1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2015, 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: Vec v0; /* initial vector */
42: Mat A; /* operator matrix */
43: EPS eps; /* eigenproblem solver context */
44: EPSType type;
45: PetscScalar target=0.5;
46: PetscInt N,m=15,nev;
47: PetscBool terse;
48: PetscViewer viewer;
50: char str[50];
52: SlepcInitialize(&argc,&argv,(char*)0,help);
54: PetscOptionsGetInt(NULL,"-m",&m,NULL);
55: N = m*(m+1)/2;
56: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
57: PetscOptionsGetScalar(NULL,"-target",&target,NULL);
58: SlepcSNPrintfScalar(str,50,target,PETSC_FALSE);
59: PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Compute the operator matrix that defines the eigensystem, Ax=kx
63: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
65: MatCreate(PETSC_COMM_WORLD,&A);
66: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
67: MatSetFromOptions(A);
68: MatSetUp(A);
69: MatMarkovModel(m,A);
71: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
72: Create the eigensolver and set various options
73: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
75: /*
76: Create eigensolver context
77: */
78: EPSCreate(PETSC_COMM_WORLD,&eps);
80: /*
81: Set operators. In this case, it is a standard eigenvalue problem
82: */
83: EPSSetOperators(eps,A,NULL);
84: EPSSetProblemType(eps,EPS_NHEP);
86: /*
87: Set the custom comparing routine in order to obtain the eigenvalues
88: closest to the target on the right only
89: */
90: EPSSetEigenvalueComparison(eps,MyEigenSort,&target);
92: /*
93: Set solver parameters at runtime
94: */
95: EPSSetFromOptions(eps);
97: /*
98: Set the initial vector. This is optional, if not done the initial
99: vector is set to random values
100: */
101: MatCreateVecs(A,&v0,NULL);
102: VecSet(v0,1.0);
103: EPSSetInitialSpace(eps,1,&v0);
105: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106: Solve the eigensystem
107: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109: EPSSolve(eps);
111: /*
112: Optional: Get some information from the solver and display it
113: */
114: EPSGetType(eps,&type);
115: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
116: EPSGetDimensions(eps,&nev,NULL,NULL);
117: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Display solution and clean up
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123: /* show detailed info unless -terse option is given by user */
124: PetscOptionsHasName(NULL,"-terse",&terse);
125: if (terse) {
126: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
127: } else {
128: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
129: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
130: EPSReasonView(eps,viewer);
131: EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
132: PetscViewerPopFormat(viewer);
133: }
134: EPSDestroy(&eps);
135: MatDestroy(&A);
136: VecDestroy(&v0);
137: SlepcFinalize();
138: return 0;
139: }
143: /*
144: Matrix generator for a Markov model of a random walk on a triangular grid.
146: This subroutine generates a test matrix that models a random walk on a
147: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
148: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
149: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
150: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
151: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
152: algorithms. The transpose of the matrix is stochastic and so it is known
153: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
154: associated with the eigenvalue unity. The problem is to calculate the steady
155: state probability distribution of the system, which is the eigevector
156: associated with the eigenvalue one and scaled in such a way that the sum all
157: the components is equal to one.
159: Note: the code will actually compute the transpose of the stochastic matrix
160: that contains the transition probabilities.
161: */
162: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)163: {
164: const PetscReal cst = 0.5/(PetscReal)(m-1);
165: PetscReal pd,pu;
166: PetscInt Istart,Iend,i,j,jmax,ix=0;
167: PetscErrorCode ierr;
170: MatGetOwnershipRange(A,&Istart,&Iend);
171: for (i=1;i<=m;i++) {
172: jmax = m-i+1;
173: for (j=1;j<=jmax;j++) {
174: ix = ix + 1;
175: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
176: if (j!=jmax) {
177: pd = cst*(PetscReal)(i+j-1);
178: /* north */
179: if (i==1) {
180: MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
181: } else {
182: MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
183: }
184: /* east */
185: if (j==1) {
186: MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
187: } else {
188: MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
189: }
190: }
191: /* south */
192: pu = 0.5 - cst*(PetscReal)(i+j-3);
193: if (j>1) {
194: MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
195: }
196: /* west */
197: if (i>1) {
198: MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
199: }
200: }
201: }
202: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
203: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
204: return(0);
205: }
209: /*
210: Function for user-defined eigenvalue ordering criterion.
212: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
213: one of them as the preferred one according to the criterion.
214: In this example, the preferred value is the one closest to the target,
215: but on the right side.
216: */
217: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)218: {
219: PetscScalar target = *(PetscScalar*)ctx;
220: PetscReal da,db;
221: PetscBool aisright,bisright;
224: if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
225: else aisright = PETSC_FALSE;
226: if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
227: else bisright = PETSC_FALSE;
228: if (aisright == bisright) {
229: /* both are on the same side of the target */
230: da = SlepcAbsEigenvalue(ar-target,ai);
231: db = SlepcAbsEigenvalue(br-target,bi);
232: if (da < db) *r = -1;
233: else if (da > db) *r = 1;
234: else *r = 0;
235: } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
236: else *r = 1; /* 'b' is on the right */
237: return(0);
238: }