1 ! Copyright (C) 2008 Doug Coleman, Michael Judge.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: arrays combinators kernel math math.analysis
4 math.functions math.order sequences sorting locals
9 [ sum ] [ length ] bi / ;
11 : geometric-mean ( seq -- x )
12 [ length ] [ product ] bi nth-root ;
14 : harmonic-mean ( seq -- x )
15 [ recip ] sigma recip ;
17 :: kth-smallest ( seq k -- elt )
18 #! Wirth's method, Algorithm's + Data structues = Programs p. 84
19 #! The algorithm modifiers seq, so we clone it
33 [ i seq nth-unsafe x < ] [ i 1 + i! ] while
34 [ x j seq nth-unsafe < ] [ j 1 - j! ] while
47 : lower-median ( seq -- elt )
48 dup dup length odd? [ midpoint@ ] [ midpoint@ 1 - ] if kth-smallest ;
50 : upper-median ( seq -- elt )
51 dup midpoint@ kth-smallest ;
53 : medians ( seq -- lower upper )
54 [ lower-median ] [ upper-median ] bi ;
57 dup length odd? [ lower-median ] [ medians + 2 / ] if ;
59 : minmax ( seq -- min max )
60 #! find the min and max of a seq in one pass
61 [ 1/0. -1/0. ] dip [ [ min ] [ max ] bi-curry bi* ] each ;
71 [ [ mean ] keep [ - sq ] with sigma ]
75 : std ( seq -- x ) var sqrt ;
77 : ste ( seq -- x ) [ std ] [ length ] bi sqrt / ;
79 : ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
80 ! finds sigma((xi-mean(x))(yi-mean(y))
81 0 [ [ [ pick ] dip swap - ] bi@ * + ] 2reduce 2nip ;
83 : (r) ( mean(x) mean(y) {x} {y} sx sy -- r )
84 * recip [ [ ((r)) ] keep length 1 - / ] dip * ;
86 : [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
87 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
89 : r ( {{x,y}...} -- r )
92 : r^2 ( {{x,y}...} -- r )
95 : least-squares ( {{x,y}...} -- alpha beta )
96 [r] { [ 2dup ] [ ] [ ] [ ] [ ] } spread
97 ! stack is mean(x) mean(y) mean(x) mean(y) {x} {y} sx sy
98 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
99 swap / * ! stack is mean(x) mean(y) beta