Actual source code: test10.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2013, 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[] = "Computes the smallest nonzero eigenvalue of the Laplacian of a graph.\n\n"
 23:   "This example illustrates EPSSetDeflationSpace(). The example graph corresponds to a "
 24:   "2-D regular mesh. The command line options are:\n"
 25:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 26:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

 28: #include <slepceps.h>

 32: int main (int argc,char **argv)
 33: {
 34:   EPS            eps;             /* eigenproblem solver context */
 35:   Mat            A;               /* operator matrix */
 36:   Vec            x;
 37:   EPSType        type;
 38:   PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
 39:   PetscScalar    w;
 40:   PetscBool      flag;

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

 45:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 46:   PetscOptionsGetInt(NULL,"-m",&m,&flag);
 47:   if (!flag) m=n;
 48:   N = n*m;
 49:   PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%D (%Dx%D grid)\n\n",N,n,m);

 51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 52:      Compute the operator matrix that defines the eigensystem, Ax=kx
 53:      In this example, A = L(G), where L is the Laplacian of graph G, i.e.
 54:      Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
 55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 57:   MatCreate(PETSC_COMM_WORLD,&A);
 58:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 59:   MatSetFromOptions(A);
 60:   MatSetUp(A);

 62:   MatGetOwnershipRange(A,&Istart,&Iend);
 63:   for (II=Istart;II<Iend;II++) {
 64:     i = II/n; j = II-i*n;
 65:     w = 0.0;
 66:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); w=w+1.0; }
 67:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); w=w+1.0; }
 68:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); w=w+1.0; }
 69:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); w=w+1.0; }
 70:     MatSetValue(A,II,II,w,INSERT_VALUES);
 71:   }

 73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 77:                 Create the eigensolver and set various options
 78:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 80:   /*
 81:      Create eigensolver context
 82:   */
 83:   EPSCreate(PETSC_COMM_WORLD,&eps);

 85:   /*
 86:      Set operators. In this case, it is a standard eigenvalue problem
 87:   */
 88:   EPSSetOperators(eps,A,NULL);
 89:   EPSSetProblemType(eps,EPS_HEP);

 91:   /*
 92:      Select portion of spectrum
 93:   */
 94:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);

 96:   /*
 97:      Set solver parameters at runtime
 98:   */
 99:   EPSSetFromOptions(eps);

101:   /*
102:      Attach deflation space: in this case, the matrix has a constant
103:      nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue
104:   */
105:   MatGetVecs(A,&x,NULL);
106:   VecSet(x,1.0);
107:   EPSSetDeflationSpace(eps,1,&x);
108:   VecDestroy(&x);

110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111:                       Solve the eigensystem
112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

114:   EPSSolve(eps);

116:   /*
117:      Optional: Get some information from the solver and display it
118:   */
119:   EPSGetType(eps,&type);
120:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
121:   EPSGetDimensions(eps,&nev,NULL,NULL);
122:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125:                     Display solution and clean up
126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

128:   EPSPrintSolution(eps,NULL);
129:   EPSDestroy(&eps);
130:   MatDestroy(&A);
131:   SlepcFinalize();
132:   return 0;
133: }