Line data Source code
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 : This example implements one of the problems found at
12 : NLEVP: A Collection of Nonlinear Eigenvalue Problems,
13 : The University of Manchester.
14 : The details of the collection can be found at:
15 : [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
16 : Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.
17 :
18 : The pdde_stability problem is a complex-symmetric QEP from the stability
19 : analysis of a discretized partial delay-differential equation. It requires
20 : complex scalars.
21 : */
22 :
23 : static char help[] = "Stability analysis of a discretized partial delay-differential equation.\n\n"
24 : "The command line options are:\n"
25 : " -m <m>, grid size, the matrices have dimension n=m*m.\n"
26 : " -c <a0,b0,a1,b1,a2,b2,phi1>, comma-separated list of 7 real parameters.\n\n";
27 :
28 : #include <slepcpep.h>
29 :
30 : #define NMAT 3
31 :
32 : /*
33 : Function for user-defined eigenvalue ordering criterion.
34 :
35 : Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
36 : one of them as the preferred one according to the criterion.
37 : In this example, the preferred value is the one with absolute value closest to 1.
38 : */
39 16630 : PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
40 : {
41 16630 : PetscReal aa,ab;
42 :
43 16630 : PetscFunctionBeginUser;
44 16630 : aa = PetscAbsReal(SlepcAbsEigenvalue(ar,ai)-PetscRealConstant(1.0));
45 16630 : ab = PetscAbsReal(SlepcAbsEigenvalue(br,bi)-PetscRealConstant(1.0));
46 16630 : *r = aa > ab ? 1 : (aa < ab ? -1 : 0);
47 16630 : PetscFunctionReturn(PETSC_SUCCESS);
48 : }
49 :
50 3 : int main(int argc,char **argv)
51 : {
52 3 : Mat A[NMAT]; /* problem matrices */
53 3 : PEP pep; /* polynomial eigenproblem solver context */
54 3 : PetscInt m=15,n,II,Istart,Iend,i,j,k;
55 3 : PetscReal h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
56 3 : PetscScalar alpha,beta,gamma;
57 3 : PetscBool flg,terse;
58 :
59 3 : PetscFunctionBeginUser;
60 3 : PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
61 : #if !defined(PETSC_USE_COMPLEX)
62 : SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires complex scalars");
63 : #endif
64 :
65 3 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
66 3 : n = m*m;
67 3 : h = PETSC_PI/(m+1);
68 3 : gamma = PetscExpScalar(PETSC_i*c[6]);
69 3 : gamma = gamma/PetscAbsScalar(gamma);
70 3 : k = 7;
71 3 : PetscCall(PetscOptionsGetRealArray(NULL,NULL,"-c",c,&k,&flg));
72 3 : PetscCheck(!flg || k==7,PETSC_COMM_WORLD,PETSC_ERR_USER,"The number of parameters -c should be 7, you provided %" PetscInt_FMT,k);
73 3 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",n,m));
74 :
75 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76 : Compute the polynomial matrices
77 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
78 :
79 : /* initialize matrices */
80 12 : for (i=0;i<NMAT;i++) {
81 9 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
82 9 : PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
83 9 : PetscCall(MatSetFromOptions(A[i]));
84 : }
85 3 : PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
86 :
87 : /* A[1] has a pattern similar to the 2D Laplacian */
88 678 : for (II=Istart;II<Iend;II++) {
89 675 : i = II/m; j = II-i*m;
90 675 : xi = (i+1)*h; xj = (j+1)*h;
91 675 : alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
92 675 : beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
93 675 : PetscCall(MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES));
94 675 : if (j>0) PetscCall(MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES));
95 675 : if (j<m-1) PetscCall(MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES));
96 675 : if (i>0) PetscCall(MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES));
97 675 : if (i<m-1) PetscCall(MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES));
98 : }
99 :
100 : /* A[0] and A[2] are diagonal */
101 678 : for (II=Istart;II<Iend;II++) {
102 675 : i = II/m; j = II-i*m;
103 675 : xi = (i+1)*h; xj = (j+1)*h;
104 675 : alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
105 675 : beta = c[4]+c[5]*xj*(PETSC_PI-xj);
106 675 : PetscCall(MatSetValue(A[0],II,II,alpha,INSERT_VALUES));
107 675 : PetscCall(MatSetValue(A[2],II,II,beta,INSERT_VALUES));
108 : }
109 :
110 : /* assemble matrices */
111 12 : for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
112 12 : for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));
113 :
114 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115 : Create the eigensolver and solve the problem
116 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117 :
118 3 : PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
119 3 : PetscCall(PEPSetOperators(pep,NMAT,A));
120 3 : PetscCall(PEPSetEigenvalueComparison(pep,MyEigenSort,NULL));
121 3 : PetscCall(PEPSetDimensions(pep,4,PETSC_DETERMINE,PETSC_DETERMINE));
122 3 : PetscCall(PEPSetFromOptions(pep));
123 3 : PetscCall(PEPSolve(pep));
124 :
125 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126 : Display solution and clean up
127 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128 :
129 : /* show detailed info unless -terse option is given by user */
130 3 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
131 3 : if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
132 : else {
133 0 : PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
134 0 : PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
135 0 : PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
136 0 : PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
137 : }
138 3 : PetscCall(PEPDestroy(&pep));
139 12 : for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
140 3 : PetscCall(SlepcFinalize());
141 : return 0;
142 : }
143 :
144 : /*TEST
145 :
146 : build:
147 : requires: complex
148 :
149 : test:
150 : suffix: 1
151 : args: -pep_type {{toar qarnoldi linear}} -pep_ncv 25 -terse
152 : requires: complex double
153 :
154 : TEST*/
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