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 : static char help[] = "Illustrates use of NEPSetEigenvalueComparison().\n\n"
12 : "This is a simplified version of ex20.\n"
13 : "The command line options are:\n"
14 : " -n <n>, where <n> = number of grid subdivisions.\n";
15 :
16 : /*
17 : Solve 1-D PDE
18 : -u'' = lambda*u
19 : on [0,1] subject to
20 : u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
21 : */
22 :
23 : #include <slepcnep.h>
24 :
25 : /*
26 : User-defined routines
27 : */
28 : PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
29 : PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
30 : PetscErrorCode MyEigenSort(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*);
31 :
32 : /*
33 : User-defined application context
34 : */
35 : typedef struct {
36 : PetscScalar kappa; /* ratio between stiffness of spring and attached mass */
37 : PetscReal h; /* mesh spacing */
38 : } ApplicationCtx;
39 :
40 1 : int main(int argc,char **argv)
41 : {
42 1 : NEP nep; /* nonlinear eigensolver context */
43 1 : Mat F,J; /* Function and Jacobian matrices */
44 1 : ApplicationCtx ctx; /* user-defined context */
45 1 : PetscScalar target;
46 1 : RG rg;
47 1 : PetscInt n=128;
48 1 : PetscBool terse;
49 :
50 1 : PetscFunctionBeginUser;
51 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
52 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
53 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n));
54 1 : ctx.h = 1.0/(PetscReal)n;
55 1 : ctx.kappa = 1.0;
56 :
57 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58 : Prepare nonlinear eigensolver context
59 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60 :
61 1 : PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
62 :
63 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
64 1 : PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
65 1 : PetscCall(MatSetFromOptions(F));
66 1 : PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
67 1 : PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
68 1 : PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));
69 :
70 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
71 1 : PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
72 1 : PetscCall(MatSetFromOptions(J));
73 1 : PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
74 1 : PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
75 1 : PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));
76 :
77 1 : PetscCall(NEPSetType(nep,NEPNLEIGS));
78 1 : PetscCall(NEPGetRG(nep,&rg));
79 1 : PetscCall(RGSetType(rg,RGINTERVAL));
80 : #if defined(PETSC_USE_COMPLEX)
81 : PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,-0.001,0.001));
82 : #else
83 1 : PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,0,0));
84 : #endif
85 1 : PetscCall(NEPSetTarget(nep,25.0));
86 1 : PetscCall(NEPSetEigenvalueComparison(nep,MyEigenSort,&target));
87 1 : PetscCall(NEPSetTolerances(nep,PETSC_SMALL,PETSC_DEFAULT));
88 1 : PetscCall(NEPSetFromOptions(nep));
89 1 : PetscCall(NEPGetTarget(nep,&target));
90 :
91 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92 : Solve the eigensystem and display the solution
93 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94 :
95 1 : PetscCall(NEPSolve(nep));
96 :
97 : /* show detailed info unless -terse option is given by user */
98 1 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
99 1 : if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
100 : else {
101 0 : PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
102 0 : PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
103 0 : PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
104 0 : PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
105 : }
106 :
107 1 : PetscCall(NEPDestroy(&nep));
108 1 : PetscCall(MatDestroy(&F));
109 1 : PetscCall(MatDestroy(&J));
110 1 : PetscCall(SlepcFinalize());
111 : return 0;
112 : }
113 :
114 : /* ------------------------------------------------------------------- */
115 : /*
116 : FormFunction - Computes Function matrix T(lambda)
117 :
118 : Input Parameters:
119 : . nep - the NEP context
120 : . lambda - the scalar argument
121 : . ctx - optional user-defined context, as set by NEPSetFunction()
122 :
123 : Output Parameters:
124 : . fun - Function matrix
125 : . B - optionally different preconditioning matrix
126 : */
127 108 : PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
128 : {
129 108 : ApplicationCtx *user = (ApplicationCtx*)ctx;
130 108 : PetscScalar A[3],c,d;
131 108 : PetscReal h;
132 108 : PetscInt i,n,j[3],Istart,Iend;
133 108 : PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
134 :
135 108 : PetscFunctionBeginUser;
136 : /*
137 : Compute Function entries and insert into matrix
138 : */
139 108 : PetscCall(MatGetSize(fun,&n,NULL));
140 108 : PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
141 108 : if (Istart==0) FirstBlock=PETSC_TRUE;
142 108 : if (Iend==n) LastBlock=PETSC_TRUE;
143 108 : h = user->h;
144 108 : c = user->kappa/(lambda-user->kappa);
145 108 : d = n;
146 :
147 : /*
148 : Interior grid points
149 : */
150 13716 : for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
151 13608 : j[0] = i-1; j[1] = i; j[2] = i+1;
152 13608 : A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
153 13608 : PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
154 : }
155 :
156 : /*
157 : Boundary points
158 : */
159 108 : if (FirstBlock) {
160 108 : i = 0;
161 108 : j[0] = 0; j[1] = 1;
162 108 : A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
163 108 : PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
164 : }
165 :
166 108 : if (LastBlock) {
167 108 : i = n-1;
168 108 : j[0] = n-2; j[1] = n-1;
169 108 : A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
170 108 : PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
171 : }
172 :
173 : /*
174 : Assemble matrix
175 : */
176 108 : PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
177 108 : PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
178 108 : if (fun != B) {
179 0 : PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
180 0 : PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
181 : }
182 108 : PetscFunctionReturn(PETSC_SUCCESS);
183 : }
184 :
185 : /* ------------------------------------------------------------------- */
186 : /*
187 : FormJacobian - Computes Jacobian matrix T'(lambda)
188 :
189 : Input Parameters:
190 : . nep - the NEP context
191 : . lambda - the scalar argument
192 : . ctx - optional user-defined context, as set by NEPSetJacobian()
193 :
194 : Output Parameters:
195 : . jac - Jacobian matrix
196 : . B - optionally different preconditioning matrix
197 : */
198 0 : PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
199 : {
200 0 : ApplicationCtx *user = (ApplicationCtx*)ctx;
201 0 : PetscScalar A[3],c;
202 0 : PetscReal h;
203 0 : PetscInt i,n,j[3],Istart,Iend;
204 0 : PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
205 :
206 0 : PetscFunctionBeginUser;
207 : /*
208 : Compute Jacobian entries and insert into matrix
209 : */
210 0 : PetscCall(MatGetSize(jac,&n,NULL));
211 0 : PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
212 0 : if (Istart==0) FirstBlock=PETSC_TRUE;
213 0 : if (Iend==n) LastBlock=PETSC_TRUE;
214 0 : h = user->h;
215 0 : c = user->kappa/(lambda-user->kappa);
216 :
217 : /*
218 : Interior grid points
219 : */
220 0 : for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
221 0 : j[0] = i-1; j[1] = i; j[2] = i+1;
222 0 : A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
223 0 : PetscCall(MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES));
224 : }
225 :
226 : /*
227 : Boundary points
228 : */
229 0 : if (FirstBlock) {
230 0 : i = 0;
231 0 : j[0] = 0; j[1] = 1;
232 0 : A[0] = -2.0*h/3.0; A[1] = -h/6.0;
233 0 : PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
234 : }
235 :
236 0 : if (LastBlock) {
237 0 : i = n-1;
238 0 : j[0] = n-2; j[1] = n-1;
239 0 : A[0] = -h/6.0; A[1] = -h/3.0-c*c;
240 0 : PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
241 : }
242 :
243 : /*
244 : Assemble matrix
245 : */
246 0 : PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
247 0 : PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
248 0 : PetscFunctionReturn(PETSC_SUCCESS);
249 : }
250 :
251 : /*
252 : Function for user-defined eigenvalue ordering criterion.
253 :
254 : Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
255 : one of them as the preferred one according to the criterion.
256 : In this example, eigenvalues are sorted with respect to the target,
257 : but those on the right of the target are preferred.
258 : */
259 196 : PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
260 : {
261 196 : PetscReal a,b;
262 196 : PetscScalar target = *(PetscScalar*)ctx;
263 :
264 196 : PetscFunctionBeginUser;
265 196 : if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
266 : else {
267 109 : a = SlepcAbsEigenvalue(ar-target,ai);
268 109 : b = SlepcAbsEigenvalue(br-target,bi);
269 109 : if (a>b) *r = 1;
270 85 : else if (a<b) *r = -1;
271 0 : else *r = 0;
272 : }
273 196 : PetscFunctionReturn(PETSC_SUCCESS);
274 : }
275 :
276 : /*TEST
277 :
278 : test:
279 : suffix: 1
280 : args: -nep_nev 4 -nep_ncv 8 -terse
281 : requires: double !complex
282 :
283 : TEST*/
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