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, but with a user-defined sorting criterion."
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 spectrum selection.\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: */
34: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);
35: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
39: int main(int argc,char **argv) 40: {
41: Mat A; /* operator matrix */
42: EPS eps; /* eigenproblem solver context */
43: EPSType type;
44: PetscScalar target=0.5;
45: PetscInt N,m=15,nev;
46: PetscBool terse;
47: PetscViewer viewer;
49: char str[50];
51: SlepcInitialize(&argc,&argv,(char*)0,help);
53: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
54: N = m*(m+1)/2;
55: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
56: PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
57: SlepcSNPrintfScalar(str,50,target,PETSC_FALSE);
58: PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Compute the operator matrix that defines the eigensystem, Ax=kx
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: MatCreate(PETSC_COMM_WORLD,&A);
65: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
66: MatSetFromOptions(A);
67: MatSetUp(A);
68: MatMarkovModel(m,A);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Create the eigensolver and set various options
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: /*
75: Create eigensolver context
76: */
77: EPSCreate(PETSC_COMM_WORLD,&eps);
79: /*
80: Set operators. In this case, it is a standard eigenvalue problem
81: */
82: EPSSetOperators(eps,A,NULL);
83: EPSSetProblemType(eps,EPS_NHEP);
85: /*
86: Set the custom comparing routine in order to obtain the eigenvalues
87: closest to the target on the right only
88: */
89: EPSSetEigenvalueComparison(eps,MyEigenSort,&target);
91: /*
92: Set solver parameters at runtime
93: */
94: EPSSetFromOptions(eps);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Solve the eigensystem
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: EPSSolve(eps);
102: /*
103: Optional: Get some information from the solver and display it
104: */
105: EPSGetType(eps,&type);
106: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
107: EPSGetDimensions(eps,&nev,NULL,NULL);
108: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
110: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111: Display solution and clean up
112: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114: /* show detailed info unless -terse option is given by user */
115: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
116: if (terse) {
117: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
118: } else {
119: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
120: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
121: EPSReasonView(eps,viewer);
122: EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
123: PetscViewerPopFormat(viewer);
124: }
125: EPSDestroy(&eps);
126: MatDestroy(&A);
127: SlepcFinalize();
128: return ierr;
129: }
133: /*
134: Matrix generator for a Markov model of a random walk on a triangular grid.
136: This subroutine generates a test matrix that models a random walk on a
137: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
138: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
139: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
140: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
141: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
142: algorithms. The transpose of the matrix is stochastic and so it is known
143: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
144: associated with the eigenvalue unity. The problem is to calculate the steady
145: state probability distribution of the system, which is the eigevector
146: associated with the eigenvalue one and scaled in such a way that the sum all
147: the components is equal to one.
149: Note: the code will actually compute the transpose of the stochastic matrix
150: that contains the transition probabilities.
151: */
152: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)153: {
154: const PetscReal cst = 0.5/(PetscReal)(m-1);
155: PetscReal pd,pu;
156: PetscInt Istart,Iend,i,j,jmax,ix=0;
157: PetscErrorCode ierr;
160: MatGetOwnershipRange(A,&Istart,&Iend);
161: for (i=1;i<=m;i++) {
162: jmax = m-i+1;
163: for (j=1;j<=jmax;j++) {
164: ix = ix + 1;
165: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
166: if (j!=jmax) {
167: pd = cst*(PetscReal)(i+j-1);
168: /* north */
169: if (i==1) {
170: MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
171: } else {
172: MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
173: }
174: /* east */
175: if (j==1) {
176: MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
177: } else {
178: MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
179: }
180: }
181: /* south */
182: pu = 0.5 - cst*(PetscReal)(i+j-3);
183: if (j>1) {
184: MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
185: }
186: /* west */
187: if (i>1) {
188: MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
189: }
190: }
191: }
192: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
193: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
194: return(0);
195: }
199: /*
200: Function for user-defined eigenvalue ordering criterion.
202: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
203: one of them as the preferred one according to the criterion.
204: In this example, the preferred value is the one closest to the target,
205: but on the right side.
206: */
207: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)208: {
209: PetscScalar target = *(PetscScalar*)ctx;
210: PetscReal da,db;
211: PetscBool aisright,bisright;
214: if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
215: else aisright = PETSC_FALSE;
216: if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
217: else bisright = PETSC_FALSE;
218: if (aisright == bisright) {
219: /* both are on the same side of the target */
220: da = SlepcAbsEigenvalue(ar-target,ai);
221: db = SlepcAbsEigenvalue(br-target,bi);
222: if (da < db) *r = -1;
223: else if (da > db) *r = 1;
224: else *r = 0;
225: } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
226: else *r = 1; /* 'b' is on the right */
227: return(0);
228: }