Re: Possible wrong matrix determinant value

[Marco Guazzone]

On Wed, May 13, 2009 at 3:09 PM, HALL, BENJAMIN            PW
<address@hidden> wrote:
>
>
> |-----Original Message-----
> |From: Marco Guazzone [mailto:address@hidden
>
> |
> |It seems the function "det()" gives a wrong determinant value for
> |certain matrices.
> |
> |Look at the following code:
> |
> |--- [code_snip] ---
> |A=[0.5560, 0.2747, 0.5406, 0.7989; 0.1089, 0.8301, 0.8917, 0.8953;
> |0.9480, 0.9732, 0.2165, 0.8832; 0.0238, 0.6754, 0.2318, 0.4503]
> |det(A);
> |--- [/code_snip] ---
> |
> |The result (on my machine: Intel Core 2 Duo+Fedora 10 x86_64) with
> |octave 3.0.3 is: -0.078647
> |
> |However, trying with other tools/libraries, the above value seems to
> |be wrong. In fact:
> |
> |With Octave 3.0.3:             -0.078647
> |With BOOST uBLAS 1.39: -0.07874537
> |With R 2.9.0:                     -0.07874537
> |With NumPy 1.2.0:             -0.078745369636711721
> |With Mathematica 7:           -0.07874537
> |
>
> Are you sure you entered exactly the same matrix into all the different
> codes?  I get the following:
>
> Octave:          -0.0786470081539579
> Mathematica:     -0.07864700815395793
> Matlab:          -0.078647008153958
> R:               -0.078647008154
>
> ===================================================
> octave-3.0.0:
> octave:1> A=[0.5560, 0.2747, 0.5406, 0.7989; 0.1089, 0.8301, 0.8917,
> 0.8953;
>> 0.9480, 0.9732, 0.2165, 0.8832; 0.0238, 0.6754, 0.2318, 0.4503]
> A =
>
>   0.556000   0.274700   0.540600   0.798900
>   0.108900   0.830100   0.891700   0.895300
>   0.948000   0.973200   0.216500   0.883200
>   0.023800   0.675400   0.231800   0.450300
>
> octave:3> dd = det(A)
> dd = -0.078647
> octave:4> format long
> octave:5> dd
> dd = -0.0786470081539579
>
>
> ===================================================
> Matlab-7.7.0:
>>> A=[0.5560, 0.2747, 0.5406, 0.7989; 0.1089, 0.8301, 0.8917, 0.8953;
> 0.9480, 0.9732, 0.2165, 0.8832; 0.0238, 0.6754, 0.2318, 0.4503]
>
> A =
>
>    0.5560    0.2747    0.5406    0.7989
>    0.1089    0.8301    0.8917    0.8953
>    0.9480    0.9732    0.2165    0.8832
>    0.0238    0.6754    0.2318    0.4503
>
>
>>> dd = det(A);
>>> format long
>>> dd
>
> dd =
>
>  -0.078647008153958
>
>
> ===================================================
> Mathematica-6.0:
> A = {{0.5560, 0.2747, 0.5406, 0.7989},
>     {0.1089, 0.8301, 0.8917, 0.8953},
>     {0.9480, 0.9732, 0.2165, 0.8832},
>     {0.0238, 0.6754, 0.2318, 0.4503} };
> A // MatrixForm
>
> d = Det[A];
>
> Out[19]= -0.078647
>
> NumberForm[Det[A], 16]
>
> Out[32]= -0.07864700815395793
>
> ===================================================
> R-2.8.1:
>
> A <- matrix( c(0.5560, 0.2747, 0.5406, 0.7989,
>               0.1089, 0.8301, 0.8917, 0.8953,
>               0.9480, 0.9732, 0.2165, 0.8832,
>               0.0238, 0.6754, 0.2318, 0.4503), nrow=4, ncol=4 )
>
> A <- t(A)     ## not that this matters for the determinant
>
>> A
>       [,1]   [,2]   [,3]   [,4]
> [1,] 0.5560 0.2747 0.5406 0.7989
> [2,] 0.1089 0.8301 0.8917 0.8953
> [3,] 0.9480 0.9732 0.2165 0.8832
> [4,] 0.0238 0.6754 0.2318 0.4503
>
>> det(A)
> [1] -0.07864701
>
>> print(sprintf("%.12f",det(A)))
> "-0.078647008154"
>

Oooooooops!!
You're right!
I really really sorry for this mistake.
Probably I fall into a cut&paste trap!

Here below are the results (matching with yours)


Octave: -0.0786470081539579
R: -0.07864701
Mathematica: -0.078647
NumPy: -0.07864700815395792


--- [octave] ---
A=[0.5560, 0.2747, 0.5406, 0.7989; 0.1089, 0.8301, 0.8917, 0.8953;
0.9480, 0.9732, 0.2165, 0.8832; 0.0238, 0.6754, 0.2318, 0.4503]

det(A)
--- [/octave] ---

==> -0.0786470081539579

--- [R] ---
A=matrix(c(0.5560, 0.2747, 0.5406, 0.7989,0.1089, 0.8301, 0.8917,
0.8953,0.9480, 0.9732, 0.2165, 0.8832,0.0238, 0.6754, 0.2318,
0.4503),nrow=4,ncol=4,byrow=T)

det(A)
--- [/R] ---

==> -0.07864701

--- [R (var2)] ---
library(Matrix)

A=Matrix(c(0.5560, 0.2747, 0.5406, 0.7989,0.1089, 0.8301, 0.8917,
0.8953,0.9480, 0.9732, 0.2165, 0.8832,0.0238, 0.6754, 0.2318,
0.4503),nrow=4,ncol=4,byrow=T)

determinant(A, log=F)
--- [/R (var2)] ---

==> -0.07864701

--- [numpy] ---
import numpy as np

A=np.matrix('0.5560, 0.2747, 0.5406, 0.7989; 0.1089, 0.8301, 0.8917,
0.8953; 0.9480, 0.9732, 0.2165, 0.8832; 0.0238, 0.6754, 0.2318,
0.4503'

np.linalg.det(A)
--- [/numpy] ---

==> -0.07864700815395792

--- [mathematica] ---
A = {{0.5560, 0.2747, 0.5406, 0.7989}, {0.1089, 0.8301, 0.8917,
  0.8953}, {0.9480, 0.9732, 0.2165, 0.8832}, {0.0238, 0.6754, 0.2318,
   0.4503}}

Det[A]
--- [/mathematica] ---

==> -0.078647


Thank you very much!!!

-- Marco