Actual source code: ex29.c

slepc-3.21.1 2024-04-26
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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[] = "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;

 39:   PetscFunctionBeginUser;
 40:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,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*/