Date: 2026-03-09T09:12:28+00:00

Actual source code: epskrylov.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: */
     10: /*
     11:    Common subroutines for all Krylov-type solvers
     12: */

     14: #include <slepc/private/epsimpl.h>
     15: #include <slepc/private/slepcimpl.h>
     16: #include <slepcblaslapack.h>

     18: /*
     19:    EPSDelayedArnoldi - This function is equivalent to BVMatArnoldi but
     20:    performs the computation in a different way. The main idea is that
     21:    reorthogonalization is delayed to the next Arnoldi step. This version is
     22:    more scalable but in some cases convergence may stagnate.
     23: */
     24: PetscErrorCode EPSDelayedArnoldi(EPS eps,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscReal *beta,PetscBool *breakdown)
     25: {
     26:   PetscInt       i,j,m=*M;
     27:   Vec            u,t;
     28:   PetscScalar    shh[100],*lhh,dot,dot2;
     29:   PetscReal      norm1=0.0,norm2=1.0;
     30:   Vec            vj,vj1,vj2=NULL;

     32:   PetscFunctionBegin;
     33:   if (m<=100) lhh = shh;
     34:   else PetscCall(PetscMalloc1(m,&lhh));
     35:   PetscCall(BVCreateVec(eps->V,&u));
     36:   PetscCall(BVCreateVec(eps->V,&t));

     38:   PetscCall(BVSetActiveColumns(eps->V,0,m));
     39:   for (j=k;j<m;j++) {
     40:     PetscCall(BVGetColumn(eps->V,j,&vj));
     41:     PetscCall(BVGetColumn(eps->V,j+1,&vj1));
     42:     PetscCall(STApply(eps->st,vj,vj1));
     43:     PetscCall(BVRestoreColumn(eps->V,j,&vj));
     44:     PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));

     46:     PetscCall(BVDotColumnBegin(eps->V,j+1,H+ldh*j));
     47:     if (j>k) {
     48:       PetscCall(BVDotColumnBegin(eps->V,j,lhh));
     49:       PetscCall(BVGetColumn(eps->V,j,&vj));
     50:       PetscCall(VecDotBegin(vj,vj,&dot));
     51:       if (j>k+1) {
     52:         PetscCall(BVNormVecBegin(eps->V,u,NORM_2,&norm2));
     53:         PetscCall(BVGetColumn(eps->V,j-2,&vj2));
     54:         PetscCall(VecDotBegin(u,vj2,&dot2));
     55:       }
     56:       PetscCall(BVDotColumnEnd(eps->V,j+1,H+ldh*j));
     57:       PetscCall(BVDotColumnEnd(eps->V,j,lhh));
     58:       PetscCall(VecDotEnd(vj,vj,&dot));
     59:       PetscCall(BVRestoreColumn(eps->V,j,&vj));
     60:       if (j>k+1) {
     61:         PetscCall(BVNormVecEnd(eps->V,u,NORM_2,&norm2));
     62:         PetscCall(VecDotEnd(u,vj2,&dot2));
     63:         PetscCall(BVRestoreColumn(eps->V,j-2,&vj2));
     64:       }
     65:       norm1 = PetscSqrtReal(PetscRealPart(dot));
     66:       for (i=0;i<j;i++) H[ldh*j+i] = H[ldh*j+i]/norm1;
     67:       H[ldh*j+j] = H[ldh*j+j]/dot;
     68:       PetscCall(BVCopyVec(eps->V,j,t));
     69:       PetscCall(BVScaleColumn(eps->V,j,1.0/norm1));
     70:       PetscCall(BVScaleColumn(eps->V,j+1,1.0/norm1));
     71:     } else PetscCall(BVDotColumnEnd(eps->V,j+1,H+ldh*j)); /* j==k */

     73:     PetscCall(BVMultColumn(eps->V,-1.0,1.0,j+1,H+ldh*j));

     75:     if (j>k) {
     76:       PetscCall(BVSetActiveColumns(eps->V,0,j));
     77:       PetscCall(BVMultVec(eps->V,-1.0,1.0,t,lhh));
     78:       PetscCall(BVSetActiveColumns(eps->V,0,m));
     79:       for (i=0;i<j;i++) H[ldh*(j-1)+i] += lhh[i];
     80:     }

     82:     if (j>k+1) {
     83:       PetscCall(BVGetColumn(eps->V,j-1,&vj1));
     84:       PetscCall(VecCopy(u,vj1));
     85:       PetscCall(BVRestoreColumn(eps->V,j-1,&vj1));
     86:       PetscCall(BVScaleColumn(eps->V,j-1,1.0/norm2));
     87:       H[ldh*(j-2)+j-1] = norm2;
     88:     }

     90:     if (j<m-1) PetscCall(VecCopy(t,u));
     91:   }

     93:   PetscCall(BVNormVec(eps->V,t,NORM_2,&norm2));
     94:   PetscCall(VecScale(t,1.0/norm2));
     95:   PetscCall(BVGetColumn(eps->V,m-1,&vj1));
     96:   PetscCall(VecCopy(t,vj1));
     97:   PetscCall(BVRestoreColumn(eps->V,m-1,&vj1));
     98:   H[ldh*(m-2)+m-1] = norm2;

    100:   PetscCall(BVDotColumn(eps->V,m,lhh));

    102:   PetscCall(BVMultColumn(eps->V,-1.0,1.0,m,lhh));
    103:   for (i=0;i<m;i++)
    104:     H[ldh*(m-1)+i] += lhh[i];

    106:   PetscCall(BVNormColumn(eps->V,m,NORM_2,beta));
    107:   PetscCall(BVScaleColumn(eps->V,m,1.0 / *beta));
    108:   *breakdown = PETSC_FALSE;

    110:   if (m>100) PetscCall(PetscFree(lhh));
    111:   PetscCall(VecDestroy(&u));
    112:   PetscCall(VecDestroy(&t));
    113:   PetscFunctionReturn(PETSC_SUCCESS);
    114: }

    116: /*
    117:    EPSDelayedArnoldi1 - This function is similar to EPSDelayedArnoldi,
    118:    but without reorthogonalization (only delayed normalization).
    119: */
    120: PetscErrorCode EPSDelayedArnoldi1(EPS eps,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscReal *beta,PetscBool *breakdown)
    121: {
    122:   PetscInt       i,j,m=*M;
    123:   PetscScalar    dot;
    124:   PetscReal      norm=0.0;
    125:   Vec            vj,vj1;

    127:   PetscFunctionBegin;
    128:   PetscCall(BVSetActiveColumns(eps->V,0,m));
    129:   for (j=k;j<m;j++) {
    130:     PetscCall(BVGetColumn(eps->V,j,&vj));
    131:     PetscCall(BVGetColumn(eps->V,j+1,&vj1));
    132:     PetscCall(STApply(eps->st,vj,vj1));
    133:     PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));
    134:     if (j>k) {
    135:       PetscCall(BVDotColumnBegin(eps->V,j+1,H+ldh*j));
    136:       PetscCall(VecDotBegin(vj,vj,&dot));
    137:       PetscCall(BVDotColumnEnd(eps->V,j+1,H+ldh*j));
    138:       PetscCall(VecDotEnd(vj,vj,&dot));
    139:       norm = PetscSqrtReal(PetscRealPart(dot));
    140:       PetscCall(BVScaleColumn(eps->V,j,1.0/norm));
    141:       H[ldh*(j-1)+j] = norm;
    142:       for (i=0;i<j;i++) H[ldh*j+i] = H[ldh*j+i]/norm;
    143:       H[ldh*j+j] = H[ldh*j+j]/dot;
    144:       PetscCall(BVScaleColumn(eps->V,j+1,1.0/norm));
    145:       *beta = norm;
    146:     } else {  /* j==k */
    147:       PetscCall(BVDotColumn(eps->V,j+1,H+ldh*j));
    148:     }
    149:     PetscCall(BVRestoreColumn(eps->V,j,&vj));
    150:     PetscCall(BVMultColumn(eps->V,-1.0,1.0,j+1,H+ldh*j));
    151:   }

    153:   *breakdown = PETSC_FALSE;
    154:   PetscFunctionReturn(PETSC_SUCCESS);
    155: }

    157: /*
    158:    EPSKrylovConvergence_Filter - Specialized version for STFILTER.
    159: */
    160: static PetscErrorCode EPSKrylovConvergence_Filter(EPS eps,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscReal gamma,PetscInt *kout)
    161: {
    162:   PetscInt       k,ninside,nconv;
    163:   PetscScalar    re,im;
    164:   PetscReal      resnorm;

    166:   PetscFunctionBegin;
    167:   ninside = 0;   /* count how many eigenvalues are located in the interval */
    168:   for (k=kini;k<kini+nits;k++) {
    169:     if (PetscRealPart(eps->eigr[k]) < gamma) break;
    170:     ninside++;
    171:   }
    172:   if (eps->trackall) getall = PETSC_TRUE;
    173:   eps->nev = ninside+kini;  /* adjust eigenvalue count */
    174:   nconv = 0;   /* count how many eigenvalues satisfy the convergence criterion */
    175:   for (k=kini;k<kini+(getall?nits:ninside);k++) {
    176:     /* eigenvalue */
    177:     re = eps->eigr[k];
    178:     im = eps->eigi[k];
    179:     PetscCall(DSVectors(eps->ds,DS_MAT_X,&k,&resnorm));
    180:     resnorm *= beta;
    181:     /* error estimate */
    182:     PetscCall((*eps->converged)(eps,re,im,resnorm,&eps->errest[k],eps->convergedctx));
    183:     if (eps->errest[k] < eps->tol) nconv++;
    184:     else if (!getall) break;
    185:   }
    186:   *kout = kini+nconv;
    187:   PetscCall(PetscInfo(eps,"Found %" PetscInt_FMT " eigenvalue approximations inside the interval (gamma=%g), k=%" PetscInt_FMT " nconv=%" PetscInt_FMT "\n",ninside,(double)gamma,k,nconv));
    188:   PetscFunctionReturn(PETSC_SUCCESS);
    189: }

    191: /*
    192:    EPSKrylovConvergence - Implements the loop that checks for convergence
    193:    in Krylov methods.

    195:    Input Parameters:
    196:      eps   - the eigensolver; some error estimates are updated in eps->errest
    197:      getall - whether all residuals must be computed
    198:      kini  - initial value of k (the loop variable)
    199:      nits  - number of iterations of the loop
    200:      V     - set of basis vectors (used only if trueresidual is activated)
    201:      nv    - number of vectors to process (dimension of Q, columns of V)
    202:      beta  - norm of f (the residual vector of the Arnoldi/Lanczos factorization)
    203:      corrf - correction factor for residual estimates (only in harmonic KS)

    205:    Output Parameters:
    206:      kout  - the first index where the convergence test failed
    207: */
    208: PetscErrorCode EPSKrylovConvergence(EPS eps,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscReal betat,PetscReal corrf,PetscInt *kout)
    209: {
    210:   PetscInt       k,newk,newk2,marker,ld,inside;
    211:   PetscScalar    re,im,*Zr,*Zi,*X;
    212:   PetscReal      resnorm,gamma,lerrest;
    213:   PetscBool      isshift,isfilter,refined,istrivial;
    214:   Vec            x=NULL,y=NULL,w[3];

    216:   PetscFunctionBegin;
    217:   if (PetscUnlikely(eps->which == EPS_ALL)) {
    218:     PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilter));
    219:     if (isfilter) {
    220:       PetscCall(STFilterGetThreshold(eps->st,&gamma));
    221:       PetscCall(EPSKrylovConvergence_Filter(eps,getall,kini,nits,beta,gamma,kout));
    222:       PetscFunctionReturn(PETSC_SUCCESS);
    223:     }
    224:   }
    225:   PetscCall(RGIsTrivial(eps->rg,&istrivial));
    226:   if (PetscUnlikely(eps->trueres)) {
    227:     PetscCall(BVCreateVec(eps->V,&x));
    228:     PetscCall(BVCreateVec(eps->V,&y));
    229:     PetscCall(BVCreateVec(eps->V,&w[0]));
    230:     PetscCall(BVCreateVec(eps->V,&w[2]));
    231: #if !defined(PETSC_USE_COMPLEX)
    232:     PetscCall(BVCreateVec(eps->V,&w[1]));
    233: #else
    234:     w[1] = NULL;
    235: #endif
    236:   }
    237:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
    238:   PetscCall(DSGetRefined(eps->ds,&refined));
    239:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&isshift));
    240:   marker = -1;
    241:   if (eps->trackall) getall = PETSC_TRUE;
    242:   for (k=kini;k<kini+nits;k++) {
    243:     /* eigenvalue */
    244:     re = eps->eigr[k];
    245:     im = eps->eigi[k];
    246:     if (!istrivial || eps->trueres || isshift || eps->conv==EPS_CONV_NORM) PetscCall(STBackTransform(eps->st,1,&re,&im));
    247:     if (PetscUnlikely(!istrivial)) {
    248:       PetscCall(RGCheckInside(eps->rg,1,&re,&im,&inside));
    249:       if (marker==-1 && inside<0) marker = k;
    250:       if (!(eps->trueres || isshift || eps->conv==EPS_CONV_NORM)) {  /* make sure eps->converged below uses the right value */
    251:         re = eps->eigr[k];
    252:         im = eps->eigi[k];
    253:       }
    254:     }
    255:     newk = k;
    256:     PetscCall(DSVectors(eps->ds,DS_MAT_X,&newk,&resnorm));
    257:     if (PetscUnlikely(eps->trueres)) {
    258:       PetscCall(DSGetArray(eps->ds,DS_MAT_X,&X));
    259:       Zr = X+k*ld;
    260:       if (newk==k+1) Zi = X+newk*ld;
    261:       else Zi = NULL;
    262:       PetscCall(EPSComputeRitzVector(eps,Zr,Zi,eps->V,x,y));
    263:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_X,&X));
    264:       PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_FALSE,re,im,x,y,w,&resnorm));
    265:     }
    266:     else if (!refined) resnorm *= beta*corrf;
    267:     /* error estimate */
    268:     PetscCall((*eps->converged)(eps,re,im,resnorm,&eps->errest[k],eps->convergedctx));
    269:     if (marker==-1 && eps->errest[k] >= eps->tol) marker = k;
    270:     if (PetscUnlikely(eps->twosided)) {
    271:       newk2 = k;
    272:       PetscCall(DSVectors(eps->ds,DS_MAT_Y,&newk2,&resnorm));
    273:       resnorm *= betat;
    274:       PetscCall((*eps->converged)(eps,re,im,resnorm,&lerrest,eps->convergedctx));
    275:       eps->errest[k] = PetscMax(eps->errest[k],lerrest);
    276:       if (marker==-1 && lerrest >= eps->tol) marker = k;
    277:     }
    278:     if (PetscUnlikely(newk==k+1)) {
    279:       eps->errest[k+1] = eps->errest[k];
    280:       k++;
    281:     }
    282:     if (marker!=-1 && !getall) break;
    283:   }
    284:   if (marker!=-1) k = marker;
    285:   *kout = k;
    286:   if (PetscUnlikely(eps->trueres)) {
    287:     PetscCall(VecDestroy(&x));
    288:     PetscCall(VecDestroy(&y));
    289:     PetscCall(VecDestroy(&w[0]));
    290:     PetscCall(VecDestroy(&w[2]));
    291: #if !defined(PETSC_USE_COMPLEX)
    292:     PetscCall(VecDestroy(&w[1]));
    293: #endif
    294:   }
    295:   PetscFunctionReturn(PETSC_SUCCESS);
    296: }

    298: PetscErrorCode EPSPseudoLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,PetscReal *cos,Vec w)
    299: {
    300:   PetscInt       j,m = *M,i,ld,l;
    301:   Vec            vj,vj1;
    302:   PetscScalar    *hwork,lhwork[100];
    303:   PetscReal      norm,norm1,norm2,t,sym=0.0,fro=0.0;
    304:   PetscBLASInt   j_,one=1;

    306:   PetscFunctionBegin;
    307:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
    308:   PetscCall(DSGetDimensions(eps->ds,NULL,&l,NULL,NULL));
    309:   if (cos) *cos = 1.0;
    310:   if (m > 100) PetscCall(PetscMalloc1(m,&hwork));
    311:   else hwork = lhwork;

    313:   PetscCall(BVSetActiveColumns(eps->V,0,m));
    314:   for (j=k;j<m;j++) {
    315:     PetscCall(BVGetColumn(eps->V,j,&vj));
    316:     PetscCall(BVGetColumn(eps->V,j+1,&vj1));
    317:     PetscCall(STApply(eps->st,vj,vj1));
    318:     PetscCall(BVRestoreColumn(eps->V,j,&vj));
    319:     PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));
    320:     PetscCall(BVOrthogonalizeColumn(eps->V,j+1,hwork,&norm,breakdown));
    321:     alpha[j] = PetscRealPart(hwork[j]);
    322:     beta[j] = PetscAbsReal(norm);
    323:     if (j==k) {
    324:       PetscReal *f;

    326:       PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&f));
    327:       for (i=0;i<l;i++) hwork[i]  = 0.0;
    328:       for (;i<j-1;i++)  hwork[i] -= f[2*ld+i];
    329:       PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&f));
    330:     }
    331:     if (j>0) {
    332:       hwork[j-1] -= beta[j-1];
    333:       PetscCall(PetscBLASIntCast(j,&j_));
    334:       sym = SlepcAbs(BLASnrm2_(&j_,hwork,&one),sym);
    335:     }
    336:     fro = SlepcAbs(fro,SlepcAbs(alpha[j],beta[j]));
    337:     if (j>0) fro = SlepcAbs(fro,beta[j-1]);
    338:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*eps->tol)) { *symmlost = PETSC_TRUE; *M=j; break; }
    339:     omega[j+1] = (norm<0.0)? -1.0: 1.0;
    340:     PetscCall(BVScaleColumn(eps->V,j+1,1.0/norm));
    341:     /* */
    342:     if (cos) {
    343:       PetscCall(BVGetColumn(eps->V,j+1,&vj1));
    344:       PetscCall(VecNorm(vj1,NORM_2,&norm1));
    345:       PetscCall(BVApplyMatrix(eps->V,vj1,w));
    346:       PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));
    347:       PetscCall(VecNorm(w,NORM_2,&norm2));
    348:       t = 1.0/(norm1*norm2);
    349:       if (*cos>t) *cos = t;
    350:     }
    351:   }
    352:   if (m > 100) PetscCall(PetscFree(hwork));
    353:   PetscFunctionReturn(PETSC_SUCCESS);
    354: }