r = PetscSqrtReal(n2)*PetscAbsReal(xa);
65 219908 *c = x1/(*r);
66 219908 *s = x2/(*r);
67
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 219908 if (type_ == 2) *r *= -1;
68
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 219908 if (type) *type = type_;
69
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 219908 if (cond) *cond = (PetscAbsReal(*c) + PetscAbsReal(*s))/PetscAbsReal(PetscAbsReal(*c) - PetscAbsReal(*s));
70
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 45433 PetscFunctionReturn(PETSC_SUCCESS);
71 }
72
73 /*
74 |c s|
75 Applies an hyperbolic rotator |s c|
76 |c s|
77 [x1 x2]|s c|
78 */
79 532453 static PetscErrorCode HRApply(PetscInt n,PetscScalar *x1,PetscInt inc1,PetscScalar *x2,PetscInt inc2,PetscReal c,PetscReal s)
80 {
81 532453 PetscInt i;
82 532453 PetscReal t;
83 532453 PetscScalar tmp;
84
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 532453 PetscFunctionBegin;
86
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 532453 if (PetscAbsReal(c)>PetscAbsReal(s)) { /* Type I */
87 455680 t = s/c;
88
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 14047996 for (i=0;i<n;i++) {
89 13592316 x1[i*inc1] = c*x1[i*inc1] + s*x2[i*inc2];
90 13592316 x2[i*inc2] = t*x1[i*inc1] + x2[i*inc2]/c;
91 }
92 } else { /* Type II */
93 76773 t = c/s;
94
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 1695381 for (i=0;i<n;i++) {
95 1618608 tmp = x1[i*inc1];
96 1618608 x1[i*inc1] = c*x1[i*inc1] + s*x2[i*inc2];
97 1618608 x2[i*inc2] = t*x1[i*inc1] + tmp/s;
98 }
99 }
100
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 532453 PetscFunctionReturn(PETSC_SUCCESS);
101 }
102
103 /*
104 Reduction to tridiagonal-diagonal form (see F. Tisseur, SIMAX 26(1), 2004).
105
106 Input:
107 A symmetric (only lower triangular part is referred)
108 s vector +1 and -1 (signature matrix)
109 Output:
110 d,e
111 s
112 Q s-orthogonal matrix with Q^T*A*Q = T (symmetric tridiagonal matrix)
113 */
114 10001 static PetscErrorCode TridiagDiag_HHR(PetscInt n,PetscScalar *A,PetscInt lda,PetscReal *s,PetscScalar* Q,PetscInt ldq,PetscBool flip,PetscReal *d,PetscReal *e,PetscInt *perm_,PetscScalar *work,PetscReal *rwork,PetscBLASInt *iwork)
115 {
116 10001 PetscInt i,j,k,*ii,*jj,i0=0,ik=0,type;
117 10001 PetscInt nwu=0;
118 10001 PetscReal *ss,cond=1.0,cs,sn,r;
119 10001 PetscScalar tau,t,*AA;
120 10001 PetscBLASInt n0,n1,ni,inc=1,m,n_,lda_,ldq_,*perm,tmp;
121 10001 PetscBool breakdown = PETSC_TRUE;
122
123
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 10001 PetscFunctionBegin;
124
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 10001 if (n<3) {
125 ✗ if (n==1) Q[0]=1;
126 ✗ if (n==2) {
127 ✗ Q[0] = Q[1+ldq] = 1;
128 ✗ Q[1] = Q[ldq] = 0;
129 }
130 ✗ PetscFunctionReturn(PETSC_SUCCESS);
131 }
132
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 10001 PetscCall(PetscBLASIntCast(lda,&lda_));
133
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 10001 PetscCall(PetscBLASIntCast(n,&n_));
134
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 10001 PetscCall(PetscBLASIntCast(ldq,&ldq_));
135 10001 ss = rwork;
136 10001 perm = iwork;
137 10001 AA = work;
138
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 229968 for (i=0;i<n;i++) PetscCall(PetscArraycpy(AA+i*n,A+i*lda,n));
139 10001 nwu += n*n;
140 10001 k=0;
141
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 20002 while (breakdown && k<n) {
142 10001 breakdown = PETSC_FALSE;
143 /* Classify (and flip) A and s according to sign */
144
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 10001 if (flip) {
145
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 229528 for (i=0;i<n;i++) {
146
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 219567 PetscCall(PetscBLASIntCast(n-1-perm_[i],&perm[i]));
147
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 219567 if (perm[i]==0) i0 = i;
148
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 219567 if (perm[i]==k) ik = i;
149 }
150 } else {
151
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 440 for (i=0;i<n;i++) {
152
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 400 PetscCall(PetscBLASIntCast(perm_[i],&perm[i]));
153
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 400 if (perm[i]==0) i0 = i;
154
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 400 if (perm[i]==k) ik = i;
155 }
156 }
157 10001 perm[ik] = 0;
158
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 10001 PetscCall(PetscBLASIntCast(k,&perm[i0]));
159 10001 i=1;
160
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 198755 while (i<n-1 && s[perm[i-1]]==s[perm[0]]) {
161
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 188754 if (s[perm[i]]!=s[perm[0]]) {
162 162033 j=i+1;
163
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 177855 while (j<n-1 && s[perm[j]]!=s[perm[0]])j++;
164 162033 tmp = perm[i]; perm[i] = perm[j]; perm[j] = tmp;
165 }
166 188754 i++;
167 }
168
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 229968 for (i=0;i<n;i++) {
169 219967 ss[i] = s[perm[i]];
170 }
171
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 10001 if (flip) {
172 ii = &j;
173 jj = &i;
174 } else {
175 40 ii = &i;
176 40 jj = &j;
177 }
178
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 229968 for (i=0;i<n;i++)
179
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 5840550 for (j=0;j<n;j++)
180 5620583 A[i+j*lda] = AA[perm[*ii]+perm[*jj]*n];
181 /* Initialize Q */
182
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183
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 219967 PetscCall(PetscArrayzero(Q+i*ldq,n));
184 219967 Q[perm[i]+i*ldq] = 1.0;
185 }
186
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 199038 for (ni=1;ni<n && ss[ni]==ss[0]; ni++);
187 10001 n0 = ni-1;
188 10001 n1 = n_-ni;
189
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 209966 for (j=0;j<n-2;j++) {
190
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 199965 PetscCall(PetscBLASIntCast(n-j-1,&m));
191 /* Forming and applying reflectors */
192
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 199965 if (n0 > 1) {
193
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 187336 PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0,A+ni-n0+j*lda,A+ni-n0+j*lda+1,&inc,&tau));
194 /* Apply reflector */
195
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 187336 if (PetscAbsScalar(tau) != 0.0) {
196 187336 t=*(A+ni-n0+j*lda); *(A+ni-n0+j*lda)=1.0;
197
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 187336 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&m,&n0,A+ni-n0+j*lda,&inc,&tau,A+j+1+(j+1)*lda,&lda_,work+nwu));
198
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 187336 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0,&m,A+ni-n0+j*lda,&inc,&tau,A+j+1+(j+1)*lda,&lda_,work+nwu));
199 /* Update Q */
200
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 187336 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0,A+ni-n0+j*lda,&inc,&tau,Q+(j+1)*ldq,&ldq_,work+nwu));
201 187336 *(A+ni-n0+j*lda) = t;
202
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 2490743 for (i=1;i<n0;i++) {
203 2303407 *(A+ni-n0+j*lda+i) = 0.0; *(A+j+(ni-n0+i)*lda) = 0.0;
204 }
205 187336 *(A+j+(ni-n0)*lda) = *(A+ni-n0+j*lda);
206 }
207 }
208
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 199965 if (n1 > 1) {
209
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 14014 PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1,A+n-n1+j*lda,A+n-n1+j*lda+1,&inc,&tau));
210 /* Apply reflector */
211
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 14014 if (PetscAbsScalar(tau) != 0.0) {
212 14014 t=*(A+n-n1+j*lda); *(A+n-n1+j*lda)=1.0;
213
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 14014 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&m,&n1,A+n-n1+j*lda,&inc,&tau,A+j+1+(n-n1)*lda,&lda_,work+nwu));
214
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 14014 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1,&m,A+n-n1+j*lda,&inc,&tau,A+n-n1+(j+1)*lda,&lda_,work+nwu));
215 /* Update Q */
216
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 14014 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1,A+n-n1+j*lda,&inc,&tau,Q+(n-n1)*ldq,&ldq_,work+nwu));
217 14014 *(A+n-n1+j*lda) = t;
218
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 96072 for (i=1;i<n1;i++) {
219 82058 *(A+n-n1+i+j*lda) = 0.0; *(A+j+(n-n1+i)*lda) = 0.0;
220 }
221 14014 *(A+j+(n-n1)*lda) = *(A+n-n1+j*lda);
222 }
223 }
224 /* Hyperbolic rotation */
225
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 199965 if (n0 > 0 && n1 > 0) {
226
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 104877 PetscCall(HRGen(PetscRealPart(A[ni-n0+j*lda]),PetscRealPart(A[n-n1+j*lda]),&type,&cs,&sn,&r,&cond));
227 /* Check condition number */
228
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 104877 if (cond > 1.0/(10*PETSC_SQRT_MACHINE_EPSILON)) {
229 ✗ breakdown = PETSC_TRUE;
230 ✗ k++;
231 ✗ PetscCheck(k<n && !flip,PETSC_COMM_SELF,PETSC_ERR_SUP,"Breakdown in construction of hyperbolic transformation");
232 break;
233 }
234 104877 A[ni-n0+j*lda] = r; A[n-n1+j*lda] = 0.0;
235 104877 A[j+(ni-n0)*lda] = r; A[j+(n-n1)*lda] = 0.0;
236 /* Apply to A */
237
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 104877 PetscCall(HRApply(m,A+j+1+(ni-n0)*lda,1,A+j+1+(n-n1)*lda,1,cs,-sn));
238
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 104877 PetscCall(HRApply(m,A+ni-n0+(j+1)*lda,lda,A+n-n1+(j+1)*lda,lda,cs,-sn));
239
240 /* Update Q */
241
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 104877 PetscCall(HRApply(n,Q+(ni-n0)*ldq,1,Q+(n-n1)*ldq,1,cs,-sn));
242
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 104877 if (type==2) {
243 8472 ss[ni-n0] = -ss[ni-n0]; ss[n-n1] = -ss[n-n1];
244 8472 n0++;ni++;n1--;
245 }
246 }
247
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 199965 if (n0>0) n0--;
248 11164 else n1--;
249 }
250 }
251
252 /* flip matrices */
253
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 10001 if (flip) {
254
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 219567 for (i=0;i<n-1;i++) {
255 209606 d[i] = PetscRealPart(A[n-i-1+(n-i-1)*lda]);
256 209606 e[i] = PetscRealPart(A[n-i-1+(n-i-2)*lda]);
257 209606 s[i] = ss[n-i-1];
258 }
259 9961 s[n-1] = ss[0];
260 9961 d[n-1] = PetscRealPart(A[0]);
261
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 229528 for (i=0;i<n;i++) PetscCall(PetscArraycpy(work+i*n,Q+i*ldq,n));
262
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263
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 5836150 for (j=0;j<n;j++)
264 5616583 Q[i+j*ldq] = work[i+(n-j-1)*n];
265 } else {
266
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 400 for (i=0;i<n-1;i++) {
267 360 d[i] = PetscRealPart(A[i+i*lda]);
268 360 e[i] = PetscRealPart(A[i+1+i*lda]);
269 360 s[i] = ss[i];
270 }
271 40 s[n-1] = ss[n-1];
272 40 d[n-1] = PetscRealPart(A[n-1 + (n-1)*lda]);
273 }
274
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 1983 PetscFunctionReturn(PETSC_SUCCESS);
275 }
276
277 335846 static PetscErrorCode MadeHRtr(PetscInt sz,PetscInt n,PetscInt idx0,PetscInt n0,PetscInt idx1,PetscInt n1,struct HRtr *tr1,struct HRtr *tr2,PetscReal *ncond,PetscScalar *work)
278 {
279 335846 PetscScalar *x,*y;
280 335846 PetscReal ncond2=1.0;
281 335846 PetscBLASInt n0_,n1_,inc=1;
282
283
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 335846 PetscFunctionBegin;
284 /* Hyperbolic transformation to make zeros in x */
285 335846 x = tr1->data;
286 335846 tr1->n[0] = n0;
287 335846 tr1->n[1] = n1;
288 335846 tr1->idx[0] = idx0;
289 335846 tr1->idx[1] = idx1;
290
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 335846 PetscCall(PetscBLASIntCast(tr1->n[0],&n0_));
291
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 335846 PetscCall(PetscBLASIntCast(tr1->n[1],&n1_));
292
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 335846 if (tr1->n[0] > 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0_,x+tr1->idx[0],x+tr1->idx[0]+1,&inc,tr1->tau));
293
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 335846 if (tr1->n[1]> 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1_,x+tr1->idx[1],x+tr1->idx[1]+1,&inc,tr1->tau+1));
294
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 335846 if (tr1->idx[0]<tr1->idx[1]) PetscCall(HRGen(PetscRealPart(x[tr1->idx[0]]),PetscRealPart(x[tr1->idx[1]]),&tr1->type,&tr1->cs,&tr1->sn,&tr1->alpha,ncond));
295 else {
296 235037 tr1->alpha = PetscRealPart(x[tr1->idx[0]]);
297 235037 *ncond = 1.0;
298 }
299
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 335846 if (sz==2) {
300 21826 y = tr2->data;
301 /* Apply first transformation to second column */
302
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 21826 if (tr1->n[0] > 1 && PetscAbsScalar(tr1->tau[0])!=0.0) {
303 20728 x[tr1->idx[0]] = 1.0;
304
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 20728 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&inc,x+tr1->idx[0],&inc,tr1->tau,y+tr1->idx[0],&n0_,work));
305 }
306
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 21826 if (tr1->n[1] > 1 && PetscAbsScalar(tr1->tau[1])!=0.0) {
307 7716 x[tr1->idx[1]] = 1.0;
308
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 7716 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&inc,x+tr1->idx[1],&inc,tr1->tau+1,y+tr1->idx[1],&n1_,work));
309 }
310
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 21826 if (tr1->idx[0]<tr1->idx[1]) PetscCall(HRApply(1,y+tr1->idx[0],1,y+tr1->idx[1],1,tr1->cs,-tr1->sn));
311 21826 tr2->n[0] = tr1->n[0];
312 21826 tr2->n[1] = tr1->n[1];
313 21826 tr2->idx[0] = tr1->idx[0];
314 21826 tr2->idx[1] = tr1->idx[1];
315
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 21826 if (tr1->idx[0]<tr1->idx[1] && tr1->type==2) {
316 10913 tr2->idx[1]++; tr2->n[1]--; tr2->n[0]++;
317 }
318
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 21826 if (tr2->n[0]>0) {
319 21826 tr2->n[0]--; tr2->idx[0]++;
320
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 21826 if (tr2->n[1]==0) tr2->idx[1] = tr2->idx[0];
321 } else {
322 ✗ tr2->n[1]--; tr2->idx[1]++; tr2->idx[0] = tr2->idx[1];
323 }
324 /* Hyperbolic transformation to make zeros in y */
325
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 21826 PetscCall(PetscBLASIntCast(tr2->n[0],&n0_));
326
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 21826 PetscCall(PetscBLASIntCast(tr2->n[1],&n1_));
327
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 21826 if (tr2->n[0] > 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0_,y+tr2->idx[0],y+tr2->idx[0]+1,&inc,tr2->tau));
328
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 21826 if (tr2->n[1]> 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1_,y+tr2->idx[1],y+tr2->idx[1]+1,&inc,tr2->tau+1));
329
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 21826 if (tr2->idx[0]<tr2->idx[1]) PetscCall(HRGen(PetscRealPart(y[tr2->idx[0]]),PetscRealPart(y[tr2->idx[1]]),&tr2->type,&tr2->cs,&tr2->sn,&tr2->alpha,&ncond2));
330 else {
331 7604 tr2->alpha = PetscRealPart(y[tr2->idx[0]]);
332 7604 ncond2 = 1.0;
333 }
334
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 21826 if (ncond2>*ncond) *ncond = ncond2;
335 }
336
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 67713 PetscFunctionReturn(PETSC_SUCCESS);
337 }
338
339 /*
340 Auxiliary function to try perform one iteration of hr routine,
341 checking condition number. If it is < tolD, apply the
342 transformation to H and R, if not, ok=false and it do nothing
343 tolE, tolerance to exchange complex pairs to improve conditioning
344 */
345 324933 static PetscErrorCode TryHRIt(PetscInt n,PetscInt j,PetscInt sz,PetscScalar *H,PetscInt ldh,PetscScalar *R,PetscInt ldr,PetscReal *s,PetscBool *exg,PetscBool *ok,PetscInt *n0,PetscInt *n1,PetscInt *idx0,PetscInt *idx1,PetscReal *cond,PetscScalar *work)
346 {
347 324933 struct HRtr *tr1,*tr2,tr1_t,tr2_t,tr1_te,tr2_te;
348 324933 PetscScalar *x,*y;
349 324933 PetscReal ncond=0,ncond_e;
350 324933 PetscInt nwu=0,i,d=1;
351 324933 PetscBLASInt n0_,n1_,inc=1,mh,mr,n_,ldr_,ldh_;
352 324933 PetscReal tolD = 1e+5;
353
354
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 324933 PetscFunctionBegin;
355
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 324933 if (cond) *cond = 1.0;
356
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 324933 PetscCall(PetscBLASIntCast(n,&n_));
357
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 324933 PetscCall(PetscBLASIntCast(ldr,&ldr_));
358
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 324933 PetscCall(PetscBLASIntCast(ldh,&ldh_));
359 324933 x = work+nwu;
360 324933 nwu += n;
361
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 324933 PetscCall(PetscArraycpy(x,R+j*ldr,n));
362 324933 *exg = PETSC_FALSE;
363 324933 *ok = PETSC_TRUE;
364 324933 tr1_t.data = x;
365
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 324933 if (sz==1) {
366 /* Hyperbolic transformation to make zeros in x */
367
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 314020 PetscCall(MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_t,NULL,&ncond,work+nwu));
368 /* Check condition number to single column*/
369
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 314020 if (ncond>tolD) *ok = PETSC_FALSE;
370 tr1 = &tr1_t;
371 tr2 = &tr2_t;
372 } else {
373 10913 y = work+nwu;
374 10913 nwu += n;
375
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 10913 PetscCall(PetscArraycpy(y,R+(j+1)*ldr,n));
376 10913 tr2_t.data = y;
377
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 10913 PetscCall(MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_t,&tr2_t,&ncond,work+nwu));
378 /* Computing hyperbolic transformations also for exchanged vectors */
379 10913 tr1_te.data = work+nwu;
380 10913 nwu += n;
381
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 10913 PetscCall(PetscArraycpy(tr1_te.data,R+(j+1)*ldr,n));
382 10913 tr2_te.data = work+nwu;
383 10913 nwu += n;
384
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 10913 PetscCall(PetscArraycpy(tr2_te.data,R+j*ldr,n));
385
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 10913 PetscCall(MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_te,&tr2_te,&ncond_e,work+nwu));
386
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 10913 if (ncond > d*ncond_e) {
387 6204 *exg = PETSC_TRUE;
388 6204 tr1 = &tr1_te;
389 6204 tr2 = &tr2_te;
390 6204 ncond = ncond_e;
391 } else {
392 tr1 = &tr1_t;
393 tr2 = &tr2_t;
394 }
395
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 10913 if (ncond>tolD) *ok = PETSC_FALSE;
396 }
397
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 324933 if (*ok) {
398 /* Everything is OK, apply transformations to R and H */
399 /* First column */
400
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 324933 if (cond && *cond<ncond) *cond = ncond;
401 324933 x = tr1->data;
402
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 324933 PetscCall(PetscBLASIntCast(tr1->n[0],&n0_));
403
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 324933 PetscCall(PetscBLASIntCast(tr1->n[1],&n1_));
404
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 324933 PetscCall(PetscBLASIntCast(n-j-sz,&mr));
405
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 324933 if (tr1->n[0] > 1 && PetscAbsScalar(tr1->tau[0])!=0.0) {
406 302394 x[tr1->idx[0]] = 1.0;
407
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 302394 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&mr,x+tr1->idx[0],&inc,tr1->tau,R+(j+sz)*ldr+tr1->idx[0],&ldr_,work+nwu));
408
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 302394 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0_,x+tr1->idx[0],&inc,tr1->tau,H+(tr1->idx[0])*ldh,&ldh_,work+nwu));
409 }
410
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 324933 if (tr1->n[1] > 1 && PetscAbsScalar(tr1->tau[1])!=0.0) {
411 50965 x[tr1->idx[1]] = 1.0;
412
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 50965 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&mr,x+tr1->idx[1],&inc,tr1->tau+1,R+(j+sz)*ldr+tr1->idx[1],&ldr_,work+nwu));
413
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 50965 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1_,x+tr1->idx[1],&inc,tr1->tau+1,H+(tr1->idx[1])*ldh,&ldh_,work+nwu));
414 }
415
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 324933 if (tr1->idx[0]<tr1->idx[1]) {
416
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 89896 PetscCall(HRApply(mr,R+(j+sz)*ldr+tr1->idx[0],ldr,R+(j+sz)*ldr+tr1->idx[1],ldr,tr1->cs,-tr1->sn));
417
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 89896 if (tr1->type==1) PetscCall(HRApply(n,H+(tr1->idx[0])*ldh,1,H+(tr1->idx[1])*ldh,1,tr1->cs,tr1->sn));
418 else {
419
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 13879 PetscCall(HRApply(n,H+(tr1->idx[0])*ldh,1,H+(tr1->idx[1])*ldh,1,-tr1->cs,-tr1->sn));
420 13879 s[tr1->idx[0]] = -s[tr1->idx[0]];
421 13879 s[tr1->idx[1]] = -s[tr1->idx[1]];
422 }
423 }
424
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 6703128 for (i=0;i<tr1->idx[0];i++) *(R+j*ldr+i) = x[i];
425
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 6567374 for (i=tr1->idx[0]+1;i<n;i++) *(R+j*ldr+i) = 0.0;
426 324933 *(R+j*ldr+tr1->idx[0]) = tr1->alpha;
427
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 324933 if (sz==2) {
428 10913 y = tr2->data;
429 /* Second column */
430
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 10913 PetscCall(PetscBLASIntCast(tr2->n[0],&n0_));
431
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 10913 PetscCall(PetscBLASIntCast(tr2->n[1],&n1_));
432
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 10913 PetscCall(PetscBLASIntCast(n-j-sz,&mr));
433
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 10913 PetscCall(PetscBLASIntCast(n-tr2->idx[0],&mh));
434
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 10913 if (tr2->n[0] > 1 && PetscAbsScalar(tr2->tau[0])!=0.0) {
435 10101 y[tr2->idx[0]] = 1.0;
436
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 10101 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&mr,y+tr2->idx[0],&inc,tr2->tau,R+(j+2)*ldr+tr2->idx[0],&ldr_,work+nwu));
437
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 10101 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0_,y+tr2->idx[0],&inc,tr2->tau,H+(tr2->idx[0])*ldh,&ldh_,work+nwu));
438 }
439
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 10913 if (tr2->n[1] > 1 && PetscAbsScalar(tr2->tau[1])!=0.0) {
440 3508 y[tr2->idx[1]] = 1.0;
441
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 3508 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&mr,y+tr2->idx[1],&inc,tr2->tau+1,R+(j+2)*ldr+tr2->idx[1],&ldr_,work+nwu));
442
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 3508 PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1_,y+tr2->idx[1],&inc,tr2->tau+1,H+(tr2->idx[1])*ldh,&ldh_,work+nwu));
443 }
444
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 10913 if (tr2->idx[0]<tr2->idx[1]) {
445
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 8102 PetscCall(HRApply(mr,R+(j+2)*ldr+tr2->idx[0],ldr,R+(j+2)*ldr+tr2->idx[1],ldr,tr2->cs,-tr2->sn));
446
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 8102 if (tr2->type==1) PetscCall(HRApply(n,H+(tr2->idx[0])*ldh,1,H+(tr2->idx[1])*ldh,1,tr2->cs,tr2->sn));
447 else {
448
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 6343 PetscCall(HRApply(n,H+(tr2->idx[0])*ldh,1,H+(tr2->idx[1])*ldh,1,-tr2->cs,-tr2->sn));
449 6343 s[tr2->idx[0]] = -s[tr2->idx[0]];
450 6343 s[tr2->idx[1]] = -s[tr2->idx[1]];
451 }
452 }
453
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 122246 for (i=0;i<tr2->idx[0]-1;i++) *(R+(j+1)*ldr+i) = y[i];
454 10913 *(R+(j+1)*ldr+tr2->idx[0]-1) = y[tr2->idx[0]-1];
455
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 268913 for (i=tr2->idx[0]+1;i<n;i++) *(R+(j+1)*ldr+i) = 0.0;
456 10913 *(R+(j+1)*ldr+tr2->idx[0]) = tr2->alpha;
457 10913 *n0 = tr2->n[0];
458 10913 *n1 = tr2->n[1];
459 10913 *idx0 = tr2->idx[0];
460 10913 *idx1 = tr2->idx[1];
461
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 10913 if (tr2->idx[0]<tr2->idx[1] && tr2->type==2) {
462 6343 (*idx1)++; (*n1)--; (*n0)++;
463 }
464 } else {
465 314020 *n0 = tr1->n[0];
466 314020 *n1 = tr1->n[1];
467 314020 *idx0 = tr1->idx[0];
468 314020 *idx1 = tr1->idx[1];
469
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 314020 if (tr1->idx[0]<tr1->idx[1] && tr1->type==2) {
470 9568 (*idx1)++; (*n1)--; (*n0)++;
471 }
472 }
473
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 324933 if (*n0>0) {
474 313560 (*n0)--; (*idx0)++;
475
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 313560 if (*n1==0) *idx1 = *idx0;
476 } else {
477 11373 (*n1)--; (*idx1)++; *idx0 = *idx1;
478 }
479 }
480
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 65465 PetscFunctionReturn(PETSC_SUCCESS);
481 }
482
483 /*
484 compute V = HR whit H s-orthogonal and R upper triangular
485 (work: work space of minimum size 6*nv)
486 */
487 10520 PetscErrorCode DSPseudoOrthog_HR(PetscInt *nv,PetscScalar *V,PetscInt ldv,PetscReal *s,PetscScalar *R,PetscInt ldr,PetscBLASInt *perm,PetscBLASInt *cmplxEig,PetscBool *breakdown,PetscScalar *work)
488 {
489 10520 PetscInt i,j,n,n0,n1,np,idx0,idx1,sz=1,k=0,nwu=0;
490 10520 PetscBLASInt t1,t2;
491 10520 PetscScalar *col1,*col2;
492 10520 PetscBool exg=PETSC_FALSE,ok=PETSC_FALSE;
493
494
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 10520 PetscFunctionBegin;
495 10520 n = *nv;
496 10520 col1 = work+nwu;
497 10520 nwu += n;
498 10520 col2 = work+nwu;
499 10520 nwu += n;
500 /* Sort R and s according to sing(s) */
501 10520 np = 0;
502
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 346366 for (i=0;i<n;i++) if (s[i]>0) np++;
503
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 10520 if (s[0]>0) n1 = np;
504 994 else n1 = n-np;
505 10520 n0 = 0;
506
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 346366 for (i=0;i<n;i++) {
507
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 335846 if (s[i]==s[0]) {
508 304251 s[n0] = s[0];
509
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 304251 PetscCall(PetscBLASIntCast(i,&perm[n0++]));
510
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 335846 } else PetscCall(PetscBLASIntCast(i,&perm[n1++]));
511 }
512
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 42115 for (i=n0;i<n;i++) s[i] = -s[0];
513 10520 n1 -= n0;
514 10520 idx0 = 0;
515 10520 idx1 = n0;
516
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 10520 if (idx1==n) idx1=idx0;
517
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 346366 for (i=0;i<n;i++) {
518
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 13672574 for (j=0;j<n;j++) R[j*ldr+i] = V[j*ldv+perm[i]];
519 }
520 /* Initialize H */
521
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522
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 335846 PetscCall(PetscArrayzero(V+i*ldv,n));
523 335846 V[perm[i]+i*ldv] = 1.0;
524 }
525
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 346366 for (i=0;i<n;i++) PetscCall(PetscBLASIntCast(i,&perm[i]));
526 j = 0;
527 335453 while (j<n-k) {
528
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 324933 if (cmplxEig[j]==0) sz=1;
529 10913 else sz=2;
530
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 324933 PetscCall(TryHRIt(n,j,sz,V,ldv,R,ldr,s,&exg,&ok,&n0,&n1,&idx0,&idx1,NULL,work+nwu));
531
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 324933 if (ok) {
532
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 324933 if (exg) cmplxEig[j] = -cmplxEig[j];
533 324933 j = j+sz;
534 } else { /* to be discarded */
535 ✗ k = k+1;
536 ✗ if (cmplxEig[j]==0) {
537 ✗ if (j<n) {
538 ✗ t1 = perm[j];
539 ✗ for (i=j;i<n-1;i++) perm[i] = perm[i+1];
540 ✗ perm[n-1] = t1;
541 ✗ t1 = cmplxEig[j];
542 ✗ for (i=j;i<n-1;i++) cmplxEig[i] = cmplxEig[i+1];
543 ✗ cmplxEig[n-1] = t1;
544 ✗ PetscCall(PetscArraycpy(col1,R+j*ldr,n));
545 ✗ for (i=j;i<n-1;i++) PetscCall(PetscArraycpy(R+i*ldr,R+(i+1)*ldr,n));
546 ✗ PetscCall(PetscArraycpy(R+(n-1)*ldr,col1,n));
547 }
548 } else {
549 ✗ k = k+1;
550 ✗ if (j<n-1) {
551 ✗ t1 = perm[j]; t2 = perm[j+1];
552 ✗ for (i=j;i<n-2;i++) perm[i] = perm[i+2];
553 ✗ perm[n-2] = t1; perm[n-1] = t2;
554 ✗ t1 = cmplxEig[j]; t2 = cmplxEig[j+1];
555 ✗ for (i=j;i<n-2;i++) cmplxEig[i] = cmplxEig[i+2];
556 ✗ cmplxEig[n-2] = t1; cmplxEig[n-1] = t2;
557 ✗ PetscCall(PetscArraycpy(col1,R+j*ldr,n));
558 ✗ PetscCall(PetscArraycpy(col2,R+(j+1)*ldr,n));
559 ✗ for (i=j;i<n-2;i++) PetscCall(PetscArraycpy(R+i*ldr,R+(i+2)*ldr,n));
560 ✗ PetscCall(PetscArraycpy(R+(n-2)*ldr,col1,n));
561
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 335453 PetscCall(PetscArraycpy(R+(n-1)*ldr,col2,n));
562 }
563 }
564 }
565 }
566
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 10520 if (k!=0) {
567 ✗ if (breakdown) *breakdown = PETSC_TRUE;
568 ✗ *nv = n-k;
569 }
570
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 2092 PetscFunctionReturn(PETSC_SUCCESS);
571 }
572
573 10500 PetscErrorCode DSGHIEPOrthogEigenv(DS ds,DSMatType mat,PetscScalar *wr,PetscScalar *wi,PetscBool accum)
574 {
575 10500 PetscInt lws,nwus=0,nwui=0,lwi,off,n,nv,ld,i,ldr,l;
576 10500 const PetscScalar *B,*W;
577 10500 PetscScalar *Q,*X,*R,*ts,szero=0.0,sone=1.0;
578 10500 PetscReal *s,vi,vr,tr,*d,*e;
579 10500 PetscBLASInt ld_,n_,nv_,*perm,*cmplxEig;
580
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 10500 PetscFunctionBegin;
582 10500 l = ds->l;
583 10500 n = ds->n-l;
584
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 10500 PetscCall(PetscBLASIntCast(n,&n_));
585 10500 ld = ds->ld;
586
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 10500 PetscCall(PetscBLASIntCast(ld,&ld_));
587 10500 off = l*ld+l;
588
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 10500 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
589
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 10500 if (!ds->compact) {
590
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 40 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
591
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 440 for (i=l;i<ds->n;i++) s[i] = PetscRealPart(B[i*ld+i]);
592
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 40 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
593 }
594 10500 lws = n*n+7*n;
595 10500 lwi = 2*n;
596
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 10500 PetscCall(DSAllocateWork_Private(ds,lws,0,lwi));
597 10500 R = ds->work+nwus;
598 10500 nwus += n*n;
599 10500 ldr = n;
600 10500 perm = ds->iwork + nwui;
601 10500 nwui += n;
602 10500 cmplxEig = ds->iwork+nwui;
603
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 10500 PetscCall(MatDenseGetArray(ds->omat[mat],&X));
604
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 335273 for (i=0;i<n;i++) {
605 #if defined(PETSC_USE_COMPLEX)
606 47006 vi = PetscImaginaryPart(wr[l+i]);
607 #else
608
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 277767 vi = wi?PetscRealPart(wi[l+i]):0.0;
609 #endif
610
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 324773 if (vi!=0) {
611 10913 cmplxEig[i] = 1;
612 10913 cmplxEig[i+1] = 2;
613 10913 i++;
614 313860 } else cmplxEig[i] = 0;
615 }
616 10500 nv = n;
617
618 /* Perform HR decomposition */
619 /* Hyperbolic rotators */
620
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 10500 PetscCall(DSPseudoOrthog_HR(&nv,X+off,ld,s+l,R,ldr,perm,cmplxEig,NULL,ds->work+nwus));
621 /* Sort wr,wi perm */
622 10500 ts = ds->work+nwus;
623
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 10500 PetscCall(PetscArraycpy(ts,wr+l,n));
624
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 346186 for (i=0;i<n;i++) wr[i+l] = ts[perm[i]];
625 #if !defined(PETSC_USE_COMPLEX)
626
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 8714 if (wi) {
627
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 8714 PetscCall(PetscArraycpy(ts,wi+l,n));
628
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 296220 for (i=0;i<n;i++) wi[i+l] = ts[perm[i]];
629 }
630 #endif
631 /* Projected Matrix */
632
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 10500 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
633
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 10500 PetscCall(PetscArrayzero(d+2*ld,ld));
634 10500 e = d+ld;
635 10500 d[l+nv-1] = PetscRealPart(wr[l+nv-1]*s[l+nv-1]);
636
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 325110 for (i=0;i<nv-1;i++) {
637
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 314610 if (cmplxEig[i]==0) { /* Real */
638 303697 d[l+i] = PetscRealPart(wr[l+i]*s[l+i]);
639 303697 e[l+i] = 0.0;
640 } else {
641 10913 vr = PetscRealPart(wr[l+i]);
642 #if defined(PETSC_USE_COMPLEX)
643 1174 vi = PetscImaginaryPart(wr[l+i]);
644 #else
645
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 9739 vi = wi?PetscRealPart(wi[l+i]):0.0;
646 #endif
647
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 10913 if (cmplxEig[i]==-1) vi = -vi;
648 10913 tr = PetscRealPart((R[i+(i+1)*ldr]/R[i+i*ldr]))*vi;
649 10913 d[l+i] = (vr-tr)*s[l+i];
650 10913 d[l+i+1] = (vr+tr)*s[l+i+1];
651 10913 e[l+i] = PetscRealPart(s[l+i]*(R[(i+1)+(i+1)*ldr]/R[i+i*ldr])*vi);
652
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 10913 if (i<nv-2) e[l+i+1] = 0.0;
653 i++;
654 }
655 }
656
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 10500 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
657
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 10500 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
658 /* accumulate previous Q */
659
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 10500 if (accum) {
660
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 10470 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
661
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 10470 PetscCall(PetscBLASIntCast(nv,&nv_));
662
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 10470 PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
663
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 10470 PetscCall(MatCopy(ds->omat[DS_MAT_Q],ds->omat[DS_MAT_W],SAME_NONZERO_PATTERN));
664
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 10470 PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_W],&W));
665
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 10470 PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&nv_,&n_,&sone,W+off,&ld_,X+off,&ld_,&szero,Q+off,&ld_));
666
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 10470 PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_W],&W));
667
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 10470 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
668 }
669 10500 ds->t = nv+l;
670
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 10500 PetscCall(MatDenseRestoreArray(ds->omat[mat],&X));
671
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 10500 if (!ds->compact) PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
672
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 2088 PetscFunctionReturn(PETSC_SUCCESS);
673 }
674
675 /*
676 Reduce to tridiagonal-diagonal pair by means of TridiagDiag_HHR.
677 */
678 10500 PetscErrorCode DSIntermediate_GHIEP(DS ds)
679 {
680 10500 PetscInt i,ld,off;
681 10500 PetscInt nwall,nwallr,nwalli;
682 10500 PetscScalar *A,*B,*Q;
683 10500 PetscReal *d,*e,*s;
684
685
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 10500 PetscFunctionBegin;
686 10500 ld = ds->ld;
687
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 10500 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
688
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 10500 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
689
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 10500 PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
690
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 10500 PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
691
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 10500 PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
692 10500 e = d+ld;
693 10500 off = ds->l+ds->l*ld;
694
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 10500 PetscCall(PetscArrayzero(Q,ld*ld));
695 10500 nwall = ld*ld+ld;
696 10500 nwallr = ld;
697 10500 nwalli = ld;
698
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 10500 PetscCall(DSAllocateWork_Private(ds,nwall,nwallr,nwalli));
699
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 357842 for (i=0;i<ds->n;i++) Q[i+i*ld]=1.0;
700
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 346186 for (i=0;i<ds->n-ds->l;i++) *(ds->perm+i)=i;
701
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 10500 if (ds->compact) {
702
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 10460 if (ds->state < DS_STATE_INTERMEDIATE) {
703
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 9961 PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
704
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 9961 PetscCall(TridiagDiag_HHR(ds->k-ds->l+1,A+off,ld,s+ds->l,Q+off,ld,PETSC_TRUE,d+ds->l,e+ds->l,ds->perm,ds->work,ds->rwork,ds->iwork));
705 9961 ds->k = ds->l;
706
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 9961 PetscCall(PetscArrayzero(d+2*ld+ds->l,ds->n-ds->l));
707 }
708 } else {
709
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 40 if (ds->state < DS_STATE_INTERMEDIATE) {
710
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 440 for (i=0;i<ds->n;i++) s[i] = PetscRealPart(B[i+i*ld]);
711
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 40 PetscCall(TridiagDiag_HHR(ds->n-ds->l,A+off,ld,s+ds->l,Q+off,ld,PETSC_FALSE,d+ds->l,e+ds->l,ds->perm,ds->work,ds->rwork,ds->iwork));
712
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 40 PetscCall(PetscArrayzero(d+2*ld,ds->n));
713 40 ds->k = ds->l;
714
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 40 PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
715 ✗ } else PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_TRUE));
716 }
717
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 10500 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
718
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 10500 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
719
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 10500 PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
720
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 10500 PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
721
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 10500 PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
722
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 2088 PetscFunctionReturn(PETSC_SUCCESS);
723 }
724