Date: 2021-02-01T14:41:56+00:00

Actual source code: ks-indef.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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:    SLEPc eigensolver: "krylovschur"

     13:    Method: Krylov-Schur for symmetric-indefinite eigenproblems
     14: */
     15: #include <slepc/private/epsimpl.h>
     16: #include "krylovschur.h"

     18: PetscErrorCode EPSSolve_KrylovSchur_Indefinite(EPS eps)
     19: {
     20:   PetscErrorCode  ierr;
     21:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
     22:   PetscInt        i,k,l,ld,nv,t,nconv=0;
     23:   Mat             U;
     24:   Vec             vomega,w=eps->work[0];
     25:   PetscScalar     *Q,*aux;
     26:   PetscReal       *a,*b,*r,beta,beta1=1.0,*omega;
     27:   PetscBool       breakdown=PETSC_FALSE,symmlost=PETSC_FALSE;

     30:   DSGetLeadingDimension(eps->ds,&ld);

     32:   /* Get the starting Lanczos vector */
     33:   EPSGetStartVector(eps,0,NULL);

     35:   /* Extract sigma[0] from BV, computed during normalization */
     36:   BVSetActiveColumns(eps->V,0,1);
     37:   VecCreateSeq(PETSC_COMM_SELF,1,&vomega);
     38:   BVGetSignature(eps->V,vomega);
     39:   VecGetArray(vomega,&aux);
     40:   DSGetArrayReal(eps->ds,DS_MAT_D,&omega);
     41:   omega[0] = PetscRealPart(aux[0]);
     42:   DSRestoreArrayReal(eps->ds,DS_MAT_D,&omega);
     43:   VecRestoreArray(vomega,&aux);
     44:   VecDestroy(&vomega);
     45:   l = 0;

     47:   /* Restart loop */
     48:   while (eps->reason == EPS_CONVERGED_ITERATING) {
     49:     eps->its++;

     51:     /* Compute an nv-step Lanczos factorization */
     52:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
     53:     DSGetArrayReal(eps->ds,DS_MAT_T,&a);
     54:     b = a + ld;
     55:     DSGetArrayReal(eps->ds,DS_MAT_D,&omega);
     56:     EPSPseudoLanczos(eps,a,b,omega,eps->nconv+l,&nv,&breakdown,&symmlost,NULL,w);
     57:     if (symmlost) {
     58:       eps->reason = EPS_DIVERGED_SYMMETRY_LOST;
     59:       if (nv==eps->nconv+l+1) { eps->nconv = nconv; break; }
     60:     }
     61:     beta = b[nv-1];
     62:     DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
     63:     DSRestoreArrayReal(eps->ds,DS_MAT_D,&omega);
     64:     DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
     65:     if (l==0) {
     66:       DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
     67:     } else {
     68:       DSSetState(eps->ds,DS_STATE_RAW);
     69:     }
     70:     BVSetActiveColumns(eps->V,eps->nconv,nv);

     72:     /* Solve projected problem */
     73:     DSSolve(eps->ds,eps->eigr,eps->eigi);
     74:     DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
     75:     DSSynchronize(eps->ds,eps->eigr,eps->eigi);

     77:     /* Check convergence */
     78:     DSGetDimensions(eps->ds,NULL,NULL,NULL,NULL,&t);
     79: #if 0
     80:     /* take into account also left residual */
     81:     BVGetColumn(eps->V,nv,&u);
     82:     VecNorm(u,NORM_2,&beta1);
     83:     BVRestoreColumn(eps->V,nv,&u);
     84:     VecNorm(w,NORM_2,&beta2);  /* w contains B*V[nv] */
     85:     beta1 = PetscMax(beta1,beta2);
     86: #endif
     87:     EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,t-eps->nconv,beta*beta1,0.0,1.0,&k);
     88:     (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
     89:     nconv = k;

     91:     /* Update l */
     92:     if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
     93:     else {
     94:       l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
     95:       l = PetscMin(l,t);
     96:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
     97:       if (*(a+ld+k+l-1)!=0) {
     98:         if (k+l<t-1) l = l+1;
     99:         else l = l-1;
    100:       }
    101:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    102:     }
    103:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

    105:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    106:       if (breakdown) SETERRQ1(PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Breakdown in Indefinite Krylov-Schur (beta=%g)",beta);
    107:       else {
    108:         /* Prepare the Rayleigh quotient for restart */
    109:         DSGetArray(eps->ds,DS_MAT_Q,&Q);
    110:         DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    111:         DSGetArrayReal(eps->ds,DS_MAT_D,&omega);
    112:         b = a + ld;
    113:         r = a + 2*ld;
    114:         for (i=k;i<k+l;i++) {
    115:           r[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
    116:         }
    117:         b[k+l-1] = r[k+l-1];
    118:         omega[k+l] = omega[nv];
    119:         DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    120:         DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    121:         DSRestoreArrayReal(eps->ds,DS_MAT_D,&omega);
    122:       }
    123:     }
    124:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    125:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    126:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
    127:     MatDestroy(&U);

    129:     /* Move restart vector and update signature */
    130:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
    131:       BVCopyColumn(eps->V,nv,k+l);
    132:       DSGetArrayReal(eps->ds,DS_MAT_D,&omega);
    133:       VecCreateSeq(PETSC_COMM_SELF,k+l,&vomega);
    134:       VecGetArray(vomega,&aux);
    135:       for (i=0;i<k+l;i++) aux[i] = omega[i];
    136:       VecRestoreArray(vomega,&aux);
    137:       BVSetActiveColumns(eps->V,0,k+l);
    138:       BVSetSignature(eps->V,vomega);
    139:       VecDestroy(&vomega);
    140:       DSRestoreArrayReal(eps->ds,DS_MAT_D,&omega);
    141:     }

    143:     eps->nconv = k;
    144:     EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv);
    145:   }
    146:   DSSetDimensions(eps->ds,eps->nconv,0,0,0);
    147:   DSSetState(eps->ds,DS_STATE_RAW);
    148:   return(0);
    149: }