/usr/share/openturns/validation/ValidCovariance.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | > restart:
> with(LinearAlgebra):
> diag:=<<sigma1,0,0>|<0,sigma2,0>|<0,0,sigma3>>;
> Cor:=<<r11,r21,r31>|<r12,r22,r32>|<r13,r23,r33>>;
> Cov:=diag.Cor.diag;
> factor(Determinant(Cov));
> iCov:=MatrixInverse(Cov);
> factor(Determinant(iCov));
[sigma1 0 0 ]
[ ]
diag := [ 0 sigma2 0 ]
[ ]
[ 0 0 sigma3]
[r11 r12 r13]
[ ]
Cor := [r21 r22 r23]
[ ]
[r31 r32 r33]
[ 2 ]
[sigma1 r11 , sigma1 r12 sigma2 , sigma1 r13 sigma3]
[ ]
Cov := [ 2 ]
[sigma2 r21 sigma1 , sigma2 r22 , sigma2 r23 sigma3]
[ ]
[ 2 ]
[sigma3 r31 sigma1 , sigma3 r32 sigma2 , sigma3 r33]
2 2 2
sigma1 sigma2 sigma3 (r11 r22 r33 - r11 r23 r32 + r21 r32 r13
- r21 r12 r33 + r31 r12 r23 - r31 r22 r13)
iCov :=
[r22 r33 - r23 r32 -r32 r13 + r12 r33 r12 r23 - r22 r13
[----------------- , - ------------------ , -----------------
[ 2 sigma2 sigma1 %1 sigma1 sigma3 %1
[ sigma1 %1
]
]
]
]
[ r21 r33 - r31 r23 r11 r33 - r13 r31
[- ----------------- , ----------------- ,
[ sigma2 sigma1 %1 2
[ sigma2 %1
r11 r23 - r13 r21]
- -----------------]
sigma2 sigma3 %1 ]
]
[r21 r32 - r31 r22 r11 r32 - r12 r31 r11 r22 - r12 r21]
[----------------- , - ----------------- , -----------------]
[sigma1 sigma3 %1 sigma2 sigma3 %1 2 ]
[ sigma3 %1 ]
%1 := r11 r22 r33 - r11 r23 r32 + r21 r32 r13 - r21 r12 r33
+ r31 r12 r23 - r31 r22 r13
2 2 2
1/(sigma1 sigma2 sigma3 (r11 r22 r33 - r11 r23 r32 + r21 r32 r13
- r21 r12 r33 + r31 r12 r23 - r31 r22 r13))
>
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