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 the use of a region for filtering; the number of wanted eigenvalues is not known a priori.\n\n"
12 : "The problem is the Brusselator wave model as in ex9.c.\n"
13 : "The command line options are:\n"
14 : " -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
15 : " -L <L>, where <L> = bifurcation parameter.\n"
16 : " -alpha <alpha>, -beta <beta>, -delta1 <delta1>, -delta2 <delta2>,\n"
17 : " where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";
18 :
19 : #include <slepceps.h>
20 :
21 : /*
22 : This example tries to compute all eigenvalues lying outside the real axis.
23 : This could be achieved by computing LARGEST_IMAGINARY eigenvalues, but
24 : here we take a different route: define a region of the complex plane where
25 : eigenvalues must be emphasized (eigenvalues outside the region are filtered
26 : out). In this case, we select the region as the complement of a thin stripe
27 : around the real axis.
28 : */
29 :
30 : PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
31 : PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);
32 : PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);
33 :
34 : typedef struct {
35 : Mat T;
36 : Vec x1,x2,y1,y2;
37 : PetscScalar alpha,beta,tau1,tau2,sigma;
38 : PetscInt lastnconv; /* last value of nconv; used in stopping test */
39 : PetscInt nreps; /* number of repetitions of nconv; used in stopping test */
40 : } CTX_BRUSSEL;
41 :
42 1 : int main(int argc,char **argv)
43 : {
44 1 : Mat A; /* eigenvalue problem matrix */
45 1 : EPS eps; /* eigenproblem solver context */
46 1 : RG rg; /* region object */
47 1 : PetscScalar delta1,delta2,L,h;
48 1 : PetscInt N=30,n,i,Istart,Iend,mpd;
49 1 : CTX_BRUSSEL *ctx;
50 1 : PetscBool terse;
51 1 : PetscViewer viewer;
52 :
53 1 : PetscFunctionBeginUser;
54 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
55 :
56 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
57 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));
58 :
59 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60 : Generate the matrix
61 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62 :
63 : /*
64 : Create shell matrix context and set default parameters
65 : */
66 1 : PetscCall(PetscNew(&ctx));
67 1 : ctx->alpha = 2.0;
68 1 : ctx->beta = 5.45;
69 1 : delta1 = 0.008;
70 1 : delta2 = 0.004;
71 1 : L = 0.51302;
72 :
73 : /*
74 : Look the command line for user-provided parameters
75 : */
76 1 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
77 1 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL));
78 1 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL));
79 1 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
80 1 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));
81 :
82 : /*
83 : Create matrix T
84 : */
85 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&ctx->T));
86 1 : PetscCall(MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N));
87 1 : PetscCall(MatSetFromOptions(ctx->T));
88 :
89 1 : PetscCall(MatGetOwnershipRange(ctx->T,&Istart,&Iend));
90 101 : for (i=Istart;i<Iend;i++) {
91 100 : if (i>0) PetscCall(MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES));
92 100 : if (i<N-1) PetscCall(MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES));
93 100 : PetscCall(MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES));
94 : }
95 1 : PetscCall(MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY));
96 1 : PetscCall(MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY));
97 1 : PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
98 :
99 : /*
100 : Fill the remaining information in the shell matrix context
101 : and create auxiliary vectors
102 : */
103 1 : h = 1.0 / (PetscReal)(N+1);
104 1 : ctx->tau1 = delta1 / ((h*L)*(h*L));
105 1 : ctx->tau2 = delta2 / ((h*L)*(h*L));
106 1 : ctx->sigma = 0.0;
107 1 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1));
108 1 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2));
109 1 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1));
110 1 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2));
111 :
112 : /*
113 : Create the shell matrix
114 : */
115 1 : PetscCall(MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A));
116 1 : PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel));
117 1 : PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel));
118 :
119 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120 : Create the eigensolver and configure the region
121 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122 :
123 1 : PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
124 1 : PetscCall(EPSSetOperators(eps,A,NULL));
125 1 : PetscCall(EPSSetProblemType(eps,EPS_NHEP));
126 :
127 : /*
128 : Define the region containing the eigenvalues of interest
129 : */
130 1 : PetscCall(EPSGetRG(eps,&rg));
131 1 : PetscCall(RGSetType(rg,RGINTERVAL));
132 1 : PetscCall(RGIntervalSetEndpoints(rg,-PETSC_INFINITY,PETSC_INFINITY,-0.01,0.01));
133 1 : PetscCall(RGSetComplement(rg,PETSC_TRUE));
134 : /* sort eigenvalue approximations wrt a target, otherwise convergence will be erratic */
135 1 : PetscCall(EPSSetTarget(eps,0.0));
136 1 : PetscCall(EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE));
137 :
138 : /*
139 : Set solver options. In particular, we must allocate sufficient
140 : storage for all eigenpairs that may converge (ncv). This is
141 : application-dependent.
142 : */
143 1 : mpd = 40;
144 1 : PetscCall(EPSSetDimensions(eps,2*mpd,3*mpd,mpd));
145 1 : PetscCall(EPSSetTolerances(eps,1e-7,2000));
146 1 : ctx->lastnconv = 0;
147 1 : ctx->nreps = 0;
148 1 : PetscCall(EPSSetStoppingTestFunction(eps,MyStoppingTest,(void*)ctx,NULL));
149 1 : PetscCall(EPSSetFromOptions(eps));
150 :
151 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152 : Solve the eigensystem and display solution
153 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154 :
155 1 : PetscCall(EPSSolve(eps));
156 :
157 : /* show detailed info unless -terse option is given by user */
158 1 : PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
159 1 : PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
160 1 : PetscCall(EPSConvergedReasonView(eps,viewer));
161 1 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
162 1 : if (!terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer));
163 1 : PetscCall(PetscViewerPopFormat(viewer));
164 :
165 1 : PetscCall(EPSDestroy(&eps));
166 1 : PetscCall(MatDestroy(&A));
167 1 : PetscCall(MatDestroy(&ctx->T));
168 1 : PetscCall(VecDestroy(&ctx->x1));
169 1 : PetscCall(VecDestroy(&ctx->x2));
170 1 : PetscCall(VecDestroy(&ctx->y1));
171 1 : PetscCall(VecDestroy(&ctx->y2));
172 1 : PetscCall(PetscFree(ctx));
173 1 : PetscCall(SlepcFinalize());
174 : return 0;
175 : }
176 :
177 550 : PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
178 : {
179 550 : PetscInt n;
180 550 : const PetscScalar *px;
181 550 : PetscScalar *py;
182 550 : CTX_BRUSSEL *ctx;
183 :
184 550 : PetscFunctionBeginUser;
185 550 : PetscCall(MatShellGetContext(A,&ctx));
186 550 : PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
187 550 : PetscCall(VecGetArrayRead(x,&px));
188 550 : PetscCall(VecGetArray(y,&py));
189 550 : PetscCall(VecPlaceArray(ctx->x1,px));
190 550 : PetscCall(VecPlaceArray(ctx->x2,px+n));
191 550 : PetscCall(VecPlaceArray(ctx->y1,py));
192 550 : PetscCall(VecPlaceArray(ctx->y2,py+n));
193 :
194 550 : PetscCall(MatMult(ctx->T,ctx->x1,ctx->y1));
195 550 : PetscCall(VecScale(ctx->y1,ctx->tau1));
196 550 : PetscCall(VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1));
197 550 : PetscCall(VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2));
198 :
199 550 : PetscCall(MatMult(ctx->T,ctx->x2,ctx->y2));
200 550 : PetscCall(VecScale(ctx->y2,ctx->tau2));
201 550 : PetscCall(VecAXPY(ctx->y2,-ctx->beta,ctx->x1));
202 550 : PetscCall(VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2));
203 :
204 550 : PetscCall(VecRestoreArrayRead(x,&px));
205 550 : PetscCall(VecRestoreArray(y,&py));
206 550 : PetscCall(VecResetArray(ctx->x1));
207 550 : PetscCall(VecResetArray(ctx->x2));
208 550 : PetscCall(VecResetArray(ctx->y1));
209 550 : PetscCall(VecResetArray(ctx->y2));
210 550 : PetscFunctionReturn(PETSC_SUCCESS);
211 : }
212 :
213 0 : PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
214 : {
215 0 : Vec d1,d2;
216 0 : PetscInt n;
217 0 : PetscScalar *pd;
218 0 : MPI_Comm comm;
219 0 : CTX_BRUSSEL *ctx;
220 :
221 0 : PetscFunctionBeginUser;
222 0 : PetscCall(MatShellGetContext(A,&ctx));
223 0 : PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
224 0 : PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
225 0 : PetscCall(VecGetArray(diag,&pd));
226 0 : PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1));
227 0 : PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2));
228 :
229 0 : PetscCall(VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma));
230 0 : PetscCall(VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma));
231 :
232 0 : PetscCall(VecDestroy(&d1));
233 0 : PetscCall(VecDestroy(&d2));
234 0 : PetscCall(VecRestoreArray(diag,&pd));
235 0 : PetscFunctionReturn(PETSC_SUCCESS);
236 : }
237 :
238 : /*
239 : Function for user-defined stopping test.
240 :
241 : Ignores the value of nev. It only takes into account the number of
242 : eigenpairs that have converged in recent outer iterations (restarts);
243 : if no new eigenvalues have converged in the last few restarts,
244 : we stop the iteration, assuming that no more eigenvalues are present
245 : inside the region.
246 : */
247 26 : PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ptr)
248 : {
249 26 : CTX_BRUSSEL *ctx = (CTX_BRUSSEL*)ptr;
250 :
251 26 : PetscFunctionBeginUser;
252 : /* check usual termination conditions, but ignoring the case nconv>=nev */
253 26 : PetscCall(EPSStoppingBasic(eps,its,max_it,nconv,PETSC_MAX_INT,reason,NULL));
254 26 : if (*reason==EPS_CONVERGED_ITERATING) {
255 : /* check if nconv is the same as before */
256 26 : if (nconv==ctx->lastnconv) ctx->nreps++;
257 : else {
258 4 : ctx->lastnconv = nconv;
259 4 : ctx->nreps = 0;
260 : }
261 : /* check if no eigenvalues converged in last 10 restarts */
262 26 : if (nconv && ctx->nreps>10) *reason = EPS_CONVERGED_USER;
263 : }
264 26 : PetscFunctionReturn(PETSC_SUCCESS);
265 : }
266 :
267 : /*TEST
268 :
269 : test:
270 : suffix: 1
271 : args: -n 100 -terse
272 : requires: !single
273 :
274 : TEST*/
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