1 ! Copyright (C) 2008 Doug Coleman, Michael Judge.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: assocs combinators generalizations kernel locals math
4 math.functions math.order sequences sequences.private sorting ;
8 [ sum ] [ length ] bi / ;
10 : geometric-mean ( seq -- x )
11 [ length ] [ product ] bi nth-root ;
13 : harmonic-mean ( seq -- x )
14 [ recip ] map-sum recip ;
16 :: kth-smallest ( seq k -- elt )
17 #! Wirth's method, Algorithm's + Data structues = Programs p. 84
18 #! The algorithm modifiers seq, so we clone it
32 [ i seq nth-unsafe x < ] [ i 1 + i! ] while
33 [ x j seq nth-unsafe < ] [ j 1 - j! ] while
35 i j seq exchange-unsafe
46 : lower-median ( seq -- elt )
47 [ ] [ ] [ length odd? ] tri
48 [ 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 [ ] [ length odd? ] bi [ lower-median ] [ medians + 2 / ] if ;
61 : (sequence>assoc) ( seq map-quot: ( x -- x' ) insert-quot: ( x' assoc -- ) assoc -- assoc )
62 [ swap curry compose each ] keep ; inline
66 : sequence>assoc! ( assoc seq map-quot: ( x -- x' ) insert-quot: ( x' assoc -- ) -- assoc )
67 4 nrot (sequence>assoc) ; inline
69 : sequence>assoc ( seq map-quot: ( x -- x' ) insert-quot: ( x' assoc -- ) exemplar -- assoc )
70 clone (sequence>assoc) ; inline
72 : sequence>hashtable ( seq map-quot: ( x -- x' ) insert-quot: ( x' assoc -- ) -- hashtable )
73 H{ } sequence>assoc ; inline
75 : histogram! ( hashtable seq -- hashtable )
76 [ ] [ inc-at ] sequence>assoc! ;
78 : histogram-by ( seq quot: ( x -- bin ) -- hashtable )
79 [ inc-at ] sequence>hashtable ; inline
81 : histogram ( seq -- hashtable )
84 : sorted-histogram ( seq -- alist )
85 histogram sort-values ;
87 : collect-pairs ( seq quot: ( x -- x' ) -- hashtable )
88 [ push-at ] sequence>hashtable ; inline
90 : collect-by ( seq quot -- hashtable )
91 [ dup ] prepose collect-pairs ; inline
95 [ ] [ [ [ second ] bi@ > ] 2keep ? ] map-reduce first ;
97 ERROR: empty-sequence ;
99 : minmax ( seq -- min max )
103 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] each
114 [ [ mean ] keep [ - sq ] with map-sum ]
118 : std ( seq -- x ) var sqrt ;
120 : ste ( seq -- x ) [ std ] [ length ] bi sqrt / ;
122 : ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
123 ! finds sigma((xi-mean(x))(yi-mean(y))
124 0 [ [ [ pick ] dip swap - ] bi@ * + ] 2reduce 2nip ;
126 : (r) ( mean(x) mean(y) {x} {y} sx sy -- r )
127 * recip [ [ ((r)) ] keep length 1 - / ] dip * ;
129 : [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
130 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
132 : r ( {{x,y}...} -- r )
135 : r^2 ( {{x,y}...} -- r )
138 : least-squares ( {{x,y}...} -- alpha beta )
139 [r] { [ 2dup ] [ ] [ ] [ ] [ ] } spread
140 ! stack is mean(x) mean(y) mean(x) mean(y) {x} {y} sx sy
141 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
142 swap / * ! stack is mean(x) mean(y) beta