Actual source code: dsgnhep.c
slepc-3.15.1 2021-05-28
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
11: #include <slepc/private/dsimpl.h>
12: #include <slepcblaslapack.h>
14: /*
15: 1) Patterns of A and B
16: DS_STATE_RAW: DS_STATE_INTERM/CONDENSED
17: 0 n-1 0 n-1
18: ------------- -------------
19: 0 |* * * * * *| 0 |* * * * * *|
20: |* * * * * *| | * * * * *|
21: |* * * * * *| | * * * *|
22: |* * * * * *| | * * * *|
23: |* * * * * *| | * *|
24: n-1 |* * * * * *| n-1 | *|
25: ------------- -------------
27: 2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
28: */
31: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY);
33: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
34: {
38: DSAllocateMat_Private(ds,DS_MAT_A);
39: DSAllocateMat_Private(ds,DS_MAT_B);
40: DSAllocateMat_Private(ds,DS_MAT_Z);
41: DSAllocateMat_Private(ds,DS_MAT_Q);
42: PetscFree(ds->perm);
43: PetscMalloc1(ld,&ds->perm);
44: PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
45: return(0);
46: }
48: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
49: {
50: PetscErrorCode ierr;
51: PetscViewerFormat format;
54: PetscViewerGetFormat(viewer,&format);
55: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
56: DSViewMat(ds,viewer,DS_MAT_A);
57: DSViewMat(ds,viewer,DS_MAT_B);
58: if (ds->state>DS_STATE_INTERMEDIATE) {
59: DSViewMat(ds,viewer,DS_MAT_Z);
60: DSViewMat(ds,viewer,DS_MAT_Q);
61: }
62: if (ds->mat[DS_MAT_X]) { DSViewMat(ds,viewer,DS_MAT_X); }
63: if (ds->mat[DS_MAT_Y]) { DSViewMat(ds,viewer,DS_MAT_Y); }
64: return(0);
65: }
67: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
68: {
70: PetscInt i;
71: PetscBLASInt n,ld,mout,info,*select,mm,inc=1,cols=1,zero=0;
72: PetscScalar *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],fone=1.0,fzero=0.0;
73: PetscReal norm,done=1.0;
74: PetscBool iscomplex = PETSC_FALSE;
75: const char *side;
78: PetscBLASIntCast(ds->n,&n);
79: PetscBLASIntCast(ds->ld,&ld);
80: if (left) {
81: X = NULL;
82: Y = &ds->mat[DS_MAT_Y][ld*(*k)];
83: side = "L";
84: } else {
85: X = &ds->mat[DS_MAT_X][ld*(*k)];
86: Y = NULL;
87: side = "R";
88: }
89: Z = left? Y: X;
90: DSAllocateWork_Private(ds,0,0,ld);
91: select = ds->iwork;
92: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
93: if (ds->state <= DS_STATE_INTERMEDIATE) {
94: DSSetIdentity(ds,DS_MAT_Q);
95: DSSetIdentity(ds,DS_MAT_Z);
96: }
97: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
98: if (ds->state < DS_STATE_CONDENSED) { DSSetState(ds,DS_STATE_CONDENSED); }
100: /* compute k-th eigenvector */
101: select[*k] = (PetscBLASInt)PETSC_TRUE;
102: #if defined(PETSC_USE_COMPLEX)
103: mm = 1;
104: DSAllocateWork_Private(ds,2*ld,2*ld,0);
105: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
106: #else
107: if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
108: mm = iscomplex? 2: 1;
109: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
110: DSAllocateWork_Private(ds,6*ld,0,0);
111: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
112: #endif
113: SlepcCheckLapackInfo("tgevc",info);
114: if (!select[*k] || mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");
116: /* accumulate and normalize eigenvectors */
117: PetscArraycpy(ds->work,Z,mm*ld);
118: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,ds->mat[left?DS_MAT_Z:DS_MAT_Q],&ld,ds->work,&ld,&fzero,Z,&ld));
119: norm = BLASnrm2_(&n,Z,&inc);
120: #if !defined(PETSC_USE_COMPLEX)
121: if (iscomplex) {
122: norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Z+ld,&inc));
123: cols = 2;
124: }
125: #endif
126: PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Z,&ld,&info));
127: SlepcCheckLapackInfo("lascl",info);
129: /* set output arguments */
130: if (iscomplex) (*k)++;
131: if (rnorm) {
132: if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
133: else *rnorm = PetscAbsScalar(Z[n-1]);
134: }
135: return(0);
136: }
138: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
139: {
141: PetscInt i;
142: PetscBLASInt n,ld,mout,info,inc = 1;
143: PetscBool iscomplex;
144: PetscScalar *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp;
145: PetscReal norm;
146: const char *side,*back;
149: PetscBLASIntCast(ds->n,&n);
150: PetscBLASIntCast(ds->ld,&ld);
151: if (left) {
152: X = NULL;
153: Y = ds->mat[DS_MAT_Y];
154: side = "L";
155: } else {
156: X = ds->mat[DS_MAT_X];
157: Y = NULL;
158: side = "R";
159: }
160: Z = left? Y: X;
161: if (ds->state <= DS_STATE_INTERMEDIATE) {
162: DSSetIdentity(ds,DS_MAT_Q);
163: DSSetIdentity(ds,DS_MAT_Z);
164: }
165: CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
166: if (ds->state>=DS_STATE_CONDENSED) {
167: /* DSSolve() has been called, backtransform with matrix Q */
168: back = "B";
169: PetscArraycpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld);
170: } else {
171: back = "A";
172: DSSetState(ds,DS_STATE_CONDENSED);
173: }
174: #if defined(PETSC_USE_COMPLEX)
175: DSAllocateWork_Private(ds,2*ld,2*ld,0);
176: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
177: #else
178: DSAllocateWork_Private(ds,6*ld,0,0);
179: PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
180: #endif
181: SlepcCheckLapackInfo("tgevc",info);
183: /* normalize eigenvectors */
184: for (i=0;i<n;i++) {
185: iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
186: norm = BLASnrm2_(&n,Z+i*ld,&inc);
187: #if !defined(PETSC_USE_COMPLEX)
188: if (iscomplex) {
189: tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
190: norm = SlepcAbsEigenvalue(norm,tmp);
191: }
192: #endif
193: tmp = 1.0 / norm;
194: PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
195: #if !defined(PETSC_USE_COMPLEX)
196: if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
197: #endif
198: if (iscomplex) i++;
199: }
200: return(0);
201: }
203: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
204: {
208: switch (mat) {
209: case DS_MAT_X:
210: case DS_MAT_Y:
211: if (k) {
212: DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
213: } else {
214: DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
215: }
216: break;
217: default:
218: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
219: }
220: return(0);
221: }
223: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
224: {
226: PetscInt i;
227: PetscBLASInt info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
228: PetscScalar *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Q = ds->mat[DS_MAT_Q],*Z = ds->mat[DS_MAT_Z],*work,*beta;
231: if (!ds->sc) return(0);
232: PetscBLASIntCast(ds->n,&n);
233: PetscBLASIntCast(ds->ld,&ld);
234: #if !defined(PETSC_USE_COMPLEX)
235: lwork = 4*n+16;
236: #else
237: lwork = 1;
238: #endif
239: liwork = 1;
240: DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
241: beta = ds->work;
242: work = ds->work + n;
243: lwork = ds->lwork - n;
244: selection = ds->iwork;
245: iwork = ds->iwork + n;
246: liwork = ds->liwork - n;
247: /* Compute the selected eigenvalue to be in the leading position */
248: DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
249: PetscArrayzero(selection,n);
250: for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
251: #if !defined(PETSC_USE_COMPLEX)
252: PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,wi,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
253: #else
254: PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
255: #endif
256: SlepcCheckLapackInfo("tgsen",info);
257: *k = mout;
258: for (i=0;i<n;i++) {
259: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
260: else wr[i] /= beta[i];
261: #if !defined(PETSC_USE_COMPLEX)
262: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
263: else wi[i] /= beta[i];
264: #endif
265: }
266: return(0);
267: }
269: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
270: {
272: PetscScalar re;
273: PetscInt i,j,pos,result;
274: PetscBLASInt ifst,ilst,info,n,ld,one=1;
275: PetscScalar *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];
276: #if !defined(PETSC_USE_COMPLEX)
277: PetscBLASInt lwork;
278: PetscScalar *work,a,safmin,scale1,scale2,im;
279: #endif
282: if (!ds->sc) return(0);
283: PetscBLASIntCast(ds->n,&n);
284: PetscBLASIntCast(ds->ld,&ld);
285: #if !defined(PETSC_USE_COMPLEX)
286: lwork = -1;
287: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
288: SlepcCheckLapackInfo("tgexc",info);
289: safmin = LAPACKlamch_("S");
290: PetscBLASIntCast((PetscInt)a,&lwork);
291: DSAllocateWork_Private(ds,lwork,0,0);
292: work = ds->work;
293: #endif
294: /* selection sort */
295: for (i=ds->l;i<n-1;i++) {
296: re = wr[i];
297: #if !defined(PETSC_USE_COMPLEX)
298: im = wi[i];
299: #endif
300: pos = 0;
301: j = i+1; /* j points to the next eigenvalue */
302: #if !defined(PETSC_USE_COMPLEX)
303: if (im != 0) j=i+2;
304: #endif
305: /* find minimum eigenvalue */
306: for (;j<n;j++) {
307: #if !defined(PETSC_USE_COMPLEX)
308: SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
309: #else
310: SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
311: #endif
312: if (result > 0) {
313: re = wr[j];
314: #if !defined(PETSC_USE_COMPLEX)
315: im = wi[j];
316: #endif
317: pos = j;
318: }
319: #if !defined(PETSC_USE_COMPLEX)
320: if (wi[j] != 0) j++;
321: #endif
322: }
323: if (pos) {
324: /* interchange blocks */
325: PetscBLASIntCast(pos+1,&ifst);
326: PetscBLASIntCast(i+1,&ilst);
327: #if !defined(PETSC_USE_COMPLEX)
328: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
329: #else
330: PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
331: #endif
332: SlepcCheckLapackInfo("tgexc",info);
333: /* recover original eigenvalues from T and S matrices */
334: for (j=i;j<n;j++) {
335: #if !defined(PETSC_USE_COMPLEX)
336: if (j<n-1 && S[j*ld+j+1] != 0.0) {
337: /* complex conjugate eigenvalue */
338: PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
339: wr[j] = re / scale1;
340: wi[j] = im / scale1;
341: wr[j+1] = a / scale2;
342: wi[j+1] = -wi[j];
343: j++;
344: } else
345: #endif
346: {
347: if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
348: else wr[j] = S[j*ld+j] / T[j*ld+j];
349: #if !defined(PETSC_USE_COMPLEX)
350: wi[j] = 0.0;
351: #endif
352: }
353: }
354: }
355: #if !defined(PETSC_USE_COMPLEX)
356: if (wi[i] != 0.0) i++;
357: #endif
358: }
359: return(0);
360: }
362: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
363: {
367: if (!rr || wr == rr) {
368: DSSort_GNHEP_Total(ds,wr,wi);
369: } else {
370: DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
371: }
372: return(0);
373: }
375: PetscErrorCode DSUpdateExtraRow_GNHEP(DS ds)
376: {
378: PetscInt i;
379: PetscBLASInt n,ld,incx=1;
380: PetscScalar *A,*B,*Q,*x,*y,one=1.0,zero=0.0;
383: PetscBLASIntCast(ds->n,&n);
384: PetscBLASIntCast(ds->ld,&ld);
385: A = ds->mat[DS_MAT_A];
386: B = ds->mat[DS_MAT_B];
387: Q = ds->mat[DS_MAT_Q];
388: DSAllocateWork_Private(ds,2*ld,0,0);
389: x = ds->work;
390: y = ds->work+ld;
391: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
392: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
393: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
394: for (i=0;i<n;i++) x[i] = PetscConj(B[n+i*ld]);
395: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
396: for (i=0;i<n;i++) B[n+i*ld] = PetscConj(y[i]);
397: ds->k = n;
398: return(0);
399: }
401: /*
402: Write zeros from the column k to n in the lower triangular part of the
403: matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
404: make (S,T) a valid Schur decompositon.
405: */
406: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
407: {
408: PetscInt i;
409: #if defined(PETSC_USE_COMPLEX)
410: PetscInt j;
411: PetscScalar s;
412: #else
414: PetscBLASInt ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
415: PetscScalar b11,b22,sr,cr,sl,cl;
416: #endif
419: #if defined(PETSC_USE_COMPLEX)
420: for (i=k; i<n; i++) {
421: /* Some functions need the diagonal elements in T be real */
422: if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
423: s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
424: for (j=0;j<=i;j++) {
425: T[ldT*i+j] *= s;
426: S[ldS*i+j] *= s;
427: }
428: T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
429: if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
430: }
431: j = i+1;
432: if (j<n) {
433: S[ldS*i+j] = 0.0;
434: if (T) T[ldT*i+j] = 0.0;
435: }
436: }
437: #else
438: PetscBLASIntCast(ldS,&ldS_);
439: PetscBLASIntCast(ldT,&ldT_);
440: PetscBLASIntCast(n,&n_);
441: for (i=k;i<n-1;i++) {
442: if (S[ldS*i+i+1] != 0.0) {
443: /* Check if T(i+1,i) and T(i,i+1) are zero */
444: if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
445: /* Check if T(i+1,i) and T(i,i+1) are negligible */
446: if (PetscAbs(T[ldT*(i+1)+i])+PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1]))*PETSC_MACHINE_EPSILON) {
447: T[ldT*i+i+1] = 0.0;
448: T[ldT*(i+1)+i] = 0.0;
449: } else {
450: /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
451: if (PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*(i+1)+i]))*PETSC_MACHINE_EPSILON) {
452: PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
453: } else if (PetscAbs(T[ldT*(i+1)+i]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*i+i+1]))*PETSC_MACHINE_EPSILON) {
454: PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
455: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
456: PetscBLASIntCast(n-i,&n_i);
457: n_i_2 = n_i - 2;
458: PetscBLASIntCast(i+2,&i_2);
459: PetscBLASIntCast(i,&i_);
460: if (b11 < 0.0) {
461: cr = -cr; sr = -sr;
462: b11 = -b11; b22 = -b22;
463: }
464: PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
465: PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
466: PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
467: PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
468: if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
469: if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
470: T[ldT*i+i] = b11; T[ldT*i+i+1] = 0.0;
471: T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
472: }
473: }
474: i++;
475: }
476: }
477: #endif
478: return(0);
479: }
481: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
482: {
484: PetscScalar *work,*beta,a;
485: PetscInt i;
486: PetscBLASInt lwork,info,n,ld,iaux;
487: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];
490: #if !defined(PETSC_USE_COMPLEX)
492: #endif
493: PetscBLASIntCast(ds->n,&n);
494: PetscBLASIntCast(ds->ld,&ld);
495: lwork = -1;
496: #if !defined(PETSC_USE_COMPLEX)
497: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
498: PetscBLASIntCast((PetscInt)a,&lwork);
499: DSAllocateWork_Private(ds,lwork+ld,0,0);
500: beta = ds->work;
501: work = beta+ds->n;
502: PetscBLASIntCast(ds->lwork-ds->n,&lwork);
503: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
504: #else
505: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
506: PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
507: DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
508: beta = ds->work;
509: work = beta+ds->n;
510: PetscBLASIntCast(ds->lwork-ds->n,&lwork);
511: PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
512: #endif
513: SlepcCheckLapackInfo("gges",info);
514: for (i=0;i<n;i++) {
515: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
516: else wr[i] /= beta[i];
517: #if !defined(PETSC_USE_COMPLEX)
518: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
519: else wi[i] /= beta[i];
520: #else
521: if (wi) wi[i] = 0.0;
522: #endif
523: }
524: return(0);
525: }
527: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
528: {
530: PetscInt ld=ds->ld,l=ds->l,k;
531: PetscMPIInt n,rank,off=0,size,ldn;
534: k = 2*(ds->n-l)*ld;
535: if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
536: if (eigr) k += (ds->n-l);
537: if (eigi) k += (ds->n-l);
538: DSAllocateWork_Private(ds,k,0,0);
539: PetscMPIIntCast(k*sizeof(PetscScalar),&size);
540: PetscMPIIntCast(ds->n-l,&n);
541: PetscMPIIntCast(ld*(ds->n-l),&ldn);
542: MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);CHKERRMPI(ierr);
543: if (!rank) {
544: MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
545: MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
546: if (ds->state>DS_STATE_RAW) {
547: MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
548: MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
549: }
550: if (eigr) {
551: MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
552: }
553: if (eigi) {
554: MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
555: }
556: }
557: MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
558: if (rank) {
559: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
560: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
561: if (ds->state>DS_STATE_RAW) {
562: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
563: MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
564: }
565: if (eigr) {
566: MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
567: }
568: if (eigi) {
569: MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
570: }
571: }
572: return(0);
573: }
575: PetscErrorCode DSTruncate_GNHEP(DS ds,PetscInt n,PetscBool trim)
576: {
577: PetscInt i,ld=ds->ld,l=ds->l;
578: PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];
581: #if defined(PETSC_USE_DEBUG)
582: /* make sure diagonal 2x2 block is not broken */
583: if (ds->state>=DS_STATE_CONDENSED && n>0 && n<ds->n && (A[n+(n-1)*ld]!=0.0 || B[n+(n-1)*ld]!=0.0)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
584: #endif
585: if (trim) {
586: if (ds->extrarow) { /* clean extra row */
587: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
588: for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
589: }
590: ds->l = 0;
591: ds->k = 0;
592: ds->n = n;
593: ds->t = ds->n; /* truncated length equal to the new dimension */
594: } else {
595: if (ds->extrarow && ds->k==ds->n) {
596: /* copy entries of extra row to the new position, then clean last row */
597: for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
598: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
599: for (i=l;i<n;i++) B[n+i*ld] = B[ds->n+i*ld];
600: for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
601: }
602: ds->k = (ds->extrarow)? n: 0;
603: ds->t = ds->n; /* truncated length equal to previous dimension */
604: ds->n = n;
605: }
606: return(0);
607: }
609: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
610: {
612: ds->ops->allocate = DSAllocate_GNHEP;
613: ds->ops->view = DSView_GNHEP;
614: ds->ops->vectors = DSVectors_GNHEP;
615: ds->ops->solve[0] = DSSolve_GNHEP;
616: ds->ops->sort = DSSort_GNHEP;
617: ds->ops->synchronize = DSSynchronize_GNHEP;
618: ds->ops->gettruncatesize = DSGetTruncateSize_Default;
619: ds->ops->truncate = DSTruncate_GNHEP;
620: ds->ops->update = DSUpdateExtraRow_GNHEP;
621: return(0);
622: }