Actual source code: ex29.c

slepc-3.7.4 2017-05-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */

 22: static char help[] = "Solves the same problem as in ex5, with a user-defined stopping test."
 23:   "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n"
 24:   "This example illustrates how the user can set a custom stopping test function.\n\n"
 25:   "The command line options are:\n"
 26:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n"
 27:   "  -seconds <s>, where <s> = maximum time in seconds allowed for computation.\n\n";

 29: #include <slepceps.h>
 30: #include <petsctime.h>

 32: /*
 33:    User-defined routines
 34: */

 36: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);
 37: PetscErrorCode MatMarkovModel(PetscInt,Mat);

 41: int main(int argc,char **argv)
 42: {
 43:   Mat                A;               /* operator matrix */
 44:   EPS                eps;             /* eigenproblem solver context */
 45:   PetscReal          seconds=2.5;     /* maximum time allowed for computation */
 46:   PetscLogDouble     deadline;        /* time to abort computation */
 47:   PetscInt           N,m=15,nconv;
 48:   PetscBool          terse;
 49:   PetscViewer        viewer;
 50:   EPSConvergedReason reason;
 51:   PetscErrorCode     ierr;

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

 55:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 56:   N = m*(m+1)/2;
 57:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
 58:   PetscOptionsGetReal(NULL,NULL,"-seconds",&seconds,NULL);
 59:   PetscPrintf(PETSC_COMM_WORLD,"Maximum time for computation is set to %g seconds.\n\n",(double)seconds);
 60:   deadline = seconds;
 61:   PetscTimeAdd(&deadline);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:      Compute the operator matrix that defines the eigensystem, Ax=kx
 65:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 67:   MatCreate(PETSC_COMM_WORLD,&A);
 68:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 69:   MatSetFromOptions(A);
 70:   MatSetUp(A);
 71:   MatMarkovModel(m,A);

 73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 74:                 Create the eigensolver and set various options
 75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 77:   EPSCreate(PETSC_COMM_WORLD,&eps);
 78:   EPSSetOperators(eps,A,NULL);
 79:   EPSSetProblemType(eps,EPS_NHEP);
 80:   EPSSetStoppingTestFunction(eps,MyStoppingTest,&deadline,NULL);
 81:   EPSSetFromOptions(eps);

 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:                       Solve the eigensystem
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 87:   EPSSolve(eps);

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:                     Display solution and clean up
 91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 93:   /* show detailed info unless -terse option is given by user */
 94:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
 95:   if (terse) {
 96:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
 97:   } else {
 98:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
 99:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
100:     EPSGetConvergedReason(eps,&reason);
101:     if (reason!=EPS_CONVERGED_USER) {
102:       EPSReasonView(eps,viewer);
103:       EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
104:     } else {
105:       EPSGetConverged(eps,&nconv);
106:       PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %D converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]);
107:     }
108:     PetscViewerPopFormat(viewer);
109:   }
110:   EPSDestroy(&eps);
111:   MatDestroy(&A);
112:   SlepcFinalize();
113:   return ierr;
114: }

118: /*
119:     Matrix generator for a Markov model of a random walk on a triangular grid.

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

134:     Note: the code will actually compute the transpose of the stochastic matrix
135:     that contains the transition probabilities.
136: */
137: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
138: {
139:   const PetscReal cst = 0.5/(PetscReal)(m-1);
140:   PetscReal       pd,pu;
141:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
142:   PetscErrorCode  ierr;

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

184: /*
185:     Function for user-defined stopping test.

187:     Checks that the computing time has not exceeded the deadline.
188: */
189: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
190: {
192:   PetscLogDouble now,deadline = *(PetscLogDouble*)ctx;

195:   /* check if usual termination conditions are met */
196:   EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL);
197:   if (*reason==EPS_CONVERGED_ITERATING) {
198:     /* check if deadline has expired */
199:     PetscTime(&now);
200:     if (now>deadline) *reason = EPS_CONVERGED_USER;
201:   }
202:   return(0);
203: }