Date: 2013-09-02T10:07:24+00:00

Actual source code: qeplin_s2.c

      1: /*

      3:    Linearization for Hermitian QEP, companion form 2.

      5:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      6:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      7:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

      9:    This file is part of SLEPc.

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

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

     20:    You  should have received a copy of the GNU Lesser General  Public  License
     21:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     22:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     23: */

     25: #include <slepc-private/qepimpl.h>         /*I "slepcqep.h" I*/
     26:  #include linearp.h

     28: /*
     29:     Given the quadratic problem (l^2*M + l*C + K)*x = 0 the following
     30:     linearization is employed:

     32:       A*z = l*B*z   where   A = [ -K   0 ]     B = [ C  M ]     z = [  x  ]
     33:                                 [  0   M ]         [ M  0 ]         [ l*x ]
     34:  */

     38: PetscErrorCode MatMult_Linear_S2A(Mat A,Vec x,Vec y)
     39: {
     40:   PetscErrorCode    ierr;
     41:   QEP_LINEAR        *ctx;
     42:   const PetscScalar *px;
     43:   PetscScalar       *py;
     44:   PetscInt          m;

     47:   MatShellGetContext(A,(void**)&ctx);
     48:   MatGetLocalSize(ctx->M,&m,NULL);
     49:   VecGetArrayRead(x,&px);
     50:   VecGetArray(y,&py);
     51:   VecPlaceArray(ctx->x1,px);
     52:   VecPlaceArray(ctx->x2,px+m);
     53:   VecPlaceArray(ctx->y1,py);
     54:   VecPlaceArray(ctx->y2,py+m);
     55:   /* y1 = -K*x1 */
     56:   MatMult(ctx->K,ctx->x1,ctx->y1);
     57:   VecScale(ctx->y1,-1.0);
     58:   /* y2 = M*x2 */
     59:   MatMult(ctx->M,ctx->x2,ctx->y2);
     60:   VecScale(ctx->y2,ctx->sfactor*ctx->sfactor);
     61:   VecResetArray(ctx->x1);
     62:   VecResetArray(ctx->x2);
     63:   VecResetArray(ctx->y1);
     64:   VecResetArray(ctx->y2);
     65:   VecRestoreArrayRead(x,&px);
     66:   VecRestoreArray(y,&py);
     67:   return(0);
     68: }

     72: PetscErrorCode MatMult_Linear_S2B(Mat B,Vec x,Vec y)
     73: {
     74:   PetscErrorCode    ierr;
     75:   QEP_LINEAR        *ctx;
     76:   const PetscScalar *px;
     77:   PetscScalar       *py;
     78:   PetscInt          m;

     81:   MatShellGetContext(B,(void**)&ctx);
     82:   MatGetLocalSize(ctx->M,&m,NULL);
     83:   VecGetArrayRead(x,&px);
     84:   VecGetArray(y,&py);
     85:   VecPlaceArray(ctx->x1,px);
     86:   VecPlaceArray(ctx->x2,px+m);
     87:   VecPlaceArray(ctx->y1,py);
     88:   VecPlaceArray(ctx->y2,py+m);
     89:   /* y1 = C*x1 + M*x2 */
     90:   MatMult(ctx->C,ctx->x1,ctx->y1);
     91:   VecScale(ctx->y1,ctx->sfactor);
     92:   MatMult(ctx->M,ctx->x2,ctx->y2);
     93:   VecAXPY(ctx->y1,ctx->sfactor*ctx->sfactor,ctx->y2);
     94:   /* y2 = M*x1 */
     95:   MatMult(ctx->M,ctx->x1,ctx->y2);
     96:   VecScale(ctx->y2,ctx->sfactor*ctx->sfactor);
     97:   VecResetArray(ctx->x1);
     98:   VecResetArray(ctx->x2);
     99:   VecResetArray(ctx->y1);
    100:   VecResetArray(ctx->y2);
    101:   VecRestoreArrayRead(x,&px);
    102:   VecRestoreArray(y,&py);
    103:   return(0);
    104: }

    108: PetscErrorCode MatGetDiagonal_Linear_S2A(Mat A,Vec diag)
    109: {
    111:   QEP_LINEAR     *ctx;
    112:   PetscScalar    *pd;
    113:   PetscInt       m;

    116:   MatShellGetContext(A,(void**)&ctx);
    117:   MatGetLocalSize(ctx->M,&m,NULL);
    118:   VecGetArray(diag,&pd);
    119:   VecPlaceArray(ctx->x1,pd);
    120:   VecPlaceArray(ctx->x2,pd+m);
    121:   MatGetDiagonal(ctx->K,ctx->x1);
    122:   VecScale(ctx->x1,-1.0);
    123:   MatGetDiagonal(ctx->M,ctx->x2);
    124:   VecScale(ctx->x2,ctx->sfactor*ctx->sfactor);
    125:   VecResetArray(ctx->x1);
    126:   VecResetArray(ctx->x2);
    127:   VecRestoreArray(diag,&pd);
    128:   return(0);
    129: }

    133: PetscErrorCode MatGetDiagonal_Linear_S2B(Mat B,Vec diag)
    134: {
    136:   QEP_LINEAR     *ctx;
    137:   PetscScalar    *pd;
    138:   PetscInt       m;

    141:   MatShellGetContext(B,(void**)&ctx);
    142:   MatGetLocalSize(ctx->M,&m,NULL);
    143:   VecGetArray(diag,&pd);
    144:   VecPlaceArray(ctx->x1,pd);
    145:   VecPlaceArray(ctx->x2,pd+m);
    146:   MatGetDiagonal(ctx->C,ctx->x1);
    147:   VecScale(ctx->x1,ctx->sfactor);
    148:   VecSet(ctx->x2,0.0);
    149:   VecResetArray(ctx->x1);
    150:   VecResetArray(ctx->x2);
    151:   VecRestoreArray(diag,&pd);
    152:   return(0);
    153: }

    157: PetscErrorCode MatCreateExplicit_Linear_S2A(MPI_Comm comm,QEP_LINEAR *ctx,Mat *A)
    158: {

    162:   SlepcMatTile(-1.0,ctx->K,0.0,ctx->M,0.0,ctx->M,ctx->sfactor*ctx->sfactor,ctx->M,A);
    163:   return(0);
    164: }

    168: PetscErrorCode MatCreateExplicit_Linear_S2B(MPI_Comm comm,QEP_LINEAR *ctx,Mat *B)
    169: {

    173:   SlepcMatTile(ctx->sfactor,ctx->C,ctx->sfactor*ctx->sfactor,ctx->M,ctx->sfactor*ctx->sfactor,ctx->M,0.0,ctx->M,B);
    174:   return(0);
    175: }