Actual source code: test9.c

slepc-3.6.1 2015-09-03
Report Typos and Errors
  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2015, 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[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid. "
 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 the initial vector.\n\n"
 25:   "The command line options are:\n"
 26:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

 28: #include <slepceps.h>

 30: /*
 31:    User-defined routines
 32: */
 33: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
 34: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);

 38: int main(int argc,char **argv)
 39: {
 40:   Vec            v0;              /* initial vector */
 41:   Mat            A;               /* operator matrix */
 42:   EPS            eps;             /* eigenproblem solver context */
 43:   EPSType        type;
 44:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
 45:   PetscInt       N,m=15,nev;
 46:   PetscScalar    origin=0.0;

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

 51:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 52:   N = m*(m+1)/2;
 53:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n\n",N,m);

 55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 56:      Compute the operator matrix that defines the eigensystem, Ax=kx
 57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 59:   MatCreate(PETSC_COMM_WORLD,&A);
 60:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 61:   MatSetFromOptions(A);
 62:   MatSetUp(A);
 63:   MatMarkovModel(m,A);

 65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 66:                 Create the eigensolver and set various options
 67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 69:   /*
 70:      Create eigensolver context
 71:   */
 72:   EPSCreate(PETSC_COMM_WORLD,&eps);

 74:   /*
 75:      Set operators. In this case, it is a standard eigenvalue problem
 76:   */
 77:   EPSSetOperators(eps,A,NULL);
 78:   EPSSetProblemType(eps,EPS_NHEP);
 79:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

 81:   /*
 82:      Set the custom comparing routine in order to obtain the eigenvalues
 83:      closest to the target on the right only
 84:   */
 85:   EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);


 88:   /*
 89:      Set solver parameters at runtime
 90:   */
 91:   EPSSetFromOptions(eps);

 93:   /*
 94:      Set the initial vector. This is optional, if not done the initial
 95:      vector is set to random values
 96:   */
 97:   MatCreateVecs(A,&v0,NULL);
 98:   VecSetValue(v0,0,-1.5,INSERT_VALUES);
 99:   VecSetValue(v0,1,2.1,INSERT_VALUES);
100:   VecAssemblyBegin(v0);
101:   VecAssemblyEnd(v0);
102:   EPSSetInitialSpace(eps,1,&v0);

104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105:                       Solve the eigensystem
106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

108:   EPSSolve(eps);

110:   /*
111:      Optional: Get some information from the solver and display it
112:   */
113:   EPSGetType(eps,&type);
114:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
115:   EPSGetDimensions(eps,&nev,NULL,NULL);
116:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

118:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119:                     Display solution and clean up
120:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

122:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
123:   EPSDestroy(&eps);
124:   MatDestroy(&A);
125:   VecDestroy(&v0);
126:   SlepcFinalize();
127:   return 0;
128: }

132: /*
133:     Matrix generator for a Markov model of a random walk on a triangular grid.

135:     This subroutine generates a test matrix that models a random walk on a
136:     triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
137:     FORTRAN subroutine to calculate the dominant invariant subspaces of a real
138:     matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
139:     papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
140:     (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
141:     algorithms. The transpose of the matrix  is stochastic and so it is known
142:     that one is an exact eigenvalue. One seeks the eigenvector of the transpose
143:     associated with the eigenvalue unity. The problem is to calculate the steady
144:     state probability distribution of the system, which is the eigevector
145:     associated with the eigenvalue one and scaled in such a way that the sum all
146:     the components is equal to one.

148:     Note: the code will actually compute the transpose of the stochastic matrix
149:     that contains the transition probabilities.
150: */
151: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
152: {
153:   const PetscReal cst = 0.5/(PetscReal)(m-1);
154:   PetscReal       pd,pu;
155:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
156:   PetscErrorCode  ierr;

159:   MatGetOwnershipRange(A,&Istart,&Iend);
160:   for (i=1;i<=m;i++) {
161:     jmax = m-i+1;
162:     for (j=1;j<=jmax;j++) {
163:       ix = ix + 1;
164:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
165:       if (j!=jmax) {
166:         pd = cst*(PetscReal)(i+j-1);
167:         /* north */
168:         if (i==1) {
169:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
170:         } else {
171:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
172:         }
173:         /* east */
174:         if (j==1) {
175:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
176:         } else {
177:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
178:         }
179:       }
180:       /* south */
181:       pu = 0.5 - cst*(PetscReal)(i+j-3);
182:       if (j>1) {
183:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
184:       }
185:       /* west */
186:       if (i>1) {
187:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
188:       }
189:     }
190:   }
191:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
192:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
193:   return(0);
194: }

198: /*
199:     Function for user-defined eigenvalue ordering criterion.

201:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
202:     one of them as the preferred one according to the criterion.
203:     In this example, the preferred value is the one furthest to the origin.
204: */
205: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
206: {
207:   PetscScalar origin = *(PetscScalar*)ctx;
208:   PetscReal   d;

211:   d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
212:   *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
213:   return(0);
214: }