Actual source code: ex5.c

slepc-3.17.2 2022-08-09
Report Typos and Errors
  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[] = "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;

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

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

 40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 41:      Compute the operator matrix that defines the eigensystem, Ax=kx
 42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51:                 Create the eigensolver and set various options
 52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 54:   /*
 55:      Create eigensolver context
 56:   */
 57:   EPSCreate(PETSC_COMM_WORLD,&eps);

 59:   /*
 60:      Set operators. In this case, it is a standard eigenvalue problem
 61:   */
 62:   EPSSetOperators(eps,A,NULL);
 63:   EPSSetProblemType(eps,EPS_NHEP);

 65:   /*
 66:      Set solver parameters at runtime
 67:   */
 68:   EPSSetFromOptions(eps);

 70:   /*
 71:      Set the initial vector. This is optional, if not done the initial
 72:      vector is set to random values
 73:   */
 74:   MatCreateVecs(A,&v0,NULL);
 75:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 76:   if (!rank) {
 77:     VecSetValue(v0,0,1.0,INSERT_VALUES);
 78:     VecSetValue(v0,1,1.0,INSERT_VALUES);
 79:     VecSetValue(v0,2,1.0,INSERT_VALUES);
 80:   }
 81:   VecAssemblyBegin(v0);
 82:   VecAssemblyEnd(v0);
 83:   EPSSetInitialSpace(eps,1,&v0);

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:                       Solve the eigensystem
 87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 89:   EPSSolve(eps);

 91:   /*
 92:      Optional: Get some information from the solver and display it
 93:   */
 94:   EPSGetType(eps,&type);
 95:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
 96:   EPSGetDimensions(eps,&nev,NULL,NULL);
 97:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:                     Display solution and clean up
101:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

103:   /* show detailed info unless -terse option is given by user */
104:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
105:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
106:   else {
107:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
108:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
109:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
110:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
111:   }
112:   EPSDestroy(&eps);
113:   MatDestroy(&A);
114:   VecDestroy(&v0);
115:   SlepcFinalize();
116:   return 0;
117: }

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

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

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

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) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
155:         else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
156:         /* east */
157:         if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
158:         else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
159:       }
160:       /* south */
161:       pu = 0.5 - cst*(PetscReal)(i+j-3);
162:       if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
163:       /* west */
164:       if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
165:     }
166:   }
167:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
168:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
169:   PetscFunctionReturn(0);
170: }

172: /*TEST

174:    test:
175:       suffix: 1
176:       nsize: 2
177:       args: -eps_largest_real -eps_nev 4 -eps_two_sided {{0 1}} -eps_krylovschur_locking {{0 1}} -ds_parallel synchronized -terse
178:       filter: sed -e "s/90424/90423/" | sed -e "s/85715/85714/"

180: TEST*/