Date: 2022-10-01T06:40:04+00:00

Actual source code: ex1.c
slepc-3.18.0 2022-10-01
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      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;

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

     30:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     31:   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:   MatCreate(PETSC_COMM_WORLD,&A);
     38:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
     39:   MatSetFromOptions(A);
     40:   MatSetUp(A);

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

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

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

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

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

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:                       Solve the eigensystem
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

    118: #if defined(PETSC_USE_COMPLEX)
    119:       re = PetscRealPart(kr);
    120:       im = PetscImaginaryPart(kr);
    121: #else
    122:       re = kr;
    123:       im = ki;
    124: #endif
    125:       if (im!=0.0) PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error);
    126:       else PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);
    127:     }
    128:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    129:   }

    131:   /*
    132:      Free work space
    133:   */
    134:   EPSDestroy(&eps);
    135:   MatDestroy(&A);
    136:   VecDestroy(&xr);
    137:   VecDestroy(&xi);
    138:   SlepcFinalize();
    139:   return 0;
    140: }