Actual source code: ex29.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[] = "Solves the same problem as in ex5, with a user-defined stopping test.\n\n"
     12:   "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n"
     13:   "This example illustrates how the user can set a custom stopping test function.\n\n"
     14:   "The command line options are:\n"
     15:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n"
     16:   "  -seconds <s>, where <s> = maximum time in seconds allowed for computation.\n\n";

     18: #include <slepceps.h>
     19: #include <petsctime.h>

     21: /*
     22:    User-defined routines
     23: */

     25: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);
     26: PetscErrorCode MatMarkovModel(PetscInt,Mat);

     28: int main(int argc,char **argv)
     29: {
     30:   Mat                A;               /* operator matrix */
     31:   EPS                eps;             /* eigenproblem solver context */
     32:   PetscReal          seconds=2.5;     /* maximum time allowed for computation */
     33:   PetscLogDouble     deadline;        /* time to abort computation */
     34:   PetscInt           N,m=15,nconv;
     35:   PetscBool          terse;
     36:   PetscViewer        viewer;
     37:   EPSConvergedReason reason;

     39:   PetscFunctionBeginUser;
     40:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     42:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     43:   N = m*(m+1)/2;
     44:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m));
     45:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-seconds",&seconds,NULL));
     46:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Maximum time for computation is set to %g seconds.\n\n",(double)seconds));
     47:   deadline = seconds;
     48:   PetscCall(PetscTimeAdd(&deadline));

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:      Compute the operator matrix that defines the eigensystem, Ax=kx
     52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     54:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     55:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     56:   PetscCall(MatSetFromOptions(A));
     57:   PetscCall(MatMarkovModel(m,A));

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:                 Create the eigensolver and set various options
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
     64:   PetscCall(EPSSetOperators(eps,A,NULL));
     65:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
     66:   PetscCall(EPSSetStoppingTestFunction(eps,MyStoppingTest,&deadline,NULL));
     67:   PetscCall(EPSSetFromOptions(eps));

     69:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     70:                       Solve the eigensystem
     71:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     73:   PetscCall(EPSSolve(eps));

     75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76:                     Display solution and clean up
     77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     79:   /* show detailed info unless -terse option is given by user */
     80:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
     81:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
     82:   else {
     83:     PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
     84:     PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
     85:     PetscCall(EPSGetConvergedReason(eps,&reason));
     86:     if (reason!=EPS_CONVERGED_USER) {
     87:       PetscCall(EPSConvergedReasonView(eps,viewer));
     88:       PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer));
     89:     } else {
     90:       PetscCall(EPSGetConverged(eps,&nconv));
     91:       PetscCall(PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %" PetscInt_FMT " converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]));
     92:     }
     93:     PetscCall(PetscViewerPopFormat(viewer));
     94:   }
     95:   PetscCall(EPSDestroy(&eps));
     96:   PetscCall(MatDestroy(&A));
     97:   PetscCall(SlepcFinalize());
     98:   return 0;
     99: }

    101: /*
    102:     Matrix generator for a Markov model of a random walk on a triangular grid.

    104:     This subroutine generates a test matrix that models a random walk on a
    105:     triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
    106:     FORTRAN subroutine to calculate the dominant invariant subspaces of a real
    107:     matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
    108:     papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
    109:     (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
    110:     algorithms. The transpose of the matrix  is stochastic and so it is known
    111:     that one is an exact eigenvalue. One seeks the eigenvector of the transpose
    112:     associated with the eigenvalue unity. The problem is to calculate the steady
    113:     state probability distribution of the system, which is the eigevector
    114:     associated with the eigenvalue one and scaled in such a way that the sum all
    115:     the components is equal to one.

    117:     Note: the code will actually compute the transpose of the stochastic matrix
    118:     that contains the transition probabilities.
    119: */
    120: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    121: {
    122:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    123:   PetscReal       pd,pu;
    124:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

    126:   PetscFunctionBeginUser;
    127:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
    128:   for (i=1;i<=m;i++) {
    129:     jmax = m-i+1;
    130:     for (j=1;j<=jmax;j++) {
    131:       ix = ix + 1;
    132:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    133:       if (j!=jmax) {
    134:         pd = cst*(PetscReal)(i+j-1);
    135:         /* north */
    136:         if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
    137:         else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
    138:         /* east */
    139:         if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
    140:         else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
    141:       }
    142:       /* south */
    143:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    144:       if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
    145:       /* west */
    146:       if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
    147:     }
    148:   }
    149:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    150:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    151:   PetscFunctionReturn(PETSC_SUCCESS);
    152: }

    154: /*
    155:     Function for user-defined stopping test.

    157:     Checks that the computing time has not exceeded the deadline.
    158: */
    159: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
    160: {
    161:   PetscLogDouble now,deadline = *(PetscLogDouble*)ctx;

    163:   PetscFunctionBeginUser;
    164:   /* check if usual termination conditions are met */
    165:   PetscCall(EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL));
    166:   if (*reason==EPS_CONVERGED_ITERATING) {
    167:     /* check if deadline has expired */
    168:     PetscCall(PetscTime(&now));
    169:     if (now>deadline) *reason = EPS_CONVERGED_USER;
    170:   }
    171:   PetscFunctionReturn(PETSC_SUCCESS);
    172: }

    174: /*TEST

    176:    test:
    177:       suffix: 1
    178:       args: -m 350 -seconds 0.6
    179:       requires: !single

    181: TEST*/