Date: 2021-09-20T09:43:58+00:00

Actual source code: ex5.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid. "
     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 the initial vector.\n\n"
     14:   "The command line options are:\n"
     15:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

     17: #include <slepceps.h>

     19: /*
     20:    User-defined routines
     21: */
     22: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     24: int main(int argc,char **argv)
     25: {
     26:   Vec            v0;              /* initial vector */
     27:   Mat            A;               /* operator matrix */
     28:   EPS            eps;             /* eigenproblem solver context */
     29:   EPSType        type;
     30:   PetscInt       N,m=15,nev;
     31:   PetscMPIInt    rank;
     32:   PetscBool      terse;

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

     37:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     38:   N = m*(m+1)/2;
     39:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n\n",N,m);

     41:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     42:      Compute the operator matrix that defines the eigensystem, Ax=kx
     43:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     45:   MatCreate(PETSC_COMM_WORLD,&A);
     46:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     47:   MatSetFromOptions(A);
     48:   MatSetUp(A);
     49:   MatMarkovModel(m,A);

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:                 Create the eigensolver and set various options
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   /*
     56:      Create eigensolver context
     57:   */
     58:   EPSCreate(PETSC_COMM_WORLD,&eps);

     60:   /*
     61:      Set operators. In this case, it is a standard eigenvalue problem
     62:   */
     63:   EPSSetOperators(eps,A,NULL);
     64:   EPSSetProblemType(eps,EPS_NHEP);

     66:   /*
     67:      Set solver parameters at runtime
     68:   */
     69:   EPSSetFromOptions(eps);

     71:   /*
     72:      Set the initial vector. This is optional, if not done the initial
     73:      vector is set to random values
     74:   */
     75:   MatCreateVecs(A,&v0,NULL);
     76:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRMPI(ierr);
     77:   if (!rank) {
     78:     VecSetValue(v0,0,1.0,INSERT_VALUES);
     79:     VecSetValue(v0,1,1.0,INSERT_VALUES);
     80:     VecSetValue(v0,2,1.0,INSERT_VALUES);
     81:   }
     82:   VecAssemblyBegin(v0);
     83:   VecAssemblyEnd(v0);
     84:   EPSSetInitialSpace(eps,1,&v0);

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:                       Solve the eigensystem
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     90:   EPSSolve(eps);

     92:   /*
     93:      Optional: Get some information from the solver and display it
     94:   */
     95:   EPSGetType(eps,&type);
     96:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
     97:   EPSGetDimensions(eps,&nev,NULL,NULL);
     98:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:                     Display solution and clean up
    102:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    104:   /* show detailed info unless -terse option is given by user */
    105:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    106:   if (terse) {
    107:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    108:   } else {
    109:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    110:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    111:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    112:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    113:   }
    114:   EPSDestroy(&eps);
    115:   MatDestroy(&A);
    116:   VecDestroy(&v0);
    117:   SlepcFinalize();
    118:   return ierr;
    119: }

    121: /*
    122:     Matrix generator for a Markov model of a random walk on a triangular grid.

    124:     This subroutine generates a test matrix that models a random walk on a
    125:     triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
    126:     FORTRAN subroutine to calculate the dominant invariant subspaces of a real
    127:     matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
    128:     papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
    129:     (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
    130:     algorithms. The transpose of the matrix  is stochastic and so it is known
    131:     that one is an exact eigenvalue. One seeks the eigenvector of the transpose
    132:     associated with the eigenvalue unity. The problem is to calculate the steady
    133:     state probability distribution of the system, which is the eigevector
    134:     associated with the eigenvalue one and scaled in such a way that the sum all
    135:     the components is equal to one.

    137:     Note: the code will actually compute the transpose of the stochastic matrix
    138:     that contains the transition probabilities.
    139: */
    140: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    141: {
    142:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    143:   PetscReal       pd,pu;
    144:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    145:   PetscErrorCode  ierr;

    148:   MatGetOwnershipRange(A,&Istart,&Iend);
    149:   for (i=1;i<=m;i++) {
    150:     jmax = m-i+1;
    151:     for (j=1;j<=jmax;j++) {
    152:       ix = ix + 1;
    153:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    154:       if (j!=jmax) {
    155:         pd = cst*(PetscReal)(i+j-1);
    156:         /* north */
    157:         if (i==1) {
    158:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    159:         } else {
    160:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    161:         }
    162:         /* east */
    163:         if (j==1) {
    164:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    165:         } else {
    166:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    167:         }
    168:       }
    169:       /* south */
    170:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    171:       if (j>1) {
    172:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    173:       }
    174:       /* west */
    175:       if (i>1) {
    176:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    177:       }
    178:     }
    179:   }
    180:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    181:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    182:   return(0);
    183: }

    185: /*TEST

    187:    test:
    188:       suffix: 1
    189:       nsize: 2
    190:       args: -eps_largest_real -eps_nev 4 -eps_two_sided {{0 1}} -eps_krylovschur_locking {{0 1}} -ds_parallel synchronized -terse
    191:       filter: sed -e "s/90424/90423/" | sed -e "s/85715/85714/"

    193: TEST*/