Actual source code: test10.c
slepc-3.15.1 2021-05-28
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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[] = "Tests multiple calls to NEPSolve(). Based on ex22.c.\n\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = number of grid subdivisions.\n"
14: " -tau <tau>, where <tau> is the delay parameter.\n\n";
16: /*
17: Solve parabolic partial differential equation with time delay tau
19: u_t = u_xx + a*u(t) + b*u(t-tau)
20: u(0,t) = u(pi,t) = 0
22: with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
24: Discretization leads to a DDE of dimension n
26: -u' = A*u(t) + B*u(t-tau)
28: which results in the nonlinear eigenproblem
30: (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
31: */
33: #include <slepcnep.h>
35: /*
36: Check if computed eigenvectors have unit norm
37: */
38: PetscErrorCode CheckNormalizedVectors(NEP nep)
39: {
41: PetscInt i,nconv;
42: Mat A;
43: Vec xr,xi;
44: PetscReal error=0.0,normr;
45: #if !defined(PETSC_USE_COMPLEX)
46: PetscReal normi;
47: #endif
50: NEPGetConverged(nep,&nconv);
51: if (nconv>0) {
52: NEPGetSplitOperatorTerm(nep,0,&A,NULL);
53: MatCreateVecs(A,&xr,&xi);
54: for (i=0;i<nconv;i++) {
55: NEPGetEigenpair(nep,i,NULL,NULL,xr,xi);
56: #if defined(PETSC_USE_COMPLEX)
57: VecNorm(xr,NORM_2,&normr);
58: error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
59: #else
60: VecNormBegin(xr,NORM_2,&normr);
61: VecNormBegin(xi,NORM_2,&normi);
62: VecNormEnd(xr,NORM_2,&normr);
63: VecNormEnd(xi,NORM_2,&normi);
64: error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
65: #endif
66: }
67: VecDestroy(&xr);
68: VecDestroy(&xi);
69: if (error>100*PETSC_MACHINE_EPSILON) {
70: PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
71: }
72: }
73: return(0);
74: }
76: int main(int argc,char **argv)
77: {
78: NEP nep; /* nonlinear eigensolver context */
79: Mat Id,A,B; /* problem matrices */
80: FN f1,f2,f3; /* functions to define the nonlinear operator */
81: Mat mats[3];
82: FN funs[3];
83: PetscScalar coeffs[2],b;
84: PetscInt n=128,Istart,Iend,i;
85: PetscReal tau=0.001,h,a=20,xi;
86: PetscBool skipnorm=PETSC_FALSE;
89: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
90: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
91: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
92: PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);
93: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
94: h = PETSC_PI/(PetscReal)(n+1);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Create functions that define the split operator
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: /* f1=-lambda */
101: FNCreate(PETSC_COMM_WORLD,&f1);
102: FNSetType(f1,FNRATIONAL);
103: coeffs[0] = -1.0; coeffs[1] = 0.0;
104: FNRationalSetNumerator(f1,2,coeffs);
106: /* f2=1.0 */
107: FNCreate(PETSC_COMM_WORLD,&f2);
108: FNSetType(f2,FNRATIONAL);
109: coeffs[0] = 1.0;
110: FNRationalSetNumerator(f2,1,coeffs);
112: /* f3=exp(-tau*lambda) */
113: FNCreate(PETSC_COMM_WORLD,&f3);
114: FNSetType(f3,FNEXP);
115: FNSetScale(f3,-tau,1.0);
117: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118: Create problem matrices
119: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: /* Identity matrix */
122: MatCreate(PETSC_COMM_WORLD,&Id);
123: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
124: MatSetFromOptions(Id);
125: MatSetUp(Id);
126: MatGetOwnershipRange(Id,&Istart,&Iend);
127: for (i=Istart;i<Iend;i++) {
128: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
129: }
130: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
131: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
132: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
134: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
135: MatCreate(PETSC_COMM_WORLD,&A);
136: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
137: MatSetFromOptions(A);
138: MatSetUp(A);
139: MatGetOwnershipRange(A,&Istart,&Iend);
140: for (i=Istart;i<Iend;i++) {
141: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
142: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
143: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
144: }
145: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
146: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
147: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
149: /* B = diag(b(xi)) */
150: MatCreate(PETSC_COMM_WORLD,&B);
151: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
152: MatSetFromOptions(B);
153: MatSetUp(B);
154: MatGetOwnershipRange(B,&Istart,&Iend);
155: for (i=Istart;i<Iend;i++) {
156: xi = (i+1)*h;
157: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
158: MatSetValue(B,i,i,b,INSERT_VALUES);
159: }
160: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
161: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
162: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
164: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: Create nonlinear eigensolver and set options
166: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168: NEPCreate(PETSC_COMM_WORLD,&nep);
169: mats[0] = A; funs[0] = f2;
170: mats[1] = Id; funs[1] = f1;
171: mats[2] = B; funs[2] = f3;
172: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
173: NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
174: NEPSetFromOptions(nep);
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Solve the eigensystem
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180: NEPSolve(nep);
181: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
182: if (!skipnorm) { CheckNormalizedVectors(nep); }
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Create problem matrices of size 2*n
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: MatDestroy(&Id);
189: MatDestroy(&A);
190: MatDestroy(&B);
191: n *= 2;
192: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
193: h = PETSC_PI/(PetscReal)(n+1);
195: /* Identity matrix */
196: MatCreate(PETSC_COMM_WORLD,&Id);
197: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
198: MatSetFromOptions(Id);
199: MatSetUp(Id);
200: MatGetOwnershipRange(Id,&Istart,&Iend);
201: for (i=Istart;i<Iend;i++) {
202: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
203: }
204: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
205: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
206: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
208: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
209: MatCreate(PETSC_COMM_WORLD,&A);
210: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
211: MatSetFromOptions(A);
212: MatSetUp(A);
213: MatGetOwnershipRange(A,&Istart,&Iend);
214: for (i=Istart;i<Iend;i++) {
215: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
216: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
217: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
218: }
219: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
220: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
221: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
223: /* B = diag(b(xi)) */
224: MatCreate(PETSC_COMM_WORLD,&B);
225: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
226: MatSetFromOptions(B);
227: MatSetUp(B);
228: MatGetOwnershipRange(B,&Istart,&Iend);
229: for (i=Istart;i<Iend;i++) {
230: xi = (i+1)*h;
231: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
232: MatSetValue(B,i,i,b,INSERT_VALUES);
233: }
234: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
235: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
236: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
238: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239: Solve again, calling NEPReset() since matrix size has changed
240: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
242: /*NEPReset(nep);*/ /* not required, will be called in NEPSetSplitOperators() */
243: mats[0] = A; funs[0] = f2;
244: mats[1] = Id; funs[1] = f1;
245: mats[2] = B; funs[2] = f3;
246: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
247: NEPSolve(nep);
248: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
249: if (!skipnorm) { CheckNormalizedVectors(nep); }
251: NEPDestroy(&nep);
252: MatDestroy(&Id);
253: MatDestroy(&A);
254: MatDestroy(&B);
255: FNDestroy(&f1);
256: FNDestroy(&f2);
257: FNDestroy(&f3);
258: SlepcFinalize();
259: return ierr;
260: }
262: /*TEST
264: testset:
265: nsize: 2
266: requires: !single
267: output_file: output/test10_1.out
268: test:
269: suffix: 1
270: args: -nep_type narnoldi -nep_target 0.55
271: test:
272: suffix: 1_rii
273: args: -nep_type rii -nep_target 0.55 -nep_rii_hermitian
274: test:
275: suffix: 1_narnoldi
276: args: -nep_type narnoldi -nep_target 0.55 -nep_narnoldi_lag_preconditioner 2
277: test:
278: suffix: 1_slp
279: args: -nep_type slp -nep_slp_st_pc_type redundant
280: test:
281: suffix: 1_interpol
282: args: -nep_type interpol -rg_type interval -rg_interval_endpoints .5,1,-.1,.1 -nep_target .7 -nep_interpol_st_pc_type redundant
283: test:
284: suffix: 1_narnoldi_sync
285: args: -nep_type narnoldi -ds_parallel synchronized
287: testset:
288: args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
289: requires: !single
290: output_file: output/test10_2.out
291: filter: sed -e "s/[+-]0\.0*i//g"
292: test:
293: suffix: 2_interpol
294: args: -nep_type interpol -nep_interpol_pep_type jd -nep_interpol_st_pc_type sor
295: test:
296: suffix: 2_nleigs
297: args: -nep_type nleigs
298: requires: complex
299: test:
300: suffix: 2_nleigs_real
301: args: -nep_type nleigs -rg_interval_endpoints .5,15
302: requires: !complex
304: TEST*/