There is a bug in Matrix package, please check it, thanks!
Matlab result:
x =
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
>> lu(x)
ans =
21.0000 22.0000 23.0000 24.0000 25.0000
0.0476 0.9524 1.9048 2.8571 3.8095
0.7619 0.2500 -0.0000 -0.0000 -0.0000
0.5238 0.5000 0.4839 0 0.0000
0.2857 0.7500 -0.0645 0 0.0000
Gsl result:
21 22 23 24 25
0.047619 0.952381 1.90476 2.85714 3.80952
0.761905 0.25 -3.44169e-015 -6.88338e-015 -1.03251e-014
0.52381 0.5 -0.0322581 -1.77636e-015 -1.66533e-015
0.285714 0.75 -0.0645161 -0 2.22045e-016
R result:
$L
5 x 5 Matrix of class "dtrMatrix"
[,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 . . . .
[2,] 0.04761905 1.00000000 . . .
[3,] 0.52380952 0.50000000 1.00000000 . .
[4,] 0.28571429 0.75000000 0.35400130 1.00000000 .
[5,] 0.76190476 0.25000000 0.50000000 0.00000000 1.00000000
$U
5 x 5 Matrix of class "dtrMatrix"
[,1] [,2] [,3] [,4] [,5]
[1,] 2.100000e+01 2.200000e+01 2.300000e+01 2.400000e+01 2.500000e+01
[2,] . 9.523810e-01 1.904762e+00 2.857143e+00 3.809524e+00
[3,] . . -1.919092e-15 -3.711332e-15 -5.614541e-15
[4,] . . . 3.781500e-16 6.288326e-16
[5,] . . . . 0.000000e+00
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