[racket] matrix-solve and approximation errors

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.orseau at 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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