Actual source code: mfnkrylov.c

slepc-3.7.4 2017-05-17
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  1: /*

  3:    SLEPc matrix function solver: "krylov"

  5:    Method: Arnoldi with Eiermann-Ernst restart

  7:    Algorithm:

  9:        Build Arnoldi approximations using f(H) for the Hessenberg matrix H,
 10:        restart by discarding the Krylov basis but keeping H.

 12:    References:

 14:        [1] M. Eiermann and O. Ernst, "A restarted Krylov subspace method
 15:            for the evaluation of matrix functions", SIAM J. Numer. Anal.
 16:            44(6):2481-2504, 2006.

 18:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 19:    SLEPc - Scalable Library for Eigenvalue Problem Computations
 20:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

 22:    This file is part of SLEPc.

 24:    SLEPc is free software: you can redistribute it and/or modify it under  the
 25:    terms of version 3 of the GNU Lesser General Public License as published by
 26:    the Free Software Foundation.

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

 33:    You  should have received a copy of the GNU Lesser General  Public  License
 34:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 35:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 36: */

 38: #include <slepc/private/mfnimpl.h>
 39: #include <slepcblaslapack.h>

 43: PetscErrorCode MFNSetUp_Krylov(MFN mfn)
 44: {
 46:   PetscInt       N;

 49:   MatGetSize(mfn->A,&N,NULL);
 50:   if (!mfn->ncv) mfn->ncv = PetscMin(30,N);
 51:   if (!mfn->max_it) mfn->max_it = 100;
 52:   MFNAllocateSolution(mfn,1);
 53:   return(0);
 54: }

 58: PetscErrorCode MFNBasicArnoldi(MFN mfn,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,PetscReal *beta,PetscBool *breakdown)
 59: {
 61:   PetscInt       j,m = *M;
 62:   Vec            vj,vj1;

 65:   BVSetActiveColumns(mfn->V,0,m);
 66:   for (j=k;j<m;j++) {
 67:     BVGetColumn(mfn->V,j,&vj);
 68:     BVGetColumn(mfn->V,j+1,&vj1);
 69:     MatMult(mfn->A,vj,vj1);
 70:     BVRestoreColumn(mfn->V,j,&vj);
 71:     BVRestoreColumn(mfn->V,j+1,&vj1);
 72:     BVOrthogonalizeColumn(mfn->V,j+1,H+ldh*j,beta,breakdown);
 73:     H[j+1+ldh*j] = *beta;
 74:     if (*breakdown) {
 75:       *M = j+1;
 76:       break;
 77:     } else {
 78:       BVScaleColumn(mfn->V,j+1,1.0/(*beta));
 79:     }
 80:   }
 81:   return(0);
 82: }

 86: PetscErrorCode MFNSolve_Krylov(MFN mfn,Vec b,Vec x)
 87: {
 89:   PetscInt       n=0,m,ld,ldh,j;
 90:   PetscBLASInt   m_,inc=1;
 91:   Mat            G=NULL,H=NULL;
 92:   Vec            F=NULL;
 93:   PetscScalar    *array,*farray,*garray,*harray;
 94:   PetscReal      beta,betaold=0.0,nrm=1.0;
 95:   PetscBool      breakdown,set,flg,symm=PETSC_FALSE;

 98:   m  = mfn->ncv;
 99:   ld = m+1;
100:   PetscCalloc1(ld*ld,&array);

102:   /* set initial vector to b/||b|| */
103:   BVInsertVec(mfn->V,0,b);
104:   BVScaleColumn(mfn->V,0,1.0/mfn->bnorm);
105:   VecSet(x,0.0);

107:   /* Restart loop */
108:   while (mfn->reason == MFN_CONVERGED_ITERATING) {
109:     mfn->its++;

111:     /* compute Arnoldi factorization */
112:     MFNBasicArnoldi(mfn,array,ld,0,&m,&beta,&breakdown);

114:     /* save previous Hessenberg matrix in G; allocate new storage for H and f(H) */
115:     if (mfn->its>1) { G = H; H = NULL; }
116:     ldh = n+m;
117:     MFN_CreateVec(ldh,&F);
118:     MFN_CreateDenseMat(ldh,&H);

120:     /* glue together the previous H and the new H obtained with Arnoldi */
121:     MatDenseGetArray(H,&harray);
122:     for (j=0;j<m;j++) {
123:       PetscMemcpy(harray+n+(j+n)*ldh,array+j*ld,m*sizeof(PetscScalar));
124:     }
125:     if (mfn->its>1) {
126:       MatDenseGetArray(G,&garray);
127:       for (j=0;j<n;j++) {
128:         PetscMemcpy(harray+j*ldh,garray+j*n,n*sizeof(PetscScalar));
129:       }
130:       MatDenseRestoreArray(G,&garray);
131:       MatDestroy(&G);
132:       harray[n+(n-1)*ldh] = betaold;
133:     }
134:     MatDenseRestoreArray(H,&harray);

136:     if (mfn->its==1) {
137:       /* set symmetry flag of H from A */
138:       MatIsHermitianKnown(mfn->A,&set,&flg);
139:       symm = set? flg: PETSC_FALSE;
140:       if (symm) {
141:         MatSetOption(H,MAT_HERMITIAN,PETSC_TRUE);
142:       }
143:     }

145:     /* evaluate f(H) */
146:     FNEvaluateFunctionMatVec(mfn->fn,H,F);

148:     /* x += ||b||*V*f(H)*e_1 */
149:     VecGetArray(F,&farray);
150:     PetscBLASIntCast(m,&m_);
151:     nrm = BLASnrm2_(&m_,farray+n,&inc);   /* relative norm of the update ||u||/||b|| */
152:     MFNMonitor(mfn,mfn->its,nrm);
153:     for (j=0;j<m;j++) farray[j+n] *= mfn->bnorm;
154:     BVSetActiveColumns(mfn->V,0,m);
155:     BVMultVec(mfn->V,1.0,1.0,x,farray+n);
156:     VecRestoreArray(F,&farray);

158:     /* check convergence */
159:     if (mfn->its>1) {
160:       if (mfn->its >= mfn->max_it) mfn->reason = MFN_DIVERGED_ITS;
161:       if (m<mfn->ncv || breakdown || beta==0.0 || nrm<mfn->tol) mfn->reason = MFN_CONVERGED_TOL;
162:     }

164:     /* restart with vector v_{m+1} */
165:     if (mfn->reason == MFN_CONVERGED_ITERATING) {
166:       BVCopyColumn(mfn->V,m,0);
167:       n += m;
168:       betaold = beta;
169:     }
170:   }

172:   MatDestroy(&H);
173:   MatDestroy(&G);
174:   VecDestroy(&F);
175:   PetscFree(array);
176:   return(0);
177: }

181: PETSC_EXTERN PetscErrorCode MFNCreate_Krylov(MFN mfn)
182: {
184:   mfn->ops->solve          = MFNSolve_Krylov;
185:   mfn->ops->setup          = MFNSetUp_Krylov;
186:   return(0);
187: }