Actual source code: ex5.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2013, 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);
37: int main(int argc,char **argv)
38: {
39: Vec v0; /* initial vector */
40: Mat A; /* operator matrix */
41: EPS eps; /* eigenproblem solver context */
42: EPSType type;
43: PetscInt N,m=15,nev;
46: SlepcInitialize(&argc,&argv,(char*)0,help);
48: PetscOptionsGetInt(NULL,"-m",&m,NULL);
49: N = m*(m+1)/2;
50: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n\n",N,m);
52: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53: Compute the operator matrix that defines the eigensystem, Ax=kx
54: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
56: MatCreate(PETSC_COMM_WORLD,&A);
57: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
58: MatSetFromOptions(A);
59: MatSetUp(A);
60: MatMarkovModel(m,A);
62: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
63: Create the eigensolver and set various options
64: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
66: /*
67: Create eigensolver context
68: */
69: EPSCreate(PETSC_COMM_WORLD,&eps);
71: /*
72: Set operators. In this case, it is a standard eigenvalue problem
73: */
74: EPSSetOperators(eps,A,NULL);
75: EPSSetProblemType(eps,EPS_NHEP);
77: /*
78: Set solver parameters at runtime
79: */
80: EPSSetFromOptions(eps);
82: /*
83: Set the initial vector. This is optional, if not done the initial
84: vector is set to random values
85: */
86: MatGetVecs(A,&v0,NULL);
87: VecSet(v0,1.0);
88: EPSSetInitialSpace(eps,1,&v0);
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Solve the eigensystem
92: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: EPSSolve(eps);
96: /*
97: Optional: Get some information from the solver and display it
98: */
99: EPSGetType(eps,&type);
100: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
101: EPSGetDimensions(eps,&nev,NULL,NULL);
102: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
104: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105: Display solution and clean up
106: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
108: EPSPrintSolution(eps,NULL);
109: EPSDestroy(&eps);
110: MatDestroy(&A);
111: VecDestroy(&v0);
112: SlepcFinalize();
113: return 0;
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: }