Actual source code: ex11.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2009, Universidad Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:       
  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 EPSAttachDeflationSpace(). 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:   Mat                  A;                  /* operator matrix */
 35:   Vec                  x;
 36:   EPS                  eps;                  /* eigenproblem solver context */
 37:   const EPSType  type;
 38:   PetscReal            error, tol, re, im;
 39:   PetscScalar          kr, ki;
 41:   PetscInt             N, n=10, m, i, j, II, J, Istart, Iend, nev, maxit, its, nconv;
 42:   PetscScalar          v, w;
 43:   PetscTruth           flag;

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

 47:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 48:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);
 49:   if( flag==PETSC_FALSE ) m=n;
 50:   N = n*m;
 51:   PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%d (%dx%d grid)\n\n",N,n,m);

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 54:      Compute the operator matrix that defines the eigensystem, Ax=kx
 55:      In this example, A = L(G), where L is the Laplacian of graph G, i.e.
 56:      Lii = degree of node i, Lij = -1 if edge (i,j) exists in G
 57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 59:   MatCreate(PETSC_COMM_WORLD,&A);
 60:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 61:   MatSetFromOptions(A);
 62: 
 63:   MatGetOwnershipRange(A,&Istart,&Iend);
 64:   for( II=Istart; II<Iend; II++ ) {
 65:     v = -1.0; i = II/n; j = II-i*n;
 66:     w = 0.0;
 67:     if(i>0) { J=II-n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 68:     if(i<m-1) { J=II+n; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 69:     if(j>0) { J=II-1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 70:     if(j<n-1) { J=II+1; MatSetValues(A,1,&II,1,&J,&v,INSERT_VALUES); w=w+1.0; }
 71:     MatSetValues(A,1,&II,1,&II,&w,INSERT_VALUES);
 72:   }

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

 77:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 78:                 Create the eigensolver and set various options
 79:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 86:   /* 
 87:      Set operators. In this case, it is a standard eigenvalue problem
 88:   */
 89:   EPSSetOperators(eps,A,PETSC_NULL);
 90:   EPSSetProblemType(eps,EPS_HEP);
 91: 
 92:   /*
 93:      Select portion of spectrum
 94:   */
 95:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);

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

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

111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
112:                       Solve the eigensystem
113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

115:   EPSSolve(eps);
116:   EPSGetIterationNumber(eps, &its);
117:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);

119:   /*
120:      Optional: Get some information from the solver and display it
121:   */
122:   EPSGetType(eps,&type);
123:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
124:   EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);
125:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
126:   EPSGetTolerances(eps,&tol,&maxit);
127:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);

129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
130:                     Display solution and clean up
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

133:   /* 
134:      Get number of converged approximate eigenpairs
135:   */
136:   EPSGetConverged(eps,&nconv);
137:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
138: 

140:   if (nconv>0) {
141:     /*
142:        Display eigenvalues and relative errors
143:     */
144:     PetscPrintf(PETSC_COMM_WORLD,
145:          "           k          ||Ax-kx||/||kx||\n"
146:          "   ----------------- ------------------\n" );

148:     for( i=0; i<nconv; i++ ) {
149:       /* 
150:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
151:         ki (imaginary part)
152:       */
153:       EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
154:       /*
155:          Compute the relative error associated to each eigenpair
156:       */
157:       EPSComputeRelativeError(eps,i,&error);

159: #ifdef PETSC_USE_COMPLEX
160:       re = PetscRealPart(kr);
161:       im = PetscImaginaryPart(kr);
162: #else
163:       re = kr;
164:       im = ki;
165: #endif 
166:       if (im!=0.0) {
167:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);
168:       } else {
169:         PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",re,error);
170:       }
171:     }
172:     PetscPrintf(PETSC_COMM_WORLD,"\n" );
173:   }
174: 
175:   /* 
176:      Free work space
177:   */
178:   EPSDestroy(eps);
179:   MatDestroy(A);
180:   SlepcFinalize();
181:   return 0;
182: }