Actual source code: ex29.c

slepc-3.18.2 2023-01-26
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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;

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

 42:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 43:   N = m*(m+1)/2;
 44:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\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) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
 83:   else {
 84:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
 85:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
 86:     EPSGetConvergedReason(eps,&reason);
 87:     if (reason!=EPS_CONVERGED_USER) {
 88:       EPSConvergedReasonView(eps,viewer);
 89:       EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
 90:     } else {
 91:       EPSGetConverged(eps,&nconv);
 92:       PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %" PetscInt_FMT " converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]);
 93:     }
 94:     PetscViewerPopFormat(viewer);
 95:   }
 96:   EPSDestroy(&eps);
 97:   MatDestroy(&A);
 98:   SlepcFinalize();
 99:   return 0;
100: }

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

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

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

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

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

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

165:   /* check if usual termination conditions are met */
166:   EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL);
167:   if (*reason==EPS_CONVERGED_ITERATING) {
168:     /* check if deadline has expired */
169:     PetscTime(&now);
170:     if (now>deadline) *reason = EPS_CONVERGED_USER;
171:   }
172:   return 0;
173: }

175: /*TEST

177:    test:
178:       suffix: 1
179:       args: -m 350 -seconds 0.6

181: TEST*/