GCC Code Coverage Report

Directory: ./
File: src/eps/tutorials/ex5.c
Date: 2025-12-10 04:20:18
Exec Total Coverage
Lines: 70 74 94.6%
Functions: 2 2 100.0%
Branches: 207 338 61.2%
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1 /*
2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 SLEPc - Scalable Library for Eigenvalue Problem Computations
4 Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
6 This file is part of SLEPc.
7 SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 */
10
11 static char help[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid.\n\n"
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 the initial vector.\n\n"
14 "The command line options are:\n"
15 " -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";
16
17 #include <slepceps.h>
18
19 /*
20 User-defined routines
21 */
22 PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
23
24 90 int main(int argc,char **argv)
25 {
26 90 Vec v0; /* initial vector */
27 90 Mat A; /* operator matrix */
28 90 EPS eps; /* eigenproblem solver context */
29 90 EPSType type;
30 90 EPSStop stop;
31 90 PetscReal thres;
32 90 PetscInt N,m=15,nev;
33 90 PetscMPIInt rank;
34 90 PetscBool terse;
35
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 90 PetscFunctionBeginUser;
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 90 PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
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 90 PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
40 90 N = m*(m+1)/2;
41
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 90 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));
42
43 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44 Compute the operator matrix that defines the eigensystem, Ax=kx
45 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
46
47
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 90 PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
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 90 PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
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 90 PetscCall(MatSetFromOptions(A));
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 90 PetscCall(MatMarkovModel(m,A));
51
52 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53 Create the eigensolver and set various options
54 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55
56 /*
57 Create eigensolver context
58 */
59
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 90 PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
60
61 /*
62 Set operators. In this case, it is a standard eigenvalue problem
63 */
64
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 90 PetscCall(EPSSetOperators(eps,A,NULL));
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 90 PetscCall(EPSSetProblemType(eps,EPS_NHEP));
66
67 /*
68 Set solver parameters at runtime
69 */
70
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 90 PetscCall(EPSSetFromOptions(eps));
71
72 /*
73 Set the initial vector. This is optional, if not done the initial
74 vector is set to random values
75 */
76
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 90 PetscCall(MatCreateVecs(A,&v0,NULL));
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 90 PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
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 90 if (!rank) {
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 50 PetscCall(VecSetValue(v0,0,1.0,INSERT_VALUES));
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 50 PetscCall(VecSetValue(v0,1,1.0,INSERT_VALUES));
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 50 PetscCall(VecSetValue(v0,2,1.0,INSERT_VALUES));
82 }
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 90 PetscCall(VecAssemblyBegin(v0));
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 90 PetscCall(VecAssemblyEnd(v0));
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 90 PetscCall(EPSSetInitialSpace(eps,1,&v0));
86
87 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88 Solve the eigensystem
89 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
90
91
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 90 PetscCall(EPSSolve(eps));
92
93 /*
94 Optional: Get some information from the solver and display it
95 */
96
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 90 PetscCall(EPSGetType(eps,&type));
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 90 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
98
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 90 PetscCall(EPSGetStoppingTest(eps,&stop));
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 90 if (stop!=EPS_STOP_THRESHOLD) {
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 80 PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
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 80 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
102 } else {
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 10 PetscCall(EPSGetThreshold(eps,&thres,NULL));
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 10 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Using threshold: %.4g\n",(double)thres));
105 }
106
107 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
108 Display solution and clean up
109 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
110
111 /* show detailed info unless -terse option is given by user */
112
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 90 PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
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 90 if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
114 else {
115 ✗ PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
116 ✗ PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
117 ✗ PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
118 ✗ PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
119 }
120
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 90 PetscCall(EPSDestroy(&eps));
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 90 PetscCall(MatDestroy(&A));
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 90 PetscCall(VecDestroy(&v0));
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 90 PetscCall(SlepcFinalize());
124 return 0;
125 }
126
127 /*
128 Matrix generator for a Markov model of a random walk on a triangular grid.
129
130 This subroutine generates a test matrix that models a random walk on a
131 triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
132 FORTRAN subroutine to calculate the dominant invariant subspaces of a real
133 matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
134 papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
135 (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
136 algorithms. The transpose of the matrix is stochastic and so it is known
137 that one is an exact eigenvalue. One seeks the eigenvector of the transpose
138 associated with the eigenvalue unity. The problem is to calculate the steady
139 state probability distribution of the system, which is the eigevector
140 associated with the eigenvalue one and scaled in such a way that the sum all
141 the components is equal to one.
142
143 Note: the code will actually compute the transpose of the stochastic matrix
144 that contains the transition probabilities.
145 */
146 90 PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
147 {
148 90 const PetscReal cst = 0.5/(PetscReal)(m-1);
149 90 PetscReal pd,pu;
150 90 PetscInt Istart,Iend,i,j,jmax,ix=0;
151
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 90 PetscFunctionBeginUser;
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 90 PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
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 1440 for (i=1;i<=m;i++) {
155 1350 jmax = m-i+1;
156
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 12150 for (j=1;j<=jmax;j++) {
157 10800 ix = ix + 1;
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 10800 if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
159
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 6000 if (j!=jmax) {
160 5250 pd = cst*(PetscReal)(i+j-1);
161 /* north */
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 5250 if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
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 4550 else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
164 /* east */
165
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 5250 if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
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 4550 else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
167 }
168 /* south */
169 6000 pu = 0.5 - cst*(PetscReal)(i+j-3);
170
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 6000 if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
171 /* west */
172
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 10800 if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
173 }
174 }
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 90 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
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 90 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
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 18 PetscFunctionReturn(PETSC_SUCCESS);
178 }
179
180 /*TEST
181
182 test:
183 suffix: 1
184 nsize: 2
185 args: -eps_largest_real -eps_nev 4 -eps_two_sided {{0 1}} -eps_krylovschur_locking {{0 1}} -ds_parallel synchronized -terse
186 filter: sed -e "s/90424/90423/" | sed -e "s/85715/85714/"
187
188 test:
189 suffix: 2
190 args: -eps_threshold_relative .9 -eps_ncv 10 -terse
191 filter: sed -e "s/-0.85714/0.85714/" | sed -e "s/90424/90423/" | sed -e "s/-1.00000, 1.00000/1.00000, -1.00000/" | sed -e "s/-0.97137, 0.97137/0.97137, -0.97137/" | sed -e "s/-0.90423, 0.90423/0.90423, -0.90423/"
192
193 TEST*/
194