Date: 2026-03-31T13:23:35+00:00

Actual source code: ex1.c

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

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Standard symmetric eigenproblem corresponding to the Laplacian operator in 1 dimension.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";

     15: #include <slepceps.h>

     17: int main(int argc,char **argv)
     18: {
     19:   Mat            A;           /* problem matrix */
     20:   EPS            eps;         /* eigenproblem solver context */
     21:   EPSType        type;
     22:   PetscReal      error,tol,re,im;
     23:   PetscScalar    kr,ki;
     24:   Vec            xr,xi;
     25:   PetscInt       n=30,i,Istart,Iend,nev,maxit,its,nconv;

     27:   PetscFunctionBeginUser;
     28:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     30:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     31:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%" PetscInt_FMT "\n\n",n));

     33:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     34:      Compute the operator matrix that defines the eigensystem, Ax=kx
     35:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     37:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     38:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
     39:   PetscCall(MatSetFromOptions(A));

     41:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     42:   for (i=Istart;i<Iend;i++) {
     43:     if (i>0) PetscCall(MatSetValue(A,i,i-1,-1.0,INSERT_VALUES));
     44:     if (i<n-1) PetscCall(MatSetValue(A,i,i+1,-1.0,INSERT_VALUES));
     45:     PetscCall(MatSetValue(A,i,i,2.0,INSERT_VALUES));
     46:   }
     47:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     48:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

     50:   PetscCall(MatCreateVecs(A,NULL,&xr));
     51:   PetscCall(MatCreateVecs(A,NULL,&xi));

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:                 Create the eigensolver and set various options
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     56:   /*
     57:      Create eigensolver context
     58:   */
     59:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

     61:   /*
     62:      Set operators. In this case, it is a standard eigenvalue problem
     63:   */
     64:   PetscCall(EPSSetOperators(eps,A,NULL));
     65:   PetscCall(EPSSetProblemType(eps,EPS_HEP));

     67:   /*
     68:      Set solver parameters at runtime
     69:   */
     70:   PetscCall(EPSSetFromOptions(eps));

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:                       Solve the eigensystem
     74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     76:   PetscCall(EPSSolve(eps));
     77:   /*
     78:      Optional: Get some information from the solver and display it
     79:   */
     80:   PetscCall(EPSGetIterationNumber(eps,&its));
     81:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
     82:   PetscCall(EPSGetType(eps,&type));
     83:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
     84:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
     85:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
     86:   PetscCall(EPSGetTolerances(eps,&tol,&maxit));
     87:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));

     89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     90:                     Display solution and clean up
     91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     92:   /*
     93:      Get number of converged approximate eigenpairs
     94:   */
     95:   PetscCall(EPSGetConverged(eps,&nconv));
     96:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv));

     98:   if (nconv>0) {
     99:     /*
    100:        Display eigenvalues and relative errors
    101:     */
    102:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
    103:          "           k          ||Ax-kx||/||kx||\n"
    104:          "   ----------------- ------------------\n"));

    106:     for (i=0;i<nconv;i++) {
    107:       /*
    108:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
    109:         ki (imaginary part)
    110:       */
    111:       PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,xr,xi));
    112:       /*
    113:          Compute the relative error associated to each eigenpair
    114:       */
    115:       PetscCall(EPSComputeError(eps,i,EPS_ERROR_RELATIVE,&error));

    117: #if defined(PETSC_USE_COMPLEX)
    118:       re = PetscRealPart(kr);
    119:       im = PetscImaginaryPart(kr);
    120: #else
    121:       re = kr;
    122:       im = ki;
    123: #endif
    124:       if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error));
    125:       else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error));
    126:     }
    127:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    128:   }

    130:   /*
    131:      Free work space
    132:   */
    133:   PetscCall(EPSDestroy(&eps));
    134:   PetscCall(MatDestroy(&A));
    135:   PetscCall(VecDestroy(&xr));
    136:   PetscCall(VecDestroy(&xi));
    137:   PetscCall(SlepcFinalize());
    138:   return 0;
    139: }