Actual source code: ex30.c
slepc-3.17.0 2022-03-31
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[] = "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";
19: #include <slepceps.h>
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: */
30: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
31: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);
32: PetscErrorCode MyStoppingTest(EPS,PetscInt,PetscInt,PetscInt,PetscInt,EPSConvergedReason*,void*);
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;
42: int main(int argc,char **argv)
43: {
44: Mat A; /* eigenvalue problem matrix */
45: EPS eps; /* eigenproblem solver context */
46: RG rg; /* region object */
47: PetscScalar delta1,delta2,L,h;
48: PetscInt N=30,n,i,Istart,Iend,mpd;
49: CTX_BRUSSEL *ctx;
50: PetscBool terse;
51: PetscViewer viewer;
53: SlepcInitialize(&argc,&argv,(char*)0,help);
55: PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
56: PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N);
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Generate the matrix
60: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62: /*
63: Create shell matrix context and set default parameters
64: */
65: PetscNew(&ctx);
66: ctx->alpha = 2.0;
67: ctx->beta = 5.45;
68: delta1 = 0.008;
69: delta2 = 0.004;
70: L = 0.51302;
72: /*
73: Look the command line for user-provided parameters
74: */
75: PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
76: PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
77: PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
78: PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
79: PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);
81: /*
82: Create matrix T
83: */
84: MatCreate(PETSC_COMM_WORLD,&ctx->T);
85: MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
86: MatSetFromOptions(ctx->T);
87: MatSetUp(ctx->T);
89: MatGetOwnershipRange(ctx->T,&Istart,&Iend);
90: for (i=Istart;i<Iend;i++) {
91: if (i>0) MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES);
92: if (i<N-1) MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES);
93: MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES);
94: }
95: MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
96: MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
97: MatGetLocalSize(ctx->T,&n,NULL);
99: /*
100: Fill the remaining information in the shell matrix context
101: and create auxiliary vectors
102: */
103: h = 1.0 / (PetscReal)(N+1);
104: ctx->tau1 = delta1 / ((h*L)*(h*L));
105: ctx->tau2 = delta2 / ((h*L)*(h*L));
106: ctx->sigma = 0.0;
107: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1);
108: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2);
109: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1);
110: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2);
112: /*
113: Create the shell matrix
114: */
115: MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
116: MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel);
117: MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel);
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Create the eigensolver and configure the region
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123: EPSCreate(PETSC_COMM_WORLD,&eps);
124: EPSSetOperators(eps,A,NULL);
125: EPSSetProblemType(eps,EPS_NHEP);
127: /*
128: Define the region containing the eigenvalues of interest
129: */
130: EPSGetRG(eps,&rg);
131: RGSetType(rg,RGINTERVAL);
132: RGIntervalSetEndpoints(rg,-PETSC_INFINITY,PETSC_INFINITY,-0.01,0.01);
133: RGSetComplement(rg,PETSC_TRUE);
134: /* sort eigenvalue approximations wrt a target, otherwise convergence will be erratic */
135: EPSSetTarget(eps,0.0);
136: EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
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: mpd = 40;
144: EPSSetDimensions(eps,2*mpd,3*mpd,mpd);
145: EPSSetTolerances(eps,1e-7,2000);
146: ctx->lastnconv = 0;
147: ctx->nreps = 0;
148: EPSSetStoppingTestFunction(eps,MyStoppingTest,(void*)ctx,NULL);
149: EPSSetFromOptions(eps);
151: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152: Solve the eigensystem and display solution
153: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: EPSSolve(eps);
157: /* show detailed info unless -terse option is given by user */
158: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
159: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
160: EPSConvergedReasonView(eps,viewer);
161: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
162: if (!terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
163: PetscViewerPopFormat(viewer);
165: EPSDestroy(&eps);
166: MatDestroy(&A);
167: MatDestroy(&ctx->T);
168: VecDestroy(&ctx->x1);
169: VecDestroy(&ctx->x2);
170: VecDestroy(&ctx->y1);
171: VecDestroy(&ctx->y2);
172: PetscFree(ctx);
173: SlepcFinalize();
174: return 0;
175: }
177: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
178: {
179: PetscInt n;
180: const PetscScalar *px;
181: PetscScalar *py;
182: CTX_BRUSSEL *ctx;
185: MatShellGetContext(A,&ctx);
186: MatGetLocalSize(ctx->T,&n,NULL);
187: VecGetArrayRead(x,&px);
188: VecGetArray(y,&py);
189: VecPlaceArray(ctx->x1,px);
190: VecPlaceArray(ctx->x2,px+n);
191: VecPlaceArray(ctx->y1,py);
192: VecPlaceArray(ctx->y2,py+n);
194: MatMult(ctx->T,ctx->x1,ctx->y1);
195: VecScale(ctx->y1,ctx->tau1);
196: VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1);
197: VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2);
199: MatMult(ctx->T,ctx->x2,ctx->y2);
200: VecScale(ctx->y2,ctx->tau2);
201: VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
202: VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2);
204: VecRestoreArrayRead(x,&px);
205: VecRestoreArray(y,&py);
206: VecResetArray(ctx->x1);
207: VecResetArray(ctx->x2);
208: VecResetArray(ctx->y1);
209: VecResetArray(ctx->y2);
210: PetscFunctionReturn(0);
211: }
213: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
214: {
215: Vec d1,d2;
216: PetscInt n;
217: PetscScalar *pd;
218: MPI_Comm comm;
219: CTX_BRUSSEL *ctx;
222: MatShellGetContext(A,&ctx);
223: PetscObjectGetComm((PetscObject)A,&comm);
224: MatGetLocalSize(ctx->T,&n,NULL);
225: VecGetArray(diag,&pd);
226: VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
227: VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);
229: VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma);
230: VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma);
232: VecDestroy(&d1);
233: VecDestroy(&d2);
234: VecRestoreArray(diag,&pd);
235: PetscFunctionReturn(0);
236: }
238: /*
239: Function for user-defined stopping test.
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: PetscErrorCode MyStoppingTest(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ptr)
248: {
249: CTX_BRUSSEL *ctx = (CTX_BRUSSEL*)ptr;
252: /* check usual termination conditions, but ignoring the case nconv>=nev */
253: EPSStoppingBasic(eps,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
254: if (*reason==EPS_CONVERGED_ITERATING) {
255: /* check if nconv is the same as before */
256: if (nconv==ctx->lastnconv) ctx->nreps++;
257: else {
258: ctx->lastnconv = nconv;
259: ctx->nreps = 0;
260: }
261: /* check if no eigenvalues converged in last 10 restarts */
262: if (nconv && ctx->nreps>10) *reason = EPS_CONVERGED_USER;
263: }
264: PetscFunctionReturn(0);
265: }
267: /*TEST
269: test:
270: suffix: 1
271: args: -n 100 -terse
272: requires: !single
274: TEST*/