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/*                      

   SLEPc eigensolver: "subspace"

   Method: Subspace Iteration

   Algorithm:

       Subspace iteration with Rayleigh-Ritz projection and locking,

       based on the SRRIT implementation.

   References:

       [1] "Subspace Iteration in SLEPc", SLEPc Technical Report STR-3,

           available at http://www.grycap.upv.es/slepc.

   Last update: Feb 2009

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain

   This file is part of SLEPc.

   SLEPc is free software: you can redistribute it and/or modify it under  the

   terms of version 3 of the GNU Lesser General Public License as published by

   the Free Software Foundation.

   SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY

   WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS

   FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for

   more details.

   You  should have received a copy of the GNU Lesser General  Public  License

   along with SLEPc. If not, see <http://www.gnu.org/licenses/>.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*/

#include <slepc-private/epsimpl.h>                /*I "slepceps.h" I*/

#include <slepcblaslapack.h>

PetscErrorCode EPSSolve_Subspace(EPS);

typedef struct {

  Vec *AV;

} EPS_SUBSPACE;

#undef __FUNCT__  

#define __FUNCT__ "EPSSetUp_Subspace"

PetscErrorCode EPSSetUp_Subspace(EPS eps)

{

  PetscErrorCode ierr;

  EPS_SUBSPACE   *ctx = (EPS_SUBSPACE*)eps->data;

  PetscFunctionBegin;

  if (eps->ncv) { /* ncv set */

    if (eps->ncv<eps->nev) SETERRQ(((PetscObject)eps)->comm,1,"The value of ncv must be at least nev");

  }

  else if (eps->mpd) { /* mpd set */

    eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd);

  }

  else { /* neither set: defaults depend on nev being small or large */

    if (eps->nev<500) eps->ncv = PetscMin(eps->n,PetscMax(2*eps->nev,eps->nev+15));

    else { eps->mpd = 500; eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd); }

  }

  if (!eps->mpd) eps->mpd = eps->ncv;

  if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);

  if (!eps->which) { ierr = EPSDefaultSetWhich(eps);CHKERRQ(ierr); }

  if (eps->which!=EPS_LARGEST_MAGNITUDE && eps->which!=EPS_TARGET_MAGNITUDE) SETERRQ(((PetscObject)eps)->comm,1,"Wrong value of eps->which");

  if (!eps->extraction) {

    ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr);

  } else if (eps->extraction!=EPS_RITZ) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Unsupported extraction type\n");

  ierr = EPSAllocateSolution(eps);CHKERRQ(ierr);

  ierr = VecDuplicateVecs(eps->t,eps->ncv,&ctx->AV);CHKERRQ(ierr);

  if (eps->ishermitian) {

    ierr = PSSetType(eps->ps,PSHEP);CHKERRQ(ierr);

  } else {

    ierr = PSSetType(eps->ps,PSNHEP);CHKERRQ(ierr);

  }

  ierr = PSAllocate(eps->ps,eps->ncv);CHKERRQ(ierr);

  ierr = EPSDefaultGetWork(eps,1);CHKERRQ(ierr);

  /* dispatch solve method */

  if (eps->leftvecs) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Left vectors not supported in this solver");

  eps->ops->solve = EPSSolve_Subspace;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSubspaceFindGroup"

/*

   EPSSubspaceFindGroup - Find a group of nearly equimodular eigenvalues, provided

   in arrays wr and wi, according to the tolerance grptol. Also the 2-norms

   of the residuals must be passed in (rsd). Arrays are processed from index

   l to index m only. The output information is:

   ngrp - number of entries of the group

   ctr  - (w(l)+w(l+ngrp-1))/2

   ae   - average of wr(l),...,wr(l+ngrp-1)

   arsd - average of rsd(l),...,rsd(l+ngrp-1)

*/

static PetscErrorCode EPSSubspaceFindGroup(PetscInt l,PetscInt m,PetscScalar *wr,PetscScalar *wi,PetscReal *rsd,PetscReal grptol,PetscInt *ngrp,PetscReal *ctr,PetscReal *ae,PetscReal *arsd)

{

  PetscInt  i;

  PetscReal rmod,rmod1;

  PetscFunctionBegin;

  *ngrp = 0;

  *ctr = 0;

  rmod = SlepcAbsEigenvalue(wr[l],wi[l]);

  for (i=l;i<m;) {

    rmod1 = SlepcAbsEigenvalue(wr[i],wi[i]);

    if (PetscAbsReal(rmod-rmod1) > grptol*(rmod+rmod1)) break;

    *ctr = (rmod+rmod1)/2.0;

    if (wi[i] != 0.0) {

      (*ngrp)+=2;

      i+=2;

    } else {

      (*ngrp)++;

      i++;

    }

  }

  *ae = 0;

  *arsd = 0;

  if (*ngrp) {

    for (i=l;i<l+*ngrp;i++) {

      (*ae) += PetscRealPart(wr[i]);

      (*arsd) += rsd[i]*rsd[i];

    }

    *ae = *ae / *ngrp;

    *arsd = PetscSqrtScalar(*arsd / *ngrp);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSubspaceResidualNorms"

/*

   EPSSubspaceResidualNorms - Computes the column norms of residual vectors

   OP*V(1:n,l:m) - V*T(1:m,l:m), where, on entry, OP*V has been computed and

   stored in AV. ldt is the leading dimension of T. On exit, rsd(l) to

   rsd(m) contain the computed norms.

*/

static PetscErrorCode EPSSubspaceResidualNorms(Vec *V,Vec *AV,PetscScalar *T,PetscInt l,PetscInt m,PetscInt ldt,Vec w,PetscReal *rsd)

{

  PetscErrorCode ierr;

  PetscInt       i,k;

  PetscScalar    t;

  PetscFunctionBegin;

  for (i=l;i<m;i++) {

    if (i==m-1 || T[i+1+ldt*i]==0.0) k=i+1;

    else k=i+2;

    ierr = VecCopy(AV[i],w);CHKERRQ(ierr);

    ierr = SlepcVecMAXPBY(w,1.0,-1.0,k,T+ldt*i,V);CHKERRQ(ierr);

    ierr = VecDot(w,w,&t);CHKERRQ(ierr);

    rsd[i] = PetscRealPart(t);

  }

  for (i=l;i<m;i++) {

    if (i == m-1) {

      rsd[i] = PetscSqrtReal(rsd[i]);  

    } else if (T[i+1+(ldt*i)]==0.0) {

      rsd[i] = PetscSqrtReal(rsd[i]);

    } else {

      rsd[i] = PetscSqrtReal((rsd[i]+rsd[i+1])/2.0);

      rsd[i+1] = rsd[i];

      i++;

    }

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSolve_Subspace"

PetscErrorCode EPSSolve_Subspace(EPS eps)

{

  PetscErrorCode ierr;

  EPS_SUBSPACE   *ctx = (EPS_SUBSPACE*)eps->data;

  PetscInt       i,k,ld,ngrp,nogrp,*itrsd,*itrsdold,

                 nxtsrr,idsrr,idort,nxtort,nv,ncv = eps->ncv,its;

  PetscScalar    *T,*U;

  PetscReal      arsd,oarsd,ctr,octr,ae,oae,*rsd,norm,tcond=1.0;

  PetscBool      breakdown;

  /* Parameters */

  PetscInt       init = 5;        /* Number of initial iterations */

  PetscReal      stpfac = 1.5,    /* Max num of iter before next SRR step */

                 alpha = 1.0,     /* Used to predict convergence of next residual */

                 beta = 1.1,      /* Used to predict convergence of next residual */

                 grptol = 1e-8,   /* Tolerance for EPSSubspaceFindGroup */

                 cnvtol = 1e-6;   /* Convergence criterion for cnv */

  PetscInt       orttol = 2;      /* Number of decimal digits whose loss

                                     can be tolerated in orthogonalization */

  PetscFunctionBegin;

  its = 0;

  ierr = PetscMalloc(sizeof(PetscReal)*ncv,&rsd);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(PetscInt)*ncv,&itrsd);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(PetscInt)*ncv,&itrsdold);CHKERRQ(ierr);

  ierr = PSGetLeadingDimension(eps->ps,&ld);CHKERRQ(ierr);

  for (i=0;i<ncv;i++) {

    rsd[i] = 0.0;

    itrsd[i] = -1;

  }

  /* Complete the initial basis with random vectors and orthonormalize them */

  k = eps->nini;

  while (k<ncv) {

    ierr = SlepcVecSetRandom(eps->V[k],eps->rand);CHKERRQ(ierr);

    ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,k,PETSC_NULL,eps->V,eps->V[k],PETSC_NULL,&norm,&breakdown);CHKERRQ(ierr);

    if (norm>0.0 && !breakdown) {

      ierr = VecScale(eps->V[k],1.0/norm);CHKERRQ(ierr);

      k++;

    }

  }

  while (eps->its<eps->max_it) {

    eps->its++;

    nv = PetscMin(eps->nconv+eps->mpd,ncv);

    ierr = PSSetDimensions(eps->ps,nv,eps->nconv,0);CHKERRQ(ierr);

    /* Find group in previously computed eigenvalues */

    ierr = EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,rsd,grptol,&nogrp,&octr,&oae,&oarsd);CHKERRQ(ierr);

    /* AV(:,idx) = OP * V(:,idx) */

    for (i=eps->nconv;i<nv;i++) {

      ierr = STApply(eps->OP,eps->V[i],ctx->AV[i]);CHKERRQ(ierr);

    }

    /* T(:,idx) = V' * AV(:,idx) */

    ierr = PSGetArray(eps->ps,PS_MAT_A,&T);CHKERRQ(ierr);

    for (i=eps->nconv;i<nv;i++) {

      ierr = VecMDot(ctx->AV[i],nv,eps->V,T+i*ld);CHKERRQ(ierr);

    }

    ierr = PSRestoreArray(eps->ps,PS_MAT_A,&T);CHKERRQ(ierr);

    ierr = PSSetState(eps->ps,PS_STATE_RAW);CHKERRQ(ierr);

    /* Solve projected problem */

    ierr = PSSolve(eps->ps,eps->eigr,eps->eigi);CHKERRQ(ierr);

    ierr = PSSort(eps->ps,eps->eigr,eps->eigi,eps->which_func,eps->which_ctx);CHKERRQ(ierr);

    /* Update vectors V(:,idx) = V * U(:,idx) */

    ierr = PSGetArray(eps->ps,PS_MAT_Q,&U);CHKERRQ(ierr);

    ierr = SlepcUpdateVectors(nv,ctx->AV,eps->nconv,nv,U,ld,PETSC_FALSE);CHKERRQ(ierr);

    ierr = SlepcUpdateVectors(nv,eps->V,eps->nconv,nv,U,ld,PETSC_FALSE);CHKERRQ(ierr);

    ierr = PSRestoreArray(eps->ps,PS_MAT_Q,&U);CHKERRQ(ierr);

    /* Convergence check */

    ierr = PSGetArray(eps->ps,PS_MAT_A,&T);CHKERRQ(ierr);

    ierr = EPSSubspaceResidualNorms(eps->V,ctx->AV,T,eps->nconv,nv,ld,eps->work[0],rsd);CHKERRQ(ierr);

    ierr = PSRestoreArray(eps->ps,PS_MAT_A,&T);CHKERRQ(ierr);

    for (i=eps->nconv;i<nv;i++) {

      itrsdold[i] = itrsd[i];

      itrsd[i] = its;

      eps->errest[i] = rsd[i];

    }

    for (;;) {

      /* Find group in currently computed eigenvalues */

      ierr = EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,eps->errest,grptol,&ngrp,&ctr,&ae,&arsd);CHKERRQ(ierr);

      if (ngrp!=nogrp) break;

      if (ngrp==0) break;

      if (PetscAbsScalar(ae-oae)>ctr*cnvtol*(itrsd[eps->nconv]-itrsdold[eps->nconv])) break;

      if (arsd>ctr*eps->tol) break;

      eps->nconv = eps->nconv + ngrp;

      if (eps->nconv>=nv) break;

    }

    ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);CHKERRQ(ierr);

    if (eps->nconv>=eps->nev) break;

    /* Compute nxtsrr (iteration of next projection step) */

    nxtsrr = PetscMin(eps->max_it,PetscMax((PetscInt)floor(stpfac*its),init));

    if (ngrp!=nogrp || ngrp==0 || arsd>=oarsd) {

      idsrr = nxtsrr - its;

    } else {

      idsrr = (PetscInt)floor(alpha+beta*(itrsdold[eps->nconv]-itrsd[eps->nconv])*log(arsd/eps->tol)/log(arsd/oarsd));

      idsrr = PetscMax(1,idsrr);

    }

    nxtsrr = PetscMin(nxtsrr,its+idsrr);

    /* Compute nxtort (iteration of next orthogonalization step) */

    ierr = PSCond(eps->ps,&tcond);CHKERRQ(ierr);

    idort = PetscMax(1,(PetscInt)floor(orttol/PetscMax(1,log10(tcond))));    

    nxtort = PetscMin(its+idort,nxtsrr);

    /* V(:,idx) = AV(:,idx) */

    for (i=eps->nconv;i<nv;i++) {

      ierr = VecCopy(ctx->AV[i],eps->V[i]);CHKERRQ(ierr);

    }

    its++;

    /* Orthogonalization loop */

    do {

      while (its<nxtort) {

        /* AV(:,idx) = OP * V(:,idx) */

        for (i=eps->nconv;i<nv;i++) {

          ierr = STApply(eps->OP,eps->V[i],ctx->AV[i]);CHKERRQ(ierr);

        }

        /* V(:,idx) = AV(:,idx) with normalization */

        for (i=eps->nconv;i<nv;i++) {

          ierr = VecCopy(ctx->AV[i],eps->V[i]);CHKERRQ(ierr);

          ierr = VecNorm(eps->V[i],NORM_INFINITY,&norm);CHKERRQ(ierr);

          ierr = VecScale(eps->V[i],1/norm);CHKERRQ(ierr);

        }

        its++;

      }

      /* Orthonormalize vectors */

      for (i=eps->nconv;i<nv;i++) {

        ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,i,PETSC_NULL,eps->V,eps->V[i],PETSC_NULL,&norm,&breakdown);CHKERRQ(ierr);

        if (breakdown) {

          ierr = SlepcVecSetRandom(eps->V[i],eps->rand);CHKERRQ(ierr);

          ierr = IPOrthogonalize(eps->ip,eps->nds,eps->DS,i,PETSC_NULL,eps->V,eps->V[i],PETSC_NULL,&norm,&breakdown);CHKERRQ(ierr);

        }

        ierr = VecScale(eps->V[i],1/norm);CHKERRQ(ierr);

      }

      nxtort = PetscMin(its+idort,nxtsrr);

    } while (its<nxtsrr);

  }

  ierr = PetscFree(rsd);CHKERRQ(ierr);

  ierr = PetscFree(itrsd);CHKERRQ(ierr);

  ierr = PetscFree(itrsdold);CHKERRQ(ierr);

  if (eps->nconv == eps->nev) eps->reason = EPS_CONVERGED_TOL;

  else eps->reason = EPS_DIVERGED_ITS;

  /* truncate Schur decomposition and change the state to raw so that

     PSVectors() computes eigenvectors from scratch */

  ierr = PSSetDimensions(eps->ps,eps->nconv,0,0);CHKERRQ(ierr);

  ierr = PSSetState(eps->ps,PS_STATE_RAW);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSReset_Subspace"

PetscErrorCode EPSReset_Subspace(EPS eps)

{

  PetscErrorCode ierr;

  EPS_SUBSPACE   *ctx = (EPS_SUBSPACE*)eps->data;

  PetscFunctionBegin;

  ierr = VecDestroyVecs(eps->ncv,&ctx->AV);CHKERRQ(ierr);

  ierr = EPSReset_Default(eps);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDestroy_Subspace"

PetscErrorCode EPSDestroy_Subspace(EPS eps)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = PetscFree(eps->data);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "EPSCreate_Subspace"

PetscErrorCode EPSCreate_Subspace(EPS eps)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = PetscNewLog(eps,EPS_SUBSPACE,&eps->data);CHKERRQ(ierr);

  eps->ops->setup                = EPSSetUp_Subspace;

  eps->ops->destroy              = EPSDestroy_Subspace;

  eps->ops->reset                = EPSReset_Subspace;

  eps->ops->backtransform        = EPSBackTransform_Default;

  eps->ops->computevectors       = EPSComputeVectors_Schur;

  PetscFunctionReturn(0);

}

EXTERN_C_END