Actual source code: test17.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[] = "Tests a user-provided preconditioner.\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: " -a <a>, where <a> is the coefficient that multiplies u in the equation.\n"
16: " -split <0/1>, to select the split form in the problem definition (enabled by default).\n";
18: /* Based on ex22.c (delay) */
20: #include <slepcnep.h>
22: /*
23: User-defined application context
24: */
25: typedef struct {
26: PetscScalar tau;
27: PetscReal a;
28: } ApplicationCtx;
30: /*
31: Create problem matrices in split form
32: */
33: PetscErrorCode BuildSplitMatrices(PetscInt n,PetscReal a,Mat *Id,Mat *A,Mat *B)
34: {
35: PetscInt i,Istart,Iend;
36: PetscReal h,xi;
37: PetscScalar b;
40: h = PETSC_PI/(PetscReal)(n+1);
42: /* Identity matrix */
43: MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,Id);
44: MatSetOption(*Id,MAT_HERMITIAN,PETSC_TRUE);
46: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
47: MatCreate(PETSC_COMM_WORLD,A);
48: MatSetSizes(*A,PETSC_DECIDE,PETSC_DECIDE,n,n);
49: MatSetFromOptions(*A);
50: MatSetUp(*A);
51: MatGetOwnershipRange(*A,&Istart,&Iend);
52: for (i=Istart;i<Iend;i++) {
53: if (i>0) MatSetValue(*A,i,i-1,1.0/(h*h),INSERT_VALUES);
54: if (i<n-1) MatSetValue(*A,i,i+1,1.0/(h*h),INSERT_VALUES);
55: MatSetValue(*A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
56: }
57: MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY);
58: MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY);
59: MatSetOption(*A,MAT_HERMITIAN,PETSC_TRUE);
61: /* B = diag(b(xi)) */
62: MatCreate(PETSC_COMM_WORLD,B);
63: MatSetSizes(*B,PETSC_DECIDE,PETSC_DECIDE,n,n);
64: MatSetFromOptions(*B);
65: MatSetUp(*B);
66: MatGetOwnershipRange(*B,&Istart,&Iend);
67: for (i=Istart;i<Iend;i++) {
68: xi = (i+1)*h;
69: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
70: MatSetValue(*B,i,i,b,INSERT_VALUES);
71: }
72: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
73: MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
74: MatSetOption(*B,MAT_HERMITIAN,PETSC_TRUE);
75: PetscFunctionReturn(0);
76: }
78: /*
79: Create preconditioner matrices (only Ap=diag(A))
80: */
81: PetscErrorCode BuildSplitPreconditioner(PetscInt n,PetscReal a,Mat *Ap)
82: {
83: PetscInt i,Istart,Iend;
84: PetscReal h;
87: h = PETSC_PI/(PetscReal)(n+1);
89: /* Ap = diag(A) */
90: MatCreate(PETSC_COMM_WORLD,Ap);
91: MatSetSizes(*Ap,PETSC_DECIDE,PETSC_DECIDE,n,n);
92: MatSetFromOptions(*Ap);
93: MatSetUp(*Ap);
94: MatGetOwnershipRange(*Ap,&Istart,&Iend);
95: for (i=Istart;i<Iend;i++) MatSetValue(*Ap,i,i,-2.0/(h*h)+a,INSERT_VALUES);
96: MatAssemblyBegin(*Ap,MAT_FINAL_ASSEMBLY);
97: MatAssemblyEnd(*Ap,MAT_FINAL_ASSEMBLY);
98: MatSetOption(*Ap,MAT_HERMITIAN,PETSC_TRUE);
99: PetscFunctionReturn(0);
100: }
102: /*
103: Compute Function matrix T(lambda)
104: */
105: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
106: {
107: ApplicationCtx *user = (ApplicationCtx*)ctx;
108: PetscInt i,n,Istart,Iend;
109: PetscReal h,xi;
110: PetscScalar b;
113: MatGetSize(fun,&n,NULL);
114: h = PETSC_PI/(PetscReal)(n+1);
115: MatGetOwnershipRange(fun,&Istart,&Iend);
116: for (i=Istart;i<Iend;i++) {
117: if (i>0) MatSetValue(fun,i,i-1,1.0/(h*h),INSERT_VALUES);
118: if (i<n-1) MatSetValue(fun,i,i+1,1.0/(h*h),INSERT_VALUES);
119: xi = (i+1)*h;
120: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
121: MatSetValue(fun,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES);
122: if (B!=fun) MatSetValue(B,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES);
123: }
124: MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
125: MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
126: if (fun != B) {
127: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
128: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
129: }
130: PetscFunctionReturn(0);
131: }
133: /*
134: Compute Jacobian matrix T'(lambda)
135: */
136: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
137: {
138: ApplicationCtx *user = (ApplicationCtx*)ctx;
139: PetscInt i,n,Istart,Iend;
140: PetscReal h,xi;
141: PetscScalar b;
144: MatGetSize(jac,&n,NULL);
145: h = PETSC_PI/(PetscReal)(n+1);
146: MatGetOwnershipRange(jac,&Istart,&Iend);
147: for (i=Istart;i<Iend;i++) {
148: xi = (i+1)*h;
149: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
150: MatSetValue(jac,i,i,-1.0-user->tau*PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES);
151: }
152: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
153: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
154: PetscFunctionReturn(0);
155: }
157: int main(int argc,char **argv)
158: {
159: NEP nep; /* nonlinear eigensolver context */
160: Mat Id,A,B,Ap,J,F,P; /* problem matrices */
161: FN f1,f2,f3; /* functions to define the nonlinear operator */
162: ApplicationCtx ctx; /* user-defined context */
163: Mat mats[3];
164: FN funs[3];
165: PetscScalar coeffs[2];
166: PetscInt n=128;
167: PetscReal tau=0.001,a=20;
168: PetscBool split=PETSC_TRUE;
170: SlepcInitialize(&argc,&argv,(char*)0,help);
171: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
172: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
173: PetscOptionsGetReal(NULL,NULL,"-a",&a,NULL);
174: PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL);
175: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g, a=%g\n\n",n,(double)tau,(double)a);
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Create nonlinear eigensolver and solve the problem
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: NEPCreate(PETSC_COMM_WORLD,&nep);
182: if (split) {
183: BuildSplitMatrices(n,a,&Id,&A,&B);
184: /* f1=-lambda */
185: FNCreate(PETSC_COMM_WORLD,&f1);
186: FNSetType(f1,FNRATIONAL);
187: coeffs[0] = -1.0; coeffs[1] = 0.0;
188: FNRationalSetNumerator(f1,2,coeffs);
189: /* f2=1.0 */
190: FNCreate(PETSC_COMM_WORLD,&f2);
191: FNSetType(f2,FNRATIONAL);
192: coeffs[0] = 1.0;
193: FNRationalSetNumerator(f2,1,coeffs);
194: /* f3=exp(-tau*lambda) */
195: FNCreate(PETSC_COMM_WORLD,&f3);
196: FNSetType(f3,FNEXP);
197: FNSetScale(f3,-tau,1.0);
198: mats[0] = A; funs[0] = f2;
199: mats[1] = Id; funs[1] = f1;
200: mats[2] = B; funs[2] = f3;
201: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
202: BuildSplitPreconditioner(n,a,&Ap);
203: mats[0] = Ap;
204: mats[1] = Id;
205: mats[2] = B;
206: NEPSetSplitPreconditioner(nep,3,mats,SAME_NONZERO_PATTERN);
207: } else {
208: /* callback form */
209: ctx.tau = tau;
210: ctx.a = a;
211: MatCreate(PETSC_COMM_WORLD,&F);
212: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
213: MatSetFromOptions(F);
214: MatSeqAIJSetPreallocation(F,3,NULL);
215: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
216: MatSetUp(F);
217: MatDuplicate(F,MAT_DO_NOT_COPY_VALUES,&P);
218: NEPSetFunction(nep,F,P,FormFunction,&ctx);
219: MatCreate(PETSC_COMM_WORLD,&J);
220: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
221: MatSetFromOptions(J);
222: MatSeqAIJSetPreallocation(J,3,NULL);
223: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
224: MatSetUp(J);
225: NEPSetJacobian(nep,J,FormJacobian,&ctx);
226: }
228: /* Set solver parameters at runtime */
229: NEPSetFromOptions(nep);
231: /* Solve the eigensystem */
232: NEPSolve(nep);
233: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
235: NEPDestroy(&nep);
236: if (split) {
237: MatDestroy(&Id);
238: MatDestroy(&A);
239: MatDestroy(&B);
240: MatDestroy(&Ap);
241: FNDestroy(&f1);
242: FNDestroy(&f2);
243: FNDestroy(&f3);
244: } else {
245: MatDestroy(&F);
246: MatDestroy(&P);
247: MatDestroy(&J);
248: }
249: SlepcFinalize();
250: return 0;
251: }
253: /*TEST
255: testset:
256: args: -a 90000 -nep_nev 2
257: requires: double
258: output_file: output/test17_1.out
259: test:
260: suffix: 1
261: args: -nep_type slp -nep_two_sided {{0 1}} -split {{0 1}}
263: testset:
264: args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
265: requires: !single
266: output_file: output/test17_2.out
267: filter: sed -e "s/[+-]0\.0*i//g"
268: test:
269: suffix: 2_interpol
270: args: -nep_type interpol -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type sor -nep_tol 1e-6 -nep_interpol_st_ksp_rtol 1e-7
271: test:
272: suffix: 2_nleigs
273: args: -nep_type nleigs -split {{0 1}}
274: requires: complex
275: test:
276: suffix: 2_nleigs_real
277: args: -nep_type nleigs -rg_interval_endpoints .5,15 -split {{0 1}} -nep_nleigs_ksp_type tfqmr
278: requires: !complex
280: testset:
281: args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -rg_ellipse_vscale 0.1 -nep_ciss_ksp_type bcgs -nep_ciss_pc_type sor
282: output_file: output/test17_3.out
283: requires: complex !single
284: test:
285: suffix: 3
286: args: -split {{0 1}}
287: test:
288: suffix: 3_par
289: nsize: 2
290: args: -nep_ciss_partitions 2
292: TEST*/