Actual source code: test10.c
slepc-3.16.1 2021-11-17
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() with different matrix size.\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"
15: " -split <0/1>, to select the split form in the problem definition (enabled by default).\n";
17: /* Based on ex22.c (delay) */
19: #include <slepcnep.h>
21: /*
22: User-defined application context
23: */
24: typedef struct {
25: PetscScalar tau;
26: PetscReal a;
27: } ApplicationCtx;
29: /*
30: Create problem matrices in split form
31: */
32: PetscErrorCode BuildSplitMatrices(PetscInt n,PetscReal a,Mat *Id,Mat *A,Mat *B)
33: {
35: PetscInt i,Istart,Iend;
36: PetscReal h,xi;
37: PetscScalar b;
40: h = PETSC_PI/(PetscReal)(n+1);
42: /* Identity matrix */
43: MatCreate(PETSC_COMM_WORLD,Id);
44: MatSetSizes(*Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
45: MatSetFromOptions(*Id);
46: MatSetUp(*Id);
47: MatGetOwnershipRange(*Id,&Istart,&Iend);
48: for (i=Istart;i<Iend;i++) {
49: MatSetValue(*Id,i,i,1.0,INSERT_VALUES);
50: }
51: MatAssemblyBegin(*Id,MAT_FINAL_ASSEMBLY);
52: MatAssemblyEnd(*Id,MAT_FINAL_ASSEMBLY);
53: MatSetOption(*Id,MAT_HERMITIAN,PETSC_TRUE);
55: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
56: MatCreate(PETSC_COMM_WORLD,A);
57: MatSetSizes(*A,PETSC_DECIDE,PETSC_DECIDE,n,n);
58: MatSetFromOptions(*A);
59: MatSetUp(*A);
60: MatGetOwnershipRange(*A,&Istart,&Iend);
61: for (i=Istart;i<Iend;i++) {
62: if (i>0) { MatSetValue(*A,i,i-1,1.0/(h*h),INSERT_VALUES); }
63: if (i<n-1) { MatSetValue(*A,i,i+1,1.0/(h*h),INSERT_VALUES); }
64: MatSetValue(*A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
65: }
66: MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY);
67: MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY);
68: MatSetOption(*A,MAT_HERMITIAN,PETSC_TRUE);
70: /* B = diag(b(xi)) */
71: MatCreate(PETSC_COMM_WORLD,B);
72: MatSetSizes(*B,PETSC_DECIDE,PETSC_DECIDE,n,n);
73: MatSetFromOptions(*B);
74: MatSetUp(*B);
75: MatGetOwnershipRange(*B,&Istart,&Iend);
76: for (i=Istart;i<Iend;i++) {
77: xi = (i+1)*h;
78: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
79: MatSetValue(*B,i,i,b,INSERT_VALUES);
80: }
81: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
82: MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
83: MatSetOption(*B,MAT_HERMITIAN,PETSC_TRUE);
84: return(0);
85: }
87: /*
88: Compute Function matrix T(lambda)
89: */
90: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
91: {
93: ApplicationCtx *user = (ApplicationCtx*)ctx;
94: PetscInt i,n,Istart,Iend;
95: PetscReal h,xi;
96: PetscScalar b;
99: MatGetSize(fun,&n,NULL);
100: h = PETSC_PI/(PetscReal)(n+1);
101: MatGetOwnershipRange(fun,&Istart,&Iend);
102: for (i=Istart;i<Iend;i++) {
103: if (i>0) { MatSetValue(fun,i,i-1,1.0/(h*h),INSERT_VALUES); }
104: if (i<n-1) { MatSetValue(fun,i,i+1,1.0/(h*h),INSERT_VALUES); }
105: xi = (i+1)*h;
106: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
107: MatSetValue(fun,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES);
108: }
109: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
110: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
111: if (fun != B) {
112: MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
113: MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
114: }
115: return(0);
116: }
118: /*
119: Compute Jacobian matrix T'(lambda)
120: */
121: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
122: {
124: ApplicationCtx *user = (ApplicationCtx*)ctx;
125: PetscInt i,n,Istart,Iend;
126: PetscReal h,xi;
127: PetscScalar b;
130: MatGetSize(jac,&n,NULL);
131: h = PETSC_PI/(PetscReal)(n+1);
132: MatGetOwnershipRange(jac,&Istart,&Iend);
133: for (i=Istart;i<Iend;i++) {
134: xi = (i+1)*h;
135: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
136: MatSetValue(jac,i,i,-1.0-user->tau*PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES);
137: }
138: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
139: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
140: return(0);
141: }
143: int main(int argc,char **argv)
144: {
145: NEP nep; /* nonlinear eigensolver context */
146: Mat Id,A,B,J,F; /* problem matrices */
147: FN f1,f2,f3; /* functions to define the nonlinear operator */
148: ApplicationCtx ctx; /* user-defined context */
149: Mat mats[3];
150: FN funs[3];
151: PetscScalar coeffs[2];
152: PetscInt n=128;
153: PetscReal tau=0.001,a=20;
154: PetscBool split=PETSC_TRUE;
157: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
158: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
159: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
160: PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL);
161: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
163: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: Create nonlinear eigensolver and set options
165: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167: NEPCreate(PETSC_COMM_WORLD,&nep);
168: NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171: First solve
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174: if (split) {
175: BuildSplitMatrices(n,a,&Id,&A,&B);
176: /* f1=-lambda */
177: FNCreate(PETSC_COMM_WORLD,&f1);
178: FNSetType(f1,FNRATIONAL);
179: coeffs[0] = -1.0; coeffs[1] = 0.0;
180: FNRationalSetNumerator(f1,2,coeffs);
181: /* f2=1.0 */
182: FNCreate(PETSC_COMM_WORLD,&f2);
183: FNSetType(f2,FNRATIONAL);
184: coeffs[0] = 1.0;
185: FNRationalSetNumerator(f2,1,coeffs);
186: /* f3=exp(-tau*lambda) */
187: FNCreate(PETSC_COMM_WORLD,&f3);
188: FNSetType(f3,FNEXP);
189: FNSetScale(f3,-tau,1.0);
190: mats[0] = A; funs[0] = f2;
191: mats[1] = Id; funs[1] = f1;
192: mats[2] = B; funs[2] = f3;
193: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
194: } else {
195: /* callback form */
196: ctx.tau = tau;
197: ctx.a = a;
198: MatCreate(PETSC_COMM_WORLD,&F);
199: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
200: MatSetFromOptions(F);
201: MatSeqAIJSetPreallocation(F,3,NULL);
202: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
203: MatSetUp(F);
204: NEPSetFunction(nep,F,F,FormFunction,&ctx);
205: MatCreate(PETSC_COMM_WORLD,&J);
206: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
207: MatSetFromOptions(J);
208: MatSeqAIJSetPreallocation(J,3,NULL);
209: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
210: MatSetUp(J);
211: NEPSetJacobian(nep,J,FormJacobian,&ctx);
212: }
214: /* Set solver parameters at runtime */
215: NEPSetFromOptions(nep);
217: /* Solve the eigensystem */
218: NEPSolve(nep);
219: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
221: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: Second solve, with problem matrices of size 2*n
223: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
225: n *= 2;
226: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
227: if (split) {
228: MatDestroy(&Id);
229: MatDestroy(&A);
230: MatDestroy(&B);
231: BuildSplitMatrices(n,a,&Id,&A,&B);
232: mats[0] = A;
233: mats[1] = Id;
234: mats[2] = B;
235: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
236: } else {
237: /* callback form */
238: MatDestroy(&F);
239: MatDestroy(&J);
240: MatCreate(PETSC_COMM_WORLD,&F);
241: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
242: MatSetFromOptions(F);
243: MatSeqAIJSetPreallocation(F,3,NULL);
244: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
245: MatSetUp(F);
246: NEPSetFunction(nep,F,F,FormFunction,&ctx);
247: MatCreate(PETSC_COMM_WORLD,&J);
248: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
249: MatSetFromOptions(J);
250: MatSeqAIJSetPreallocation(J,3,NULL);
251: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
252: MatSetUp(J);
253: NEPSetJacobian(nep,J,FormJacobian,&ctx);
254: }
256: /* Solve the eigensystem */
257: NEPSolve(nep);
258: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
260: NEPDestroy(&nep);
261: if (split) {
262: MatDestroy(&Id);
263: MatDestroy(&A);
264: MatDestroy(&B);
265: FNDestroy(&f1);
266: FNDestroy(&f2);
267: FNDestroy(&f3);
268: } else {
269: MatDestroy(&F);
270: MatDestroy(&J);
271: }
272: SlepcFinalize();
273: return ierr;
274: }
276: /*TEST
278: testset:
279: nsize: 2
280: requires: !single
281: output_file: output/test10_1.out
282: test:
283: suffix: 1
284: args: -nep_type narnoldi -nep_target 0.55
285: test:
286: suffix: 1_rii
287: args: -nep_type rii -nep_target 0.55 -nep_rii_hermitian -split {{0 1}}
288: test:
289: suffix: 1_narnoldi
290: args: -nep_type narnoldi -nep_target 0.55 -nep_narnoldi_lag_preconditioner 2
291: test:
292: suffix: 1_slp
293: args: -nep_type slp -nep_slp_st_pc_type redundant -split {{0 1}}
294: test:
295: suffix: 1_interpol
296: args: -nep_type interpol -rg_type interval -rg_interval_endpoints .5,1,-.1,.1 -nep_target .7 -nep_interpol_st_pc_type redundant
297: test:
298: suffix: 1_narnoldi_sync
299: args: -nep_type narnoldi -ds_parallel synchronized
301: testset:
302: args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
303: requires: !single
304: output_file: output/test10_2.out
305: filter: sed -e "s/[+-]0\.0*i//g"
306: test:
307: suffix: 2_interpol
308: args: -nep_type interpol -nep_interpol_pep_type jd -nep_interpol_st_pc_type sor
309: test:
310: suffix: 2_nleigs
311: args: -nep_type nleigs -split {{0 1}}
312: requires: complex
313: test:
314: suffix: 2_nleigs_real
315: args: -nep_type nleigs -rg_interval_endpoints .5,15 -split {{0 1}}
316: requires: !complex
318: TEST*/