Actual source code: ex5.c

slepc-3.20.1 2023-11-27
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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[] = "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:   PetscFunctionBeginUser;
 35:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

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

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

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

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

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

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

 66:   /*
 67:      Set solver parameters at runtime
 68:   */
 69:   PetscCall(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:   PetscCall(MatCreateVecs(A,&v0,NULL));
 76:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
 77:   if (!rank) {
 78:     PetscCall(VecSetValue(v0,0,1.0,INSERT_VALUES));
 79:     PetscCall(VecSetValue(v0,1,1.0,INSERT_VALUES));
 80:     PetscCall(VecSetValue(v0,2,1.0,INSERT_VALUES));
 81:   }
 82:   PetscCall(VecAssemblyBegin(v0));
 83:   PetscCall(VecAssemblyEnd(v0));
 84:   PetscCall(EPSSetInitialSpace(eps,1,&v0));

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

 90:   PetscCall(EPSSolve(eps));

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

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

104:   /* show detailed info unless -terse option is given by user */
105:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
106:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
107:   else {
108:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
109:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
110:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
111:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
112:   }
113:   PetscCall(EPSDestroy(&eps));
114:   PetscCall(MatDestroy(&A));
115:   PetscCall(VecDestroy(&v0));
116:   PetscCall(SlepcFinalize());
117:   return 0;
118: }

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

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

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

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

173: /*TEST

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

181: TEST*/