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) 2002-2011, Universitat Politecnica de Valencia, Spain

  9:    This file is part of SLEPc.
 10:       
 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 <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;
 45: 
 47:   MatShellGetContext(A,(void**)&ctx);
 48:   MatGetLocalSize(ctx->M,&m,PETSC_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;
 79: 
 81:   MatShellGetContext(B,(void**)&ctx);
 82:   MatGetLocalSize(ctx->M,&m,PETSC_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;
114: 
116:   MatShellGetContext(A,(void**)&ctx);
117:   MatGetLocalSize(ctx->M,&m,PETSC_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;
139: 
141:   MatShellGetContext(B,(void**)&ctx);
142:   MatGetLocalSize(ctx->M,&m,PETSC_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: {
160: 
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: }