Line | Branch | Exec | Source |
---|---|---|---|
1 | /* | ||
2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
5 | |||
6 | This file is part of SLEPc. | ||
7 | SLEPc is distributed under a 2-clause BSD license (see LICENSE). | ||
8 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
9 | */ | ||
10 | |||
11 | static char help[] = "Test the NEPProjectOperator() function.\n\n" | ||
12 | "This is based on ex22.\n" | ||
13 | "The command line options are:\n" | ||
14 | " -n <n>, where <n> = number of grid subdivisions.\n" | ||
15 | " -tau <tau>, where <tau> is the delay parameter.\n"; | ||
16 | |||
17 | /* | ||
18 | Solve parabolic partial differential equation with time delay tau | ||
19 | |||
20 | u_t = u_xx + a*u(t) + b*u(t-tau) | ||
21 | u(0,t) = u(pi,t) = 0 | ||
22 | |||
23 | with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)). | ||
24 | |||
25 | Discretization leads to a DDE of dimension n | ||
26 | |||
27 | -u' = A*u(t) + B*u(t-tau) | ||
28 | |||
29 | which results in the nonlinear eigenproblem | ||
30 | |||
31 | (-lambda*I + A + exp(-tau*lambda)*B)*u = 0 | ||
32 | */ | ||
33 | |||
34 | #include <slepcnep.h> | ||
35 | |||
36 | 10 | int main(int argc,char **argv) | |
37 | { | ||
38 | 10 | NEP nep; | |
39 | 10 | Mat Id,A,B,mats[3]; | |
40 | 10 | FN f1,f2,f3,funs[3]; | |
41 | 10 | BV V; | |
42 | 10 | DS ds; | |
43 | 10 | Vec v; | |
44 | 10 | PetscScalar coeffs[2],b,*M; | |
45 | 10 | PetscInt n=32,Istart,Iend,i,j,k,nc; | |
46 | 10 | PetscReal tau=0.001,h,a=20,xi; | |
47 | |||
48 |
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10 | PetscFunctionBeginUser; |
49 |
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10 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
50 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
51 |
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10 | PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL)); |
52 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n",n,(double)tau)); |
53 | 10 | h = PETSC_PI/(PetscReal)(n+1); | |
54 | |||
55 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
56 | Create nonlinear eigensolver context | ||
57 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
58 | |||
59 |
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10 | PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep)); |
60 | |||
61 | /* Identity matrix */ | ||
62 |
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10 | PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id)); |
63 |
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10 | PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE)); |
64 | |||
65 | /* A = 1/h^2*tridiag(1,-2,1) + a*I */ | ||
66 |
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10 | PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); |
67 |
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10 | PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n)); |
68 |
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10 | PetscCall(MatSetFromOptions(A)); |
69 |
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10 | PetscCall(MatGetOwnershipRange(A,&Istart,&Iend)); |
70 |
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330 | for (i=Istart;i<Iend;i++) { |
71 |
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320 | if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES)); |
72 |
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320 | if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES)); |
73 |
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320 | PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES)); |
74 | } | ||
75 |
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10 | PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); |
76 |
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10 | PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); |
77 |
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10 | PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE)); |
78 | |||
79 | /* B = diag(b(xi)) */ | ||
80 |
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10 | PetscCall(MatCreate(PETSC_COMM_WORLD,&B)); |
81 |
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10 | PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n)); |
82 |
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10 | PetscCall(MatSetFromOptions(B)); |
83 |
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10 | PetscCall(MatGetOwnershipRange(B,&Istart,&Iend)); |
84 |
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330 | for (i=Istart;i<Iend;i++) { |
85 | 320 | xi = (i+1)*h; | |
86 | 320 | b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI)); | |
87 |
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320 | PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES)); |
88 | } | ||
89 |
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10 | PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); |
90 |
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10 | PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); |
91 |
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10 | PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE)); |
92 | |||
93 | /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */ | ||
94 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f1)); |
95 |
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10 | PetscCall(FNSetType(f1,FNRATIONAL)); |
96 | 10 | coeffs[0] = -1.0; coeffs[1] = 0.0; | |
97 |
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10 | PetscCall(FNRationalSetNumerator(f1,2,coeffs)); |
98 | |||
99 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f2)); |
100 |
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10 | PetscCall(FNSetType(f2,FNRATIONAL)); |
101 | 10 | coeffs[0] = 1.0; | |
102 |
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10 | PetscCall(FNRationalSetNumerator(f2,1,coeffs)); |
103 | |||
104 |
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10 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f3)); |
105 |
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10 | PetscCall(FNSetType(f3,FNEXP)); |
106 |
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10 | PetscCall(FNSetScale(f3,-tau,1.0)); |
107 | |||
108 | /* Set the split operator */ | ||
109 | 10 | mats[0] = A; funs[0] = f2; | |
110 | 10 | mats[1] = Id; funs[1] = f1; | |
111 | 10 | mats[2] = B; funs[2] = f3; | |
112 |
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10 | PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN)); |
113 |
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10 | PetscCall(NEPSetType(nep,NEPNARNOLDI)); |
114 |
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10 | PetscCall(NEPSetFromOptions(nep)); |
115 | |||
116 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
117 | Project the NEP | ||
118 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
119 | |||
120 |
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10 | PetscCall(NEPSetUp(nep)); |
121 |
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10 | PetscCall(NEPGetBV(nep,&V)); |
122 |
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10 | PetscCall(BVGetSizes(V,NULL,NULL,&nc)); |
123 |
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60 | for (i=0;i<nc;i++) { |
124 |
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50 | PetscCall(BVGetColumn(V,i,&v)); |
125 |
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50 | PetscCall(VecSetValue(v,i,1.0,INSERT_VALUES)); |
126 |
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50 | PetscCall(VecAssemblyBegin(v)); |
127 |
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50 | PetscCall(VecAssemblyEnd(v)); |
128 |
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50 | PetscCall(BVRestoreColumn(V,i,&v)); |
129 | } | ||
130 |
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10 | PetscCall(NEPGetDS(nep,&ds)); |
131 |
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10 | PetscCall(DSSetType(ds,DSNEP)); |
132 |
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10 | PetscCall(DSNEPSetFN(ds,3,funs)); |
133 |
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10 | PetscCall(DSAllocate(ds,nc)); |
134 |
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10 | PetscCall(DSSetDimensions(ds,nc,0,0)); |
135 |
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10 | PetscCall(NEPProjectOperator(nep,0,nc)); |
136 | |||
137 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
138 | Display projected matrices and clean up | ||
139 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
140 | |||
141 |
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40 | for (k=0;k<3;k++) { |
142 |
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30 | PetscCall(DSGetArray(ds,DSMatExtra[k],&M)); |
143 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%" PetscInt_FMT " = \n",k)); |
144 |
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180 | for (i=0;i<nc;i++) { |
145 |
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900 | for (j=0;j<nc;j++) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %.5g",(double)PetscRealPart(M[i+j*nc]))); |
146 |
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150 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n")); |
147 | } | ||
148 |
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30 | PetscCall(DSRestoreArray(ds,DSMatExtra[k],&M)); |
149 | } | ||
150 | |||
151 |
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10 | PetscCall(NEPDestroy(&nep)); |
152 |
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10 | PetscCall(MatDestroy(&Id)); |
153 |
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10 | PetscCall(MatDestroy(&A)); |
154 |
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10 | PetscCall(MatDestroy(&B)); |
155 |
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10 | PetscCall(FNDestroy(&f1)); |
156 |
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10 | PetscCall(FNDestroy(&f2)); |
157 |
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10 | PetscCall(FNDestroy(&f3)); |
158 |
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10 | PetscCall(SlepcFinalize()); |
159 | return 0; | ||
160 | } | ||
161 | |||
162 | /*TEST | ||
163 | |||
164 | test: | ||
165 | suffix: 1 | ||
166 | args: -nep_ncv 5 | ||
167 | |||
168 | TEST*/ | ||
169 |