Hi Laurent,
I think the underlying problem is that the matrix is *very* close to
an invertible one:
> (matrix-determinant
(matrix [[ 1 0 9/10 1]
[ 0 1 1/10 1]
[ 9/10 1/10 82/100 1]
[ 1 1 1 0]]))
0
/Jens Axel
2014-04-16 12:02 GMT+02:00 Laurent <laurent.ors...@gmail.com>:
> Forgot to mention that with the true value of n=0.82, this of course returns
> the correct solution:
> (let ([n 0.82 #;(+ (* .9 .9)(* .1 .1))])
>
> (matrix-solve
> (matrix [[ 1 0 .9 1]
> [ 0 1 .1 1]
> [.9 .1 n 1]
> [ 1 1 1 0]])
> (col-matrix [0 0 0 1])))
> ; -> (array #[#[0.38] #[0.4866666666666667] #[0.13333333333333333] #[-0.5]])
>
>
> On Wed, Apr 16, 2014 at 11:10 AM, Laurent <laurent.ors...@gmail.com> wrote:
>>
>> I've just been bitten by a bad case of floating-point error with
>> `matrix-solve` (and a bad CPU that has some floating-point issues):
>>
>> (let ([n 0.8200000000000001 #;(+ (* .9 .9)(* .1 .1))])
>> (matrix-solve
>> (matrix [[ 1 0 .9 1]
>> [ 0 1 .1 1]
>> [.9 .1 n 1]
>> [ 1 1 1 0]])
>> (col-matrix [0 0 0 1])))
>> ; -> (array #[#[0.0] #[0.5] #[0.0] #[-0.5]])
>>
>> But clearly here M×X≠B, as is easily seen on the last row.
>> I've seen other situations where the approximation leads to an approximate
>> solution (which is okay of course), but this is the first case I see where
>> the result is completely off.
>>
>> I have no idea if anything can be done about it, though (apart from
>> throwing my computer through the window and buy a better one).
>>
>> Laurent
>
>
>
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