Actual source code: ex13.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:       SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:       Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain

  6:       This file is part of SLEPc. See the README file for conditions of use
  7:       and additional information.
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Generalized Symmetric eigenproblem.\n\n"
 12:   "The problem is Ax = lambda Bx, with:\n"
 13:   "   A = Laplacian operator in 2-D\n"
 14:   "   B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"
 15:   "The command line options are:\n"
 16:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 17:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n"
 18:   "  -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";

 20:  #include slepceps.h

 24: int main( int argc, char **argv )
 25: {
 26:   Mat                  A, B;                  /* matrices */
 27:   EPS                  eps;                  /* eigenproblem solver context */
 28:   EPSType              type;
 29:   PetscReal            error, tol, re, im;
 30:   PetscScalar          kr, ki;
 32:   PetscInt             N, n=10, m, Istart, Iend, II, J;
 33:   int                  nev, maxit, i, j, its, nconv, nulldim=0;
 34:   PetscScalar          v;
 35:   PetscTruth           flag;

 37:   SlepcInitialize(&argc,&argv,(char*)0,help);

 39:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 40:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);
 41:   if( flag==PETSC_FALSE ) m=n;
 42:   N = n*m;
 43:   PetscOptionsGetInt(PETSC_NULL,"-nulldim",&nulldim,PETSC_NULL);
 44:   PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%d (%dx%d grid), null(B)=%d\n\n",N,n,m,nulldim);

 46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 47:      Compute the matrices that define the eigensystem, Ax=kBx
 48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 50:   MatCreate(PETSC_COMM_WORLD,&A);
 51:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 52:   MatSetFromOptions(A);
 53: 
 54:   MatCreate(PETSC_COMM_WORLD,&B);
 55:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
 56:   MatSetFromOptions(B);

 58:   MatGetOwnershipRange(A,&Istart,&Iend);
 59:   for( II=Istart; II<Iend; II++ ) {
 60:     v = -1.0; i = II/n; j = II-i*n;
 61:     if(i>0) { J=II-n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); }
 62:     if(i<m-1) { J=II+n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); }
 63:     if(j>0) { J=II-1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); }
 64:     if(j<n-1) { J=II+1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); }
 65:     v=4.0; MatSetValues(A,1,&II,1,&II,&v,INSERT_VALUES);
 66:     if (II>=nulldim) { v=4.0; MatSetValues(B,1,&II,1,&II,&v,INSERT_VALUES); }
 67:   }

 69:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 70:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 71:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 72:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 75:                 Create the eigensolver and set various options
 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 78:   /* 
 79:      Create eigensolver context
 80:   */
 81:   EPSCreate(PETSC_COMM_WORLD,&eps);

 83:   /* 
 84:      Set operators. In this case, it is a generalized eigenvalue problem
 85:   */
 86:   EPSSetOperators(eps,A,B);
 87:   EPSSetProblemType(eps,EPS_GHEP);

 89:   /*
 90:      Set solver parameters at runtime
 91:   */
 92:   EPSSetFromOptions(eps);

 94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 95:                       Solve the eigensystem
 96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 98:   EPSSolve(eps);
 99:   EPSGetIterationNumber(eps, &its);
100:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);

102:   /*
103:      Optional: Get some information from the solver and display it
104:   */
105:   EPSGetType(eps,&type);
106:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
107:   EPSGetDimensions(eps,&nev,PETSC_NULL);
108:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
109:   EPSGetTolerances(eps,&tol,&maxit);
110:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);

112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
113:                     Display solution and clean up
114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

116:   /* 
117:      Get number of converged approximate eigenpairs
118:   */
119:   EPSGetConverged(eps,&nconv);
120:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
121: 

123:   if (nconv>0) {
124:     /*
125:        Display eigenvalues and relative errors
126:     */
127:     PetscPrintf(PETSC_COMM_WORLD,
128:          "           k          ||Ax-kBx||/||kx||\n"
129:          "   ----------------- ------------------\n" );

131:     for( i=0; i<nconv; i++ ) {
132:       /* 
133:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
134:         ki (imaginary part)
135:       */
136:       EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
137:       /*
138:          Compute the relative error associated to each eigenpair
139:       */
140:       EPSComputeRelativeError(eps,i,&error);

142: #ifdef PETSC_USE_COMPLEX
143:       re = PetscRealPart(kr);
144:       im = PetscImaginaryPart(kr);
145: #else
146:       re = kr;
147:       im = ki;
148: #endif 
149:       if (im!=0.0) {
150:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12f\n",re,im,error);
151:       } else {
152:         PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12f\n",re,error);
153:       }
154:     }
155:     PetscPrintf(PETSC_COMM_WORLD,"\n" );
156:   }
157: 
158:   /* 
159:      Free work space
160:   */
161:   EPSDestroy(eps);
162:   MatDestroy(A);
163:   SlepcFinalize();
164:   return 0;
165: }