Date: 2022-03-31T15:29:14+00:00

Actual source code: test40.c
slepc-3.17.0 2022-03-31
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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[] = "Test two-sided Krylov-Schur without calling EPSSetFromOptions (based on ex5.c).\n\n"
     12:   "The command line options are:\n"
     13:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

     15: #include <slepceps.h>

     17: /*
     18:    User-defined routines
     19: */
     20: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     22: int main(int argc,char **argv)
     23: {
     24:   Mat            A;               /* operator matrix */
     25:   EPS            eps;             /* eigenproblem solver context */
     26:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
     27:   PetscInt       N,m=15,nev;

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

     31:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     32:   N = m*(m+1)/2;
     33:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m);

     35:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     36:      Compute the operator matrix that defines the eigensystem, Ax=kx
     37:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     39:   MatCreate(PETSC_COMM_WORLD,&A);
     40:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     41:   MatSetFromOptions(A);
     42:   MatSetUp(A);
     43:   MatMarkovModel(m,A);

     45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     46:                 Create the eigensolver and set various options
     47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     49:   EPSCreate(PETSC_COMM_WORLD,&eps);
     50:   EPSSetOperators(eps,A,NULL);
     51:   EPSSetProblemType(eps,EPS_NHEP);
     52:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);
     53:   EPSSetDimensions(eps,4,PETSC_DEFAULT,PETSC_DEFAULT);
     54:   EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
     55:   EPSSetTwoSided(eps,PETSC_TRUE);

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:                       Solve the eigensystem
     59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     61:   EPSSolve(eps);
     62:   EPSGetDimensions(eps,&nev,NULL,NULL);
     63:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

     65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66:                     Display solution and clean up
     67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     69:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
     70:   EPSDestroy(&eps);
     71:   MatDestroy(&A);
     72:   SlepcFinalize();
     73:   return 0;
     74: }

     76: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
     77: {
     78:   const PetscReal cst = 0.5/(PetscReal)(m-1);
     79:   PetscReal       pd,pu;
     80:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

     83:   MatGetOwnershipRange(A,&Istart,&Iend);
     84:   for (i=1;i<=m;i++) {
     85:     jmax = m-i+1;
     86:     for (j=1;j<=jmax;j++) {
     87:       ix = ix + 1;
     88:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
     89:       if (j!=jmax) {
     90:         pd = cst*(PetscReal)(i+j-1);
     91:         /* north */
     92:         if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
     93:         else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
     94:         /* east */
     95:         if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
     96:         else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
     97:       }
     98:       /* south */
     99:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    100:       if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    101:       /* west */
    102:       if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    103:     }
    104:   }
    105:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    106:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    107:   PetscFunctionReturn(0);
    108: }

    110: /*TEST

    112:    test:
    113:       requires: !single

    115: TEST*/