Actual source code: ex29.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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[] = "Solves the same problem as in ex5, with a user-defined stopping test."
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 a custom stopping test function.\n\n"
14: "The command line options are:\n"
15: " -m <m>, where <m> = number of grid subdivisions in each dimension.\n"
16: " -seconds <s>, where <s> = maximum time in seconds allowed for computation.\n\n";
18: #include <slepceps.h>
19: #include <petsctime.h>
21: /*
22: User-defined routines
23: */
25: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);
26: PetscErrorCode MatMarkovModel(PetscInt,Mat);
28: int main(int argc,char **argv)
29: {
30: Mat A; /* operator matrix */
31: EPS eps; /* eigenproblem solver context */
32: PetscReal seconds=2.5; /* maximum time allowed for computation */
33: PetscLogDouble deadline; /* time to abort computation */
34: PetscInt N,m=15,nconv;
35: PetscBool terse;
36: PetscViewer viewer;
37: EPSConvergedReason reason;
38: PetscErrorCode ierr;
40: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
42: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
43: N = m*(m+1)/2;
44: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
45: PetscOptionsGetReal(NULL,NULL,"-seconds",&seconds,NULL);
46: PetscPrintf(PETSC_COMM_WORLD,"Maximum time for computation is set to %g seconds.\n\n",(double)seconds);
47: deadline = seconds;
48: PetscTimeAdd(&deadline);
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Compute the operator matrix that defines the eigensystem, Ax=kx
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: MatCreate(PETSC_COMM_WORLD,&A);
55: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
56: MatSetFromOptions(A);
57: MatSetUp(A);
58: MatMarkovModel(m,A);
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Create the eigensolver and set various options
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: EPSCreate(PETSC_COMM_WORLD,&eps);
65: EPSSetOperators(eps,A,NULL);
66: EPSSetProblemType(eps,EPS_NHEP);
67: EPSSetStoppingTestFunction(eps,MyStoppingTest,&deadline,NULL);
68: EPSSetFromOptions(eps);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Solve the eigensystem
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: EPSSolve(eps);
76: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
77: Display solution and clean up
78: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
80: /* show detailed info unless -terse option is given by user */
81: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
82: if (terse) {
83: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
84: } else {
85: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
86: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
87: EPSGetConvergedReason(eps,&reason);
88: if (reason!=EPS_CONVERGED_USER) {
89: EPSReasonView(eps,viewer);
90: EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
91: } else {
92: EPSGetConverged(eps,&nconv);
93: PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %D converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]);
94: }
95: PetscViewerPopFormat(viewer);
96: }
97: EPSDestroy(&eps);
98: MatDestroy(&A);
99: SlepcFinalize();
100: return ierr;
101: }
103: /*
104: Matrix generator for a Markov model of a random walk on a triangular grid.
106: This subroutine generates a test matrix that models a random walk on a
107: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
108: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
109: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
110: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
111: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
112: algorithms. The transpose of the matrix is stochastic and so it is known
113: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
114: associated with the eigenvalue unity. The problem is to calculate the steady
115: state probability distribution of the system, which is the eigevector
116: associated with the eigenvalue one and scaled in such a way that the sum all
117: the components is equal to one.
119: Note: the code will actually compute the transpose of the stochastic matrix
120: that contains the transition probabilities.
121: */
122: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
123: {
124: const PetscReal cst = 0.5/(PetscReal)(m-1);
125: PetscReal pd,pu;
126: PetscInt Istart,Iend,i,j,jmax,ix=0;
127: PetscErrorCode ierr;
130: MatGetOwnershipRange(A,&Istart,&Iend);
131: for (i=1;i<=m;i++) {
132: jmax = m-i+1;
133: for (j=1;j<=jmax;j++) {
134: ix = ix + 1;
135: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
136: if (j!=jmax) {
137: pd = cst*(PetscReal)(i+j-1);
138: /* north */
139: if (i==1) {
140: MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
141: } else {
142: MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
143: }
144: /* east */
145: if (j==1) {
146: MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
147: } else {
148: MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
149: }
150: }
151: /* south */
152: pu = 0.5 - cst*(PetscReal)(i+j-3);
153: if (j>1) {
154: MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
155: }
156: /* west */
157: if (i>1) {
158: MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
159: }
160: }
161: }
162: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
163: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
164: return(0);
165: }
167: /*
168: Function for user-defined stopping test.
170: Checks that the computing time has not exceeded the deadline.
171: */
172: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
173: {
175: PetscLogDouble now,deadline = *(PetscLogDouble*)ctx;
178: /* check if usual termination conditions are met */
179: EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL);
180: if (*reason==EPS_CONVERGED_ITERATING) {
181: /* check if deadline has expired */
182: PetscTime(&now);
183: if (now>deadline) *reason = EPS_CONVERGED_USER;
184: }
185: return(0);
186: }
188: /*TEST
190: test:
191: suffix: 1
192: args: -m 350
194: TEST*/