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, but with a user-defined sorting criterion."
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 spectrum selection.\n\n"
14: "The command line options are:\n"
15: " -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";
17: #include <slepceps.h> 19: /*
20: User-defined routines
21: */
23: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);
24: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
26: int main(int argc,char **argv) 27: {
28: Mat A; /* operator matrix */
29: EPS eps; /* eigenproblem solver context */
30: EPSType type;
31: PetscScalar target=0.5;
32: PetscInt N,m=15,nev;
33: PetscBool terse;
34: PetscViewer viewer;
35: char str[50];
37: SlepcInitialize(&argc,&argv,(char*)0,help);
39: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
40: N = m*(m+1)/2;
41: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m);
42: PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
43: SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE);
44: PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);
46: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47: Compute the operator matrix that defines the eigensystem, Ax=kx
48: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
50: MatCreate(PETSC_COMM_WORLD,&A);
51: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
52: MatSetFromOptions(A);
53: MatSetUp(A);
54: MatMarkovModel(m,A);
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Create the eigensolver and set various options
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: /*
61: Create eigensolver context
62: */
63: EPSCreate(PETSC_COMM_WORLD,&eps);
65: /*
66: Set operators. In this case, it is a standard eigenvalue problem
67: */
68: EPSSetOperators(eps,A,NULL);
69: EPSSetProblemType(eps,EPS_NHEP);
71: /*
72: Set the custom comparing routine in order to obtain the eigenvalues
73: closest to the target on the right only
74: */
75: EPSSetEigenvalueComparison(eps,MyEigenSort,&target);
77: /*
78: Set solver parameters at runtime
79: */
80: EPSSetFromOptions(eps);
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Solve the eigensystem
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: EPSSolve(eps);
88: /*
89: Optional: Get some information from the solver and display it
90: */
91: EPSGetType(eps,&type);
92: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
93: EPSGetDimensions(eps,&nev,NULL,NULL);
94: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Display solution and clean up
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: /* show detailed info unless -terse option is given by user */
101: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
102: if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
103: else {
104: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
105: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
106: EPSConvergedReasonView(eps,viewer);
107: EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
108: PetscViewerPopFormat(viewer);
109: }
110: EPSDestroy(&eps);
111: MatDestroy(&A);
112: SlepcFinalize();
113: return 0;
114: }
116: /*
117: Matrix generator for a Markov model of a random walk on a triangular grid.
119: This subroutine generates a test matrix that models a random walk on a
120: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
121: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
122: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
123: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
124: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
125: algorithms. The transpose of the matrix is stochastic and so it is known
126: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
127: associated with the eigenvalue unity. The problem is to calculate the steady
128: state probability distribution of the system, which is the eigevector
129: associated with the eigenvalue one and scaled in such a way that the sum all
130: the components is equal to one.
132: Note: the code will actually compute the transpose of the stochastic matrix
133: that contains the transition probabilities.
134: */
135: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)136: {
137: const PetscReal cst = 0.5/(PetscReal)(m-1);
138: PetscReal pd,pu;
139: PetscInt Istart,Iend,i,j,jmax,ix=0;
142: MatGetOwnershipRange(A,&Istart,&Iend);
143: for (i=1;i<=m;i++) {
144: jmax = m-i+1;
145: for (j=1;j<=jmax;j++) {
146: ix = ix + 1;
147: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
148: if (j!=jmax) {
149: pd = cst*(PetscReal)(i+j-1);
150: /* north */
151: if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
152: else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
153: /* east */
154: if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
155: else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
156: }
157: /* south */
158: pu = 0.5 - cst*(PetscReal)(i+j-3);
159: if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
160: /* west */
161: if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
162: }
163: }
164: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
165: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
166: PetscFunctionReturn(0);
167: }
169: /*
170: Function for user-defined eigenvalue ordering criterion.
172: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
173: one of them as the preferred one according to the criterion.
174: In this example, the preferred value is the one closest to the target,
175: but on the right side.
176: */
177: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)178: {
179: PetscScalar target = *(PetscScalar*)ctx;
180: PetscReal da,db;
181: PetscBool aisright,bisright;
184: if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
185: else aisright = PETSC_FALSE;
186: if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
187: else bisright = PETSC_FALSE;
188: if (aisright == bisright) {
189: /* both are on the same side of the target */
190: da = SlepcAbsEigenvalue(ar-target,ai);
191: db = SlepcAbsEigenvalue(br-target,bi);
192: if (da < db) *r = -1;
193: else if (da > db) *r = 1;
194: else *r = 0;
195: } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
196: else *r = 1; /* 'b' is on the right */
197: PetscFunctionReturn(0);
198: }
200: /*TEST
202: test:
203: suffix: 1
204: args: -eps_nev 4 -terse
205: requires: !single
206: filter: sed -e "s/[+-]0\.0*i//g"
208: TEST*/