Actual source code: dvd_blas.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:       
  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY 
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS 
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for 
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */

 22: #include <private/vecimplslepc.h>
 23:  #include davidson.h

 25: PetscLogEvent SLEPC_SlepcDenseMatProd = 0;
 26: PetscLogEvent SLEPC_SlepcDenseNorm = 0;
 27: PetscLogEvent SLEPC_SlepcDenseOrth = 0;
 28: PetscLogEvent SLEPC_SlepcDenseCopy = 0;
 29: PetscLogEvent SLEPC_VecsMult = 0;

 31: void dvd_sum_local(void *in, void *out, PetscMPIInt *cnt,MPI_Datatype *t);
 32: PetscErrorCode VecsMultS_copy_func(PetscScalar *out, PetscInt size_out,
 33:                                    void *ptr);

 37: /*
 38:   Compute C <- a*A*B + b*C, where
 39:     ldC, the leading dimension of C,
 40:     ldA, the leading dimension of A,
 41:     rA, cA, rows and columns of A,
 42:     At, if true use the transpose of A instead,
 43:     ldB, the leading dimension of B,
 44:     rB, cB, rows and columns of B,
 45:     Bt, if true use the transpose of B instead
 46: */
 47: PetscErrorCode SlepcDenseMatProd(PetscScalar *C, PetscInt _ldC, PetscScalar b,
 48:   PetscScalar a,
 49:   const PetscScalar *A, PetscInt _ldA, PetscInt rA, PetscInt cA, PetscBool At,
 50:   const PetscScalar *B, PetscInt _ldB, PetscInt rB, PetscInt cB, PetscBool Bt)
 51: {
 52:   PetscErrorCode  ierr;
 53:   PetscInt        tmp;
 54:   PetscBLASInt    m, n, k, ldA = _ldA, ldB = _ldB, ldC = _ldC;
 55:   const char      *N = "N", *T = "C", *qA = N, *qB = N;


 59:   if ((rA == 0) || (cB == 0)) { return(0); }

 64:   PetscLogEventBegin(SLEPC_SlepcDenseMatProd,0,0,0,0);

 66:   /* Transpose if needed */
 67:   if (At) tmp = rA, rA = cA, cA = tmp, qA = T;
 68:   if (Bt) tmp = rB, rB = cB, cB = tmp, qB = T;
 69: 
 70:   /* Check size */
 71:   if (cA != rB) {
 72:     SETERRQ(PETSC_COMM_SELF,1, "Matrix dimensions do not match");
 73:   }
 74: 
 75:   /* Do stub */
 76:   if ((rA == 1) && (cA == 1) && (cB == 1)) {
 77:     if (!At && !Bt) *C = *A * *B;
 78:     else if (At && !Bt) *C = PetscConj(*A) * *B;
 79:     else if (!At && Bt) *C = *A * PetscConj(*B);
 80:     else *C = PetscConj(*A) * PetscConj(*B);
 81:     m = n = k = 1;
 82:   } else {
 83:     m = rA; n = cB; k = cA;
 84:     BLASgemm_(qA, qB, &m, &n, &k, &a, (PetscScalar*)A, &ldA, (PetscScalar*)B,
 85:               &ldB, &b, C, &ldC);
 86:   }

 88:   PetscLogFlops(m*n*2*k);
 89:   PetscLogEventEnd(SLEPC_SlepcDenseMatProd,0,0,0,0);

 91:   return(0);
 92: }

 96: /*
 97:   Compute C <- A*B, where
 98:     sC, structure of C,
 99:     ldC, the leading dimension of C,
100:     sA, structure of A,
101:     ldA, the leading dimension of A,
102:     rA, cA, rows and columns of A,
103:     At, if true use the transpose of A instead,
104:     sB, structure of B,
105:     ldB, the leading dimension of B,
106:     rB, cB, rows and columns of B,
107:     Bt, if true use the transpose of B instead
108: */
109: PetscErrorCode SlepcDenseMatProdTriang(
110:   PetscScalar *C, MatType_t sC, PetscInt ldC,
111:   const PetscScalar *A, MatType_t sA, PetscInt ldA, PetscInt rA, PetscInt cA,
112:   PetscBool At,
113:   const PetscScalar *B, MatType_t sB, PetscInt ldB, PetscInt rB, PetscInt cB,
114:   PetscBool Bt)
115: {
116:   PetscErrorCode  ierr;
117:   PetscInt        tmp;
118:   PetscScalar     one=1.0, zero=0.0;
119:   PetscBLASInt    rC, cC, _ldA = ldA, _ldB = ldB, _ldC = ldC;


123:   if ((rA == 0) || (cB == 0)) { return(0); }

128:   /* Transpose if needed */
129:   if (At) tmp = rA, rA = cA, cA = tmp;
130:   if (Bt) tmp = rB, rB = cB, cB = tmp;
131: 
132:   /* Check size */
133:   if (cA != rB) SETERRQ(PETSC_COMM_SELF,1, "Matrix dimensions do not match");
134:   if (sB != 0) SETERRQ(PETSC_COMM_SELF,1, "Matrix type not supported for B");

136:   /* Optimized version: trivial case */
137:   if ((rA == 1) && (cA == 1) && (cB == 1)) {
138:     if (!At && !Bt)     *C = *A * *B;
139:     else if (At && !Bt) *C = PetscConj(*A) * *B;
140:     else if (!At && Bt) *C = *A * PetscConj(*B);
141:     else if (At && Bt)  *C = PetscConj(*A) * PetscConj(*B);
142:     return(0);
143:   }
144: 
145:   /* Optimized versions: sA == 0 && sB == 0 */
146:   if ((sA == 0) && (sB == 0)) {
147:     if (At) tmp = rA, rA = cA, cA = tmp;
148:     if (Bt) tmp = rB, rB = cB, cB = tmp;
149:     SlepcDenseMatProd(C, ldC, 0.0, 1.0, A, ldA, rA, cA, At, B, ldB, rB,
150:                              cB, Bt);
151:     PetscFunctionReturn(ierr);
152:   }

154:   /* Optimized versions: A hermitian && (B not triang) */
155:   if (DVD_IS(sA,DVD_MAT_HERMITIAN) &&
156:       DVD_ISNOT(sB,DVD_MAT_UTRIANG) &&
157:       DVD_ISNOT(sB,DVD_MAT_LTRIANG)    ) {
158:     PetscLogEventBegin(SLEPC_SlepcDenseMatProd,0,0,0,0);
159:     rC = rA; cC = cB;
160:     BLAShemm_("L", DVD_ISNOT(sA,DVD_MAT_LTRIANG)?"U":"L", &rC, &cC, &one,
161:               (PetscScalar*)A, &_ldA, (PetscScalar*)B, &_ldB, &zero, C, &_ldC);
162:     PetscLogFlops(rA*cB*cA);
163:     PetscLogEventEnd(SLEPC_SlepcDenseMatProd,0,0,0,0);
164:     return(0);
165:   }

167:   /* Optimized versions: B hermitian && (A not triang) */
168:   if (DVD_IS(sB,DVD_MAT_HERMITIAN) &&
169:       DVD_ISNOT(sA,DVD_MAT_UTRIANG) &&
170:       DVD_ISNOT(sA,DVD_MAT_LTRIANG)    ) {
171:     PetscLogEventBegin(SLEPC_SlepcDenseMatProd,0,0,0,0);
172:     rC = rA; cC = cB;
173:     BLAShemm_("R", DVD_ISNOT(sB,DVD_MAT_LTRIANG)?"U":"L", &rC, &cC, &one,
174:               (PetscScalar*)B, &_ldB, (PetscScalar*)A, &_ldA, &zero, C, &_ldC);
175:     PetscLogFlops(rA*cB*cA);
176:     PetscLogEventEnd(SLEPC_SlepcDenseMatProd,0,0,0,0);
177:     return(0);
178:   }
179: 
180:   SETERRQ(PETSC_COMM_SELF,1, "Matrix type not supported for A");
181: }

185: /*
186:   Normalize the columns of the matrix A, where
187:     ldA, the leading dimension of A,
188:     rA, cA, rows and columns of A.
189:   if eigi is given, the pairs of contiguous columns i i+1 such as eigi[i] != 0
190:   are normalized as being one column.
191: */
192: PetscErrorCode SlepcDenseNorm(PetscScalar *A, PetscInt ldA, PetscInt _rA,
193:                               PetscInt cA, PetscScalar *eigi)
194: {
195:   PetscErrorCode  ierr;
196:   PetscInt        i;
197:   PetscScalar     norm, norm0;
198:   PetscBLASInt    rA = _rA, one=1;


204:   PetscLogEventBegin(SLEPC_SlepcDenseNorm,0,0,0,0);

206:   for(i=0; i<cA; i++) {
207:     if(eigi && eigi[i] != 0.0) {
208:       norm = BLASnrm2_(&rA, &A[i*ldA], &one);
209:       norm0 = BLASnrm2_(&rA, &A[(i+1)*ldA], &one);
210:       norm = 1.0/PetscSqrtScalar(norm*norm + norm0*norm0);
211:       BLASscal_(&rA, &norm, &A[i*ldA], &one);
212:       BLASscal_(&rA, &norm, &A[(i+1)*ldA], &one);
213:       i++;
214:     } else {
215:       norm = BLASnrm2_(&rA, &A[i*ldA], &one);
216:       norm = 1.0 / norm;
217:       BLASscal_(&rA, &norm, &A[i*ldA], &one);
218:      }
219:   }

221:   PetscLogEventEnd(SLEPC_SlepcDenseNorm,0,0,0,0);

223:   return(0);
224: }
225: 

229: /*
230:   Compute A <- orth(A), where
231:     ldA, the leading dimension of A,
232:     rA, cA, rows and columns of A,
233:     auxS, auxiliary vector of more size than cA+min(rA,cA),
234:     lauxS, size of auxS,
235:     ncA, new number of columns of A
236: */
237: PetscErrorCode SlepcDenseOrth(PetscScalar *A, PetscInt _ldA, PetscInt _rA,
238:                               PetscInt _cA, PetscScalar *auxS, PetscInt _lauxS,
239:                               PetscInt *ncA)
240: {
241:   PetscErrorCode  ierr;
242:   PetscBLASInt    ldA = _ldA, rA = _rA, cA = _cA,
243:                   info, ltau = PetscMin(_cA, _rA), lw = _lauxS - ltau;
244:   PetscScalar     *tau = auxS, *w = tau + ltau;


248:   /* Quick exit */
249:   if ((_rA == 0) || (cA == 0)) { return(0); }

254:   /* Memory check */
255:   if (lw < cA) SETERRQ(PETSC_COMM_SELF,1, "Insufficient memory for xGEQRF");
256: 
257:   PetscLogEventBegin(SLEPC_SlepcDenseOrth,0,0,0,0);
258:   LAPACKgeqrf_(&rA, &cA, A, &ldA, tau, w, &lw, &info);
259:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB, "Error in Lapack xGEQRF %d", info);
260:   LAPACKorgqr_(&rA, &ltau, &ltau, A, &ldA, tau, w, &lw, &info);
261:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB, "Error in Lapack xORGQR %d", info);
262:   PetscLogEventEnd(SLEPC_SlepcDenseOrth,0,0,0,0);

264:   if (ncA) *ncA = ltau;

266:   return(0);
267: }

271: /*
272:   Y <- X, where
273:   ldX, leading dimension of X,
274:   rX, cX, rows and columns of X
275:   ldY, leading dimension of Y
276: */
277: PetscErrorCode SlepcDenseCopy(PetscScalar *Y, PetscInt ldY, PetscScalar *X,
278:                               PetscInt ldX, PetscInt rX, PetscInt cX)
279: {
280:   PetscErrorCode  ierr;
281:   PetscInt        i;


287:   if ((ldX < rX) || (ldY < rX)) {
288:     SETERRQ(PETSC_COMM_SELF,1, "Leading dimension error");
289:   }
290: 
291:   /* Quick exit */
292:   if (Y == X) {
293:     if (ldX != ldY) {
294:       SETERRQ(PETSC_COMM_SELF,1, "Leading dimension error");
295:     }
296:     return(0);
297:   }

299:   PetscLogEventBegin(SLEPC_SlepcDenseCopy,0,0,0,0);
300:   for(i=0; i<cX; i++) {
301:     PetscMemcpy(&Y[ldY*i], &X[ldX*i], sizeof(PetscScalar)*rX);
302: 
303:   }
304:   PetscLogEventEnd(SLEPC_SlepcDenseCopy,0,0,0,0);

306:   return(0);
307: }

311: /*
312:   Y <- X, where
313:   ldX, leading dimension of X,
314:   rX, cX, rows and columns of X
315:   ldY, leading dimension of Y
316: */
317: PetscErrorCode SlepcDenseCopyTriang(PetscScalar *Y, MatType_t sY, PetscInt ldY,
318:                                     PetscScalar *X, MatType_t sX, PetscInt ldX,
319:                                     PetscInt rX, PetscInt cX)
320: {
321:   PetscErrorCode  ierr;
322:   PetscInt        i,j,c;


328:   if ((ldX < rX) || (ldY < rX)) {
329:     SETERRQ(PETSC_COMM_SELF,1, "Leading dimension error");
330:   }

332:   if (sY == 0 && sX == 0) {
333:     SlepcDenseCopy(Y, ldY, X, ldX, rX, cX);
334:     return(0);
335:   }

337:   if (rX != cX) {
338:     SETERRQ(PETSC_COMM_SELF,1, "Rectangular matrices not supported");
339:   }

341:   if (DVD_IS(sX,DVD_MAT_UTRIANG) &&
342:       DVD_ISNOT(sX,DVD_MAT_LTRIANG)) {        /* UpTr to ... */
343:     if (DVD_IS(sY,DVD_MAT_UTRIANG) &&
344:         DVD_ISNOT(sY,DVD_MAT_LTRIANG))        /* ... UpTr, */
345:       c = 0;                                      /*     so copy */
346:     else if(DVD_ISNOT(sY,DVD_MAT_UTRIANG) &&
347:             DVD_IS(sY,DVD_MAT_LTRIANG))       /* ... LoTr, */
348:       c = 1;                                      /*     so transpose */
349:     else                                          /* ... Full, */
350:       c = 2;                                      /*     so reflect from up */
351:   } else if (DVD_ISNOT(sX,DVD_MAT_UTRIANG) &&
352:              DVD_IS(sX,DVD_MAT_LTRIANG)) {    /* LoTr to ... */
353:     if (DVD_IS(sY,DVD_MAT_UTRIANG) &&
354:         DVD_ISNOT(sY,DVD_MAT_LTRIANG))        /* ... UpTr, */
355:       c = 1;                                      /*     so transpose */
356:     else if(DVD_ISNOT(sY,DVD_MAT_UTRIANG) &&
357:             DVD_IS(sY,DVD_MAT_LTRIANG))       /* ... LoTr, */
358:       c = 0;                                      /*     so copy */
359:     else                                          /* ... Full, */
360:       c = 3;                                      /*     so reflect fr. down */
361:   } else                                          /* Full to any, */
362:     c = 0;                                        /*     so copy */
363: 
364:   PetscLogEventBegin(SLEPC_SlepcDenseCopy,0,0,0,0);

366:   switch(c) {
367:   case 0: /* copy */
368:     for(i=0; i<cX; i++) {
369:       PetscMemcpy(&Y[ldY*i], &X[ldX*i], sizeof(PetscScalar)*rX);
370: 
371:     }
372:     break;

374:   case 1: /* transpose */
375:     for(i=0; i<cX; i++)
376:       for(j=0; j<rX; j++)
377:         Y[ldY*j+i] = PetscConj(X[ldX*i+j]);
378:     break;

380:   case 2: /* reflection from up */
381:     for(i=0; i<cX; i++)
382:       for(j=0; j<PetscMin(i+1,rX); j++)
383:         Y[ldY*j+i] = PetscConj(Y[ldY*i+j] = X[ldX*i+j]);
384:     break;

386:   case 3: /* reflection from down */
387:     for(i=0; i<cX; i++)
388:       for(j=i; j<rX; j++)
389:         Y[ldY*j+i] = PetscConj(Y[ldY*i+j] = X[ldX*i+j]);
390:     break;
391:   }
392:   PetscLogEventEnd(SLEPC_SlepcDenseCopy,0,0,0,0);

394:   return(0);
395: }


400: /*
401:   Compute Y[0..cM-1] <- alpha * X[0..cX-1] * M + beta * Y[0..cM-1],
402:   where X and Y are contiguous global vectors.
403: */
404: PetscErrorCode SlepcUpdateVectorsZ(Vec *Y, PetscScalar beta, PetscScalar alpha,
405:   Vec *X, PetscInt cX, const PetscScalar *M, PetscInt ldM, PetscInt rM,
406:   PetscInt cM)
407: {
408:   PetscErrorCode  ierr;


412:   SlepcUpdateVectorsS(Y, 1, beta, alpha, X, cX, 1, M, ldM, rM, cM);
413: 

415:   return(0);
416: }


421: /*
422:   Compute Y[0:dY:cM*dY-1] <- alpha * X[0:dX:cX-1] * M + beta * Y[0:dY:cM*dY-1],
423:   where X and Y are contiguous global vectors.
424: */
425: PetscErrorCode SlepcUpdateVectorsS(Vec *Y, PetscInt dY, PetscScalar beta,
426:   PetscScalar alpha, Vec *X, PetscInt cX, PetscInt dX, const PetscScalar *M,
427:   PetscInt ldM, PetscInt rM, PetscInt cM)
428: {
429:   PetscErrorCode    ierr;
430:   const PetscScalar *px;
431:   PetscScalar       *py;
432:   PetscInt          rX, rY, ldX, ldY, i, rcX;

435:   SlepcValidVecsContiguous(Y,cM*dY,1);
436:   SlepcValidVecsContiguous(X,cX,5);

439:   /* Compute the real number of columns */
440:   rcX = cX/dX;
441:   if (rcX != rM) {
442:     SETERRQ(((PetscObject)*Y)->comm,1, "Matrix dimensions do not match");
443:   }

445:   if ((rcX == 0) || (rM == 0) || (cM == 0)) {
446:     return(0);
447:   } else if ((Y + cM <= X) || (X + cX <= Y) ||
448:              ((X != Y) && ((PetscMax(dX,dY))%(PetscMin(dX,dY))!=0))) {
449:     /* If Y[0..cM-1] and X[0..cX-1] are not overlapped... */

451:     /* Get the dense matrices and dimensions associated to Y and X */
452:     VecGetLocalSize(X[0], &rX);
453:     VecGetLocalSize(Y[0], &rY);
454:     if (rX != rY) {
455:       SETERRQ(((PetscObject)*Y)->comm,1, "The multivectors do not have the same dimension");
456:     }
457:     VecGetArrayRead(X[0], &px);
458:     VecGetArray(Y[0], &py);

460:     /* Update the strides */
461:     ldX = rX*dX; ldY= rY*dY;

463:     /* Do operation */
464:     SlepcDenseMatProd(py, ldY, beta, alpha, px, ldX, rX, rcX,
465:                     PETSC_FALSE, M, ldM, rM, cM, PETSC_FALSE);
466: 
467:     VecRestoreArrayRead(X[0], &px);
468:     VecRestoreArray(Y[0], &py);
469:     for(i=1; i<cM; i++) {
470:       PetscObjectStateIncrease((PetscObject)Y[dY*i]);
471:     }

473:   } else if ((Y >= X) && (beta == 0.0) && (dY == dX)) {
474:     /* If not, call to SlepcUpdateVectors */
475:     SlepcUpdateStrideVectors(cX, X, Y-X, dX, Y-X+cM*dX, M-ldM*(Y-X),
476:                                     ldM, PETSC_FALSE);
477:     if (alpha != 1.0)
478:       for (i=0; i<cM; i++) {
479:         VecScale(Y[i], alpha);
480:       }
481:   } else {
482:     SETERRQ(((PetscObject)*Y)->comm,1, "Unsupported case");
483:   }

485:   return(0);
486: }

490: /*
491:   Compute X <- alpha * X[0:dX:cX-1] * M
492:   where X is a matrix with non-consecutive columns
493: */
494: PetscErrorCode SlepcUpdateVectorsD(Vec *X, PetscInt cX, PetscScalar alpha,
495:   const PetscScalar *M, PetscInt ldM, PetscInt rM, PetscInt cM,
496:   PetscScalar *work, PetscInt lwork)
497: {
499:   PetscScalar    **px, *Y, *Z;
500:   PetscInt       rX, i, j, rY, rY0, ldY;

503:   SlepcValidVecsContiguous(X,cX,1);

507:   if (cX != rM) {
508:     SETERRQ(((PetscObject)*X)->comm,1, "Matrix dimensions do not match");
509:   }

511:   rY = (lwork/2)/cX;
512:   if (rY <= 0) {
513:     SETERRQ(((PetscObject)*X)->comm,1, "Insufficient work space given");
514:   }
515:   Y = work; Z = &Y[cX*rY]; ldY = rY;

517:   if ((cX == 0) || (rM == 0) || (cM == 0)) {
518:     return(0);
519:   }

521:   /* Get the dense vectors associated to the columns of X */
522:   PetscMalloc(sizeof(Vec)*cX, &px);
523:   for(i=0; i<cX; i++) {
524:     VecGetArray(X[i], &px[i]);
525:   }
526:   VecGetLocalSize(X[0], &rX);

528:   for(i=0, rY0=0; i<rX; i+=rY0) {
529:     rY0 = PetscMin(rY, rX-i);

531:     /* Y <- X[i0:i1,:] */
532:     for(j=0; j<cX; j++) {
533:       SlepcDenseCopy(&Y[ldY*j], ldY, px[j]+i, rX, rY0, 1);
534: 
535:     }

537:     /* Z <- Y * M */
538:     SlepcDenseMatProd(Z, ldY, 0.0, alpha, Y, ldY, rY0, cX, PETSC_FALSE,
539:                                                  M, ldM, rM, cM, PETSC_FALSE);
540: 

542:     /* X <- Z */
543:     for(j=0; j<cM; j++) {
544:       SlepcDenseCopy(px[j]+i, rX, &Z[j*ldY], ldY, rY0, 1);
545: 
546:     }
547:   }

549:   for(i=0; i<cX; i++) {
550:     VecRestoreArray(X[i], &px[i]);
551:   }
552:   PetscFree(px);

554:   return(0);
555: }



561: /* Computes M <- [ M(0:sU-1,  0:sV-1) W(0:sU-1,  sV:eV-1) ]
562:                  [ W(sU:eU-1, 0:sV-1) W(sU:eU-1, sV:eV-1) ]
563:   where W = U' * V.
564:   workS0 and workS1 are an auxiliary scalar vector of size
565:   (eU-sU)*sV*(sU!=0)+(eV-sV)*eU. But, if sU == 0, sV == 0 and eU == ldM, only workS0
566:   is needed, and of size eU*eV.
567: */
568: PetscErrorCode VecsMult(PetscScalar *M, MatType_t sM, PetscInt ldM,
569:                         Vec *U, PetscInt sU, PetscInt eU,
570:                         Vec *V, PetscInt sV, PetscInt eV,
571:                         PetscScalar *workS0, PetscScalar *workS1)
572: {
573:   PetscErrorCode    ierr;
574:   PetscInt          ldU, ldV, i, j, k, ms = (eU-sU)*sV*(sU==0?0:1)+(eV-sV)*eU;
575:   const PetscScalar *pu, *pv;
576:   PetscScalar       *W, *Wr;


580:   /* Check if quick exit */
581:   if ((eU-sU == 0) || (eV-sV == 0))
582:     return(0);

584:   SlepcValidVecsContiguous(U,eU,4);
585:   SlepcValidVecsContiguous(V,eV,7);
587: 
588:   /* Get the dense matrices and dimensions associated to U and V */
589:   VecGetLocalSize(U[0], &ldU);
590:   VecGetLocalSize(V[0], &ldV);
591:   if (ldU != ldV) {
592:     SETERRQ(((PetscObject)*U)->comm,1, "Matrix dimensions do not match");
593:   }
594:   VecGetArrayRead(U[0], &pu);
595:   VecGetArrayRead(V[0], &pv);

597:   if (workS0) {
599:     W = workS0;
600:   } else {
601:     PetscMalloc(sizeof(PetscScalar)*ms, &W);
602: 
603:   }

605:   PetscLogEventBegin(SLEPC_VecsMult,0,0,0,0);

607:   if ((sU == 0) && (sV == 0) && (eU == ldM)) {
608:     /* Use the smart memory usage version */

610:     /* W <- U' * V */
611:     SlepcDenseMatProdTriang(W, sM, eU,
612:                                    pu, 0, ldU, ldU, eU, PETSC_TRUE,
613:                                    pv, 0, ldV, ldV, eV, PETSC_FALSE);
614: 
615: 
616:     /* ReduceAll(W, SUM) */
617:     MPI_Allreduce(W, M, eU*eV, MPIU_SCALAR, MPIU_SUM,
618:                          ((PetscObject)U[0])->comm);
619:   /* Full M matrix */
620:   } else if (DVD_ISNOT(sM,DVD_MAT_UTRIANG) &&
621:              DVD_ISNOT(sM,DVD_MAT_LTRIANG)) {
622:     if (workS1) {
624:       Wr = workS1;
625:       if (PetscAbs(PetscMin(W-workS1, workS1-W)) < ms) {
626:         SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!");
627:       }
628:     } else {
629:       PetscMalloc(sizeof(PetscScalar)*ms, &Wr);
630: 
631:     }
632: 
633:     /* W(0:(eU-sU)*sV-1) <- U(sU:eU-1)' * V(0:sV-1) */
634:     if (sU > 0) {
635:       SlepcDenseMatProd(W, eU-sU, 0.0, 1.0,
636:                                pu+ldU*sU, ldU, ldU, eU-sU, PETSC_TRUE,
637:                                pv       , ldV, ldV, sV,    PETSC_FALSE);
638: 
639:     }
640: 
641:     /* W((eU-sU)*sV:(eU-sU)*sV+(eV-sV)*eU-1) <- U(0:eU-1)' * V(sV:eV-1) */
642:     SlepcDenseMatProd(W+(eU-sU)*sV*(sU > 0?1:0), eU, 0.0, 1.0,
643:                              pu,        ldU, ldU, eU,    PETSC_TRUE,
644:                              pv+ldV*sV, ldV, ldV, eV-sV, PETSC_FALSE);
645: 
646: 
647:     /* ReduceAll(W, SUM) */
648:     MPI_Allreduce(W, Wr, ms, MPIU_SCALAR,
649:                       MPIU_SUM, ((PetscObject)U[0])->comm);
650: 
651:     /* M(...,...) <- W */
652:     k = 0;
653:     if (sU > 0) for (i=0; i<sV; i++)
654:       for (j=ldM*i+sU; j<ldM*i+eU; j++,k++) M[j] = Wr[k];
655:     for (i=sV; i<eV; i++)
656:       for (j=ldM*i; j<ldM*i+eU; j++,k++) M[j] = Wr[k];
657: 
658:     if (!workS1) {
659:       PetscFree(Wr);
660:     }

662:   /* Upper triangular M matrix */
663:   } else if (DVD_IS(sM,DVD_MAT_UTRIANG) &&
664:              DVD_ISNOT(sM,DVD_MAT_LTRIANG)) {
665:     if (workS1) {
667:       Wr = workS1;
668:       if (PetscAbs(PetscMin(W-workS1,workS1-W)) < (eV-sV)*eU) {
669:         SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!");
670:       }
671:     } else {
672:       PetscMalloc(sizeof(PetscScalar)*(eV-sV)*eU, &Wr);
673: 
674:     }
675: 
676:     /* W(0:(eV-sV)*eU-1) <- U(0:eU-1)' * V(sV:eV-1) */
677:     SlepcDenseMatProd(W,         eU,  0.0, 1.0,
678:                              pu,        ldU, ldU, eU,    PETSC_TRUE,
679:                              pv+ldV*sV, ldV, ldV, eV-sV, PETSC_FALSE);
680: 
681: 
682:     /* ReduceAll(W, SUM) */
683:     MPI_Allreduce(W, Wr, (eV-sV)*eU, MPIU_SCALAR, MPIU_SUM,
684:                          ((PetscObject)U[0])->comm);
685: 
686:     /* M(...,...) <- W */
687:     for (i=sV,k=0; i<eV; i++)
688:         for (j=ldM*i; j<ldM*i+eU; j++,k++) M[j] = Wr[k];

690:     if (!workS1) {
691:       PetscFree(Wr);
692:     }

694:   /* Lower triangular M matrix */
695:   } else if (DVD_ISNOT(sM,DVD_MAT_UTRIANG) &&
696:              DVD_IS(sM,DVD_MAT_LTRIANG)) {
697:     if (workS1) {
699:       Wr = workS1;
700:       if (PetscMin(W - workS1, workS1 - W) < (eU-sU)*eV) {
701:         SETERRQ(PETSC_COMM_SELF,1, "Consistency broken!");
702:       }
703:     } else {
704:       PetscMalloc(sizeof(PetscScalar)*(eU-sU)*eV, &Wr);
705: 
706:     }
707: 
708:     /* W(0:(eU-sU)*eV-1) <- U(sU:eU-1)' * V(0:eV-1) */
709:     SlepcDenseMatProd(W, eU-sU, 0.0, 1.0,
710:                              pu+ldU*sU, ldU, ldU, eU-sU, PETSC_TRUE,
711:                              pv       , ldV, ldV, eV,    PETSC_FALSE);
712: 
713: 
714:     /* ReduceAll(W, SUM) */
715:     MPI_Allreduce(W, Wr, (eU-sU)*eV, MPIU_SCALAR, MPIU_SUM,
716:                          ((PetscObject)U[0])->comm);
717: 
718:     /* M(...,...) <- W */
719:     for (i=0,k=0; i<eV; i++)
720:       for (j=ldM*i+sU; j<ldM*i+eU; j++,k++) M[j] = Wr[k];
721: 
722:     if (!workS1) {
723:       PetscFree(Wr);
724:     }
725:   }

727:   PetscLogEventEnd(SLEPC_VecsMult,0,0,0,0);

729:   if (!workS0) {
730:     PetscFree(W);
731:   }

733:   VecRestoreArrayRead(U[0], &pu);
734:   VecRestoreArrayRead(V[0], &pv);
735:   return(0);
736: }


741: /* Computes M <- [ M(0:sU-1,  0:sV-1) W(0:sU-1,  sV:eV-1) ]
742:                  [ W(sU:eU-1, 0:sV-1) W(sU:eU-1, sV:eV-1) ]
743:   where W = local_U' * local_V. Needs VecsMultIb for completing the operation!
744:   workS0 and workS1 are an auxiliary scalar vector of size
745:   (eU-sU)*sV+(eV-sV)*eU. But, if sU == 0, sV == 0 and eU == ldM, only workS0
746:   is needed, and of size eU*eV.
747: */
748: PetscErrorCode VecsMultIa(PetscScalar *M, MatType_t sM, PetscInt ldM,
749:                           Vec *U, PetscInt sU, PetscInt eU,
750:                           Vec *V, PetscInt sV, PetscInt eV)
751: {
752:   PetscErrorCode  ierr;
753:   PetscInt        ldU, ldV;
754:   PetscScalar     *pu, *pv;


758:   /* Check if quick exit */
759:   if ((eU-sU == 0) || (eV-sV == 0))
760:     return(0);
761: 
762:   SlepcValidVecsContiguous(U,eU,4);
763:   SlepcValidVecsContiguous(V,eV,7);

766:   /* Get the dense matrices and dimensions associated to U and V */
767:   VecGetLocalSize(U[0], &ldU);
768:   VecGetLocalSize(V[0], &ldV);
769:   if (ldU != ldV) {
770:     SETERRQ(((PetscObject)*U)->comm,1, "Matrix dimensions do not match");
771:   }
772:   VecGetArray(U[0], &pu);
773:   VecGetArray(V[0], &pv);

775:   if ((sU == 0) && (sV == 0) && (eU == ldM)) {
776:     /* M <- local_U' * local_V */
777:     SlepcDenseMatProdTriang(M, sM, eU,
778:                                    pu, 0, ldU, ldU, eU, PETSC_TRUE,
779:                                    pv, 0, ldV, ldV, eV, PETSC_FALSE);
780: 
781: 
782:   /* Full M matrix */
783:   } else if (DVD_ISNOT(sM,DVD_MAT_UTRIANG) &&
784:              DVD_ISNOT(sM,DVD_MAT_LTRIANG)) {
785:     /* M(sU:eU-1,0:sV-1) <- U(sU:eU-1)' * V(0:sV-1) */
786:     SlepcDenseMatProd(&M[sU], ldM, 0.0, 1.0,
787:                              pu+ldU*sU, ldU, ldU, eU-sU, PETSC_TRUE,
788:                              pv       , ldV, ldV, sV,    PETSC_FALSE);
789: 
790: 
791:     /* M(0:eU-1,sV:eV-1) <- U(0:eU-1)' * V(sV:eV-1) */
792:     SlepcDenseMatProd(&M[ldM*sV], ldM, 0.0, 1.0,
793:                              pu,        ldU, ldU, eU,    PETSC_TRUE,
794:                              pv+ldV*sV, ldV, ldV, eV-sV, PETSC_FALSE);
795: 
796: 
797:   /* Other structures */
798:   } else SETERRQ(((PetscObject)*U)->comm,1, "Matrix structure not supported");

800:   VecRestoreArray(U[0], &pu);
801:   PetscObjectStateDecrease((PetscObject)U[0]);
802:   VecRestoreArray(V[0], &pv);
803:   PetscObjectStateDecrease((PetscObject)V[0]);

805:   return(0);
806: }


811: /* Computes M <- nprocs*M
812:   where nprocs is the number of processors.
813: */
814: PetscErrorCode VecsMultIc(PetscScalar *M, MatType_t sM, PetscInt ldM,
815:                           PetscInt rM, PetscInt cM, Vec V)
816: {
817:   int        i,j,n;


821:   /* Check if quick exit */
822:   if ((rM == 0) || (cM == 0))
823:     return(0);
825: 
826:   if (sM != 0) SETERRQ(((PetscObject)V)->comm,1, "Matrix structure not supported");

828:   MPI_Comm_size(((PetscObject)V)->comm, &n);

830:   for(i=0; i<cM; i++)
831:     for(j=0; j<rM; j++)
832:       M[ldM*i+j]/= (PetscScalar)n;

834:   return(0);
835: }


840: /* Computes N <- Allreduce( [ M(0:sU-1,  0:sV-1) W(0:sU-1,  sV:eV-1) ] )
841:                           ( [ W(sU:eU-1, 0:sV-1) W(sU:eU-1, sV:eV-1) ] )
842:   where W = U' * V.
843:   workS0 and workS1 are an auxiliary scalar vector of size
844:   (eU-sU)*sV+(eV-sV)*eU. But, if sU == 0, sV == 0 and eU == ldM, only workS0
845:   is needed, and of size eU*eV.
846: */
847: PetscErrorCode VecsMultIb(PetscScalar *M, MatType_t sM, PetscInt ldM,
848:                           PetscInt rM, PetscInt cM, PetscScalar *auxS,
849:                           Vec V)
850: {
851:   PetscErrorCode  ierr;
852:   PetscScalar     *W, *Wr;


856:   /* Check if quick exit */
857:   if ((rM == 0) || (cM == 0))
858:     return(0);
861: 
862:   if (auxS)
863:     W = auxS;
864:   else {
865:     PetscMalloc(sizeof(PetscScalar)*rM*cM*2, &W);
866: 
867:   }
868:   Wr = W + rM*cM;

870:   PetscLogEventBegin(SLEPC_VecsMult,0,0,0,0);

872:   if (sM == 0) {
873:     /* W <- M */
874:     SlepcDenseCopy(W, rM, M, ldM, rM, cM);

876:     /* Wr <- ReduceAll(W, SUM) */
877:     MPI_Allreduce(W, Wr, rM*cM, MPIU_SCALAR, MPIU_SUM,
878:                          ((PetscObject)V)->comm);

880:     /* M <- Wr */
881:     SlepcDenseCopy(M, ldM, Wr, rM, rM, cM);

883:   /* Other structures */
884:   } else SETERRQ(((PetscObject)V)->comm,1, "Matrix structure not supported");

886:   PetscLogEventEnd(SLEPC_VecsMult,0,0,0,0);

888:   if (!auxS) {
889:     PetscFree(W);
890:   }

892:   return(0);
893: }


898: /* Computes M <- [ M(0:sU-1,  0:sV-1) W(0:sU-1,  sV:eV-1) ]
899:                  [ W(sU:eU-1, 0:sV-1) W(sU:eU-1, sV:eV-1) ]
900:   where W = U' * V.
901:   r, a DvdReduction structure,
902:   sr, an structure DvdMult_copy_func.
903: */
904: PetscErrorCode VecsMultS(PetscScalar *M, MatType_t sM, PetscInt ldM,
905:                          Vec *U, PetscInt sU, PetscInt eU,
906:                          Vec *V, PetscInt sV, PetscInt eV, DvdReduction *r,
907:                          DvdMult_copy_func *sr)
908: {
909:   PetscErrorCode    ierr;
910:   PetscInt          ldU, ldV, ms = (eU-sU)*sV*(sU==0?0:1)+(eV-sV)*eU;
911:   const PetscScalar *pu, *pv;
912:   PetscScalar       *W;


916:   /* Check if quick exit */
917:   if ((eU-sU == 0) || (eV-sV == 0))
918:     return(0);
919: 
920:   SlepcValidVecsContiguous(U,eU,4);
921:   SlepcValidVecsContiguous(V,eV,7);

924:   /* Get the dense matrices and dimensions associated to U and V */
925:   VecGetLocalSize(U[0], &ldU);
926:   VecGetLocalSize(V[0], &ldV);
927:   if (ldU != ldV) {
928:     SETERRQ(((PetscObject)*U)->comm,1, "Matrix dimensions do not match");
929:   }
930:   VecGetArrayRead(U[0], &pu);
931:   VecGetArrayRead(V[0], &pv);

933:   PetscLogEventBegin(SLEPC_VecsMult,0,0,0,0);

935:   if ((sU == 0) && (sV == 0)) {
936:     /* Use the smart memory usage version */

938:     /* Add the reduction to r */
939:     SlepcAllReduceSum(r, eU*eV, VecsMultS_copy_func, sr, &W);
940: 

942:     /* W <- U' * V */
943:     SlepcDenseMatProdTriang(W, sM, eU,
944:                                    pu, 0, ldU, ldU, eU, PETSC_TRUE,
945:                                    pv, 0, ldV, ldV, eV, PETSC_FALSE);
946: 
947: 
948:     /* M <- ReduceAll(W, SUM) */
949:     sr->M = M;    sr->ld = ldM;
950:     sr->i0 = 0;   sr->i1 = eV;    sr->s0 = sU;    sr->e0 = eU;
951:                   sr->i2 = eV;

953:   /* Full M matrix */
954:   } else if (DVD_ISNOT(sM,DVD_MAT_UTRIANG) &&
955:              DVD_ISNOT(sM,DVD_MAT_LTRIANG)) {
956:     /* Add the reduction to r */
957:     SlepcAllReduceSum(r, ms, VecsMultS_copy_func, sr, &W);
958: 

960:     /* W(0:(eU-sU)*sV-1) <- U(sU:eU-1)' * V(0:sV-1) */
961:     SlepcDenseMatProd(W, eU-sU, 0.0, 1.0,
962:                              pu+ldU*sU, ldU, ldU, eU-sU, PETSC_TRUE,
963:                              pv       , ldV, ldV, sV,    PETSC_FALSE);
964: 
965: 
966:     /* W((eU-sU)*sV:(eU-sU)*sV+(eV-sV)*eU-1) <- U(0:eU-1)' * V(sV:eV-1) */
967:     SlepcDenseMatProd(W+(eU-sU)*sV*(sU > 0?1:0), eU, 0.0, 1.0,
968:                              pu,        ldU, ldU, eU,    PETSC_TRUE,
969:                              pv+ldV*sV, ldV, ldV, eV-sV, PETSC_FALSE);
970: 
971: 
972:     /* M <- ReduceAll(W, SUM) */
973:     sr->M = M;            sr->ld = ldM;
974:     sr->i0 = sU>0?0:sV;   sr->i1 = sV;    sr->s0 = sU;    sr->e0 = eU;
975:                           sr->i2 = eV;    sr->s1 = 0;     sr->e1 = eU;

977:   /* Upper triangular M matrix */
978:   } else if (DVD_IS(sM,DVD_MAT_UTRIANG) &&
979:              DVD_ISNOT(sM,DVD_MAT_LTRIANG)) {
980:     /* Add the reduction to r */
981:     SlepcAllReduceSum(r, (eV-sV)*eU, VecsMultS_copy_func, sr, &W);
982: 
983: 
984:     /* W(0:(eV-sV)*eU-1) <- U(0:eU-1)' * V(sV:eV-1) */
985:     SlepcDenseMatProd(W,         eU,  0.0, 1.0,
986:                              pu,        ldU, ldU, eU,    PETSC_TRUE,
987:                              pv+ldV*sV, ldV, ldV, eV-sV, PETSC_FALSE);
988: 
989: 
990:     /* M <- ReduceAll(W, SUM) */
991:     sr->M = M;    sr->ld = ldM;
992:     sr->i0 = sV;  sr->i1 = eV;    sr->s0 = 0;     sr->e0 = eU;
993:                   sr->i2 = eV;
994: 
995:   /* Lower triangular M matrix */
996:   } else if (DVD_ISNOT(sM,DVD_MAT_UTRIANG) &&
997:              DVD_IS(sM,DVD_MAT_LTRIANG)) {
998:     /* Add the reduction to r */
999:     SlepcAllReduceSum(r, (eU-sU)*eV, VecsMultS_copy_func, sr, &W);
1000: 
1001: 
1002:     /* W(0:(eU-sU)*eV-1) <- U(sU:eU-1)' * V(0:eV-1) */
1003:     SlepcDenseMatProd(W, eU-sU, 0.0, 1.0,
1004:                              pu+ldU*sU, ldU, ldU, eU-sU, PETSC_TRUE,
1005:                              pv       , ldV, ldV, eV,    PETSC_FALSE);
1006: 
1007: 
1008:     /* ReduceAll(W, SUM) */
1009:     sr->M = M;    sr->ld = ldM;
1010:     sr->i0 = 0;   sr->i1 = eV;    sr->s0 = sU;    sr->e0 = eU;
1011:                   sr->i2 = eV;
1012:   }

1014:   PetscLogEventEnd(SLEPC_VecsMult,0,0,0,0);

1016:   VecRestoreArrayRead(U[0], &pu);
1017:   VecRestoreArrayRead(V[0], &pv);
1018:   return(0);
1019: }

1023: PetscErrorCode VecsMultS_copy_func(PetscScalar *out, PetscInt size_out,
1024:                                    void *ptr)
1025: {
1026:   PetscInt        i, j, k;
1027:   DvdMult_copy_func
1028:                   *sr = (DvdMult_copy_func*)ptr;


1033:   for (i=sr->i0,k=0; i<sr->i1; i++)
1034:     for (j=sr->ld*i+sr->s0; j<sr->ld*i+sr->e0; j++,k++) sr->M[j] = out[k];
1035:   for (i=sr->i1; i<sr->i2; i++)
1036:     for (j=sr->ld*i+sr->s1; j<sr->ld*i+sr->e1; j++,k++) sr->M[j] = out[k];

1038:   if (k != size_out) SETERRQ(PETSC_COMM_SELF,1, "Wrong size");

1040:   return(0);
1041: }

1045: /* Orthonormalize a chunk of parallel vector.
1046:    NOTE: wS0 and wS1 must be of size n*n.
1047: */
1048: PetscErrorCode VecsOrthonormalize(Vec *V, PetscInt n, PetscScalar *wS0,
1049:                                   PetscScalar *wS1)
1050: {
1051:   PetscErrorCode  ierr;
1052:   PetscBLASInt    nn = n, info, ld;
1053:   PetscInt        ldV, i;
1054:   PetscScalar     *H, *T, one=1.0, *pv;
1055: 

1058:   if (!wS0) {
1059:     PetscMalloc(sizeof(PetscScalar)*n*n, &H);
1060:   } else {
1062:     H = wS0;
1063:   }
1064:   if (!wS1) {
1065:     PetscMalloc(sizeof(PetscScalar)*n*n, &T);
1066:   } else {
1068:     T = wS1;
1069:   }

1071:   /* H <- V' * V */
1072:   VecsMult(H, 0, n, V, 0, n, V, 0, n, T, PETSC_NULL);

1074:   /* H <- chol(H) */
1075:   LAPACKpbtrf_("U", &nn, &nn, H, &nn, &info);
1076:   if (info) SETERRQ1(((PetscObject)*V)->comm,PETSC_ERR_LIB, "Error in Lapack PBTRF %d", info);

1078:   /* V <- V * inv(H) */
1079:   VecGetLocalSize(V[0], &ldV);
1080:   VecGetArray(V[0], &pv);
1081:   ld = ldV;
1082:   BLAStrsm_("R", "U", "N", "N", &ld, &nn, &one, H, &nn, pv, &ld);
1083:   VecRestoreArray(V[0], &pv);
1084:   for(i=1; i<n; i++) {
1085:     PetscObjectStateIncrease((PetscObject)V[i]);
1086:   }

1088:   if (!wS0) {
1089:     PetscFree(H);
1090:   }
1091:   if (!wS1) {
1092:     PetscFree(T);
1093:   }
1094: 
1095:   return(0);
1096: }

1100: /* 
1101:   Sum up several arrays with only one call to MPIReduce.
1102: */
1103: PetscErrorCode SlepcAllReduceSumBegin(DvdReductionChunk *ops,
1104:                                       PetscInt max_size_ops,
1105:                                       PetscScalar *in, PetscScalar *out,
1106:                                       PetscInt max_size_in, DvdReduction *r,
1107:                                       MPI_Comm comm)
1108: {

1113:   r->in = in;
1114:   r->out = out;
1115:   r->size_in = 0;
1116:   r->max_size_in = max_size_in;
1117:   r->ops = ops;
1118:   r->size_ops = 0;
1119:   r->max_size_ops = max_size_ops;
1120:   r->comm = comm;

1122:   return(0);
1123: }

1127: PetscErrorCode SlepcAllReduceSum(DvdReduction *r, PetscInt size_in,
1128:                                  DvdReductionPostF f, void *ptr,
1129:                                  PetscScalar **in)
1130: {

1133:   *in = r->in + r->size_in;
1134:   r->ops[r->size_ops].out = r->out + r->size_in;
1135:   r->ops[r->size_ops].size_out = size_in;
1136:   r->ops[r->size_ops].f = f;
1137:   r->ops[r->size_ops].ptr = ptr;
1138:   if (++(r->size_ops) > r->max_size_ops) {
1139:     SETERRQ(PETSC_COMM_SELF,1, "max_size_ops is not large enough");
1140:   }
1141:   if ((r->size_in+= size_in) > r->max_size_in) {
1142:     SETERRQ(PETSC_COMM_SELF,1, "max_size_in is not large enough");
1143:   }

1145:   return(0);
1146: }


1151: PetscErrorCode SlepcAllReduceSumEnd(DvdReduction *r)
1152: {
1153:   PetscErrorCode  ierr;
1154:   PetscInt        i;


1158:   /* Check if quick exit */
1159:   if (r->size_ops == 0)
1160:     return(0);

1162:   /* Call the MPIAllReduce routine */
1163:   MPI_Allreduce(r->in, r->out, r->size_in, MPIU_SCALAR, MPIU_SUM,
1164:                        r->comm);

1166:   /* Call the postponed routines */
1167:   for(i=0; i<r->size_ops; i++) {
1168:     r->ops[i].f(r->ops[i].out, r->ops[i].size_out, r->ops[i].ptr);
1169: 
1170:   }

1172:   /* Tag the operation as done */
1173:   r->size_ops = 0;

1175:   return(0);
1176: }


1181: /* auxS: size_cX+V_new_e */
1182: PetscErrorCode dvd_orthV(IP ip, Vec *DS, PetscInt size_DS, Vec *cX,
1183:                          PetscInt size_cX, Vec *V, PetscInt V_new_s,
1184:                          PetscInt V_new_e, PetscScalar *auxS,
1185:                          PetscRandom rand)
1186: {
1187:   PetscErrorCode  ierr;
1188:   PetscInt        i, j;
1189:   PetscBool       lindep;
1190:   PetscReal       norm;
1191:   PetscScalar     *auxS0 = auxS;
1192: 
1194: 
1195:   /* Orthonormalize V with IP */
1196:   for (i=V_new_s; i<V_new_e; i++) {
1197:     for(j=0; j<3; j++) {
1198:       if (j>0) { SlepcVecSetRandom(V[i], rand);  }
1199:       if (cX + size_cX == V) {
1200:         /* If cX and V are contiguous, orthogonalize in one step */
1201:         IPOrthogonalize(ip, size_DS, DS, size_cX+i, PETSC_NULL, cX,
1202:                                V[i], auxS0, &norm, &lindep);
1203:       } else if (DS) {
1204:         /* Else orthogonalize first against DS, and then against cX and V */
1205:         IPOrthogonalize(ip, size_DS, DS, size_cX, PETSC_NULL, cX,
1206:                                V[i], auxS0, PETSC_NULL, &lindep);
1207:         if(!lindep) {
1208:           IPOrthogonalize(ip, 0, PETSC_NULL, i, PETSC_NULL, V,
1209:                                  V[i], auxS0, &norm, &lindep);
1210:         }
1211:       } else {
1212:         /* Else orthogonalize first against cX and then against V */
1213:         IPOrthogonalize(ip, size_cX, cX, i, PETSC_NULL, V,
1214:                                V[i], auxS0, &norm, &lindep);
1215:       }
1216:       if(!lindep && (norm > PETSC_MACHINE_EPSILON)) break;
1217:       PetscInfo1(ip,"Orthonormalization problems adding the vector %D to the searching subspace\n",i);
1218:     }
1219:     if(lindep || (norm < PETSC_MACHINE_EPSILON)) {
1220:         SETERRQ(((PetscObject)ip)->comm,1, "Error during orthonormalization of eigenvectors");
1221:     }
1222:     VecScale(V[i], 1.0/norm);
1223:   }
1224: 
1225:   return(0);
1226: }


1231: /* auxS: size_cX+V_new_e+1 */
1232: PetscErrorCode dvd_BorthV(IP ip, Vec *DS, Vec *BDS, PetscInt size_DS, Vec *cX,
1233:                          Vec *BcX, PetscInt size_cX, Vec *V, Vec *BV,
1234:                          PetscInt V_new_s, PetscInt V_new_e,
1235:                          PetscScalar *auxS, PetscRandom rand)
1236: {
1237:   PetscErrorCode  ierr;
1238:   PetscInt        i, j;
1239:   PetscBool       lindep;
1240:   PetscReal       norm;
1241:   PetscScalar     *auxS0 = auxS;
1242: 
1244: 
1245:   /* Orthonormalize V with IP */
1246:   for (i=V_new_s; i<V_new_e; i++) {
1247:     for(j=0; j<3; j++) {
1248:       if (j>0) { SlepcVecSetRandom(V[i], rand);  }
1249:       if (cX + size_cX == V) {
1250:         /* If cX and V are contiguous, orthogonalize in one step */
1251:         IPBOrthogonalize(ip, size_DS, DS, BDS, size_cX+i, PETSC_NULL, cX, BcX,
1252:                                V[i], BV[i], auxS0, &norm, &lindep);
1253:       } else if (DS) {
1254:         /* Else orthogonalize first against DS, and then against cX and V */
1255:         IPBOrthogonalize(ip, size_DS, DS, BDS, size_cX, PETSC_NULL, cX, BcX,
1256:                                V[i], BV[i], auxS0, PETSC_NULL, &lindep);
1257:         if(!lindep) {
1258:           IPBOrthogonalize(ip, 0, PETSC_NULL, PETSC_NULL, i, PETSC_NULL, V, BV,
1259:                                   V[i], BV[i], auxS0, &norm, &lindep);
1260:         }
1261:       } else {
1262:         /* Else orthogonalize first against cX and then against V */
1263:         IPBOrthogonalize(ip, size_cX, cX, BcX, i, PETSC_NULL, V, BV,
1264:                                 V[i], BV[i], auxS0, &norm, &lindep);
1265:       }
1266:       if(!lindep && (norm > PETSC_MACHINE_EPSILON)) break;
1267:       PetscInfo1(ip, "Orthonormalization problems adding the vector %d to the searching subspace\n", i);
1268: 
1269:     }
1270:     if(lindep || (norm < PETSC_MACHINE_EPSILON)) {
1271:         SETERRQ(((PetscObject)ip)->comm,1, "Error during the orthonormalization of the eigenvectors!");
1272:     }
1273:     VecScale(V[i], 1.0/norm);
1274:     VecScale(BV[i], 1.0/norm);
1275:   }
1276: 
1277:   return(0);
1278: }
1279: 
1282: /*
1283:   Compute eigenvectors associated to the Schur decomposition (S, T) and
1284:   save the left vectors in pY and the right vectors in pX, where
1285:   n, size of the eigenproblem
1286:   ldS, ldT, leading dimension of S and T
1287:   ldpX, ldpY, leading dimension of pX and pY
1288:   auxS, auxiliar scalar of length:
1289:     double standard 3n, double generalized 6n,
1290:     complex standard 3n, complex generalized 3n
1291:   size_auxS, the length of auxS
1292:   doProd, if true pX and pY return the eigenvectors premultiplied by the input vectors stored in pX and pY respectively
1293: */
1294: PetscErrorCode dvd_compute_eigenvectors(PetscInt n_, PetscScalar *S,
1295:   PetscInt ldS_, PetscScalar *T, PetscInt ldT_, PetscScalar *pX,
1296:   PetscInt ldpX_, PetscScalar *pY, PetscInt ldpY_, PetscScalar *auxS,
1297:   PetscInt size_auxS, PetscBool doProd)
1298: {
1299: #if defined(SLEPC_MISSING_LAPACK_GGEV)
1301:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GGEV - Lapack routine is unavailable.");
1302: #else
1303:   PetscBLASInt    n, ldpX, ldpY, nout, info, ldS, ldT;
1304:   const char      *side, *howmny;
1305: #if defined(PETSC_USE_COMPLEX)
1306:   PetscReal       *auxR;
1307: #endif
1308: 
1315:   n = PetscBLASIntCast(n_);
1316:   ldpX = PetscBLASIntCast(PetscMax(ldpX_,1));
1317:   ldpY = PetscBLASIntCast(PetscMax(ldpY_,1));
1318:   ldS = PetscBLASIntCast(PetscMax(ldS_,1));
1319:   ldT = PetscBLASIntCast(PetscMax(ldT_,1));

1321:   if (pX && pY) side = "B";
1322:   else if (pX)  side = "R";
1323:   else if (pY)  side = "L";
1324:   else { return(0); }

1326:   howmny = doProd?"B":"A";

1328:   if (T) {
1329:     /* [eigr, pX] = eig(S, T) */
1330: #if defined(PETSC_USE_COMPLEX)
1331:     auxR = (PetscReal*)auxS; auxS = (PetscScalar*)(auxR+2*n); size_auxS-= 2*n;
1332:     if (size_auxS < 2*n)
1333:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Insufficient work space for xTGEVC");
1334:     LAPACKtgevc_(side,howmny,PETSC_NULL,&n,S,&ldS,T,&ldT,pY,&ldpY,pX,&ldpX,&n,&nout,auxS,auxR,&info);
1335:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTGEVC %d",info);
1336: #else
1337:     if (size_auxS < 6*n)
1338:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Insufficient work space for xTGEVC");
1339:     LAPACKtgevc_(side,howmny,PETSC_NULL,&n,S,&ldS,T,&ldT,pY,&ldpY,pX,&ldpX,&n,&nout,auxS,&info);
1340: #endif
1341:   } else {
1342:     /* [eigr, pX] = eig(S) */
1343: #if defined(PETSC_USE_COMPLEX)
1344:     auxR = (PetscReal*)auxS; auxS = (PetscScalar*)(auxR+n); size_auxS-= n;
1345:     if (size_auxS < 2*n)
1346:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Insufficient work space for xTREVC");
1347:     LAPACKtrevc_(side,howmny,PETSC_NULL,&n,S,&ldS,pY,&ldpY,pX,&ldpX,&n,&nout,auxS,auxR,&info);
1348: #else
1349:     if (size_auxS < 3*n)
1350:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Insufficient work space for xTREVC");
1351:     LAPACKtrevc_(side,howmny,PETSC_NULL,&n,S,&ldS,pY,&ldpY,pX,&ldpX,&n,&nout,auxS,&info);
1352: #endif
1353:     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xTREVC %d",info);
1354:   }
1355:   return(0);
1356: #endif
1357: }


1362: PetscErrorCode EPSSortDenseHEP(EPS eps, PetscInt n, PetscInt k, PetscScalar *w, PetscScalar *V, PetscInt ldV)
1363: {
1364:   PetscInt        i, j, result, pos;
1365:   PetscReal       re;
1366:   PetscScalar     t;
1367:   PetscBLASInt    n_,one=1;
1368:   PetscErrorCode  ierr;

1373:   n_ = PetscBLASIntCast(n);

1375:   /* selection sort */
1376:   for (i=k;i<n-1;i++) {
1377:     re = PetscRealPart(w[i]);
1378:     pos = 0;
1379:     /* find minimum eigenvalue */
1380:     for (j=i+1;j<n;j++) {
1381:       EPSCompareEigenvalues(eps,re,0,PetscRealPart(w[j]),0,&result);
1382:       if (result > 0) {
1383:         re = PetscRealPart(w[j]);
1384:         pos = j;
1385:       }
1386:     }
1387:     /* interchange the pairs i and pos */
1388:     if (pos) {
1389:       BLASswap_(&n_, &V[ldV*pos], &one, &V[ldV*i], &one);
1390:       t = w[i]; w[i] = w[pos]; w[pos] = t;
1391:     }
1392:   }

1394:   return(0);
1395: }

1399: /* Write zeros from the column k to n in the lower triangular part of the
1400:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
1401:    make (S,T) a valid Schur decompositon.
1402: */
1403: PetscErrorCode EPSCleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *eigi,PetscScalar *X,PetscInt ldX,PetscBool doProd)
1404: {
1405:   PetscInt        i, j;
1406: #if defined(PETSC_USE_COMPLEX)
1407:   PetscScalar     s;
1408: #endif


1414:   if (!doProd && X) {
1415:     for (i=0; i<n; i++) for (j=0; j<n; j++) X[ldX*i+j] = 0.0;
1416:     for (i=0; i<n; i++) X[ldX*i+i] = 1.0;
1417:   }

1419: #if defined(PETSC_USE_COMPLEX)
1420:   for (i=k; i<n; i++) {
1421:     /* Some functions need the diagonal elements in T be real */
1422:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
1423:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
1424:       for(j=0; j<=i; j++)
1425:         T[ldT*i+j]*= s,
1426:         S[ldS*i+j]*= s;
1427:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
1428:       if (X) for(j=0; j<n; j++) X[ldX*i+j]*= s;
1429:     }
1430:     if ((j=i+1) < n) {
1431:       S[ldS*i+j] = 0.0;
1432:       if (T) T[ldT*i+j] = 0.0;
1433:     }
1434:   }
1435: #else
1436:   for (i=k; i<n; i++) {
1437:     if (S[ldS*i+i+1] != 0.0 && eigi && eigi[i] != 0.0) {
1438:       if ((j=i+2) < n) S[ldS*(i+1)+j] = 0.0;
1439:       if (T) {
1440:         /* T[ldT*(i+1)+i] = 0.0; */
1441:         {
1442:           /* Check if T(i+1,i) is negligible */
1443:           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) {
1444:             PetscBLASInt    ldS_,ldT_,n_i,n_i_1,one=1,n_,i_1,i_;
1445:             PetscScalar     b11,b22,sr,cr,sl,cl;
1446:             ldS_ = PetscBLASIntCast(ldS);
1447:             ldT_ = PetscBLASIntCast(ldT);
1448:             n_i = PetscBLASIntCast(n-i);
1449:             n_i_1 = n_i - 1;
1450:             i_1 = PetscBLASIntCast(i+1);
1451:             i_ = PetscBLASIntCast(i);
1452:             n_ = PetscBLASIntCast(n);
1453:             LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl);
1454:             if (b11 < 0.0) { cr=-cr; sr=-sr; b11=-b11; b22=-b22; }
1455:             BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl);
1456:             BLASrot_(&i_1,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr);
1457:             if (n_i_1>0) BLASrot_(&n_i_1,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i],&ldT_,&cl,&sl);
1458:             BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr);
1459:             if (X) BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr);
1460:             T[ldT*i+i] = b11; T[ldT*i+i+1] = T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
1461:           } else {
1462:             T[ldT*(i+1)+i] = T[ldT*i+i+1] = 0.0;
1463:           }
1464:         }
1465:         if ((j=i+1) < n) T[ldT*i+j] = 0.0;
1466:         if ((j=i+2) < n) T[ldT*(i+1)+j] = 0.0;
1467:       }
1468:       i++;
1469:     } else {
1470:       if ((j=i+1) < n) {
1471:         S[ldS*i+j] = 0.0;
1472:         if (T) T[ldT*i+j] = 0.0;
1473:       }
1474:     }
1475:   }
1476: #endif

1478:   return(0);
1479: }