Actual source code: ex5.c
slepc-3.21.0 2024-03-30
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(MatMarkovModel(m,A));
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Create the eigensolver and set various options
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: /*
55: Create eigensolver context
56: */
57: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
59: /*
60: Set operators. In this case, it is a standard eigenvalue problem
61: */
62: PetscCall(EPSSetOperators(eps,A,NULL));
63: PetscCall(EPSSetProblemType(eps,EPS_NHEP));
65: /*
66: Set solver parameters at runtime
67: */
68: PetscCall(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: PetscCall(MatCreateVecs(A,&v0,NULL));
75: PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
76: if (!rank) {
77: PetscCall(VecSetValue(v0,0,1.0,INSERT_VALUES));
78: PetscCall(VecSetValue(v0,1,1.0,INSERT_VALUES));
79: PetscCall(VecSetValue(v0,2,1.0,INSERT_VALUES));
80: }
81: PetscCall(VecAssemblyBegin(v0));
82: PetscCall(VecAssemblyEnd(v0));
83: PetscCall(EPSSetInitialSpace(eps,1,&v0));
85: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
86: Solve the eigensystem
87: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: PetscCall(EPSSolve(eps));
91: /*
92: Optional: Get some information from the solver and display it
93: */
94: PetscCall(EPSGetType(eps,&type));
95: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
96: PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
97: PetscCall(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: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
105: if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
106: else {
107: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
108: PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
109: PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
110: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
111: }
112: PetscCall(EPSDestroy(&eps));
113: PetscCall(MatDestroy(&A));
114: PetscCall(VecDestroy(&v0));
115: PetscCall(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;
144: PetscFunctionBeginUser;
145: PetscCall(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) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
155: else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
156: /* east */
157: if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
158: else PetscCall(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) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
163: /* west */
164: if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
165: }
166: }
167: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
168: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
169: PetscFunctionReturn(PETSC_SUCCESS);
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*/