Date: 2026-03-31T13:23:31+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 - Implements the loop that checks for convergence
    159:    in Krylov methods.

    161:    Input Parameters:
    162:      eps   - the eigensolver; some error estimates are updated in eps->errest
    163:      getall - whether all residuals must be computed
    164:      kini  - initial value of k (the loop variable)
    165:      nits  - number of iterations of the loop
    166:      V     - set of basis vectors (used only if trueresidual is activated)
    167:      nv    - number of vectors to process (dimension of Q, columns of V)
    168:      beta  - norm of f (the residual vector of the Arnoldi/Lanczos factorization)
    169:      corrf - correction factor for residual estimates (only in harmonic KS)

    171:    Output Parameters:
    172:      kout  - the first index where the convergence test failed
    173: */
    174: PetscErrorCode EPSKrylovConvergence(EPS eps,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal beta,PetscReal betat,PetscReal corrf,PetscInt *kout)
    175: {
    176:   PetscInt       k,newk,newk2,marker,ld,inside;
    177:   PetscScalar    re,im,*Zr,*Zi,*X;
    178:   PetscReal      resnorm,lerrest;
    179:   PetscBool      isshift,refined,istrivial;
    180:   Vec            x=NULL,y=NULL,w[3];

    182:   PetscFunctionBegin;
    183:   PetscCall(RGIsTrivial(eps->rg,&istrivial));
    184:   if (PetscUnlikely(eps->trueres)) {
    185:     PetscCall(BVCreateVec(eps->V,&x));
    186:     PetscCall(BVCreateVec(eps->V,&y));
    187:     PetscCall(BVCreateVec(eps->V,&w[0]));
    188:     PetscCall(BVCreateVec(eps->V,&w[2]));
    189: #if !defined(PETSC_USE_COMPLEX)
    190:     PetscCall(BVCreateVec(eps->V,&w[1]));
    191: #else
    192:     w[1] = NULL;
    193: #endif
    194:   }
    195:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
    196:   PetscCall(DSGetRefined(eps->ds,&refined));
    197:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&isshift));
    198:   marker = -1;
    199:   if (eps->trackall) getall = PETSC_TRUE;
    200:   for (k=kini;k<kini+nits;k++) {
    201:     /* eigenvalue */
    202:     re = eps->eigr[k];
    203:     im = eps->eigi[k];
    204:     if (!istrivial || eps->trueres || isshift || eps->conv==EPS_CONV_NORM) PetscCall(STBackTransform(eps->st,1,&re,&im));
    205:     if (PetscUnlikely(!istrivial)) {
    206:       PetscCall(RGCheckInside(eps->rg,1,&re,&im,&inside));
    207:       if (marker==-1 && inside<0) marker = k;
    208:       if (!(eps->trueres || isshift || eps->conv==EPS_CONV_NORM)) {  /* make sure eps->converged below uses the right value */
    209:         re = eps->eigr[k];
    210:         im = eps->eigi[k];
    211:       }
    212:     }
    213:     newk = k;
    214:     PetscCall(DSVectors(eps->ds,DS_MAT_X,&newk,&resnorm));
    215:     if (PetscUnlikely(eps->trueres)) {
    216:       PetscCall(DSGetArray(eps->ds,DS_MAT_X,&X));
    217:       Zr = X+k*ld;
    218:       if (newk==k+1) Zi = X+newk*ld;
    219:       else Zi = NULL;
    220:       PetscCall(EPSComputeRitzVector(eps,Zr,Zi,eps->V,x,y));
    221:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_X,&X));
    222:       PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_FALSE,re,im,x,y,w,&resnorm));
    223:     }
    224:     else if (!refined) resnorm *= beta*corrf;
    225:     /* error estimate */
    226:     PetscCall((*eps->converged)(eps,re,im,resnorm,&eps->errest[k],eps->convergedctx));
    227:     if (marker==-1 && eps->errest[k] >= eps->tol) marker = k;
    228:     if (PetscUnlikely(eps->twosided)) {
    229:       newk2 = k;
    230:       PetscCall(DSVectors(eps->ds,DS_MAT_Y,&newk2,&resnorm));
    231:       resnorm *= betat;
    232:       PetscCall((*eps->converged)(eps,re,im,resnorm,&lerrest,eps->convergedctx));
    233:       eps->errest[k] = PetscMax(eps->errest[k],lerrest);
    234:       if (marker==-1 && lerrest >= eps->tol) marker = k;
    235:     }
    236:     if (PetscUnlikely(newk==k+1)) {
    237:       eps->errest[k+1] = eps->errest[k];
    238:       k++;
    239:     }
    240:     if (marker!=-1 && !getall) break;
    241:   }
    242:   if (marker!=-1) k = marker;
    243:   *kout = k;
    244:   if (PetscUnlikely(eps->trueres)) {
    245:     PetscCall(VecDestroy(&x));
    246:     PetscCall(VecDestroy(&y));
    247:     PetscCall(VecDestroy(&w[0]));
    248:     PetscCall(VecDestroy(&w[2]));
    249: #if !defined(PETSC_USE_COMPLEX)
    250:     PetscCall(VecDestroy(&w[1]));
    251: #endif
    252:   }
    253:   PetscFunctionReturn(PETSC_SUCCESS);
    254: }

    256: PetscErrorCode EPSPseudoLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,PetscReal *omega,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscBool *symmlost,PetscReal *cos,Vec w)
    257: {
    258:   PetscInt       j,m = *M,i,ld,l;
    259:   Vec            vj,vj1;
    260:   PetscScalar    *hwork,lhwork[100];
    261:   PetscReal      norm,norm1,norm2,t,sym=0.0,fro=0.0;
    262:   PetscBLASInt   j_,one=1;

    264:   PetscFunctionBegin;
    265:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
    266:   PetscCall(DSGetDimensions(eps->ds,NULL,&l,NULL,NULL));
    267:   if (cos) *cos = 1.0;
    268:   if (m > 100) PetscCall(PetscMalloc1(m,&hwork));
    269:   else hwork = lhwork;

    271:   PetscCall(BVSetActiveColumns(eps->V,0,m));
    272:   for (j=k;j<m;j++) {
    273:     PetscCall(BVGetColumn(eps->V,j,&vj));
    274:     PetscCall(BVGetColumn(eps->V,j+1,&vj1));
    275:     PetscCall(STApply(eps->st,vj,vj1));
    276:     PetscCall(BVRestoreColumn(eps->V,j,&vj));
    277:     PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));
    278:     PetscCall(BVOrthogonalizeColumn(eps->V,j+1,hwork,&norm,breakdown));
    279:     alpha[j] = PetscRealPart(hwork[j]);
    280:     beta[j] = PetscAbsReal(norm);
    281:     if (j==k) {
    282:       PetscReal *f;

    284:       PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&f));
    285:       for (i=0;i<l;i++) hwork[i]  = 0.0;
    286:       for (;i<j-1;i++)  hwork[i] -= f[2*ld+i];
    287:       PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&f));
    288:     }
    289:     if (j>0) {
    290:       hwork[j-1] -= beta[j-1];
    291:       PetscCall(PetscBLASIntCast(j,&j_));
    292:       sym = SlepcAbs(BLASnrm2_(&j_,hwork,&one),sym);
    293:     }
    294:     fro = SlepcAbs(fro,SlepcAbs(alpha[j],beta[j]));
    295:     if (j>0) fro = SlepcAbs(fro,beta[j-1]);
    296:     if (sym/fro>PetscMax(PETSC_SQRT_MACHINE_EPSILON,10*eps->tol)) { *symmlost = PETSC_TRUE; *M=j; break; }
    297:     omega[j+1] = (norm<0.0)? -1.0: 1.0;
    298:     PetscCall(BVScaleColumn(eps->V,j+1,1.0/norm));
    299:     /* */
    300:     if (cos) {
    301:       PetscCall(BVGetColumn(eps->V,j+1,&vj1));
    302:       PetscCall(VecNorm(vj1,NORM_2,&norm1));
    303:       PetscCall(BVApplyMatrix(eps->V,vj1,w));
    304:       PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));
    305:       PetscCall(VecNorm(w,NORM_2,&norm2));
    306:       t = 1.0/(norm1*norm2);
    307:       if (*cos>t) *cos = t;
    308:     }
    309:   }
    310:   if (m > 100) PetscCall(PetscFree(hwork));
    311:   PetscFunctionReturn(PETSC_SUCCESS);
    312: }