1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2014, 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;
48: char str[50];
50: SlepcInitialize(&argc,&argv,(char*)0,help);
52: PetscOptionsGetInt(NULL,"-m",&m,NULL);
53: N = m*(m+1)/2;
54: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
55: PetscOptionsGetScalar(NULL,"-target",&target,NULL);
56: SlepcSNPrintfScalar(str,50,target,PETSC_FALSE);
57: PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Compute the operator matrix that defines the eigensystem, Ax=kx
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: MatCreate(PETSC_COMM_WORLD,&A);
64: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
65: MatSetFromOptions(A);
66: MatSetUp(A);
67: MatMarkovModel(m,A);
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Create the eigensolver and set various options
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
73: /*
74: Create eigensolver context
75: */
76: EPSCreate(PETSC_COMM_WORLD,&eps);
78: /*
79: Set operators. In this case, it is a standard eigenvalue problem
80: */
81: EPSSetOperators(eps,A,NULL);
82: EPSSetProblemType(eps,EPS_NHEP);
84: /*
85: Set the custom comparing routine in order to obtain the eigenvalues
86: closest to the target on the right only
87: */
88: EPSSetEigenvalueComparison(eps,MyEigenSort,&target);
90: /*
91: Set solver parameters at runtime
92: */
93: EPSSetFromOptions(eps);
95: /*
96: Set the initial vector. This is optional, if not done the initial
97: vector is set to random values
98: */
99: MatGetVecs(A,&v0,NULL);
100: VecSet(v0,1.0);
101: EPSSetInitialSpace(eps,1,&v0);
103: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: Solve the eigensystem
105: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107: EPSSolve(eps);
109: /*
110: Optional: Get some information from the solver and display it
111: */
112: EPSGetType(eps,&type);
113: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
114: EPSGetDimensions(eps,&nev,NULL,NULL);
115: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
117: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118: Display solution and clean up
119: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: EPSPrintSolution(eps,NULL);
122: EPSDestroy(&eps);
123: MatDestroy(&A);
124: VecDestroy(&v0);
125: SlepcFinalize();
126: return 0;
127: }
131: /*
132: Matrix generator for a Markov model of a random walk on a triangular grid.
134: This subroutine generates a test matrix that models a random walk on a
135: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
136: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
137: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
138: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
139: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
140: algorithms. The transpose of the matrix is stochastic and so it is known
141: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
142: associated with the eigenvalue unity. The problem is to calculate the steady
143: state probability distribution of the system, which is the eigevector
144: associated with the eigenvalue one and scaled in such a way that the sum all
145: the components is equal to one.
147: Note: the code will actually compute the transpose of the stochastic matrix
148: that contains the transition probabilities.
149: */
150: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)151: {
152: const PetscReal cst = 0.5/(PetscReal)(m-1);
153: PetscReal pd,pu;
154: PetscInt Istart,Iend,i,j,jmax,ix=0;
155: PetscErrorCode ierr;
158: MatGetOwnershipRange(A,&Istart,&Iend);
159: for (i=1;i<=m;i++) {
160: jmax = m-i+1;
161: for (j=1;j<=jmax;j++) {
162: ix = ix + 1;
163: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
164: if (j!=jmax) {
165: pd = cst*(PetscReal)(i+j-1);
166: /* north */
167: if (i==1) {
168: MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
169: } else {
170: MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
171: }
172: /* east */
173: if (j==1) {
174: MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
175: } else {
176: MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
177: }
178: }
179: /* south */
180: pu = 0.5 - cst*(PetscReal)(i+j-3);
181: if (j>1) {
182: MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
183: }
184: /* west */
185: if (i>1) {
186: MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
187: }
188: }
189: }
190: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
191: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
192: return(0);
193: }
197: /*
198: Function for user-defined eigenvalue ordering criterion.
200: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
201: one of them as the preferred one according to the criterion.
202: In this example, the preferred value is the one closest to the target,
203: but on the right side.
204: */
205: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)206: {
207: PetscScalar target = *(PetscScalar*)ctx;
208: PetscReal da,db;
209: PetscBool aisright,bisright;
212: if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
213: else aisright = PETSC_FALSE;
214: if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
215: else bisright = PETSC_FALSE;
216: if (aisright == bisright) {
217: /* both are on the same side of the target */
218: da = SlepcAbsEigenvalue(ar-target,ai);
219: db = SlepcAbsEigenvalue(br-target,bi);
220: if (da < db) *r = -1;
221: else if (da > db) *r = 1;
222: else *r = 0;
223: } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
224: else *r = 1; /* 'b' is on the right */
225: return(0);
226: }