Actual source code: dsgnhep.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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: */
30: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY);
32: static PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
33: {
34: PetscFunctionBegin;
35: PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
36: PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
37: PetscCall(DSAllocateMat_Private(ds,DS_MAT_Z));
38: PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
39: PetscCall(PetscFree(ds->perm));
40: PetscCall(PetscMalloc1(ld,&ds->perm));
41: PetscFunctionReturn(PETSC_SUCCESS);
42: }
44: static PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
45: {
46: PetscViewerFormat format;
48: PetscFunctionBegin;
49: PetscCall(PetscViewerGetFormat(viewer,&format));
50: if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(PETSC_SUCCESS);
51: PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
52: PetscCall(DSViewMat(ds,viewer,DS_MAT_B));
53: if (ds->state>DS_STATE_INTERMEDIATE) {
54: PetscCall(DSViewMat(ds,viewer,DS_MAT_Z));
55: PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
56: }
57: if (ds->omat[DS_MAT_X]) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
58: if (ds->omat[DS_MAT_Y]) PetscCall(DSViewMat(ds,viewer,DS_MAT_Y));
59: PetscFunctionReturn(PETSC_SUCCESS);
60: }
62: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
63: {
64: PetscInt i;
65: PetscBLASInt n,ld,mout,*select,mm,inc=1,cols=1,zero=0;
66: PetscScalar *X,*Y,*XY,*Z,*Q,*A,*B,fone=1.0,fzero=0.0;
67: PetscReal norm,done=1.0;
68: PetscBool iscomplex = PETSC_FALSE;
69: const char *side;
71: PetscFunctionBegin;
72: PetscCall(PetscBLASIntCast(ds->n,&n));
73: PetscCall(PetscBLASIntCast(ds->ld,&ld));
74: if (left) {
75: X = NULL;
76: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Y],&Y));
77: side = "L";
78: } else {
79: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
80: Y = NULL;
81: side = "R";
82: }
83: XY = left? Y: X;
84: PetscCall(DSAllocateWork_Private(ds,0,0,ld));
85: select = ds->iwork;
86: for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
87: if (ds->state <= DS_STATE_INTERMEDIATE) {
88: PetscCall(DSSetIdentity(ds,DS_MAT_Q));
89: PetscCall(DSSetIdentity(ds,DS_MAT_Z));
90: }
91: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
92: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
93: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
94: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
95: PetscCall(CleanDenseSchur(n,0,A,ld,B,ld,Q,ld,Z,ld));
96: if (ds->state < DS_STATE_CONDENSED) PetscCall(DSSetState(ds,DS_STATE_CONDENSED));
98: /* compute k-th eigenvector */
99: select[*k] = (PetscBLASInt)PETSC_TRUE;
100: #if PetscDefined(USE_COMPLEX)
101: mm = 1;
102: PetscCall(DSAllocateWork_Private(ds,2*ld,2*ld,0));
103: PetscCallLAPACKInfo("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,PetscSafePointerPlusOffset(Y,(*k)*ld),&ld,PetscSafePointerPlusOffset(X,(*k)*ld),&ld,&mm,&mout,ds->work,ds->rwork,&info));
104: #else
105: if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
106: mm = iscomplex? 2: 1;
107: if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
108: PetscCall(DSAllocateWork_Private(ds,6*ld,0,0));
109: PetscCallLAPACKInfo("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,PetscSafePointerPlusOffset(Y,(*k)*ld),&ld,PetscSafePointerPlusOffset(X,(*k)*ld),&ld,&mm,&mout,ds->work,&info));
110: #endif
111: PetscCheck(select[*k] && mout==mm,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");
112: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
113: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
115: /* accumulate and normalize eigenvectors */
116: PetscCall(PetscArraycpy(ds->work,XY+(*k)*ld,mm*ld));
117: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,left?Z:Q,&ld,ds->work,&ld,&fzero,XY+(*k)*ld,&ld));
118: norm = BLASnrm2_(&n,XY+(*k)*ld,&inc);
119: #if !PetscDefined(USE_COMPLEX)
120: if (iscomplex) {
121: norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,XY+(*k+1)*ld,&inc));
122: cols = 2;
123: }
124: #endif
125: PetscCallLAPACKInfo("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,XY+(*k)*ld,&ld,&info));
126: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
127: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
129: /* set output arguments */
130: if (rnorm) {
131: if (iscomplex) *rnorm = SlepcAbsEigenvalue(XY[n-1+(*k)*ld],XY[n-1+(*k+1)*ld]);
132: else *rnorm = PetscAbsScalar(XY[n-1+(*k)*ld]);
133: }
134: if (iscomplex) (*k)++;
135: PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&XY));
136: PetscFunctionReturn(PETSC_SUCCESS);
137: }
139: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
140: {
141: PetscInt i;
142: PetscBLASInt n,ld,mout,inc = 1;
143: PetscBool iscomplex;
144: PetscScalar *X,*Y,*XY,*Q,*Z,*A,*B,tmp;
145: PetscReal norm;
146: const char *side,*back;
148: PetscFunctionBegin;
149: PetscCall(PetscBLASIntCast(ds->n,&n));
150: PetscCall(PetscBLASIntCast(ds->ld,&ld));
151: if (left) {
152: X = NULL;
153: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Y],&Y));
154: side = "L";
155: } else {
156: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
157: Y = NULL;
158: side = "R";
159: }
160: XY = left? Y: X;
161: if (ds->state <= DS_STATE_INTERMEDIATE) {
162: PetscCall(DSSetIdentity(ds,DS_MAT_Q));
163: PetscCall(DSSetIdentity(ds,DS_MAT_Z));
164: }
165: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
166: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
167: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
168: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
169: PetscCall(CleanDenseSchur(n,0,A,ld,B,ld,Q,ld,Z,ld));
170: if (ds->state>=DS_STATE_CONDENSED) {
171: /* DSSolve() has been called, backtransform with matrix Q */
172: back = "B";
173: PetscCall(PetscArraycpy(left?Y:X,left?Z:Q,ld*ld));
174: } else {
175: back = "A";
176: PetscCall(DSSetState(ds,DS_STATE_CONDENSED));
177: }
178: #if PetscDefined(USE_COMPLEX)
179: PetscCall(DSAllocateWork_Private(ds,2*ld,2*ld,0));
180: PetscCallLAPACKInfo("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
181: #else
182: PetscCall(DSAllocateWork_Private(ds,6*ld,0,0));
183: PetscCallLAPACKInfo("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
184: #endif
185: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
186: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
188: /* normalize eigenvectors */
189: for (i=0;i<n;i++) {
190: iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
191: norm = BLASnrm2_(&n,XY+i*ld,&inc);
192: #if !PetscDefined(USE_COMPLEX)
193: if (iscomplex) {
194: tmp = BLASnrm2_(&n,XY+(i+1)*ld,&inc);
195: norm = SlepcAbsEigenvalue(norm,tmp);
196: }
197: #endif
198: tmp = 1.0 / norm;
199: PetscCallBLAS("BLASscal",BLASscal_(&n,&tmp,XY+i*ld,&inc));
200: #if !PetscDefined(USE_COMPLEX)
201: if (iscomplex) PetscCallBLAS("BLASscal",BLASscal_(&n,&tmp,XY+(i+1)*ld,&inc));
202: #endif
203: if (iscomplex) i++;
204: }
205: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
206: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
207: PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&XY));
208: PetscFunctionReturn(PETSC_SUCCESS);
209: }
211: static PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
212: {
213: PetscFunctionBegin;
214: switch (mat) {
215: case DS_MAT_X:
216: case DS_MAT_Y:
217: if (k) PetscCall(DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE));
218: else PetscCall(DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE));
219: break;
220: default:
221: SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
222: }
223: PetscFunctionReturn(PETSC_SUCCESS);
224: }
226: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
227: {
228: PetscInt i;
229: PetscBLASInt n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
230: PetscScalar *S,*T,*Q,*Z,*work,*beta;
232: PetscFunctionBegin;
233: if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
234: PetscCall(PetscBLASIntCast(ds->n,&n));
235: PetscCall(PetscBLASIntCast(ds->ld,&ld));
236: #if !PetscDefined(USE_COMPLEX)
237: lwork = 4*n+16;
238: #else
239: lwork = 1;
240: #endif
241: liwork = 1;
242: PetscCall(DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n));
243: beta = ds->work;
244: work = ds->work + n;
245: PetscCall(PetscBLASIntCast(ds->lwork-n,&lwork));
246: selection = ds->iwork;
247: iwork = ds->iwork + n;
248: PetscCall(PetscBLASIntCast(ds->liwork-n,&liwork));
249: /* Compute the selected eigenvalue to be in the leading position */
250: PetscCall(DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE));
251: PetscCall(PetscArrayzero(selection,n));
252: for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
253: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&S));
254: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&T));
255: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
256: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
257: #if !PetscDefined(USE_COMPLEX)
258: PetscCallLAPACKInfo("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));
259: #else
260: PetscCallLAPACKInfo("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));
261: #endif
262: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&S));
263: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&T));
264: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
265: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
266: *k = mout;
267: for (i=0;i<n;i++) {
268: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
269: else wr[i] /= beta[i];
270: #if !PetscDefined(USE_COMPLEX)
271: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
272: else wi[i] /= beta[i];
273: #endif
274: }
275: PetscFunctionReturn(PETSC_SUCCESS);
276: }
278: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
279: {
280: PetscScalar re;
281: PetscInt i,j,pos,result;
282: PetscBLASInt ifst,ilst,n,ld,one=1;
283: PetscScalar *S,*T,*Z,*Q;
284: #if !PetscDefined(USE_COMPLEX)
285: PetscBLASInt lwork;
286: PetscScalar *work,a,safmin,scale1,scale2,im;
287: #endif
289: PetscFunctionBegin;
290: if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
291: PetscCall(PetscBLASIntCast(ds->n,&n));
292: PetscCall(PetscBLASIntCast(ds->ld,&ld));
293: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&S));
294: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&T));
295: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
296: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
297: #if !PetscDefined(USE_COMPLEX)
298: lwork = -1;
299: PetscCallLAPACKInfo("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
300: safmin = LAPACKlamch_("S");
301: PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
302: PetscCall(DSAllocateWork_Private(ds,lwork,0,0));
303: work = ds->work;
304: #endif
305: /* selection sort */
306: for (i=ds->l;i<n-1;i++) {
307: re = wr[i];
308: #if !PetscDefined(USE_COMPLEX)
309: im = wi[i];
310: #endif
311: pos = 0;
312: j = i+1; /* j points to the next eigenvalue */
313: #if !PetscDefined(USE_COMPLEX)
314: if (im != 0) j=i+2;
315: #endif
316: /* find minimum eigenvalue */
317: for (;j<n;j++) {
318: #if !PetscDefined(USE_COMPLEX)
319: PetscCall(SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result));
320: #else
321: PetscCall(SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result));
322: #endif
323: if (result > 0) {
324: re = wr[j];
325: #if !PetscDefined(USE_COMPLEX)
326: im = wi[j];
327: #endif
328: pos = j;
329: }
330: #if !PetscDefined(USE_COMPLEX)
331: if (wi[j] != 0) j++;
332: #endif
333: }
334: if (pos) {
335: /* interchange blocks */
336: PetscCall(PetscBLASIntCast(pos+1,&ifst));
337: PetscCall(PetscBLASIntCast(i+1,&ilst));
338: #if !PetscDefined(USE_COMPLEX)
339: PetscCallLAPACKInfo("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
340: #else
341: PetscCallLAPACKInfo("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
342: #endif
343: /* recover original eigenvalues from T and S matrices */
344: for (j=i;j<n;j++) {
345: #if !PetscDefined(USE_COMPLEX)
346: if (j<n-1 && S[j*ld+j+1] != 0.0) {
347: /* complex conjugate eigenvalue */
348: PetscCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
349: wr[j] = re / scale1;
350: wi[j] = im / scale1;
351: wr[j+1] = a / scale2;
352: wi[j+1] = -wi[j];
353: j++;
354: } else
355: #endif
356: {
357: if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
358: else wr[j] = S[j*ld+j] / T[j*ld+j];
359: #if !PetscDefined(USE_COMPLEX)
360: wi[j] = 0.0;
361: #endif
362: }
363: }
364: }
365: #if !PetscDefined(USE_COMPLEX)
366: if (wi[i] != 0.0) i++;
367: #endif
368: }
369: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&S));
370: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&T));
371: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
372: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
373: PetscFunctionReturn(PETSC_SUCCESS);
374: }
376: static PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
377: {
378: PetscFunctionBegin;
379: if (!rr || wr == rr) PetscCall(DSSort_GNHEP_Total(ds,wr,wi));
380: else PetscCall(DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k));
381: PetscFunctionReturn(PETSC_SUCCESS);
382: }
384: static PetscErrorCode DSUpdateExtraRow_GNHEP(DS ds)
385: {
386: PetscInt i;
387: PetscBLASInt n,ld,incx=1;
388: PetscScalar *A,*B,*x,*y,one=1.0,zero=0.0;
389: const PetscScalar *Q;
391: PetscFunctionBegin;
392: PetscCall(PetscBLASIntCast(ds->n,&n));
393: PetscCall(PetscBLASIntCast(ds->ld,&ld));
394: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
395: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
396: PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
397: PetscCall(DSAllocateWork_Private(ds,2*ld,0,0));
398: x = ds->work;
399: y = ds->work+ld;
400: for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
401: PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
402: for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
403: for (i=0;i<n;i++) x[i] = PetscConj(B[n+i*ld]);
404: PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
405: for (i=0;i<n;i++) B[n+i*ld] = PetscConj(y[i]);
406: ds->k = n;
407: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
408: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
409: PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
410: PetscFunctionReturn(PETSC_SUCCESS);
411: }
413: /*
414: Write zeros from the column k to n in the lower triangular part of the
415: matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
416: make (S,T) a valid Schur decompositon.
417: */
418: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
419: {
420: PetscInt i;
421: #if PetscDefined(USE_COMPLEX)
422: PetscInt j;
423: PetscScalar s;
424: #else
425: PetscBLASInt ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
426: PetscScalar b11,b22,sr,cr,sl,cl;
427: #endif
429: PetscFunctionBegin;
430: #if PetscDefined(USE_COMPLEX)
431: for (i=k; i<n; i++) {
432: /* Some functions need the diagonal elements in T be real */
433: if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
434: s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
435: for (j=0;j<=i;j++) {
436: T[ldT*i+j] *= s;
437: S[ldS*i+j] *= s;
438: }
439: T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
440: if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
441: }
442: j = i+1;
443: if (j<n) {
444: S[ldS*i+j] = 0.0;
445: if (T) T[ldT*i+j] = 0.0;
446: }
447: }
448: #else
449: PetscCall(PetscBLASIntCast(ldS,&ldS_));
450: PetscCall(PetscBLASIntCast(ldT,&ldT_));
451: PetscCall(PetscBLASIntCast(n,&n_));
452: for (i=k;i<n-1;i++) {
453: if (S[ldS*i+i+1] != 0.0) {
454: /* Check if T(i+1,i) and T(i,i+1) are zero */
455: if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
456: /* Check if T(i+1,i) and T(i,i+1) are negligible */
457: 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) {
458: T[ldT*i+i+1] = 0.0;
459: T[ldT*(i+1)+i] = 0.0;
460: } else {
461: /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
462: 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) {
463: PetscCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
464: } 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) {
465: PetscCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
466: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
467: PetscCall(PetscBLASIntCast(n-i,&n_i));
468: n_i_2 = n_i - 2;
469: PetscCall(PetscBLASIntCast(i+2,&i_2));
470: PetscCall(PetscBLASIntCast(i,&i_));
471: if (b11 < 0.0) {
472: cr = -cr; sr = -sr;
473: b11 = -b11; b22 = -b22;
474: }
475: PetscCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
476: PetscCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
477: PetscCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
478: PetscCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
479: if (X) PetscCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
480: if (Y) PetscCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
481: T[ldT*i+i] = b11; T[ldT*i+i+1] = 0.0;
482: T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
483: }
484: }
485: i++;
486: }
487: }
488: #endif
489: PetscFunctionReturn(PETSC_SUCCESS);
490: }
492: static PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
493: {
494: PetscScalar *work,*beta,a;
495: PetscInt i;
496: PetscBLASInt lwork,n,ld,iaux;
497: PetscScalar *A,*B,*Z,*Q;
498: PetscBool usegges3=(ds->method==1)?PETSC_TRUE:PETSC_FALSE;
500: PetscFunctionBegin;
501: #if !PetscDefined(USE_COMPLEX)
502: PetscAssertPointer(wi,3);
503: #endif
504: PetscCall(PetscBLASIntCast(ds->n,&n));
505: PetscCall(PetscBLASIntCast(ds->ld,&ld));
506: lwork = -1;
507: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
508: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
509: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
510: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
511: #if !PetscDefined(USE_COMPLEX)
512: if (usegges3) PetscCallLAPACKInfo("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
513: else PetscCallLAPACKInfo("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
514: PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
515: PetscCall(DSAllocateWork_Private(ds,lwork+ld,0,0));
516: beta = ds->work;
517: work = beta+ds->n;
518: PetscCall(PetscBLASIntCast(ds->lwork-ds->n,&lwork));
519: if (usegges3) PetscCallLAPACKInfo("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
520: else PetscCallLAPACKInfo("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
521: #else
522: if (usegges3) PetscCallLAPACKInfo("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
523: else PetscCallLAPACKInfo("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
524: PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
525: PetscCall(DSAllocateWork_Private(ds,lwork+ld,8*ld,0));
526: beta = ds->work;
527: work = beta+ds->n;
528: PetscCall(PetscBLASIntCast(ds->lwork-ds->n,&lwork));
529: if (usegges3) PetscCallLAPACKInfo("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
530: else PetscCallLAPACKInfo("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
531: #endif
532: for (i=0;i<n;i++) {
533: if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
534: else wr[i] /= beta[i];
535: #if !PetscDefined(USE_COMPLEX)
536: if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
537: else wi[i] /= beta[i];
538: #else
539: if (wi) wi[i] = 0.0;
540: #endif
541: }
542: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
543: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
544: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
545: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
546: PetscFunctionReturn(PETSC_SUCCESS);
547: }
549: #if !PetscDefined(HAVE_MPIUNI)
550: static PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
551: {
552: PetscInt ld=ds->ld,l=ds->l,k;
553: PetscMPIInt n,rank,off=0,size,ldn;
554: PetscScalar *A,*B,*Q,*Z;
556: PetscFunctionBegin;
557: k = 2*(ds->n-l)*ld;
558: if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
559: if (eigr) k += (ds->n-l);
560: if (eigi) k += (ds->n-l);
561: PetscCall(DSAllocateWork_Private(ds,k,0,0));
562: PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
563: PetscCall(PetscMPIIntCast(ds->n-l,&n));
564: PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
565: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
566: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
567: if (ds->state>DS_STATE_RAW) {
568: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
569: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
570: }
571: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
572: if (!rank) {
573: PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
574: PetscCallMPI(MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
575: if (ds->state>DS_STATE_RAW) {
576: PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
577: PetscCallMPI(MPI_Pack(Z+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
578: }
579: if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
580: #if !PetscDefined(USE_COMPLEX)
581: if (eigi) PetscCallMPI(MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
582: #endif
583: }
584: PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
585: if (rank) {
586: PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
587: PetscCallMPI(MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
588: if (ds->state>DS_STATE_RAW) {
589: PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
590: PetscCallMPI(MPI_Unpack(ds->work,size,&off,Z+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
591: }
592: if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
593: #if !PetscDefined(USE_COMPLEX)
594: if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
595: #endif
596: }
597: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
598: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
599: if (ds->state>DS_STATE_RAW) {
600: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
601: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
602: }
603: PetscFunctionReturn(PETSC_SUCCESS);
604: }
605: #endif
607: static PetscErrorCode DSTruncate_GNHEP(DS ds,PetscInt n,PetscBool trim)
608: {
609: PetscInt i,ld=ds->ld,l=ds->l;
610: PetscScalar *A,*B;
612: PetscFunctionBegin;
613: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
614: PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
615: #if PetscDefined(USE_DEBUG)
616: /* make sure diagonal 2x2 block is not broken */
617: PetscCheck(ds->state<DS_STATE_CONDENSED || n==0 || n==ds->n || (A[n+(n-1)*ld]==0.0 && B[n+(n-1)*ld]==0.0),PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
618: #endif
619: if (trim) {
620: if (ds->extrarow) { /* clean extra row */
621: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
622: for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
623: }
624: ds->l = 0;
625: ds->k = 0;
626: ds->n = n;
627: ds->t = ds->n; /* truncated length equal to the new dimension */
628: } else {
629: if (ds->extrarow && ds->k==ds->n) {
630: /* copy entries of extra row to the new position, then clean last row */
631: for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
632: for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
633: for (i=l;i<n;i++) B[n+i*ld] = B[ds->n+i*ld];
634: for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
635: }
636: ds->k = ds->extrarow? n: 0;
637: ds->t = ds->n; /* truncated length equal to previous dimension */
638: ds->n = n;
639: }
640: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
641: PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
642: PetscFunctionReturn(PETSC_SUCCESS);
643: }
645: /*MC
646: DSGNHEP - Dense Generalized Non-Hermitian Eigenvalue Problem.
648: Notes:
649: The problem is expressed as $AX = BX\Lambda$, where $(A,B)$ is the input
650: matrix pencil. $\Lambda$ is a diagonal matrix whose diagonal elements are the
651: arguments of `DSSolve()`. After solve, $(A,B)$ is overwritten with the
652: generalized (real) Schur form $(S,T) = (Z^*AQ,Z^*BQ)$, with the first
653: matrix being upper quasi-triangular and the second one triangular.
655: Used DS matrices:
656: + `DS_MAT_A` - first problem matrix
657: . `DS_MAT_B` - second problem matrix
658: . `DS_MAT_Q` - first orthogonal/unitary transformation that reduces to
659: generalized (real) Schur form
660: - `DS_MAT_Z` - second orthogonal/unitary transformation that reduces to
661: generalized (real) Schur form
663: Implemented methods:
664: + 0 - QZ iteration (`_gges`)
665: - 1 - blocked QZ iteration (`_gges3`, if available)
667: Level: beginner
669: .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`
670: M*/
671: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
672: {
673: PetscFunctionBegin;
674: ds->ops->allocate = DSAllocate_GNHEP;
675: ds->ops->view = DSView_GNHEP;
676: ds->ops->vectors = DSVectors_GNHEP;
677: ds->ops->solve[0] = DSSolve_GNHEP;
678: #if !defined(SLEPC_MISSING_LAPACK_GGES3)
679: ds->ops->solve[1] = DSSolve_GNHEP;
680: #endif
681: ds->ops->sort = DSSort_GNHEP;
682: #if !PetscDefined(HAVE_MPIUNI)
683: ds->ops->synchronize = DSSynchronize_GNHEP;
684: #endif
685: ds->ops->gettruncatesize = DSGetTruncateSize_Default;
686: ds->ops->truncate = DSTruncate_GNHEP;
687: ds->ops->update = DSUpdateExtraRow_GNHEP;
688: PetscFunctionReturn(PETSC_SUCCESS);
689: }