Actual source code: ex18.c
slepc-3.21.0 2024-03-30
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: PetscFunctionBeginUser;
38: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
40: PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
41: N = m*(m+1)/2;
42: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m));
43: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL));
44: PetscCall(SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE));
45: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str));
47: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
48: Compute the operator matrix that defines the eigensystem, Ax=kx
49: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
52: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
53: PetscCall(MatSetFromOptions(A));
54: PetscCall(MatMarkovModel(m,A));
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Create the eigensolver and set various options
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: /*
61: Create eigensolver context
62: */
63: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
65: /*
66: Set operators. In this case, it is a standard eigenvalue problem
67: */
68: PetscCall(EPSSetOperators(eps,A,NULL));
69: PetscCall(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: PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&target));
77: /*
78: Set solver parameters at runtime
79: */
80: PetscCall(EPSSetFromOptions(eps));
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Solve the eigensystem
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: PetscCall(EPSSolve(eps));
88: /*
89: Optional: Get some information from the solver and display it
90: */
91: PetscCall(EPSGetType(eps,&type));
92: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
93: PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
94: PetscCall(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: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
102: if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
103: else {
104: PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
105: PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
106: PetscCall(EPSConvergedReasonView(eps,viewer));
107: PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer));
108: PetscCall(PetscViewerPopFormat(viewer));
109: }
110: PetscCall(EPSDestroy(&eps));
111: PetscCall(MatDestroy(&A));
112: PetscCall(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;
141: PetscFunctionBeginUser;
142: PetscCall(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) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
152: else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
153: /* east */
154: if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
155: else PetscCall(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) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
160: /* west */
161: if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
162: }
163: }
164: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
165: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
166: PetscFunctionReturn(PETSC_SUCCESS);
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;
183: PetscFunctionBeginUser;
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(PETSC_SUCCESS);
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*/