Actual source code: test8.c

slepc-3.7.2 2016-07-19
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

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

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

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */

 22: static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
 23:   "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
 24:   "The command line options are:\n"
 25:   "  -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";

 27: #include <slepceps.h>
 28: #include <petscblaslapack.h>

 30: /*
 31:    User-defined routines
 32: */
 33: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
 34: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);

 38: int main(int argc,char **argv)
 39: {
 40:   Mat            A;               /* operator matrix */
 41:   EPS            eps;             /* eigenproblem solver context */
 42:   EPSType        type;
 43:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
 44:   PetscMPIInt    size;
 45:   PetscInt       N,n=10,nev;

 48:   SlepcInitialize(&argc,&argv,(char*)0,help);
 49:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 50:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only");

 52:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 53:   N = n*n;
 54:   PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%D (%Dx%D grid)\n\n",N,n,n);

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57:      Compute the operator matrix that defines the eigensystem, Ax=kx
 58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 60:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
 61:   MatSetFromOptions(A);
 62:   MatShellSetOperation(A,MATOP_MULT,(void(*)())MatMult_Laplacian2D);
 63:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatMult_Laplacian2D);
 64:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Laplacian2D);

 66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 67:                 Create the eigensolver and set various options
 68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 70:   /*
 71:      Create eigensolver context
 72:   */
 73:   EPSCreate(PETSC_COMM_WORLD,&eps);

 75:   /*
 76:      Set operators. In this case, it is a standard eigenvalue problem
 77:   */
 78:   EPSSetOperators(eps,A,NULL);
 79:   EPSSetProblemType(eps,EPS_HEP);
 80:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

 82:   /*
 83:      Set solver parameters at runtime
 84:   */
 85:   EPSSetFromOptions(eps);

 87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 88:                       Solve the eigensystem
 89:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 91:   EPSSolve(eps);

 93:   /*
 94:      Optional: Get some information from the solver and display it
 95:   */
 96:   EPSGetType(eps,&type);
 97:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
 98:   EPSGetDimensions(eps,&nev,NULL,NULL);
 99:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:                     Display solution and clean up
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

105:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
106:   EPSDestroy(&eps);
107:   MatDestroy(&A);
108:   SlepcFinalize();
109:   return ierr;
110: }

112: /*
113:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
114:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
115:     DU on the superdiagonal.
116:  */
117: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
118: {
119:   PetscScalar dd,dl,du;
120:   int         j;

122:   dd  = 4.0;
123:   dl  = -1.0;
124:   du  = -1.0;

126:   y[0] =  dd*x[0] + du*x[1];
127:   for (j=1;j<nx-1;j++)
128:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
129:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
130: }

134: /*
135:     Matrix-vector product subroutine for the 2D Laplacian.

137:     The matrix used is the 2 dimensional discrete Laplacian on unit square with
138:     zero Dirichlet boundary condition.

140:     Computes y <-- A*x, where A is the block tridiagonal matrix

142:                  | T -I          |
143:                  |-I  T -I       |
144:              A = |   -I  T       |
145:                  |        ...  -I|
146:                  |           -I T|

148:     The subroutine TV is called to compute y<--T*x.
149:  */
150: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
151: {
152:   void              *ctx;
153:   int               nx,lo,i,j;
154:   const PetscScalar *px;
155:   PetscScalar       *py;
156:   PetscErrorCode    ierr;

159:   MatShellGetContext(A,&ctx);
160:   nx = *(int*)ctx;
161:   VecGetArrayRead(x,&px);
162:   VecGetArray(y,&py);

164:   tv(nx,&px[0],&py[0]);
165:   for (i=0;i<nx;i++) py[i] -= px[nx+i];

167:   for (j=2;j<nx;j++) {
168:     lo = (j-1)*nx;
169:     tv(nx,&px[lo],&py[lo]);
170:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
171:   }

173:   lo = (nx-1)*nx;
174:   tv(nx,&px[lo],&py[lo]);
175:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

177:   VecRestoreArrayRead(x,&px);
178:   VecRestoreArray(y,&py);
179:   return(0);
180: }

184: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
185: {

189:   VecSet(diag,4.0);
190:   return(0);
191: }