On Tue, Feb 5, 2013 at 5:58 PM, Doug Coleman <doug.cole...@gmail.com> wrote:
> If you interested in finding the determinant of a matrix, the easiest way
> is probably to bind to LAPACK or LINPACK using our Fortran FFI. Take a look
> at extra/math/blas/ffi for an example.
>
> I ended up writing the whole thing... It's really inefficient, as it makes
> temporary matrices. You'd probably want some kind of virtual-matrix or
> matrix view with the row/column removed.
>
> : 2x2-det ( mat -- x )
> first2 [ [ first ] [ second ] bi* * ] [ [ second ] [ first ] bi* * ]
> 2bi - ;
>
> : row-col-pairs ( row matrix -- seq )
> 2dup length < [ nip 0 swap ] unless
> length iota [ 2array ] with map ;
>
> : sub-matrices ( row matrix -- seq )
> [ nip ] [ row-col-pairs ] 2bi
> [ first2 [ swap remove-nth ] dip '[ _ swap remove-nth ] map ] with { }
> map-as ;
>
> :: laplace-expansion ( row matrix -- x )
> matrix length 2 = [ matrix 2x2-det ] [
> 0 matrix [ nth ] [ sub-matrices ] 2bi ! cheat, always expand on
> first row for recursive case
> [ row swap laplace-expansion ] map
> v* [ odd? [ neg ] when ] map-index sum
> ] if ;
>
> : determinant ( matrix -- x )
> ! TODO: Check for square matrix here
> 0 swap laplace-expansion ;
>
> 0 { { 1 2 3 } { 4 5 6 } { 7 8 9 } } laplace-expansion .
> 0
> 1 { { 1 2 3 } { 4 5 6 } { 7 8 9 } } laplace-expansion .
> 0
> 2 { { 1 2 3 } { 4 5 6 } { 7 8 9 } } laplace-expansion .
> 0
>
> { { 40 39 38 37 } { 1 1 1 831 } { 22 22 1110 299 } { 13 14 15 17 } }
> determinant
>
> http://www.wolframalpha.com/input/?i=Determinant%5B%5B40%2C39%2C38%2C37%5D%2C%5B1%2C1%2C1%2C831%5D%2C%5B22%2C22%2C1110%2C299%5D%2C%5B13%2C14%2C15%2C17%5D%5D
>
>
> If you have time, try adding a more efficient version to arrays.shaped?
> (Or bind to LINPACK or implement a better algorithm!)
>
> Have fun,
> Doug
>
Ok Doug. Made an attempt to roll my own determinant.
Had fun writing a bunch of helper words, but got stuck on the important
part, the recursive case.
The compiler doesn't like the stack effects in the if statement in my
recursive case.
Think I'm at the point where I can't proceed without a suggestion.
- Leonard
determinant-tests.factor
Description: Binary data
determinant.factor
Description: Binary data
------------------------------------------------------------------------------ Precog is a next-generation analytics platform capable of advanced analytics on semi-structured data. The platform includes APIs for building apps and a phenomenal toolset for data science. Developers can use our toolset for easy data analysis & visualization. Get a free account! http://www2.precog.com/precogplatform/slashdotnewsletter
_______________________________________________ Factor-talk mailing list Factor-talk@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/factor-talk
