Line data Source code
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 6258 : static PetscErrorCode HRGen(PetscReal x1,PetscReal x2,PetscInt *type,PetscReal *c,PetscReal *s,PetscReal *r,PetscReal *cond)
39 : {
40 6258 : PetscReal t,n2,xa,xb;
41 6258 : PetscInt type_;
42 :
43 6258 : PetscFunctionBegin;
44 6258 : if (x2==0.0) {
45 0 : *r = PetscAbsReal(x1); *c = (x1>=0.0)?1.0:-1.0; *s = 0.0;
46 0 : if (type) *type = 1;
47 0 : PetscFunctionReturn(PETSC_SUCCESS);
48 : }
49 6258 : if (PetscAbsReal(x1) == PetscAbsReal(x2)) {
50 : /* hyperbolic rotation doesn't exist */
51 0 : *c = *s = *r = 0.0;
52 0 : if (type) *type = 0;
53 0 : *cond = PETSC_MAX_REAL;
54 0 : PetscFunctionReturn(PETSC_SUCCESS);
55 : }
56 :
57 6258 : if (PetscAbsReal(x1)>PetscAbsReal(x2)) {
58 : xa = x1; xb = x2; type_ = 1;
59 : } else {
60 1528 : xa = x2; xb = x1; type_ = 2;
61 : }
62 6258 : t = xb/xa;
63 6258 : n2 = PetscAbsReal(1 - t*t);
64 6258 : *r = PetscSqrtReal(n2)*PetscAbsReal(xa);
65 6258 : *c = x1/(*r);
66 6258 : *s = x2/(*r);
67 6258 : if (type_ == 2) *r *= -1;
68 6258 : if (type) *type = type_;
69 6258 : if (cond) *cond = (PetscAbsReal(*c) + PetscAbsReal(*s))/PetscAbsReal(PetscAbsReal(*c) - PetscAbsReal(*s));
70 6258 : 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 12263 : static PetscErrorCode HRApply(PetscInt n,PetscScalar *x1,PetscInt inc1,PetscScalar *x2,PetscInt inc2,PetscReal c,PetscReal s)
80 : {
81 12263 : PetscInt i;
82 12263 : PetscReal t;
83 12263 : PetscScalar tmp;
84 :
85 12263 : PetscFunctionBegin;
86 12263 : if (PetscAbsReal(c)>PetscAbsReal(s)) { /* Type I */
87 9387 : t = s/c;
88 674897 : for (i=0;i<n;i++) {
89 665510 : x1[i*inc1] = c*x1[i*inc1] + s*x2[i*inc2];
90 665510 : x2[i*inc2] = t*x1[i*inc1] + x2[i*inc2]/c;
91 : }
92 : } else { /* Type II */
93 2876 : t = c/s;
94 93305 : for (i=0;i<n;i++) {
95 90429 : tmp = x1[i*inc1];
96 90429 : x1[i*inc1] = c*x1[i*inc1] + s*x2[i*inc2];
97 90429 : x2[i*inc2] = t*x1[i*inc1] + tmp/s;
98 : }
99 : }
100 12263 : 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 : */
114 324 : 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 : {
116 324 : PetscInt i,j,k,*ii,*jj,i0=0,ik=0,tmp,type;
117 324 : PetscInt nwu=0;
118 324 : PetscReal *ss,cond=1.0,cs,sn,r;
119 324 : PetscScalar tau,t,*AA;
120 324 : PetscBLASInt n0,n1,ni,inc=1,m,n_,lda_,ldq_,*perm;
121 324 : PetscBool breakdown = PETSC_TRUE;
122 :
123 324 : PetscFunctionBegin;
124 324 : if (n<3) {
125 0 : if (n==1) Q[0]=1;
126 0 : if (n==2) {
127 0 : Q[0] = Q[1+ldq] = 1;
128 0 : Q[1] = Q[ldq] = 0;
129 : }
130 0 : PetscFunctionReturn(PETSC_SUCCESS);
131 : }
132 324 : PetscCall(PetscBLASIntCast(lda,&lda_));
133 324 : PetscCall(PetscBLASIntCast(n,&n_));
134 324 : PetscCall(PetscBLASIntCast(ldq,&ldq_));
135 324 : ss = rwork;
136 324 : perm = iwork;
137 324 : AA = work;
138 4987 : for (i=0;i<n;i++) PetscCall(PetscArraycpy(AA+i*n,A+i*lda,n));
139 324 : nwu += n*n;
140 324 : k=0;
141 648 : while (breakdown && k<n) {
142 324 : breakdown = PETSC_FALSE;
143 : /* Classify (and flip) A and s according to sign */
144 324 : if (flip) {
145 4943 : for (i=0;i<n;i++) {
146 4623 : perm[i] = n-1-perm_[i];
147 4623 : if (perm[i]==0) i0 = i;
148 4623 : if (perm[i]==k) ik = i;
149 : }
150 : } else {
151 44 : for (i=0;i<n;i++) {
152 40 : perm[i] = perm_[i];
153 40 : if (perm[i]==0) i0 = i;
154 40 : if (perm[i]==k) ik = i;
155 : }
156 : }
157 324 : perm[ik] = 0;
158 324 : perm[i0] = k;
159 324 : i=1;
160 3264 : while (i<n-1 && s[perm[i-1]]==s[perm[0]]) {
161 2940 : if (s[perm[i]]!=s[perm[0]]) {
162 721 : j=i+1;
163 2342 : while (j<n-1 && s[perm[j]]!=s[perm[0]])j++;
164 721 : tmp = perm[i]; perm[i] = perm[j]; perm[j] = tmp;
165 : }
166 2940 : i++;
167 : }
168 4987 : for (i=0;i<n;i++) {
169 4663 : ss[i] = s[perm[i]];
170 : }
171 324 : if (flip) {
172 : ii = &j;
173 : jj = &i;
174 : } else {
175 4 : ii = &i;
176 4 : jj = &j;
177 : }
178 4987 : for (i=0;i<n;i++)
179 123542 : for (j=0;j<n;j++)
180 118879 : A[i+j*lda] = AA[perm[*ii]+perm[*jj]*n];
181 : /* Initialize Q */
182 4987 : for (i=0;i<n;i++) {
183 4663 : PetscCall(PetscArrayzero(Q+i*ldq,n));
184 4663 : Q[perm[i]+i*ldq] = 1.0;
185 : }
186 3336 : for (ni=1;ni<n && ss[ni]==ss[0]; ni++);
187 324 : n0 = ni-1;
188 324 : n1 = n_-ni;
189 4339 : for (j=0;j<n-2;j++) {
190 4015 : PetscCall(PetscBLASIntCast(n-j-1,&m));
191 : /* Forming and applying reflectors */
192 4015 : if (n0 > 1) {
193 2840 : PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0,A+ni-n0+j*lda,A+ni-n0+j*lda+1,&inc,&tau));
194 : /* Apply reflector */
195 2840 : if (PetscAbsScalar(tau) != 0.0) {
196 2840 : t=*(A+ni-n0+j*lda); *(A+ni-n0+j*lda)=1.0;
197 2840 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&m,&n0,A+ni-n0+j*lda,&inc,&tau,A+j+1+(j+1)*lda,&lda_,work+nwu));
198 2840 : 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 2840 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0,A+ni-n0+j*lda,&inc,&tau,Q+(j+1)*ldq,&ldq_,work+nwu));
201 2840 : *(A+ni-n0+j*lda) = t;
202 47317 : for (i=1;i<n0;i++) {
203 44477 : *(A+ni-n0+j*lda+i) = 0.0; *(A+j+(ni-n0+i)*lda) = 0.0;
204 : }
205 2840 : *(A+j+(ni-n0)*lda) = *(A+ni-n0+j*lda);
206 : }
207 : }
208 4015 : if (n1 > 1) {
209 1301 : PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1,A+n-n1+j*lda,A+n-n1+j*lda+1,&inc,&tau));
210 : /* Apply reflector */
211 1301 : if (PetscAbsScalar(tau) != 0.0) {
212 1301 : t=*(A+n-n1+j*lda); *(A+n-n1+j*lda)=1.0;
213 1301 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&m,&n1,A+n-n1+j*lda,&inc,&tau,A+j+1+(n-n1)*lda,&lda_,work+nwu));
214 1301 : 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 1301 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1,A+n-n1+j*lda,&inc,&tau,Q+(n-n1)*ldq,&ldq_,work+nwu));
217 1301 : *(A+n-n1+j*lda) = t;
218 9366 : for (i=1;i<n1;i++) {
219 8065 : *(A+n-n1+i+j*lda) = 0.0; *(A+j+(n-n1+i)*lda) = 0.0;
220 : }
221 1301 : *(A+j+(n-n1)*lda) = *(A+n-n1+j*lda);
222 : }
223 : }
224 : /* Hyperbolic rotation */
225 4015 : if (n0 > 0 && n1 > 0) {
226 227 : PetscCall(HRGen(PetscRealPart(A[ni-n0+j*lda]),PetscRealPart(A[n-n1+j*lda]),&type,&cs,&sn,&r,&cond));
227 : /* Check condition number */
228 227 : if (cond > 1.0/(10*PETSC_SQRT_MACHINE_EPSILON)) {
229 0 : breakdown = PETSC_TRUE;
230 0 : k++;
231 0 : PetscCheck(k<n && !flip,PETSC_COMM_SELF,PETSC_ERR_SUP,"Breakdown in construction of hyperbolic transformation");
232 : break;
233 : }
234 227 : A[ni-n0+j*lda] = r; A[n-n1+j*lda] = 0.0;
235 227 : A[j+(ni-n0)*lda] = r; A[j+(n-n1)*lda] = 0.0;
236 : /* Apply to A */
237 227 : PetscCall(HRApply(m,A+j+1+(ni-n0)*lda,1,A+j+1+(n-n1)*lda,1,cs,-sn));
238 227 : PetscCall(HRApply(m,A+ni-n0+(j+1)*lda,lda,A+n-n1+(j+1)*lda,lda,cs,-sn));
239 :
240 : /* Update Q */
241 227 : PetscCall(HRApply(n,Q+(ni-n0)*ldq,1,Q+(n-n1)*ldq,1,cs,-sn));
242 227 : if (type==2) {
243 97 : ss[ni-n0] = -ss[ni-n0]; ss[n-n1] = -ss[n-n1];
244 97 : n0++;ni++;n1--;
245 : }
246 : }
247 4015 : if (n0>0) n0--;
248 1125 : else n1--;
249 : }
250 : }
251 :
252 : /* flip matrices */
253 324 : if (flip) {
254 4623 : for (i=0;i<n-1;i++) {
255 4303 : d[i] = PetscRealPart(A[n-i-1+(n-i-1)*lda]);
256 4303 : e[i] = PetscRealPart(A[n-i-1+(n-i-2)*lda]);
257 4303 : s[i] = ss[n-i-1];
258 : }
259 320 : s[n-1] = ss[0];
260 320 : d[n-1] = PetscRealPart(A[0]);
261 4943 : for (i=0;i<n;i++) PetscCall(PetscArraycpy(work+i*n,Q+i*ldq,n));
262 4943 : for (i=0;i<n;i++)
263 123102 : for (j=0;j<n;j++)
264 118479 : Q[i+j*ldq] = work[i+(n-j-1)*n];
265 : } else {
266 40 : for (i=0;i<n-1;i++) {
267 36 : d[i] = PetscRealPart(A[i+i*lda]);
268 36 : e[i] = PetscRealPart(A[i+1+i*lda]);
269 36 : s[i] = ss[i];
270 : }
271 4 : s[n-1] = ss[n-1];
272 4 : d[n-1] = PetscRealPart(A[n-1 + (n-1)*lda]);
273 : }
274 324 : PetscFunctionReturn(PETSC_SUCCESS);
275 : }
276 :
277 10635 : 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 10635 : PetscScalar *x,*y;
280 10635 : PetscReal ncond2=1.0;
281 10635 : PetscBLASInt n0_,n1_,inc=1;
282 :
283 10635 : PetscFunctionBegin;
284 : /* Hyperbolic transformation to make zeros in x */
285 10635 : x = tr1->data;
286 10635 : tr1->n[0] = n0;
287 10635 : tr1->n[1] = n1;
288 10635 : tr1->idx[0] = idx0;
289 10635 : tr1->idx[1] = idx1;
290 10635 : PetscCall(PetscBLASIntCast(tr1->n[0],&n0_));
291 10635 : PetscCall(PetscBLASIntCast(tr1->n[1],&n1_));
292 10635 : if (tr1->n[0] > 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0_,x+tr1->idx[0],x+tr1->idx[0]+1,&inc,tr1->tau));
293 10635 : if (tr1->n[1]> 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1_,x+tr1->idx[1],x+tr1->idx[1]+1,&inc,tr1->tau+1));
294 10635 : 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 5099 : tr1->alpha = PetscRealPart(x[tr1->idx[0]]);
297 5099 : *ncond = 1.0;
298 : }
299 10635 : if (sz==2) {
300 578 : y = tr2->data;
301 : /* Apply first transformation to second column */
302 578 : if (tr1->n[0] > 1 && PetscAbsScalar(tr1->tau[0])!=0.0) {
303 524 : x[tr1->idx[0]] = 1.0;
304 524 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&inc,x+tr1->idx[0],&inc,tr1->tau,y+tr1->idx[0],&n0_,work));
305 : }
306 578 : if (tr1->n[1] > 1 && PetscAbsScalar(tr1->tau[1])!=0.0) {
307 466 : x[tr1->idx[1]] = 1.0;
308 466 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&inc,x+tr1->idx[1],&inc,tr1->tau+1,y+tr1->idx[1],&n1_,work));
309 : }
310 578 : if (tr1->idx[0]<tr1->idx[1]) PetscCall(HRApply(1,y+tr1->idx[0],1,y+tr1->idx[1],1,tr1->cs,-tr1->sn));
311 578 : tr2->n[0] = tr1->n[0];
312 578 : tr2->n[1] = tr1->n[1];
313 578 : tr2->idx[0] = tr1->idx[0];
314 578 : tr2->idx[1] = tr1->idx[1];
315 578 : if (tr1->idx[0]<tr1->idx[1] && tr1->type==2) {
316 289 : tr2->idx[1]++; tr2->n[1]--; tr2->n[0]++;
317 : }
318 578 : if (tr2->n[0]>0) {
319 578 : tr2->n[0]--; tr2->idx[0]++;
320 578 : if (tr2->n[1]==0) tr2->idx[1] = tr2->idx[0];
321 : } else {
322 0 : tr2->n[1]--; tr2->idx[1]++; tr2->idx[0] = tr2->idx[1];
323 : }
324 : /* Hyperbolic transformation to make zeros in y */
325 578 : PetscCall(PetscBLASIntCast(tr2->n[0],&n0_));
326 578 : PetscCall(PetscBLASIntCast(tr2->n[1],&n1_));
327 578 : if (tr2->n[0] > 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0_,y+tr2->idx[0],y+tr2->idx[0]+1,&inc,tr2->tau));
328 578 : if (tr2->n[1]> 1) PetscCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1_,y+tr2->idx[1],y+tr2->idx[1]+1,&inc,tr2->tau+1));
329 578 : 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 83 : tr2->alpha = PetscRealPart(y[tr2->idx[0]]);
332 83 : ncond2 = 1.0;
333 : }
334 578 : if (ncond2>*ncond) *ncond = ncond2;
335 : }
336 10635 : 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 10346 : 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 10346 : struct HRtr *tr1,*tr2,tr1_t,tr2_t,tr1_te,tr2_te;
348 10346 : PetscScalar *x,*y;
349 10346 : PetscReal ncond=0,ncond_e;
350 10346 : PetscInt nwu=0,i,d=1;
351 10346 : PetscBLASInt n0_,n1_,inc=1,mh,mr,n_,ldr_,ldh_;
352 10346 : PetscReal tolD = 1e+5;
353 :
354 10346 : PetscFunctionBegin;
355 10346 : if (cond) *cond = 1.0;
356 10346 : PetscCall(PetscBLASIntCast(n,&n_));
357 10346 : PetscCall(PetscBLASIntCast(ldr,&ldr_));
358 10346 : PetscCall(PetscBLASIntCast(ldh,&ldh_));
359 10346 : x = work+nwu;
360 10346 : nwu += n;
361 10346 : PetscCall(PetscArraycpy(x,R+j*ldr,n));
362 10346 : *exg = PETSC_FALSE;
363 10346 : *ok = PETSC_TRUE;
364 10346 : tr1_t.data = x;
365 10346 : if (sz==1) {
366 : /* Hyperbolic transformation to make zeros in x */
367 10057 : PetscCall(MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_t,NULL,&ncond,work+nwu));
368 : /* Check condition number to single column*/
369 10057 : if (ncond>tolD) *ok = PETSC_FALSE;
370 : tr1 = &tr1_t;
371 : tr2 = &tr2_t;
372 : } else {
373 289 : y = work+nwu;
374 289 : nwu += n;
375 289 : PetscCall(PetscArraycpy(y,R+(j+1)*ldr,n));
376 289 : tr2_t.data = y;
377 289 : PetscCall(MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_t,&tr2_t,&ncond,work+nwu));
378 : /* Computing hyperbolic transformations also for exchanged vectors */
379 289 : tr1_te.data = work+nwu;
380 289 : nwu += n;
381 289 : PetscCall(PetscArraycpy(tr1_te.data,R+(j+1)*ldr,n));
382 289 : tr2_te.data = work+nwu;
383 289 : nwu += n;
384 289 : PetscCall(PetscArraycpy(tr2_te.data,R+j*ldr,n));
385 289 : PetscCall(MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_te,&tr2_te,&ncond_e,work+nwu));
386 289 : if (ncond > d*ncond_e) {
387 188 : *exg = PETSC_TRUE;
388 188 : tr1 = &tr1_te;
389 188 : tr2 = &tr2_te;
390 188 : ncond = ncond_e;
391 : } else {
392 : tr1 = &tr1_t;
393 : tr2 = &tr2_t;
394 : }
395 289 : if (ncond>tolD) *ok = PETSC_FALSE;
396 : }
397 10346 : if (*ok) {
398 : /* Everything is OK, apply transformations to R and H */
399 : /* First column */
400 10346 : if (cond && *cond<ncond) *cond = ncond;
401 10346 : x = tr1->data;
402 10346 : PetscCall(PetscBLASIntCast(tr1->n[0],&n0_));
403 10346 : PetscCall(PetscBLASIntCast(tr1->n[1],&n1_));
404 10346 : PetscCall(PetscBLASIntCast(n-j-sz,&mr));
405 10346 : if (tr1->n[0] > 1 && PetscAbsScalar(tr1->tau[0])!=0.0) {
406 9162 : x[tr1->idx[0]] = 1.0;
407 9162 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&mr,x+tr1->idx[0],&inc,tr1->tau,R+(j+sz)*ldr+tr1->idx[0],&ldr_,work+nwu));
408 9162 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0_,x+tr1->idx[0],&inc,tr1->tau,H+(tr1->idx[0])*ldh,&ldh_,work+nwu));
409 : }
410 10346 : if (tr1->n[1] > 1 && PetscAbsScalar(tr1->tau[1])!=0.0) {
411 5033 : x[tr1->idx[1]] = 1.0;
412 5033 : 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 5033 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1_,x+tr1->idx[1],&inc,tr1->tau+1,H+(tr1->idx[1])*ldh,&ldh_,work+nwu));
414 : }
415 10346 : if (tr1->idx[0]<tr1->idx[1]) {
416 5247 : PetscCall(HRApply(mr,R+(j+sz)*ldr+tr1->idx[0],ldr,R+(j+sz)*ldr+tr1->idx[1],ldr,tr1->cs,-tr1->sn));
417 5247 : 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 {
419 977 : PetscCall(HRApply(n,H+(tr1->idx[0])*ldh,1,H+(tr1->idx[1])*ldh,1,-tr1->cs,-tr1->sn));
420 977 : s[tr1->idx[0]] = -s[tr1->idx[0]];
421 977 : s[tr1->idx[1]] = -s[tr1->idx[1]];
422 : }
423 : }
424 307526 : for (i=0;i<tr1->idx[0];i++) *(R+j*ldr+i) = x[i];
425 307520 : for (i=tr1->idx[0]+1;i<n;i++) *(R+j*ldr+i) = 0.0;
426 10346 : *(R+j*ldr+tr1->idx[0]) = tr1->alpha;
427 10346 : if (sz==2) {
428 289 : y = tr2->data;
429 : /* Second column */
430 289 : PetscCall(PetscBLASIntCast(tr2->n[0],&n0_));
431 289 : PetscCall(PetscBLASIntCast(tr2->n[1],&n1_));
432 289 : PetscCall(PetscBLASIntCast(n-j-sz,&mr));
433 289 : PetscCall(PetscBLASIntCast(n-tr2->idx[0],&mh));
434 289 : if (tr2->n[0] > 1 && PetscAbsScalar(tr2->tau[0])!=0.0) {
435 248 : y[tr2->idx[0]] = 1.0;
436 248 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&mr,y+tr2->idx[0],&inc,tr2->tau,R+(j+2)*ldr+tr2->idx[0],&ldr_,work+nwu));
437 248 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0_,y+tr2->idx[0],&inc,tr2->tau,H+(tr2->idx[0])*ldh,&ldh_,work+nwu));
438 : }
439 289 : if (tr2->n[1] > 1 && PetscAbsScalar(tr2->tau[1])!=0.0) {
440 219 : y[tr2->idx[1]] = 1.0;
441 219 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&mr,y+tr2->idx[1],&inc,tr2->tau+1,R+(j+2)*ldr+tr2->idx[1],&ldr_,work+nwu));
442 219 : PetscCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1_,y+tr2->idx[1],&inc,tr2->tau+1,H+(tr2->idx[1])*ldh,&ldh_,work+nwu));
443 : }
444 289 : if (tr2->idx[0]<tr2->idx[1]) {
445 255 : PetscCall(HRApply(mr,R+(j+2)*ldr+tr2->idx[0],ldr,R+(j+2)*ldr+tr2->idx[1],ldr,tr2->cs,-tr2->sn));
446 255 : 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 {
448 171 : PetscCall(HRApply(n,H+(tr2->idx[0])*ldh,1,H+(tr2->idx[1])*ldh,1,-tr2->cs,-tr2->sn));
449 171 : s[tr2->idx[0]] = -s[tr2->idx[0]];
450 171 : s[tr2->idx[1]] = -s[tr2->idx[1]];
451 : }
452 : }
453 9534 : for (i=0;i<tr2->idx[0]-1;i++) *(R+(j+1)*ldr+i) = y[i];
454 289 : *(R+(j+1)*ldr+tr2->idx[0]-1) = y[tr2->idx[0]-1];
455 9829 : for (i=tr2->idx[0]+1;i<n;i++) *(R+(j+1)*ldr+i) = 0.0;
456 289 : *(R+(j+1)*ldr+tr2->idx[0]) = tr2->alpha;
457 289 : *n0 = tr2->n[0];
458 289 : *n1 = tr2->n[1];
459 289 : *idx0 = tr2->idx[0];
460 289 : *idx1 = tr2->idx[1];
461 289 : if (tr2->idx[0]<tr2->idx[1] && tr2->type==2) {
462 171 : (*idx1)++; (*n1)--; (*n0)++;
463 : }
464 : } else {
465 10057 : *n0 = tr1->n[0];
466 10057 : *n1 = tr1->n[1];
467 10057 : *idx0 = tr1->idx[0];
468 10057 : *idx1 = tr1->idx[1];
469 10057 : if (tr1->idx[0]<tr1->idx[1] && tr1->type==2) {
470 880 : (*idx1)++; (*n1)--; (*n0)++;
471 : }
472 : }
473 10346 : if (*n0>0) {
474 9548 : (*n0)--; (*idx0)++;
475 9548 : if (*n1==0) *idx1 = *idx0;
476 : } else {
477 798 : (*n1)--; (*idx1)++; *idx0 = *idx1;
478 : }
479 : }
480 10346 : 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 : */
487 374 : PetscErrorCode DSPseudoOrthog_HR(PetscInt *nv,PetscScalar *V,PetscInt ldv,PetscReal *s,PetscScalar *R,PetscInt ldr,PetscBLASInt *perm,PetscBLASInt *cmplxEig,PetscBool *breakdown,PetscScalar *work)
488 : {
489 374 : PetscInt i,j,n,n0,n1,np,idx0,idx1,sz=1,k=0,t1,t2,nwu=0;
490 374 : PetscScalar *col1,*col2;
491 374 : PetscBool exg=PETSC_FALSE,ok=PETSC_FALSE;
492 :
493 374 : PetscFunctionBegin;
494 374 : n = *nv;
495 374 : col1 = work+nwu;
496 374 : nwu += n;
497 374 : col2 = work+nwu;
498 374 : nwu += n;
499 : /* Sort R and s according to sing(s) */
500 374 : np = 0;
501 11009 : for (i=0;i<n;i++) if (s[i]>0) np++;
502 374 : if (s[0]>0) n1 = np;
503 65 : else n1 = n-np;
504 374 : n0 = 0;
505 11009 : for (i=0;i<n;i++) {
506 10635 : if (s[i]==s[0]) {
507 8689 : s[n0] = s[0];
508 8689 : perm[n0++] = i;
509 1946 : } else perm[n1++] = i;
510 : }
511 2320 : for (i=n0;i<n;i++) s[i] = -s[0];
512 374 : n1 -= n0;
513 374 : idx0 = 0;
514 374 : idx1 = n0;
515 374 : if (idx1==n) idx1=idx0;
516 11009 : for (i=0;i<n;i++) {
517 634698 : for (j=0;j<n;j++) R[j*ldr+i] = V[j*ldv+perm[i]];
518 : }
519 : /* Initialize H */
520 11009 : for (i=0;i<n;i++) {
521 10635 : PetscCall(PetscArrayzero(V+i*ldv,n));
522 10635 : V[perm[i]+i*ldv] = 1.0;
523 : }
524 11009 : for (i=0;i<n;i++) perm[i] = i;
525 : j = 0;
526 10720 : while (j<n-k) {
527 10346 : if (cmplxEig[j]==0) sz=1;
528 289 : else sz=2;
529 10346 : PetscCall(TryHRIt(n,j,sz,V,ldv,R,ldr,s,&exg,&ok,&n0,&n1,&idx0,&idx1,NULL,work+nwu));
530 10346 : if (ok) {
531 10346 : if (exg) cmplxEig[j] = -cmplxEig[j];
532 10346 : j = j+sz;
533 : } else { /* to be discarded */
534 0 : k = k+1;
535 0 : if (cmplxEig[j]==0) {
536 0 : if (j<n) {
537 0 : t1 = perm[j];
538 0 : for (i=j;i<n-1;i++) perm[i] = perm[i+1];
539 0 : perm[n-1] = t1;
540 0 : t1 = cmplxEig[j];
541 0 : for (i=j;i<n-1;i++) cmplxEig[i] = cmplxEig[i+1];
542 0 : cmplxEig[n-1] = t1;
543 0 : PetscCall(PetscArraycpy(col1,R+j*ldr,n));
544 0 : for (i=j;i<n-1;i++) PetscCall(PetscArraycpy(R+i*ldr,R+(i+1)*ldr,n));
545 0 : PetscCall(PetscArraycpy(R+(n-1)*ldr,col1,n));
546 : }
547 : } else {
548 0 : k = k+1;
549 0 : if (j<n-1) {
550 0 : t1 = perm[j]; t2 = perm[j+1];
551 0 : for (i=j;i<n-2;i++) perm[i] = perm[i+2];
552 0 : perm[n-2] = t1; perm[n-1] = t2;
553 0 : t1 = cmplxEig[j]; t2 = cmplxEig[j+1];
554 0 : for (i=j;i<n-2;i++) cmplxEig[i] = cmplxEig[i+2];
555 0 : cmplxEig[n-2] = t1; cmplxEig[n-1] = t2;
556 0 : PetscCall(PetscArraycpy(col1,R+j*ldr,n));
557 0 : PetscCall(PetscArraycpy(col2,R+(j+1)*ldr,n));
558 0 : for (i=j;i<n-2;i++) PetscCall(PetscArraycpy(R+i*ldr,R+(i+2)*ldr,n));
559 0 : PetscCall(PetscArraycpy(R+(n-2)*ldr,col1,n));
560 10720 : PetscCall(PetscArraycpy(R+(n-1)*ldr,col2,n));
561 : }
562 : }
563 : }
564 : }
565 374 : if (k!=0) {
566 0 : if (breakdown) *breakdown = PETSC_TRUE;
567 0 : *nv = n-k;
568 : }
569 374 : PetscFunctionReturn(PETSC_SUCCESS);
570 : }
571 :
572 372 : PetscErrorCode DSGHIEPOrthogEigenv(DS ds,DSMatType mat,PetscScalar *wr,PetscScalar *wi,PetscBool accum)
573 : {
574 372 : PetscInt lws,nwus=0,nwui=0,lwi,off,n,nv,ld,i,ldr,l;
575 372 : const PetscScalar *B,*W;
576 372 : PetscScalar *Q,*X,*R,*ts,szero=0.0,sone=1.0;
577 372 : PetscReal *s,vi,vr,tr,*d,*e;
578 372 : PetscBLASInt ld_,n_,nv_,*perm,*cmplxEig;
579 :
580 372 : PetscFunctionBegin;
581 372 : l = ds->l;
582 372 : n = ds->n-l;
583 372 : PetscCall(PetscBLASIntCast(n,&n_));
584 372 : ld = ds->ld;
585 372 : PetscCall(PetscBLASIntCast(ld,&ld_));
586 372 : off = l*ld+l;
587 372 : PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
588 372 : if (!ds->compact) {
589 4 : PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_B],&B));
590 44 : for (i=l;i<ds->n;i++) s[i] = PetscRealPart(B[i*ld+i]);
591 4 : PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_B],&B));
592 : }
593 372 : lws = n*n+7*n;
594 372 : lwi = 2*n;
595 372 : PetscCall(DSAllocateWork_Private(ds,lws,0,lwi));
596 372 : R = ds->work+nwus;
597 372 : nwus += n*n;
598 372 : ldr = n;
599 372 : perm = ds->iwork + nwui;
600 372 : nwui += n;
601 372 : cmplxEig = ds->iwork+nwui;
602 372 : PetscCall(MatDenseGetArray(ds->omat[mat],&X));
603 10702 : for (i=0;i<n;i++) {
604 : #if defined(PETSC_USE_COMPLEX)
605 10330 : vi = PetscImaginaryPart(wr[l+i]);
606 : #else
607 : vi = wi?PetscRealPart(wi[l+i]):0.0;
608 : #endif
609 10330 : if (vi!=0) {
610 289 : cmplxEig[i] = 1;
611 289 : cmplxEig[i+1] = 2;
612 289 : i++;
613 10041 : } else cmplxEig[i] = 0;
614 : }
615 372 : nv = n;
616 :
617 : /* Perform HR decomposition */
618 : /* Hyperbolic rotators */
619 372 : PetscCall(DSPseudoOrthog_HR(&nv,X+off,ld,s+l,R,ldr,perm,cmplxEig,NULL,ds->work+nwus));
620 : /* Sort wr,wi perm */
621 372 : ts = ds->work+nwus;
622 372 : PetscCall(PetscArraycpy(ts,wr+l,n));
623 10991 : for (i=0;i<n;i++) wr[i+l] = ts[perm[i]];
624 : #if !defined(PETSC_USE_COMPLEX)
625 : if (wi) {
626 : PetscCall(PetscArraycpy(ts,wi+l,n));
627 : for (i=0;i<n;i++) wi[i+l] = ts[perm[i]];
628 : }
629 : #endif
630 : /* Projected Matrix */
631 372 : PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
632 372 : PetscCall(PetscArrayzero(d+2*ld,ld));
633 372 : e = d+ld;
634 372 : d[l+nv-1] = PetscRealPart(wr[l+nv-1]*s[l+nv-1]);
635 10356 : for (i=0;i<nv-1;i++) {
636 9984 : if (cmplxEig[i]==0) { /* Real */
637 9695 : d[l+i] = PetscRealPart(wr[l+i]*s[l+i]);
638 9695 : e[l+i] = 0.0;
639 : } else {
640 289 : vr = PetscRealPart(wr[l+i]);
641 : #if defined(PETSC_USE_COMPLEX)
642 289 : vi = PetscImaginaryPart(wr[l+i]);
643 : #else
644 : vi = wi?PetscRealPart(wi[l+i]):0.0;
645 : #endif
646 289 : if (cmplxEig[i]==-1) vi = -vi;
647 289 : tr = PetscRealPart((R[i+(i+1)*ldr]/R[i+i*ldr]))*vi;
648 289 : d[l+i] = (vr-tr)*s[l+i];
649 289 : d[l+i+1] = (vr+tr)*s[l+i+1];
650 289 : e[l+i] = PetscRealPart(s[l+i]*(R[(i+1)+(i+1)*ldr]/R[i+i*ldr])*vi);
651 289 : if (i<nv-2) e[l+i+1] = 0.0;
652 : i++;
653 : }
654 : }
655 372 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
656 372 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
657 : /* accumulate previous Q */
658 372 : if (accum) {
659 369 : PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
660 369 : PetscCall(PetscBLASIntCast(nv,&nv_));
661 369 : PetscCall(DSAllocateMat_Private(ds,DS_MAT_W));
662 369 : PetscCall(MatCopy(ds->omat[DS_MAT_Q],ds->omat[DS_MAT_W],SAME_NONZERO_PATTERN));
663 369 : PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_W],&W));
664 369 : PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&nv_,&n_,&sone,W+off,&ld_,X+off,&ld_,&szero,Q+off,&ld_));
665 369 : PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_W],&W));
666 369 : PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
667 : }
668 372 : ds->t = nv+l;
669 372 : PetscCall(MatDenseRestoreArray(ds->omat[mat],&X));
670 372 : if (!ds->compact) PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
671 372 : PetscFunctionReturn(PETSC_SUCCESS);
672 : }
673 :
674 : /*
675 : Reduce to tridiagonal-diagonal pair by means of TridiagDiag_HHR.
676 : */
677 372 : PetscErrorCode DSIntermediate_GHIEP(DS ds)
678 : {
679 372 : PetscInt i,ld,off;
680 372 : PetscInt nwall,nwallr,nwalli;
681 372 : PetscScalar *A,*B,*Q;
682 372 : PetscReal *d,*e,*s;
683 :
684 372 : PetscFunctionBegin;
685 372 : ld = ds->ld;
686 372 : PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
687 372 : PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
688 372 : PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
689 372 : PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
690 372 : PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
691 372 : e = d+ld;
692 372 : off = ds->l+ds->l*ld;
693 372 : PetscCall(PetscArrayzero(Q,ld*ld));
694 372 : nwall = ld*ld+ld;
695 372 : nwallr = ld;
696 372 : nwalli = ld;
697 372 : PetscCall(DSAllocateWork_Private(ds,nwall,nwallr,nwalli));
698 12197 : for (i=0;i<ds->n;i++) Q[i+i*ld]=1.0;
699 10991 : for (i=0;i<ds->n-ds->l;i++) *(ds->perm+i)=i;
700 372 : if (ds->compact) {
701 368 : if (ds->state < DS_STATE_INTERMEDIATE) {
702 320 : PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
703 320 : 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));
704 320 : ds->k = ds->l;
705 320 : PetscCall(PetscArrayzero(d+2*ld+ds->l,ds->n-ds->l));
706 : }
707 : } else {
708 4 : if (ds->state < DS_STATE_INTERMEDIATE) {
709 44 : for (i=0;i<ds->n;i++) s[i] = PetscRealPart(B[i+i*ld]);
710 4 : 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));
711 4 : PetscCall(PetscArrayzero(d+2*ld,ds->n));
712 4 : ds->k = ds->l;
713 4 : PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_FALSE));
714 0 : } else PetscCall(DSSwitchFormat_GHIEP(ds,PETSC_TRUE));
715 : }
716 372 : PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
717 372 : PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
718 372 : PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
719 372 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
720 372 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
721 372 : PetscFunctionReturn(PETSC_SUCCESS);
722 : }
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