Actual source code: invit.c
slepc-3.7.1 2016-05-27
1: /*
3: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
4: SLEPc - Scalable Library for Eigenvalue Problem Computations
5: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
7: This file is part of SLEPc.
9: SLEPc is free software: you can redistribute it and/or modify it under the
10: terms of version 3 of the GNU Lesser General Public License as published by
11: the Free Software Foundation.
13: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
14: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
15: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
16: more details.
18: You should have received a copy of the GNU Lesser General Public License
19: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
20: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
21: */
22: #include <slepc/private/dsimpl.h>
23: #include <slepcblaslapack.h>
25: struct HRtr
26: {
27: PetscScalar *data;
28: PetscInt m;
29: PetscInt idx[2];
30: PetscInt n[2];
31: PetscScalar tau[2];
32: PetscReal alpha;
33: PetscReal cs;
34: PetscReal sn;
35: PetscInt type;
36: };
40: /*
41: Generates a hyperbolic rotation
42: if x1*x1 - x2*x2 != 0
43: r = sqrt(|x1*x1 - x2*x2|)
44: c = x1/r s = x2/r
46: | c -s||x1| |d*r|
47: |-s c||x2| = | 0 |
48: where d = 1 for type==1 and -1 for type==2
49: Returns the condition number of the reduction
50: */
51: static PetscErrorCode HRGen(PetscReal x1,PetscReal x2,PetscInt *type,PetscReal *c,PetscReal *s,PetscReal *r,PetscReal *cond)
52: {
53: PetscReal t,n2,xa,xb;
54: PetscInt type_;
57: if (x2==0.0) {
58: *r = PetscAbsReal(x1);
59: *c = (x1>=0)?1.0:-1.0;
60: *s = 0.0;
61: if (type) *type = 1;
62: return(0);
63: }
64: if (PetscAbsReal(x1) == PetscAbsReal(x2)) {
65: /* hyperbolic rotation doesn't exist */
66: *c = 0.0;
67: *s = 0.0;
68: *r = 0.0;
69: if (type) *type = 0;
70: *cond = PETSC_MAX_REAL;
71: return(0);
72: }
74: if (PetscAbsReal(x1)>PetscAbsReal(x2)) {
75: xa = x1; xb = x2; type_ = 1;
76: } else {
77: xa = x2; xb = x1; type_ = 2;
78: }
79: t = xb/xa;
80: n2 = PetscAbsReal(1 - t*t);
81: *r = PetscSqrtReal(n2)*PetscAbsReal(xa);
82: *c = x1/(*r);
83: *s = x2/(*r);
84: if (type_ == 2) *r *= -1;
85: if (type) *type = type_;
86: if (cond) *cond = (PetscAbsReal(*c) + PetscAbsReal(*s))/PetscAbsReal(PetscAbsReal(*c) - PetscAbsReal(*s));
87: return(0);
88: }
92: /*
93: |c s|
94: Applies an hyperbolic rotator |s c|
95: |c s|
96: [x1 x2]|s c|
97: */
98: static PetscErrorCode HRApply(PetscInt n,PetscScalar *x1,PetscInt inc1,PetscScalar *x2,PetscInt inc2,PetscReal c,PetscReal s)
99: {
100: PetscInt i;
101: PetscReal t;
102: PetscScalar tmp;
105: if (PetscAbsReal(c)>PetscAbsReal(s)) { /* Type I */
106: t = s/c;
107: for (i=0;i<n;i++) {
108: x1[i*inc1] = c*x1[i*inc1] + s*x2[i*inc2];
109: x2[i*inc2] = t*x1[i*inc1] + x2[i*inc2]/c;
110: }
111: } else { /* Type II */
112: t = c/s;
113: for (i=0;i<n;i++) {
114: tmp = x1[i*inc1];
115: x1[i*inc1] = c*x1[i*inc1] + s*x2[i*inc2];
116: x2[i*inc2] = t*x1[i*inc1] + tmp/s;
117: }
118: }
119: return(0);
120: }
124: /*
125: Reduction to tridiagonal-diagonal form (see F. Tisseur, SIMAX 26(1), 2004).
127: Input:
128: A symmetric (only lower triangular part is referred)
129: s vector +1 and -1 (signature matrix)
130: Output:
131: d,e
132: s
133: Q s-orthogonal matrix with Q^T*A*Q = T (symmetric tridiagonal matrix)
134: */
135: 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)
136: {
137: #if defined(SLEPC_MISSING_LAPACK_LARFG) || defined(SLEPC_MISSING_LAPACK_LARF)
139: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LARFG/LARF - Lapack routines are unavailable");
140: #else
142: PetscInt i,j,k,*ii,*jj,i0=0,ik=0,tmp,type;
143: PetscInt nwu=0;
144: PetscReal *ss,cond=1.0,cs,sn,r;
145: PetscScalar tau,t,*AA;
146: PetscBLASInt n0,n1,ni,inc=1,m,n_,lda_,ldq_,*perm;
147: PetscBool breakdown = PETSC_TRUE;
150: if (n<3) {
151: if (n==1) Q[0]=1;
152: if (n==2) {
153: Q[0] = Q[1+ldq] = 1;
154: Q[1] = Q[ldq] = 0;
155: }
156: return(0);
157: }
158: PetscBLASIntCast(lda,&lda_);
159: PetscBLASIntCast(n,&n_);
160: PetscBLASIntCast(ldq,&ldq_);
161: ss = rwork;
162: perm = iwork;
163: AA = work;
164: for (i=0;i<n;i++) {
165: PetscMemcpy(AA+i*n,A+i*lda,n*sizeof(PetscScalar));
166: }
167: nwu += n*n;
168: k=0;
169: while (breakdown && k<n) {
170: breakdown = PETSC_FALSE;
171: /* Classify (and flip) A and s according to sign */
172: if (flip) {
173: for (i=0;i<n;i++) {
174: perm[i] = n-1-perm_[i];
175: if (perm[i]==0) i0 = i;
176: if (perm[i]==k) ik = i;
177: }
178: } else {
179: for (i=0;i<n;i++) {
180: perm[i] = perm_[i];
181: if (perm[i]==0) i0 = i;
182: if (perm[i]==k) ik = i;
183: }
184: }
185: perm[ik] = 0;
186: perm[i0] = k;
187: i=1;
188: while (i<n-1 && s[perm[i-1]]==s[perm[0]]) {
189: if (s[perm[i]]!=s[perm[0]]) {
190: j=i+1;
191: while (j<n-1 && s[perm[j]]!=s[perm[0]])j++;
192: tmp = perm[i]; perm[i] = perm[j]; perm[j] = tmp;
193: }
194: i++;
195: }
196: for (i=0;i<n;i++) {
197: ss[i] = s[perm[i]];
198: }
199: if (flip) {
200: ii = &j;
201: jj = &i;
202: } else {
203: ii = &i;
204: jj = &j;
205: }
206: for (i=0;i<n;i++)
207: for (j=0;j<n;j++)
208: A[i+j*lda] = AA[perm[*ii]+perm[*jj]*n];
209: /* Initialize Q */
210: for (i=0;i<n;i++) {
211: PetscMemzero(Q+i*ldq,n*sizeof(PetscScalar));
212: Q[perm[i]+i*ldq] = 1.0;
213: }
214: for (ni=1;ni<n && ss[ni]==ss[0]; ni++);
215: n0 = ni-1;
216: n1 = n_-ni;
217: for (j=0;j<n-2;j++) {
218: PetscBLASIntCast(n-j-1,&m);
219: /* Forming and applying reflectors */
220: if (n0 > 1) {
221: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0,A+ni-n0+j*lda,A+ni-n0+j*lda+1,&inc,&tau));
222: /* Apply reflector */
223: if (PetscAbsScalar(tau) != 0.0) {
224: t=*(A+ni-n0+j*lda); *(A+ni-n0+j*lda)=1.0;
225: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&m,&n0,A+ni-n0+j*lda,&inc,&tau,A+j+1+(j+1)*lda,&lda_,work+nwu));
226: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0,&m,A+ni-n0+j*lda,&inc,&tau,A+j+1+(j+1)*lda,&lda_,work+nwu));
227: /* Update Q */
228: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0,A+ni-n0+j*lda,&inc,&tau,Q+(j+1)*ldq,&ldq_,work+nwu));
229: *(A+ni-n0+j*lda) = t;
230: for (i=1;i<n0;i++) {
231: *(A+ni-n0+j*lda+i) = 0.0; *(A+j+(ni-n0+i)*lda) = 0.0;
232: }
233: *(A+j+(ni-n0)*lda) = *(A+ni-n0+j*lda);
234: }
235: }
236: if (n1 > 1) {
237: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1,A+n-n1+j*lda,A+n-n1+j*lda+1,&inc,&tau));
238: /* Apply reflector */
239: if (PetscAbsScalar(tau) != 0.0) {
240: t=*(A+n-n1+j*lda); *(A+n-n1+j*lda)=1.0;
241: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&m,&n1,A+n-n1+j*lda,&inc,&tau,A+j+1+(n-n1)*lda,&lda_,work+nwu));
242: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1,&m,A+n-n1+j*lda,&inc,&tau,A+n-n1+(j+1)*lda,&lda_,work+nwu));
243: /* Update Q */
244: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1,A+n-n1+j*lda,&inc,&tau,Q+(n-n1)*ldq,&ldq_,work+nwu));
245: *(A+n-n1+j*lda) = t;
246: for (i=1;i<n1;i++) {
247: *(A+n-n1+i+j*lda) = 0.0; *(A+j+(n-n1+i)*lda) = 0.0;
248: }
249: *(A+j+(n-n1)*lda) = *(A+n-n1+j*lda);
250: }
251: }
252: /* Hyperbolic rotation */
253: if (n0 > 0 && n1 > 0) {
254: HRGen(PetscRealPart(A[ni-n0+j*lda]),PetscRealPart(A[n-n1+j*lda]),&type,&cs,&sn,&r,&cond);
255: /* Check condition number */
256: if (cond > 1.0/(10*PETSC_SQRT_MACHINE_EPSILON)) {
257: breakdown = PETSC_TRUE;
258: k++;
259: if (k==n || flip)
260: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Breakdown in construction of hyperbolic transformation");
261: break;
262: }
263: A[ni-n0+j*lda] = r; A[n-n1+j*lda] = 0.0;
264: A[j+(ni-n0)*lda] = r; A[j+(n-n1)*lda] = 0.0;
265: /* Apply to A */
266: HRApply(m,A+j+1+(ni-n0)*lda,1,A+j+1+(n-n1)*lda,1,cs,-sn);
267: HRApply(m,A+ni-n0+(j+1)*lda,lda,A+n-n1+(j+1)*lda,lda,cs,-sn);
269: /* Update Q */
270: HRApply(n,Q+(ni-n0)*ldq,1,Q+(n-n1)*ldq,1,cs,-sn);
271: if (type==2) {
272: ss[ni-n0] = -ss[ni-n0]; ss[n-n1] = -ss[n-n1];
273: n0++;ni++;n1--;
274: }
275: }
276: if (n0>0) n0--;
277: else n1--;
278: }
279: }
281: /* flip matrices */
282: if (flip) {
283: for (i=0;i<n-1;i++) {
284: d[i] = PetscRealPart(A[n-i-1+(n-i-1)*lda]);
285: e[i] = PetscRealPart(A[n-i-1+(n-i-2)*lda]);
286: s[i] = ss[n-i-1];
287: }
288: s[n-1] = ss[0];
289: d[n-1] = PetscRealPart(A[0]);
290: for (i=0;i<n;i++) {
291: ierr=PetscMemcpy(work+i*n,Q+i*ldq,n*sizeof(PetscScalar));
292: }
293: for (i=0;i<n;i++)
294: for (j=0;j<n;j++)
295: Q[i+j*ldq] = work[i+(n-j-1)*n];
296: } else {
297: for (i=0;i<n-1;i++) {
298: d[i] = PetscRealPart(A[i+i*lda]);
299: e[i] = PetscRealPart(A[i+1+i*lda]);
300: s[i] = ss[i];
301: }
302: s[n-1] = ss[n-1];
303: d[n-1] = PetscRealPart(A[n-1 + (n-1)*lda]);
304: }
305: return(0);
306: #endif
307: }
311: 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)
312: {
313: #if defined(SLEPC_MISSING_LAPACK_LARFG) || defined(SLEPC_MISSING_LAPACK_LARF)
315: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LARFG/LARF - Lapack routines are unavailable");
316: #else
318: PetscScalar *x,*y;
319: PetscReal ncond2;
320: PetscBLASInt n0_,n1_,inc=1;
323: /* Hyperbolic transformation to make zeros in x */
324: x = tr1->data;
325: tr1->n[0] = n0;
326: tr1->n[1] = n1;
327: tr1->idx[0] = idx0;
328: tr1->idx[1] = idx1;
329: PetscBLASIntCast(tr1->n[0],&n0_);
330: PetscBLASIntCast(tr1->n[1],&n1_);
331: if (tr1->n[0] > 1) {
332: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0_,x+tr1->idx[0],x+tr1->idx[0]+1,&inc,tr1->tau));
333: }
334: if (tr1->n[1]> 1) {
335: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1_,x+tr1->idx[1],x+tr1->idx[1]+1,&inc,tr1->tau+1));
336: }
337: if (tr1->idx[0]<tr1->idx[1]) {
338: HRGen(PetscRealPart(x[tr1->idx[0]]),PetscRealPart(x[tr1->idx[1]]),&(tr1->type),&(tr1->cs),&(tr1->sn),&(tr1->alpha),ncond);
339: } else {
340: tr1->alpha = PetscRealPart(x[tr1->idx[0]]);
341: *ncond = 1.0;
342: }
343: if (sz==2) {
344: y = tr2->data;
345: /* Apply first transformation to second column */
346: if (tr1->n[0] > 1 && PetscAbsScalar(tr1->tau[0])!=0.0) {
347: x[tr1->idx[0]] = 1.0;
348: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&inc,x+tr1->idx[0],&inc,tr1->tau,y+tr1->idx[0],&n0_,work));
349: }
350: if (tr1->n[1] > 1 && PetscAbsScalar(tr1->tau[1])!=0.0) {
351: x[tr1->idx[1]] = 1.0;
352: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&inc,x+tr1->idx[1],&inc,tr1->tau+1,y+tr1->idx[1],&n1_,work));
353: }
354: if (tr1->idx[0]<tr1->idx[1]) {
355: HRApply(1,y+tr1->idx[0],1,y+tr1->idx[1],1,tr1->cs,-tr1->sn);
356: }
357: tr2->n[0] = tr1->n[0];
358: tr2->n[1] = tr1->n[1];
359: tr2->idx[0] = tr1->idx[0];
360: tr2->idx[1] = tr1->idx[1];
361: if (tr1->idx[0]<tr1->idx[1] && tr1->type==2) {
362: tr2->idx[1]++; tr2->n[1]--; tr2->n[0]++;
363: }
364: if (tr2->n[0]>0) {
365: tr2->n[0]--; tr2->idx[0]++;
366: if (tr2->n[1]==0) tr2->idx[1] = tr2->idx[0];
367: } else {
368: tr2->n[1]--; tr2->idx[1]++; tr2->idx[0] = tr2->idx[1];
369: }
370: /* Hyperbolic transformation to make zeros in y */
371: PetscBLASIntCast(tr2->n[0],&n0_);
372: PetscBLASIntCast(tr2->n[1],&n1_);
373: if (tr2->n[0] > 1) {
374: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n0_,y+tr2->idx[0],y+tr2->idx[0]+1,&inc,tr2->tau));
375: }
376: if (tr2->n[1]> 1) {
377: PetscStackCallBLAS("LAPACKlarfg",LAPACKlarfg_(&n1_,y+tr2->idx[1],y+tr2->idx[1]+1,&inc,tr2->tau+1));
378: }
379: if (tr2->idx[0]<tr2->idx[1]) {
380: HRGen(PetscRealPart(y[tr2->idx[0]]),PetscRealPart(y[tr2->idx[1]]),&(tr2->type),&(tr2->cs),&(tr2->sn),&(tr2->alpha),&ncond2);
381: } else {
382: tr2->alpha = PetscRealPart(y[tr2->idx[0]]);
383: ncond2 = 1.0;
384: }
385: if (ncond2>*ncond) *ncond = ncond2;
386: }
387: return(0);
388: #endif
389: }
393: /*
394: Auxiliary function to try perform one iteration of hr routine,
395: checking condition number. If it is < tolD, apply the
396: transformation to H and R, if not, ok=false and it do nothing
397: tolE, tolerance to exchange complex pairs to improve conditioning
398: */
399: 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)
400: {
401: #if defined(SLEPC_MISSING_LAPACK_LARF)
403: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LARF - Lapack routine is unavailable");
404: #else
406: struct HRtr *tr1,*tr2,tr1_t,tr2_t,tr1_te,tr2_te;
407: PetscScalar *x,*y;
408: PetscReal ncond,ncond_e;
409: PetscInt nwu=0,i,d=1;
410: PetscBLASInt n0_,n1_,inc=1,mh,mr,n_,ldr_,ldh_;
411: PetscReal tolD = 1e+5;
414: if (cond) *cond = 1.0;
415: PetscBLASIntCast(n,&n_);
416: PetscBLASIntCast(ldr,&ldr_);
417: PetscBLASIntCast(ldh,&ldh_);
418: x = work+nwu;
419: nwu += n;
420: PetscMemcpy(x,R+j*ldr,n*sizeof(PetscScalar));
421: *exg = PETSC_FALSE;
422: *ok = PETSC_TRUE;
423: tr1_t.data = x;
424: if (sz==1) {
425: /* Hyperbolic transformation to make zeros in x */
426: MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_t,NULL,&ncond,work+nwu);
427: /* Check condition number to single column*/
428: if (ncond>tolD) {
429: *ok = PETSC_FALSE;
430: }
431: tr1 = &tr1_t;
432: tr2 = &tr2_t;
433: } else {
434: y = work+nwu;
435: nwu += n;
436: PetscMemcpy(y,R+(j+1)*ldr,n*sizeof(PetscScalar));
437: tr2_t.data = y;
438: MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_t,&tr2_t,&ncond,work+nwu);
439: /* Computing hyperbolic transformations also for exchanged vectors */
440: tr1_te.data = work+nwu;
441: nwu += n;
442: PetscMemcpy(tr1_te.data,R+(j+1)*ldr,n*sizeof(PetscScalar));
443: tr2_te.data = work+nwu;
444: nwu += n;
445: PetscMemcpy(tr2_te.data,R+j*ldr,n*sizeof(PetscScalar));
446: MadeHRtr(sz,n,*idx0,*n0,*idx1,*n1,&tr1_te,&tr2_te,&ncond_e,work+nwu);
447: if (ncond > d*ncond_e) {
448: *exg = PETSC_TRUE;
449: tr1 = &tr1_te;
450: tr2 = &tr2_te;
451: ncond = ncond_e;
452: } else {
453: tr1 = &tr1_t;
454: tr2 = &tr2_t;
455: }
456: if (ncond>tolD) *ok = PETSC_FALSE;
457: }
458: if (*ok) {
459: /* Everything is OK, apply transformations to R and H */
460: /* First column */
461: if (cond && *cond<ncond) *cond = ncond;
462: x = tr1->data;
463: PetscBLASIntCast(tr1->n[0],&n0_);
464: PetscBLASIntCast(tr1->n[1],&n1_);
465: PetscBLASIntCast(n-j-sz,&mr);
466: if (tr1->n[0] > 1 && PetscAbsScalar(tr1->tau[0])!=0.0) {
467: x[tr1->idx[0]] = 1.0;
468: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&mr,x+tr1->idx[0],&inc,tr1->tau,R+(j+sz)*ldr+tr1->idx[0],&ldr_,work+nwu));
469: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0_,x+tr1->idx[0],&inc,tr1->tau,H+(tr1->idx[0])*ldh,&ldh_,work+nwu));
470: }
471: if (tr1->n[1] > 1 && PetscAbsScalar(tr1->tau[1])!=0.0) {
472: x[tr1->idx[1]] = 1.0;
473: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&mr,x+tr1->idx[1],&inc,tr1->tau+1,R+(j+sz)*ldr+tr1->idx[1],&ldr_,work+nwu));
474: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1_,x+tr1->idx[1],&inc,tr1->tau+1,H+(tr1->idx[1])*ldh,&ldh_,work+nwu));
475: }
476: if (tr1->idx[0]<tr1->idx[1]) {
477: HRApply(mr,R+(j+sz)*ldr+tr1->idx[0],ldr,R+(j+sz)*ldr+tr1->idx[1],ldr,tr1->cs,-tr1->sn);
478: if (tr1->type==1) {
479: HRApply(n,H+(tr1->idx[0])*ldh,1,H+(tr1->idx[1])*ldh,1,tr1->cs,tr1->sn);
480: } else {
481: HRApply(n,H+(tr1->idx[0])*ldh,1,H+(tr1->idx[1])*ldh,1,-tr1->cs,-tr1->sn);
482: s[tr1->idx[0]] = -s[tr1->idx[0]];
483: s[tr1->idx[1]] = -s[tr1->idx[1]];
484: }
485: }
486: for (i=0;i<tr1->idx[0];i++) *(R+j*ldr+i) = x[i];
487: for (i=tr1->idx[0]+1;i<n;i++) *(R+j*ldr+i) = 0.0;
488: *(R+j*ldr+tr1->idx[0]) = tr1->alpha;
489: if (sz==2) {
490: y = tr2->data;
491: /* Second column */
492: PetscBLASIntCast(tr2->n[0],&n0_);
493: PetscBLASIntCast(tr2->n[1],&n1_);
494: PetscBLASIntCast(n-j-sz,&mr);
495: PetscBLASIntCast(n-tr2->idx[0],&mh);
496: if (tr2->n[0] > 1 && PetscAbsScalar(tr2->tau[0])!=0.0) {
497: y[tr2->idx[0]] = 1.0;
498: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n0_,&mr,y+tr2->idx[0],&inc,tr2->tau,R+(j+2)*ldr+tr2->idx[0],&ldr_,work+nwu));
499: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n0_,y+tr2->idx[0],&inc,tr2->tau,H+(tr2->idx[0])*ldh,&ldh_,work+nwu));
500: }
501: if (tr2->n[1] > 1 && PetscAbsScalar(tr2->tau[1])!=0.0) {
502: y[tr2->idx[1]] = 1.0;
503: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("L",&n1_,&mr,y+tr2->idx[1],&inc,tr2->tau+1,R+(j+2)*ldr+tr2->idx[1],&ldr_,work+nwu));
504: PetscStackCallBLAS("LAPACKlarf",LAPACKlarf_("R",&n_,&n1_,y+tr2->idx[1],&inc,tr2->tau+1,H+(tr2->idx[1])*ldh,&ldh_,work+nwu));
505: }
506: if (tr2->idx[0]<tr2->idx[1]) {
507: HRApply(mr,R+(j+2)*ldr+tr2->idx[0],ldr,R+(j+2)*ldr+tr2->idx[1],ldr,tr2->cs,-tr2->sn);
508: if (tr2->type==1) {
509: HRApply(n,H+(tr2->idx[0])*ldh,1,H+(tr2->idx[1])*ldh,1,tr2->cs,tr2->sn);
510: } else {
511: HRApply(n,H+(tr2->idx[0])*ldh,1,H+(tr2->idx[1])*ldh,1,-tr2->cs,-tr2->sn);
512: s[tr2->idx[0]] = -s[tr2->idx[0]];
513: s[tr2->idx[1]] = -s[tr2->idx[1]];
514: }
515: }
516: for (i=0;i<tr2->idx[0]-1;i++) *(R+(j+1)*ldr+i) = y[i];
517: *(R+(j+1)*ldr+tr2->idx[0]-1) = y[tr2->idx[0]-1];
518: for (i=tr2->idx[0]+1;i<n;i++) *(R+(j+1)*ldr+i) = 0.0;
519: *(R+(j+1)*ldr+tr2->idx[0]) = tr2->alpha;
520: *n0 = tr2->n[0];
521: *n1 = tr2->n[1];
522: *idx0 = tr2->idx[0];
523: *idx1 = tr2->idx[1];
524: if (tr2->idx[0]<tr2->idx[1] && tr2->type==2) {
525: (*idx1)++; (*n1)--; (*n0)++;
526: }
527: } else {
528: *n0 = tr1->n[0];
529: *n1 = tr1->n[1];
530: *idx0 = tr1->idx[0];
531: *idx1 = tr1->idx[1];
532: if (tr1->idx[0]<tr1->idx[1] && tr1->type==2) {
533: (*idx1)++; (*n1)--; (*n0)++;
534: }
535: }
536: if (*n0>0) {
537: (*n0)--; (*idx0)++;
538: if (*n1==0) *idx1 = *idx0;
539: } else {
540: (*n1)--; (*idx1)++; *idx0 = *idx1;
541: }
542: }
543: return(0);
544: #endif
545: }
549: /*
550: compute V = HR whit H s-orthogonal and R upper triangular
551: */
552: static PetscErrorCode PseudoOrthog_HR(PetscInt *nv,PetscScalar *V,PetscInt ldv,PetscReal *s,PetscScalar *R,PetscInt ldr,PetscBLASInt *perm,PetscBLASInt *cmplxEig,PetscBool *breakdown,PetscScalar *work)
553: {
555: PetscInt i,j,n,n0,n1,np,idx0,idx1,sz=1,k=0,t1,t2,nwu=0;
556: PetscScalar *col1,*col2;
557: PetscBool exg=PETSC_FALSE,ok=PETSC_FALSE;
560: n = *nv;
561: col1 = work+nwu;
562: nwu += n;
563: col2 = work+nwu;
564: nwu += n;
565: /* Sort R and s according to sing(s) */
566: np = 0;
567: for (i=0;i<n;i++) if (s[i]>0) np++;
568: if (s[0]>0) n1 = np;
569: else n1 = n-np;
570: n0 = 0;
571: for (i=0;i<n;i++) {
572: if (s[i]==s[0]) {
573: s[n0] = s[0];
574: perm[n0++] = i;
575: } else perm[n1++] = i;
576: }
577: for (i=n0;i<n;i++) s[i] = -s[0];
578: n1 -= n0;
579: idx0 = 0;
580: idx1 = n0;
581: if (idx1==n) idx1=idx0;
582: for (i=0;i<n;i++) {
583: for (j=0;j<n;j++) R[j*ldr+i] = V[j*ldv+perm[i]];
584: }
585: /* Initialize H */
586: for (i=0;i<n;i++) {
587: PetscMemzero(V+i*ldv,n*sizeof(PetscScalar));
588: V[perm[i]+i*ldv] = 1.0;
589: }
590: for (i=0;i<n;i++) perm[i] = i;
591: j = 0;
592: while (j<n-k) {
593: if (cmplxEig[j]==0) sz=1;
594: else sz=2;
595: TryHRIt(n,j,sz,V,ldv,R,ldr,s,&exg,&ok,&n0,&n1,&idx0,&idx1,NULL,work+nwu);
596: if (ok) {
597: if (exg) cmplxEig[j] = -cmplxEig[j];
598: j = j+sz;
599: } else { /* to be discarded */
600: k = k+1;
601: if (cmplxEig[j]==0) {
602: if (j<n) {
603: t1 = perm[j];
604: for (i=j;i<n-1;i++) perm[i] = perm[i+1];
605: perm[n-1] = t1;
606: t1 = cmplxEig[j];
607: for (i=j;i<n-1;i++) cmplxEig[i] = cmplxEig[i+1];
608: cmplxEig[n-1] = t1;
609: PetscMemcpy(col1,R+j*ldr,n*sizeof(PetscScalar));
610: for (i=j;i<n-1;i++) {
611: PetscMemcpy(R+i*ldr,R+(i+1)*ldr,n*sizeof(PetscScalar));
612: }
613: PetscMemcpy(R+(n-1)*ldr,col1,n*sizeof(PetscScalar));
614: }
615: } else {
616: k = k+1;
617: if (j<n-1) {
618: t1 = perm[j];
619: t2 = perm[j+1];
620: for (i=j;i<n-2;i++) perm[i] = perm[i+2];
621: perm[n-2] = t1;
622: perm[n-1] = t2;
623: t1 = cmplxEig[j];
624: t2 = cmplxEig[j+1];
625: for (i=j;i<n-2;i++) cmplxEig[i] = cmplxEig[i+2];
626: cmplxEig[n-2] = t1;
627: cmplxEig[n-1] = t2;
628: PetscMemcpy(col1,R+j*ldr,n*sizeof(PetscScalar));
629: PetscMemcpy(col2,R+(j+1)*ldr,n*sizeof(PetscScalar));
630: for (i=j;i<n-2;i++) {
631: PetscMemcpy(R+i*ldr,R+(i+2)*ldr,n*sizeof(PetscScalar));
632: }
633: PetscMemcpy(R+(n-2)*ldr,col1,n*sizeof(PetscScalar));
634: PetscMemcpy(R+(n-1)*ldr,col2,n*sizeof(PetscScalar));
635: }
636: }
637: }
638: }
639: if (k!=0) {
640: if (breakdown) *breakdown = PETSC_TRUE;
641: *nv = n-k;
642: }
643: return(0);
644: }
648: PetscErrorCode DSGHIEPOrthogEigenv(DS ds,DSMatType mat,PetscScalar *wr,PetscScalar *wi,PetscBool accum)
649: {
651: PetscInt lws,nwus=0,nwui=0,lwi;
652: PetscInt off,n,nv,ld,i,ldr,l;
653: PetscScalar *W,*X,*R,*ts,zeroS=0.0,oneS=1.0;
654: PetscReal *s,vi,vr,tr,*d,*e;
655: PetscBLASInt ld_,n_,nv_,*perm,*cmplxEig;
658: l = ds->l;
659: n = ds->n-l;
660: PetscBLASIntCast(n,&n_);
661: ld = ds->ld;
662: PetscBLASIntCast(ld,&ld_);
663: off = l*ld+l;
664: s = ds->rmat[DS_MAT_D];
665: if (!ds->compact) {
666: for (i=l;i<ds->n;i++) s[i] = PetscRealPart(*(ds->mat[DS_MAT_B]+i*ld+i));
667: }
668: lws = n*n+7*n;
669: lwi = 2*n;
670: DSAllocateWork_Private(ds,lws,0,lwi);
671: R = ds->work+nwus;
672: nwus += n*n;
673: ldr = n;
674: perm = ds->iwork + nwui;
675: nwui += n;
676: cmplxEig = ds->iwork+nwui;
677: X = ds->mat[mat];
678: for (i=0;i<n;i++) {
679: #if defined(PETSC_USE_COMPLEX)
680: vi = PetscImaginaryPart(wr[l+i]);
681: #else
682: vi = PetscRealPart(wi[l+i]);
683: #endif
684: if (vi!=0) {
685: cmplxEig[i] = 1;
686: cmplxEig[i+1] = 2;
687: i++;
688: } else cmplxEig[i] = 0;
689: }
690: nv = n;
691:
692: /* Perform HR decomposition */
693: /* Hyperbolic rotators */
694: PseudoOrthog_HR(&nv,X+off,ld,s+l,R,ldr,perm,cmplxEig,NULL,ds->work+nwus);
695: /* Sort wr,wi perm */
696: ts = ds->work+nwus;
697: PetscMemcpy(ts,wr+l,n*sizeof(PetscScalar));
698: for (i=0;i<n;i++) wr[i+l] = ts[perm[i]];
699: #if !defined(PETSC_USE_COMPLEX)
700: PetscMemcpy(ts,wi+l,n*sizeof(PetscScalar));
701: for (i=0;i<n;i++) wi[i+l] = ts[perm[i]];
702: #endif
703: /* Projected Matrix */
704: PetscMemzero(ds->rmat[DS_MAT_T]+2*ld,ld*sizeof(PetscReal));
705: d = ds->rmat[DS_MAT_T];
706: e = d+ld;
707: for (i=0;i<nv;i++) {
708: if (cmplxEig[i]==0) { /* Real */
709: d[l+i] = PetscRealPart(wr[l+i]*s[l+i]);
710: e[l+i] = 0.0;
711: } else {
712: vr = PetscRealPart(wr[l+i]);
713: #if defined(PETSC_USE_COMPLEX)
714: vi = PetscImaginaryPart(wr[l+i]);
715: #else
716: vi = PetscRealPart(wi[l+i]);
717: #endif
718: if (cmplxEig[i]==-1) vi = -vi;
719: tr = PetscRealPart((R[i+(i+1)*ldr]/R[i+i*ldr]))*vi;
720: d[l+i] = (vr-tr)*s[l+i];
721: d[l+i+1] = (vr+tr)*s[l+i+1];
722: e[l+i] = PetscRealPart(s[l+i]*(R[(i+1)+(i+1)*ldr]/R[i+i*ldr])*vi);
723: e[l+i+1] = 0.0;
724: i++;
725: }
726: }
727: /* accumulate previous Q */
728: if (accum) {
729: PetscBLASIntCast(nv,&nv_);
730: DSAllocateMat_Private(ds,DS_MAT_W);
731: W = ds->mat[DS_MAT_W];
732: DSCopyMatrix_Private(ds,DS_MAT_W,DS_MAT_Q);
733: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&nv_,&n_,&oneS,W+off,&ld_,X+off,&ld_,&zeroS,ds->mat[DS_MAT_Q]+off,&ld_));
734: } else {
735: PetscMemzero(ds->mat[DS_MAT_Q],ld*ld*sizeof(PetscScalar));
736: for (i=0;i<ds->l;i++) *(ds->mat[DS_MAT_Q]+i+i*ld) = 1.0;
737: for (i=0;i<n;i++) { PetscMemcpy(ds->mat[DS_MAT_Q]+off+i*ld,X+off+i*ld,n*sizeof(PetscScalar)); }
738: }
739: ds->t = nv+l;
740: if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
741: return(0);
742: }
746: /*
747: Reduce to tridiagonal-diagonal pair by means of TridiagDiag_HHR.
748: */
749: PetscErrorCode DSIntermediate_GHIEP(DS ds)
750: {
752: PetscInt i,ld,off;
753: PetscInt nwall,nwallr,nwalli;
754: PetscScalar *A,*B,*Q;
755: PetscReal *d,*e,*s;
758: ld = ds->ld;
759: A = ds->mat[DS_MAT_A];
760: B = ds->mat[DS_MAT_B];
761: Q = ds->mat[DS_MAT_Q];
762: d = ds->rmat[DS_MAT_T];
763: e = ds->rmat[DS_MAT_T]+ld;
764: s = ds->rmat[DS_MAT_D];
765: off = ds->l+ds->l*ld;
766: PetscMemzero(Q,ld*ld*sizeof(PetscScalar));
767: nwall = ld*ld+ld;
768: nwallr = ld;
769: nwalli = ld;
770: DSAllocateWork_Private(ds,nwall,nwallr,nwalli);
771: for (i=0;i<ds->n;i++) Q[i+i*ld]=1.0;
772: for (i=0;i<ds->n-ds->l;i++) *(ds->perm+i)=i;
773: if (ds->compact) {
774: if (ds->state < DS_STATE_INTERMEDIATE) {
775: DSSwitchFormat_GHIEP(ds,PETSC_FALSE);
776: 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);
777: ds->k = ds->l;
778: PetscMemzero(d+2*ld+ds->l,(ds->n-ds->l)*sizeof(PetscReal));
779: }
780: } else {
781: if (ds->state < DS_STATE_INTERMEDIATE) {
782: for (i=0;i<ds->n;i++) s[i] = PetscRealPart(B[i+i*ld]);
783: 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);
784: PetscMemzero(d+2*ld,(ds->n)*sizeof(PetscReal));
785: ds->k = ds->l;
786: DSSwitchFormat_GHIEP(ds,PETSC_FALSE);
787: } else {
788: DSSwitchFormat_GHIEP(ds,PETSC_TRUE);
789: }
790: }
791: return(0);
792: }