Date: 2021-02-01T14:42:03+00:00

Actual source code: ex29.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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."
     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;
     38:   PetscErrorCode     ierr;

     40:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

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

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

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:                 Create the eigensolver and set various options
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:                       Solve the eigensystem
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     74:   EPSSolve(eps);

     76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     77:                     Display solution and clean up
     78:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     80:   /* show detailed info unless -terse option is given by user */
     81:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
     82:   if (terse) {
     83:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
     84:   } else {
     85:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     86:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
     87:     EPSGetConvergedReason(eps,&reason);
     88:     if (reason!=EPS_CONVERGED_USER) {
     89:       EPSConvergedReasonView(eps,viewer);
     90:       EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
     91:     } else {
     92:       EPSGetConverged(eps,&nconv);
     93:       PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %D converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]);
     94:     }
     95:     PetscViewerPopFormat(viewer);
     96:   }
     97:   EPSDestroy(&eps);
     98:   MatDestroy(&A);
     99:   SlepcFinalize();
    100:   return ierr;
    101: }

    103: /*
    104:     Matrix generator for a Markov model of a random walk on a triangular grid.

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

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

    130:   MatGetOwnershipRange(A,&Istart,&Iend);
    131:   for (i=1;i<=m;i++) {
    132:     jmax = m-i+1;
    133:     for (j=1;j<=jmax;j++) {
    134:       ix = ix + 1;
    135:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    136:       if (j!=jmax) {
    137:         pd = cst*(PetscReal)(i+j-1);
    138:         /* north */
    139:         if (i==1) {
    140:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    141:         } else {
    142:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    143:         }
    144:         /* east */
    145:         if (j==1) {
    146:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    147:         } else {
    148:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    149:         }
    150:       }
    151:       /* south */
    152:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    153:       if (j>1) {
    154:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    155:       }
    156:       /* west */
    157:       if (i>1) {
    158:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    159:       }
    160:     }
    161:   }
    162:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    163:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    164:   return(0);
    165: }

    167: /*
    168:     Function for user-defined stopping test.

    170:     Checks that the computing time has not exceeded the deadline.
    171: */
    172: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
    173: {
    175:   PetscLogDouble now,deadline = *(PetscLogDouble*)ctx;

    178:   /* check if usual termination conditions are met */
    179:   EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL);
    180:   if (*reason==EPS_CONVERGED_ITERATING) {
    181:     /* check if deadline has expired */
    182:     PetscTime(&now);
    183:     if (now>deadline) *reason = EPS_CONVERGED_USER;
    184:   }
    185:   return(0);
    186: }

    188: /*TEST

    190:    test:
    191:       suffix: 1
    192:       args: -m 350 -seconds 0.6

    194: TEST*/