Actual source code: ex29.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[] = "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;
39: PetscFunctionBeginUser;
40: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
42: PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
43: N = m*(m+1)/2;
44: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m));
45: PetscCall(PetscOptionsGetReal(NULL,NULL,"-seconds",&seconds,NULL));
46: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Maximum time for computation is set to %g seconds.\n\n",(double)seconds));
47: deadline = seconds;
48: PetscCall(PetscTimeAdd(&deadline));
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Compute the operator matrix that defines the eigensystem, Ax=kx
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
55: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
56: PetscCall(MatSetFromOptions(A));
57: PetscCall(MatMarkovModel(m,A));
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Create the eigensolver and set various options
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
64: PetscCall(EPSSetOperators(eps,A,NULL));
65: PetscCall(EPSSetProblemType(eps,EPS_NHEP));
66: PetscCall(EPSSetStoppingTestFunction(eps,MyStoppingTest,&deadline,NULL));
67: PetscCall(EPSSetFromOptions(eps));
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Solve the eigensystem
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
73: PetscCall(EPSSolve(eps));
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Display solution and clean up
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: /* show detailed info unless -terse option is given by user */
80: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
81: if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
82: else {
83: PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
84: PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
85: PetscCall(EPSGetConvergedReason(eps,&reason));
86: if (reason!=EPS_CONVERGED_USER) {
87: PetscCall(EPSConvergedReasonView(eps,viewer));
88: PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer));
89: } else {
90: PetscCall(EPSGetConverged(eps,&nconv));
91: PetscCall(PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %" PetscInt_FMT " converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]));
92: }
93: PetscCall(PetscViewerPopFormat(viewer));
94: }
95: PetscCall(EPSDestroy(&eps));
96: PetscCall(MatDestroy(&A));
97: PetscCall(SlepcFinalize());
98: return 0;
99: }
101: /*
102: Matrix generator for a Markov model of a random walk on a triangular grid.
104: This subroutine generates a test matrix that models a random walk on a
105: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
106: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
107: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
108: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
109: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
110: algorithms. The transpose of the matrix is stochastic and so it is known
111: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
112: associated with the eigenvalue unity. The problem is to calculate the steady
113: state probability distribution of the system, which is the eigevector
114: associated with the eigenvalue one and scaled in such a way that the sum all
115: the components is equal to one.
117: Note: the code will actually compute the transpose of the stochastic matrix
118: that contains the transition probabilities.
119: */
120: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
121: {
122: const PetscReal cst = 0.5/(PetscReal)(m-1);
123: PetscReal pd,pu;
124: PetscInt Istart,Iend,i,j,jmax,ix=0;
126: PetscFunctionBeginUser;
127: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
128: for (i=1;i<=m;i++) {
129: jmax = m-i+1;
130: for (j=1;j<=jmax;j++) {
131: ix = ix + 1;
132: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
133: if (j!=jmax) {
134: pd = cst*(PetscReal)(i+j-1);
135: /* north */
136: if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
137: else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
138: /* east */
139: if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
140: else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
141: }
142: /* south */
143: pu = 0.5 - cst*(PetscReal)(i+j-3);
144: if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
145: /* west */
146: if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
147: }
148: }
149: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
150: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
151: PetscFunctionReturn(PETSC_SUCCESS);
152: }
154: /*
155: Function for user-defined stopping test.
157: Checks that the computing time has not exceeded the deadline.
158: */
159: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
160: {
161: PetscLogDouble now,deadline = *(PetscLogDouble*)ctx;
163: PetscFunctionBeginUser;
164: /* check if usual termination conditions are met */
165: PetscCall(EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL));
166: if (*reason==EPS_CONVERGED_ITERATING) {
167: /* check if deadline has expired */
168: PetscCall(PetscTime(&now));
169: if (now>deadline) *reason = EPS_CONVERGED_USER;
170: }
171: PetscFunctionReturn(PETSC_SUCCESS);
172: }
174: /*TEST
176: test:
177: suffix: 1
178: args: -m 350 -seconds 0.6
179: requires: !single
181: TEST*/