1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2016, 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[] = "Solves the same problem as in ex5, with a user-defined stopping test."
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 a custom stopping test function.\n\n"
25: "The command line options are:\n"
26: " -m <m>, where <m> = number of grid subdivisions in each dimension.\n"
27: " -seconds <s>, where <s> = maximum time in seconds allowed for computation.\n\n";
29: #include <slepceps.h>
30: #include <petsctime.h>
32: /*
33: User-defined routines
34: */
36: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);
37: PetscErrorCode MatMarkovModel(PetscInt,Mat);
41: int main(int argc,char **argv) 42: {
43: Mat A; /* operator matrix */
44: EPS eps; /* eigenproblem solver context */
45: PetscReal seconds=2.5; /* maximum time allowed for computation */
46: PetscLogDouble deadline; /* time to abort computation */
47: PetscInt N,m=15,nconv;
48: PetscBool terse;
49: PetscViewer viewer;
50: EPSConvergedReason reason;
51: PetscErrorCode ierr;
53: SlepcInitialize(&argc,&argv,(char*)0,help);
55: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
56: N = m*(m+1)/2;
57: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
58: PetscOptionsGetReal(NULL,NULL,"-seconds",&seconds,NULL);
59: PetscPrintf(PETSC_COMM_WORLD,"Maximum time for computation is set to %g seconds.\n\n",(double)seconds);
60: deadline = seconds;
61: PetscTimeAdd(&deadline);
63: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
64: Compute the operator matrix that defines the eigensystem, Ax=kx
65: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
67: MatCreate(PETSC_COMM_WORLD,&A);
68: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
69: MatSetFromOptions(A);
70: MatSetUp(A);
71: MatMarkovModel(m,A);
73: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
74: Create the eigensolver and set various options
75: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
77: EPSCreate(PETSC_COMM_WORLD,&eps);
78: EPSSetOperators(eps,A,NULL);
79: EPSSetProblemType(eps,EPS_NHEP);
80: EPSSetStoppingTestFunction(eps,MyStoppingTest,&deadline,NULL);
81: EPSSetFromOptions(eps);
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Solve the eigensystem
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: EPSSolve(eps);
89: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
90: Display solution and clean up
91: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: /* show detailed info unless -terse option is given by user */
94: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
95: if (terse) {
96: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
97: } else {
98: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
99: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
100: EPSGetConvergedReason(eps,&reason);
101: if (reason!=EPS_CONVERGED_USER) {
102: EPSReasonView(eps,viewer);
103: EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
104: } else {
105: EPSGetConverged(eps,&nconv);
106: PetscViewerASCIIPrintf(viewer,"Eigensolve finished with %D converged eigenpairs; reason=%s\n",nconv,EPSConvergedReasons[reason]);
107: }
108: PetscViewerPopFormat(viewer);
109: }
110: EPSDestroy(&eps);
111: MatDestroy(&A);
112: SlepcFinalize();
113: return ierr;
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: }
184: /*
185: Function for user-defined stopping test.
187: Checks that the computing time has not exceeded the deadline.
188: */
189: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)190: {
192: PetscLogDouble now,deadline = *(PetscLogDouble*)ctx;
195: /* check if usual termination conditions are met */
196: EPSStoppingBasic(eps,its,max_it,nconv,nev,reason,NULL);
197: if (*reason==EPS_CONVERGED_ITERATING) {
198: /* check if deadline has expired */
199: PetscTime(&now);
200: if (now>deadline) *reason = EPS_CONVERGED_USER;
201: }
202: return(0);
203: }