Line | Branch | Exec | Source |
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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[] = "Computes the action of the square root of the 2-D Laplacian.\n\n" | ||
12 | "The command line options are:\n" | ||
13 | " -n <n>, where <n> = number of grid subdivisions in x dimension.\n" | ||
14 | " -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n" | ||
15 | "To draw the solution run with -mfn_view_solution draw -draw_pause -1\n\n"; | ||
16 | |||
17 | #include <slepcmfn.h> | ||
18 | |||
19 | 10 | int main(int argc,char **argv) | |
20 | { | ||
21 | 10 | Mat A; /* problem matrix */ | |
22 | 10 | MFN mfn; | |
23 | 10 | FN f; | |
24 | 10 | PetscReal norm,tol; | |
25 | 10 | Vec v,y,z; | |
26 | 10 | PetscInt N,n=10,m,Istart,Iend,i,j,II; | |
27 | 10 | PetscBool flag; | |
28 | |||
29 |
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10 | PetscFunctionBeginUser; |
30 |
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10 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
31 | |||
32 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
33 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag)); |
34 |
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10 | if (!flag) m=n; |
35 | 10 | N = n*m; | |
36 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSquare root of Laplacian y=sqrt(A)*e_1, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m)); |
37 | |||
38 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
39 | Compute the discrete 2-D Laplacian, A | ||
40 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
41 | |||
42 |
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10 | PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); |
43 |
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10 | PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N)); |
44 |
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10 | PetscCall(MatSetFromOptions(A)); |
45 | |||
46 |
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10 | PetscCall(MatGetOwnershipRange(A,&Istart,&Iend)); |
47 |
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1010 | for (II=Istart;II<Iend;II++) { |
48 | 1000 | i = II/n; j = II-i*n; | |
49 |
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1000 | if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES)); |
50 |
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1000 | if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES)); |
51 |
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1000 | if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES)); |
52 |
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1000 | if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES)); |
53 |
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1000 | PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES)); |
54 | } | ||
55 | |||
56 |
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10 | PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); |
57 |
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10 | PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); |
58 | |||
59 | /* set symmetry flag so that solver can exploit it */ | ||
60 |
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10 | PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE)); |
61 | |||
62 | /* set v = e_1 */ | ||
63 |
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10 | PetscCall(MatCreateVecs(A,NULL,&v)); |
64 |
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10 | PetscCall(VecSetValue(v,0,1.0,INSERT_VALUES)); |
65 |
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10 | PetscCall(VecAssemblyBegin(v)); |
66 |
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10 | PetscCall(VecAssemblyEnd(v)); |
67 |
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10 | PetscCall(VecDuplicate(v,&y)); |
68 |
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10 | PetscCall(VecDuplicate(v,&z)); |
69 | |||
70 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
71 | Create the solver, set the matrix and the function | ||
72 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
73 |
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10 | PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn)); |
74 |
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10 | PetscCall(MFNSetOperator(mfn,A)); |
75 |
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10 | PetscCall(MFNGetFN(mfn,&f)); |
76 |
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10 | PetscCall(FNSetType(f,FNSQRT)); |
77 |
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10 | PetscCall(MFNSetErrorIfNotConverged(mfn,PETSC_TRUE)); |
78 |
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10 | PetscCall(MFNSetFromOptions(mfn)); |
79 | |||
80 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
81 | First solve: y=sqrt(A)*v | ||
82 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
83 | |||
84 |
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10 | PetscCall(MFNSolve(mfn,v,y)); |
85 |
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10 | PetscCall(VecNorm(y,NORM_2,&norm)); |
86 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Intermediate vector has norm %g\n",(double)norm)); |
87 | |||
88 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
89 | Second solve: z=sqrt(A)*y and compare against A*v | ||
90 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
91 | |||
92 |
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10 | PetscCall(MFNSolve(mfn,y,z)); |
93 |
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10 | PetscCall(MFNGetTolerances(mfn,&tol,NULL)); |
94 | |||
95 |
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10 | PetscCall(MatMult(A,v,y)); /* overwrite y */ |
96 |
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10 | PetscCall(VecAXPY(y,-1.0,z)); |
97 |
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10 | PetscCall(VecNorm(y,NORM_2,&norm)); |
98 | |||
99 |
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10 | if (norm<tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error norm is less than the requested tolerance\n\n")); |
100 | ✗ | else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error norm larger than tolerance: %3.1e\n\n",(double)norm)); | |
101 | |||
102 | /* | ||
103 | Free work space | ||
104 | */ | ||
105 |
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10 | PetscCall(MFNDestroy(&mfn)); |
106 |
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10 | PetscCall(MatDestroy(&A)); |
107 |
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10 | PetscCall(VecDestroy(&v)); |
108 |
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10 | PetscCall(VecDestroy(&y)); |
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10 | PetscCall(VecDestroy(&z)); |
110 |
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10 | PetscCall(SlepcFinalize()); |
111 | return 0; | ||
112 | } | ||
113 | |||
114 | /*TEST | ||
115 | |||
116 | test: | ||
117 | suffix: 1 | ||
118 | args: -mfn_tol 1e-4 | ||
119 | |||
120 | TEST*/ | ||
121 |