Actual source code: test22.c
slepc-3.17.2 2022-08-09
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 how to obtain invariant subspaces. "
12: "Based on ex9.\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 computes the eigenvalues with largest real part of the
23: following matrix
25: A = [ tau1*T+(beta-1)*I alpha^2*I
26: -beta*I tau2*T-alpha^2*I ],
28: where
30: T = tridiag{1,-2,1}
31: h = 1/(n+1)
32: tau1 = delta1/(h*L)^2
33: tau2 = delta2/(h*L)^2
34: */
36: /* Matrix operations */
37: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
38: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);
40: typedef struct {
41: Mat T;
42: Vec x1,x2,y1,y2;
43: PetscScalar alpha,beta,tau1,tau2,sigma;
44: } CTX_BRUSSEL;
46: int main(int argc,char **argv)
47: {
48: EPS eps;
49: Mat A;
50: Vec *Q,v;
51: PetscScalar delta1,delta2,L,h,kr,ki;
52: PetscReal errest,tol,re,im,lev;
53: PetscInt N=30,n,i,j,Istart,Iend,nev,nconv;
54: CTX_BRUSSEL *ctx;
55: PetscBool errok,trueres;
57: SlepcInitialize(&argc,&argv,(char*)0,help);
58: PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
59: PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N);
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Generate the matrix
63: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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: PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
73: PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
74: PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
75: PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
76: PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);
78: /* Create matrix T */
79: MatCreate(PETSC_COMM_WORLD,&ctx->T);
80: MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
81: MatSetFromOptions(ctx->T);
82: MatSetUp(ctx->T);
83: MatGetOwnershipRange(ctx->T,&Istart,&Iend);
84: for (i=Istart;i<Iend;i++) {
85: if (i>0) MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES);
86: if (i<N-1) MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES);
87: MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES);
88: }
89: MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
90: MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
91: MatGetLocalSize(ctx->T,&n,NULL);
93: /* Fill the remaining information in the shell matrix context
94: and create auxiliary vectors */
95: h = 1.0 / (PetscReal)(N+1);
96: ctx->tau1 = delta1 / ((h*L)*(h*L));
97: ctx->tau2 = delta2 / ((h*L)*(h*L));
98: ctx->sigma = 0.0;
99: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1);
100: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2);
101: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1);
102: VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2);
104: /* Create the shell matrix */
105: MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
106: MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel);
107: MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel);
109: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: Create the eigensolver and solve the problem
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
113: EPSCreate(PETSC_COMM_WORLD,&eps);
114: EPSSetOperators(eps,A,NULL);
115: EPSSetProblemType(eps,EPS_NHEP);
116: EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
117: EPSSetTrueResidual(eps,PETSC_FALSE);
118: EPSSetFromOptions(eps);
119: EPSSolve(eps);
121: EPSGetTrueResidual(eps,&trueres);
122: /*if (trueres) PetscPrintf(PETSC_COMM_WORLD," Computing true residuals explicitly\n\n");*/
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Display solution and clean up
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128: EPSGetDimensions(eps,&nev,NULL,NULL);
129: EPSGetTolerances(eps,&tol,NULL);
130: EPSGetConverged(eps,&nconv);
131: if (nconv<nev) PetscPrintf(PETSC_COMM_WORLD," Problem: less than %" PetscInt_FMT " eigenvalues converged\n\n",nev);
132: else {
133: /* Check that all converged eigenpairs satisfy the requested tolerance
134: (in this example we use the solver's error estimate instead of computing
135: the residual norm explicitly) */
136: errok = PETSC_TRUE;
137: for (i=0;i<nev;i++) {
138: EPSGetErrorEstimate(eps,i,&errest);
139: EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL);
140: errok = (errok && errest<5.0*SlepcAbsEigenvalue(kr,ki)*tol)? PETSC_TRUE: PETSC_FALSE;
141: }
142: if (!errok) PetscPrintf(PETSC_COMM_WORLD," Problem: some of the first %" PetscInt_FMT " relative errors are higher than the tolerance\n\n",nev);
143: else {
144: PetscPrintf(PETSC_COMM_WORLD," All requested eigenvalues computed up to the required tolerance:");
145: for (i=0;i<=(nev-1)/8;i++) {
146: PetscPrintf(PETSC_COMM_WORLD,"\n ");
147: for (j=0;j<PetscMin(8,nev-8*i);j++) {
148: EPSGetEigenpair(eps,8*i+j,&kr,&ki,NULL,NULL);
149: #if defined(PETSC_USE_COMPLEX)
150: re = PetscRealPart(kr);
151: im = PetscImaginaryPart(kr);
152: #else
153: re = kr;
154: im = ki;
155: #endif
156: if (PetscAbs(re)/PetscAbs(im)<PETSC_SMALL) re = 0.0;
157: if (PetscAbs(im)/PetscAbs(re)<PETSC_SMALL) im = 0.0;
158: if (im!=0.0) PetscPrintf(PETSC_COMM_WORLD,"%.5f%+.5fi",(double)re,(double)im);
159: else PetscPrintf(PETSC_COMM_WORLD,"%.5f",(double)re);
160: if (8*i+j+1<nev) PetscPrintf(PETSC_COMM_WORLD,", ");
161: }
162: }
163: PetscPrintf(PETSC_COMM_WORLD,"\n\n");
164: }
165: }
167: /* Get an orthogonal basis of the invariant subspace and check it is indeed
168: orthogonal (note that eigenvectors are not orthogonal in this case) */
169: if (nconv>1) {
170: MatCreateVecs(A,&v,NULL);
171: VecDuplicateVecs(v,nconv,&Q);
172: EPSGetInvariantSubspace(eps,Q);
173: VecCheckOrthonormality(Q,nconv,NULL,nconv,NULL,NULL,&lev);
174: if (lev<10*tol) PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n");
175: else PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)lev);
176: VecDestroyVecs(nconv,&Q);
177: VecDestroy(&v);
178: }
180: EPSDestroy(&eps);
181: MatDestroy(&A);
182: MatDestroy(&ctx->T);
183: VecDestroy(&ctx->x1);
184: VecDestroy(&ctx->x2);
185: VecDestroy(&ctx->y1);
186: VecDestroy(&ctx->y2);
187: PetscFree(ctx);
188: SlepcFinalize();
189: return 0;
190: }
192: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
193: {
194: PetscInt n;
195: const PetscScalar *px;
196: PetscScalar *py;
197: CTX_BRUSSEL *ctx;
200: MatShellGetContext(A,&ctx);
201: MatGetLocalSize(ctx->T,&n,NULL);
202: VecGetArrayRead(x,&px);
203: VecGetArray(y,&py);
204: VecPlaceArray(ctx->x1,px);
205: VecPlaceArray(ctx->x2,px+n);
206: VecPlaceArray(ctx->y1,py);
207: VecPlaceArray(ctx->y2,py+n);
209: MatMult(ctx->T,ctx->x1,ctx->y1);
210: VecScale(ctx->y1,ctx->tau1);
211: VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1);
212: VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2);
214: MatMult(ctx->T,ctx->x2,ctx->y2);
215: VecScale(ctx->y2,ctx->tau2);
216: VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
217: VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2);
219: VecRestoreArrayRead(x,&px);
220: VecRestoreArray(y,&py);
221: VecResetArray(ctx->x1);
222: VecResetArray(ctx->x2);
223: VecResetArray(ctx->y1);
224: VecResetArray(ctx->y2);
225: PetscFunctionReturn(0);
226: }
228: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
229: {
230: Vec d1,d2;
231: PetscInt n;
232: PetscScalar *pd;
233: MPI_Comm comm;
234: CTX_BRUSSEL *ctx;
237: MatShellGetContext(A,&ctx);
238: PetscObjectGetComm((PetscObject)A,&comm);
239: MatGetLocalSize(ctx->T,&n,NULL);
240: VecGetArray(diag,&pd);
241: VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
242: VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);
244: VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma);
245: VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma);
247: VecDestroy(&d1);
248: VecDestroy(&d2);
249: VecRestoreArray(diag,&pd);
250: PetscFunctionReturn(0);
251: }
253: /*TEST
255: test:
256: suffix: 1
257: args: -eps_nev 4 -eps_true_residual {{0 1}}
258: requires: !single
260: test:
261: suffix: 2
262: args: -eps_nev 4 -eps_true_residual -eps_balance oneside -eps_tol 1e-7
263: requires: !single
265: test:
266: suffix: 3
267: args: -n 50 -eps_nev 4 -eps_ncv 16 -eps_type subspace -eps_largest_magnitude -bv_orthog_block {{gs tsqr chol tsqrchol svqb}}
268: requires: !single
270: TEST*/