Actual source code: ex3.c

slepc-3.20.1 2023-11-27
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

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

 16: #include <slepceps.h>

 18: /*
 19:    User-defined routines
 20: */
 21: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
 22: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);

 24: int main(int argc,char **argv)
 25: {
 26:   Mat            A;               /* operator matrix */
 27:   EPS            eps;             /* eigenproblem solver context */
 28:   EPSType        type;
 29:   PetscMPIInt    size;
 30:   PetscInt       N,n=10,nev;
 31:   PetscBool      terse;

 33:   PetscFunctionBeginUser;
 34:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
 35:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
 36:   PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");

 38:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 39:   N = n*n;
 40:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n));

 42:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43:        Create the operator matrix that defines the eigensystem, Ax=kx
 44:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 46:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A));
 47:   PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D));
 48:   PetscCall(MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D));
 49:   PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D));

 51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 52:                 Create the eigensolver and set various options
 53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 55:   /*
 56:      Create eigensolver context
 57:   */
 58:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

 60:   /*
 61:      Set operators. In this case, it is a standard eigenvalue problem
 62:   */
 63:   PetscCall(EPSSetOperators(eps,A,NULL));
 64:   PetscCall(EPSSetProblemType(eps,EPS_HEP));

 66:   /*
 67:      Set solver parameters at runtime
 68:   */
 69:   PetscCall(EPSSetFromOptions(eps));

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:                       Solve the eigensystem
 73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 75:   PetscCall(EPSSolve(eps));

 77:   /*
 78:      Optional: Get some information from the solver and display it
 79:   */
 80:   PetscCall(EPSGetType(eps,&type));
 81:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
 82:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
 83:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:                     Display solution and clean up
 87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 89:   /* show detailed info unless -terse option is given by user */
 90:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
 91:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
 92:   else {
 93:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
 94:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
 95:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
 96:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
 97:   }
 98:   PetscCall(EPSDestroy(&eps));
 99:   PetscCall(MatDestroy(&A));
100:   PetscCall(SlepcFinalize());
101:   return 0;
102: }

104: /*
105:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
106:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
107:     DU on the superdiagonal.
108:  */
109: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
110: {
111:   PetscScalar dd,dl,du;
112:   int         j;

114:   dd  = 4.0;
115:   dl  = -1.0;
116:   du  = -1.0;

118:   y[0] =  dd*x[0] + du*x[1];
119:   for (j=1;j<nx-1;j++)
120:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
121:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
122: }

124: /*
125:     Matrix-vector product subroutine for the 2D Laplacian.

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

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

132:                  | T -I          |
133:                  |-I  T -I       |
134:              A = |   -I  T       |
135:                  |        ...  -I|
136:                  |           -I T|

138:     The subroutine TV is called to compute y<--T*x.
139:  */
140: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
141: {
142:   void              *ctx;
143:   int               nx,lo,i,j;
144:   const PetscScalar *px;
145:   PetscScalar       *py;

147:   PetscFunctionBeginUser;
148:   PetscCall(MatShellGetContext(A,&ctx));
149:   nx = *(int*)ctx;
150:   PetscCall(VecGetArrayRead(x,&px));
151:   PetscCall(VecGetArray(y,&py));

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

156:   for (j=2;j<nx;j++) {
157:     lo = (j-1)*nx;
158:     tv(nx,&px[lo],&py[lo]);
159:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
160:   }

162:   lo = (nx-1)*nx;
163:   tv(nx,&px[lo],&py[lo]);
164:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

166:   PetscCall(VecRestoreArrayRead(x,&px));
167:   PetscCall(VecRestoreArray(y,&py));
168:   PetscFunctionReturn(PETSC_SUCCESS);
169: }

171: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
172: {
173:   PetscFunctionBeginUser;
174:   PetscCall(VecSet(diag,4.0));
175:   PetscFunctionReturn(PETSC_SUCCESS);
176: }

178: /*TEST

180:    test:
181:       suffix: 1
182:       args: -n 72 -eps_nev 4 -eps_ncv 20 -terse
183:       requires: !single

185: TEST*/