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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[] = "Test dense LME functions.\n\n"; | ||
12 | |||
13 | #include <slepclme.h> | ||
14 | |||
15 | 10 | int main(int argc,char **argv) | |
16 | { | ||
17 | 10 | LME lme; | |
18 | 10 | Mat A,B,C,X; | |
19 | 10 | PetscInt i,j,n=10,k=2; | |
20 | 10 | PetscScalar *As,*Bs,*Cs,*Xs; | |
21 | 10 | PetscViewer viewer; | |
22 | 10 | PetscBool verbose; | |
23 | |||
24 |
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10 | PetscFunctionBeginUser; |
25 |
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10 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
26 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
27 |
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10 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL)); |
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10 | PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose)); |
29 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Dense matrix equations, n=%" PetscInt_FMT ".\n",n)); |
30 | |||
31 | /* Create LME object */ | ||
32 |
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10 | PetscCall(LMECreate(PETSC_COMM_WORLD,&lme)); |
33 | |||
34 | /* Set up viewer */ | ||
35 |
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10 | PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer)); |
36 |
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10 | if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB)); |
37 | |||
38 | /* Create matrices */ | ||
39 |
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10 | PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A)); |
40 |
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10 | PetscCall(PetscObjectSetName((PetscObject)A,"A")); |
41 |
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10 | PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&B)); |
42 |
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10 | PetscCall(PetscObjectSetName((PetscObject)B,"B")); |
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10 | PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,k,NULL,&C)); |
44 |
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10 | PetscCall(PetscObjectSetName((PetscObject)C,"C")); |
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10 | PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&X)); |
46 |
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10 | PetscCall(PetscObjectSetName((PetscObject)X,"X")); |
47 | |||
48 | /* Fill A with an upper Hessenberg Toeplitz matrix */ | ||
49 |
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10 | PetscCall(MatDenseGetArray(A,&As)); |
50 |
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110 | for (i=0;i<n;i++) As[i+i*n]=3.0-(PetscReal)n/2; |
51 |
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100 | for (i=0;i<n-1;i++) As[i+1+i*n]=0.5; |
52 |
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30 | for (j=1;j<3;j++) { |
53 |
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190 | for (i=0;i<n-j;i++) As[i+(i+j)*n]=1.0; |
54 | } | ||
55 |
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10 | PetscCall(MatDenseRestoreArray(A,&As)); |
56 | |||
57 |
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10 | if (verbose) { |
58 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n")); | |
59 | ✗ | PetscCall(MatView(A,viewer)); | |
60 | } | ||
61 | |||
62 | /* Fill B with the 1-D Laplacian matrix */ | ||
63 |
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10 | PetscCall(MatDenseGetArray(B,&Bs)); |
64 |
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110 | for (i=0;i<n;i++) Bs[i+i*n]=2.0; |
65 |
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100 | for (i=0;i<n-1;i++) { Bs[i+1+i*n]=-1; Bs[i+(i+1)*n]=-1; } |
66 |
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10 | PetscCall(MatDenseRestoreArray(B,&Bs)); |
67 | |||
68 |
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10 | if (verbose) { |
69 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix B - - - - - - - -\n")); | |
70 | ✗ | PetscCall(MatView(B,viewer)); | |
71 | } | ||
72 | |||
73 | /* Solve Lyapunov equation A*X+X*A'= -B */ | ||
74 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solving Lyapunov equation for B\n")); |
75 |
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10 | PetscCall(MatDenseGetArray(A,&As)); |
76 |
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10 | PetscCall(MatDenseGetArray(B,&Bs)); |
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10 | PetscCall(MatDenseGetArray(X,&Xs)); |
78 |
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10 | PetscCall(LMEDenseLyapunov(lme,n,As,n,Bs,n,Xs,n)); |
79 |
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10 | PetscCall(MatDenseRestoreArray(A,&As)); |
80 |
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10 | PetscCall(MatDenseRestoreArray(B,&Bs)); |
81 |
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10 | PetscCall(MatDenseRestoreArray(X,&Xs)); |
82 |
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10 | if (verbose) { |
83 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solution X - - - - - - - -\n")); | |
84 | ✗ | PetscCall(MatView(X,viewer)); | |
85 | } | ||
86 | |||
87 | /* Fill C with a full-rank nx2 matrix */ | ||
88 |
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10 | PetscCall(MatDenseGetArray(C,&Cs)); |
89 |
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30 | for (i=0;i<k;i++) Cs[i+i*n] = (i%2)? -1.0: 1.0; |
90 |
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10 | PetscCall(MatDenseRestoreArray(C,&Cs)); |
91 | |||
92 |
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10 | if (verbose) { |
93 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix C - - - - - - - -\n")); | |
94 | ✗ | PetscCall(MatView(C,viewer)); | |
95 | } | ||
96 | |||
97 | /* Solve Lyapunov equation A*X+X*A'= -C*C' */ | ||
98 |
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10 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solving Lyapunov equation for C (Cholesky)\n")); |
99 |
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10 | PetscCall(MatDenseGetArray(A,&As)); |
100 |
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10 | PetscCall(MatDenseGetArray(C,&Cs)); |
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10 | PetscCall(MatDenseGetArray(X,&Xs)); |
102 |
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10 | PetscCall(LMEDenseHessLyapunovChol(lme,n,As,n,2,Cs,n,Xs,n,NULL)); |
103 |
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10 | PetscCall(MatDenseRestoreArray(A,&As)); |
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10 | PetscCall(MatDenseRestoreArray(C,&Cs)); |
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10 | PetscCall(MatDenseRestoreArray(X,&Xs)); |
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10 | if (verbose) { |
107 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solution X - - - - - - - -\n")); | |
108 | ✗ | PetscCall(MatView(X,viewer)); | |
109 | } | ||
110 | |||
111 |
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10 | PetscCall(MatDestroy(&A)); |
112 |
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10 | PetscCall(MatDestroy(&B)); |
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10 | PetscCall(MatDestroy(&C)); |
114 |
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10 | PetscCall(MatDestroy(&X)); |
115 |
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10 | PetscCall(LMEDestroy(&lme)); |
116 |
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10 | PetscCall(SlepcFinalize()); |
117 | return 0; | ||
118 | } | ||
119 | |||
120 | /*TEST | ||
121 | |||
122 | test: | ||
123 | args: -info :lme | ||
124 | requires: double | ||
125 | filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/1e-\\1/g" | ||
126 | |||
127 | TEST*/ | ||
128 |