USING: kernel math math.functions math.derivatives accessors words
generalizations sequences generic.parser fry locals compiler.units
continuations quotations combinators macros make ;
IN: math.dual
TUPLE: dual ordinary-part epsilon-part ;
C: dual
! Ordinary numbers implement the dual protocol by returning themselves as the
! ordinary part, and 0 as the epsilon part.
M: number ordinary-part>> ;
M: number epsilon-part>> drop 0 ;
: unpack-dual ( dual -- ordinary-part epsilon-part )
[ ordinary-part>> ] [ epsilon-part>> ] bi ;
> ] _ napply _ execute ] ;
MACRO:: chain-rule ( derivative-list n -- x )
n n n n derivative-list n 1+ n
'[ [ [ epsilon-part>> ] _ napply ] _ nkeep [ ordinary-part>> ] _ napply
_ nweave
_ _ nspread
_ nsum ] ;
PRIVATE>
! dual-op is similar to execute, but promotes the word to operate on duals.
! Uses the "derivative" word-prop, which holds a list of quotations giving the
! partial derivative of the word with respect to each of its argumets.
:: [dual-op] ( word -- quot )
word "derivative" word-prop :> derivative-list
derivative-list length :> n
word n '[ _ _ ordinary-op ]
n
derivative-list n '[ _ _ chain-rule ]
'[ _ _ nkeep @ ] ;
MACRO: dual-op ( word -- ) [dual-op] ;
: define-dual-method ( word -- )
[ \ dual swap create-method-in ] keep [dual-op] define ;
! Specialize math functions to operate on dual numbers.
<< { sqrt exp log sin cos tan sinh cosh tanh atan }
[ define-dual-method ] each >>
! Inverse methods { asin, acos, asinh, acosh, atanh } are not generic,
! so there is no way to specialize them for dual numbers.
! Arithmetic methods are not generic (yet?), so we have to define special
! versions of them to operate on dual numbers.
: d+ ( x y -- x+y ) \ + dual-op ;
: d- ( x y -- x+y ) \ - dual-op ;
: d* ( x y -- x*y ) \ * dual-op ;
: d/ ( x y -- x/y ) \ / dual-op ;
: d^ ( x y -- x^y ) \ ^ dual-op ;