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
On Tue, Feb 5, 2013 at 1:32 PM, Leonard P <leonard14...@gmail.com> wrote:
> Anyone know off-hand of an idiomatic way to do the Laplace expansion of an
> nxn matrix?
>
>
>
>
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