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.functions
4 math.order sequences sorting locals sequences.private
9 [ sum ] [ length ] bi / ;
11 : geometric-mean ( seq -- x )
12 [ length ] [ product ] bi nth-root ;
14 : harmonic-mean ( seq -- x )
15 [ recip ] map-sum 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
36 i j seq exchange-unsafe
47 : lower-median ( seq -- elt )
48 [ ] [ ] [ length odd? ] tri
49 [ midpoint@ ] [ midpoint@ 1 - ] if kth-smallest ;
51 : upper-median ( seq -- elt )
52 dup midpoint@ kth-smallest ;
54 : medians ( seq -- lower upper )
55 [ lower-median ] [ upper-median ] bi ;
58 [ ] [ length odd? ] bi [ lower-median ] [ medians + 2 / ] if ;
62 : (sequence>assoc) ( seq quot assoc -- assoc )
63 [ swap curry each ] keep ; inline
67 : sequence>assoc* ( assoc seq quot: ( obj assoc -- ) -- assoc )
68 rot (sequence>assoc) ; inline
70 : sequence>assoc ( seq quot: ( obj assoc -- ) exemplar -- assoc )
71 clone (sequence>assoc) ; inline
73 : sequence>hashtable ( seq quot: ( obj hashtable -- ) -- hashtable )
74 H{ } sequence>assoc ; inline
76 : histogram* ( hashtable seq -- hashtable )
77 [ inc-at ] sequence>assoc* ;
79 : histogram ( seq -- hashtable )
80 [ inc-at ] sequence>hashtable ;
82 : sorted-histogram ( seq -- alist )
83 histogram >alist sort-values ;
85 : collect-values ( seq quot: ( obj hashtable -- ) -- hash )
86 '[ [ dup @ ] dip push-at ] sequence>hashtable ; inline
90 [ ] [ [ [ second ] bi@ > ] 2keep ? ] map-reduce first ;
92 ERROR: empty-sequence ;
94 : minmax ( seq -- min max )
98 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] each
109 [ [ mean ] keep [ - sq ] with map-sum ]
113 : std ( seq -- x ) var sqrt ;
115 : ste ( seq -- x ) [ std ] [ length ] bi sqrt / ;
117 : ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
118 ! finds sigma((xi-mean(x))(yi-mean(y))
119 0 [ [ [ pick ] dip swap - ] bi@ * + ] 2reduce 2nip ;
121 : (r) ( mean(x) mean(y) {x} {y} sx sy -- r )
122 * recip [ [ ((r)) ] keep length 1 - / ] dip * ;
124 : [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
125 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
127 : r ( {{x,y}...} -- r )
130 : r^2 ( {{x,y}...} -- r )
133 : least-squares ( {{x,y}...} -- alpha beta )
134 [r] { [ 2dup ] [ ] [ ] [ ] [ ] } spread
135 ! stack is mean(x) mean(y) mean(x) mean(y) {x} {y} sx sy
136 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
137 swap / * ! stack is mean(x) mean(y) beta