Actual source code: ex1.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[] = "Standard symmetric eigenproblem corresponding to the Laplacian operator in 1 dimension.\n\n"
 23:   "The command line options are:\n"
 24:   "  -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";

 26: #include <slepceps.h>

 30: int main(int argc,char **argv)
 31: {
 32:   Mat            A;           /* problem matrix */
 33:   EPS            eps;         /* eigenproblem solver context */
 34:   EPSType        type;
 35:   PetscReal      error,tol,re,im;
 36:   PetscScalar    kr,ki,value[3];
 37:   Vec            xr,xi;
 38:   PetscInt       n=30,i,Istart,Iend,col[3],nev,maxit,its,nconv;
 39:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

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

 44:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 45:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%D\n\n",n);

 47:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48:      Compute the operator matrix that defines the eigensystem, Ax=kx
 49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 51:   MatCreate(PETSC_COMM_WORLD,&A);
 52:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 53:   MatSetFromOptions(A);
 54:   MatSetUp(A);

 56:   MatGetOwnershipRange(A,&Istart,&Iend);
 57:   if (Istart==0) FirstBlock=PETSC_TRUE;
 58:   if (Iend==n) LastBlock=PETSC_TRUE;
 59:   value[0]=-1.0; value[1]=2.0; value[2]=-1.0;
 60:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
 61:     col[0]=i-1; col[1]=i; col[2]=i+1;
 62:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 63:   }
 64:   if (LastBlock) {
 65:     i=n-1; col[0]=n-2; col[1]=n-1;
 66:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 67:   }
 68:   if (FirstBlock) {
 69:     i=0; col[0]=0; col[1]=1; value[0]=2.0; value[1]=-1.0;
 70:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 71:   }

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

 76:   MatGetVecs(A,NULL,&xr);
 77:   MatGetVecs(A,NULL,&xi);

 79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 80:                 Create the eigensolver and set various options
 81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 82:   /*
 83:      Create eigensolver context
 84:   */
 85:   EPSCreate(PETSC_COMM_WORLD,&eps);

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

 93:   /*
 94:      Set solver parameters at runtime
 95:   */
 96:   EPSSetFromOptions(eps);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:                       Solve the eigensystem
100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:                     Display solution and clean up
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
118:   /*
119:      Get number of converged approximate eigenpairs
120:   */
121:   EPSGetConverged(eps,&nconv);
122:   PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %D\n\n",nconv);

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

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

143: #if defined(PETSC_USE_COMPLEX)
144:       re = PetscRealPart(kr);
145:       im = PetscImaginaryPart(kr);
146: #else
147:       re = kr;
148:       im = ki;
149: #endif
150:       if (im!=0.0) {
151:         PetscPrintf(PETSC_COMM_WORLD," %9F%+9F j %12G\n",re,im,error);
152:       } else {
153:         PetscPrintf(PETSC_COMM_WORLD,"   %12F       %12G\n",re,error);
154:       }
155:     }
156:     PetscPrintf(PETSC_COMM_WORLD,"\n");
157:   }

159:   /*
160:      Free work space
161:   */
162:   EPSDestroy(&eps);
163:   MatDestroy(&A);
164:   VecDestroy(&xr);
165:   VecDestroy(&xi);
166:   SlepcFinalize();
167:   return 0;
168: }