Actual source code: ex11.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[] = "Computes the smallest nonzero eigenvalue of the Laplacian of a graph.\n\n"
 12:   "This example illustrates EPSAttachDeflationSpace(). The example graph corresponds to a "
 13:   "2-D regular mesh. The command line options are:\n"
 14:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 15:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

 17:  #include slepceps.h

 21: int main( int argc, char **argv )
 22: {
 23:   Mat                  A;                  /* operator matrix */
 24:   Vec                  x;
 25:   EPS                  eps;                  /* eigenproblem solver context */
 26:   EPSType              type;
 27:   PetscReal            error, tol, re, im;
 28:   PetscScalar          kr, ki;
 30:   int                  nev, maxit, its, nconv;
 31:   PetscInt             N, n=10, m, i, j, II, J, Istart, Iend;
 32:   PetscScalar          v, w;
 33:   PetscTruth           flag;

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

 37:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 38:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);
 39:   if( flag==PETSC_FALSE ) m=n;
 40:   N = n*m;
 41:   PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%d (%dx%d grid)\n\n",N,n,m);

 43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 44:      Compute the operator matrix that defines the eigensystem, Ax=kx
 45:      In this example, A = L(G), where L is the Laplacian of graph G, i.e.
 46:      Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
 47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 49:   MatCreate(PETSC_COMM_WORLD,&A);
 50:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 51:   MatSetFromOptions(A);
 52: 
 53:   MatGetOwnershipRange(A,&Istart,&Iend);
 54:   for( II=Istart; II<Iend; II++ ) {
 55:     v = -1.0; i = II/n; j = II-i*n;
 56:     w = 0.0;
 57:     if(i>0) { J=II-n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 58:     if(i<m-1) { J=II+n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 59:     if(j>0) { J=II-1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 60:     if(j<n-1) { J=II+1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 61:     MatSetValues(A,1,&II,1,&II,&w,INSERT_VALUES);
 62:   }

 64:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 65:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 68:                 Create the eigensolver and set various options
 69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 76:   /* 
 77:      Set operators. In this case, it is a standard eigenvalue problem
 78:   */
 79:   EPSSetOperators(eps,A,PETSC_NULL);
 80:   EPSSetProblemType(eps,EPS_HEP);
 81: 
 82:   /*
 83:      Select portion of spectrum
 84:   */
 85:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);

 87:   /*
 88:      Set solver parameters at runtime
 89:   */
 90:   EPSSetFromOptions(eps);

 92:   /*
 93:      Attach deflation space: in this case, the matrix has a constant 
 94:      nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue
 95:   */
 96:   MatGetVecs(A,&x,PETSC_NULL);
 97:   VecSet(x,1.0);
 98:   EPSAttachDeflationSpace(eps,1,&x,PETSC_FALSE);
 99:   VecDestroy(x);

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
102:                       Solve the eigensystem
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

105:   EPSSolve(eps);
106:   EPSGetIterationNumber(eps, &its);
107:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);

109:   /*
110:      Optional: Get some information from the solver and display it
111:   */
112:   EPSGetType(eps,&type);
113:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
114:   EPSGetDimensions(eps,&nev,PETSC_NULL);
115:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
116:   EPSGetTolerances(eps,&tol,&maxit);
117:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);

119:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
120:                     Display solution and clean up
121:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

123:   /* 
124:      Get number of converged approximate eigenpairs
125:   */
126:   EPSGetConverged(eps,&nconv);
127:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
128: 

130:   if (nconv>0) {
131:     /*
132:        Display eigenvalues and relative errors
133:     */
134:     PetscPrintf(PETSC_COMM_WORLD,
135:          "           k          ||Ax-kx||/||kx||\n"
136:          "   ----------------- ------------------\n" );

138:     for( i=0; i<nconv; i++ ) {
139:       /* 
140:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
141:         ki (imaginary part)
142:       */
143:       EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
144:       /*
145:          Compute the relative error associated to each eigenpair
146:       */
147:       EPSComputeRelativeError(eps,i,&error);

149: #ifdef PETSC_USE_COMPLEX
150:       re = PetscRealPart(kr);
151:       im = PetscImaginaryPart(kr);
152: #else
153:       re = kr;
154:       im = ki;
155: #endif 
156:       if (im!=0.0) {
157:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);
158:       } else {
159:         PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",re,error);
160:       }
161:     }
162:     PetscPrintf(PETSC_COMM_WORLD,"\n" );
163:   }
164: 
165:   /* 
166:      Free work space
167:   */
168:   EPSDestroy(eps);
169:   MatDestroy(A);
170:   SlepcFinalize();
171:   return 0;
172: }