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 math.vectors sequences
5 sequences.private sorting fry arrays grouping sets ;
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 ;
19 :: ((kth-object)) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
20 #! Wirth's method, Algorithm's + Data structues = Programs p. 84
21 #! The algorithm modifiers seq, so we clone it
22 k seq bounds-check 2drop
35 [ i seq nth-quot call x quot call ] [ i 1 + i! ] while
36 [ x j seq nth-quot call quot call ] [ j 1 - j! ] while
38 i j seq exchange-quot call
49 : (kth-object) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
50 [ clone ] 4dip ((kth-object)) ; inline
52 : kth-object-unsafe ( seq k quot: ( x y -- ? ) -- elt )
53 [ [ nth-unsafe ] [ exchange-unsafe ] ] dip (kth-object) ; inline
55 : kth-objects-unsafe ( seq kths quot: ( x y -- ? ) -- elts )
57 '[ [ nth-unsafe ] [ exchange-unsafe ] _ ((kth-object)) ] with map ; inline
61 : kth-object ( seq k quot: ( x y -- ? ) -- elt )
62 [ [ nth ] [ exchange ] ] dip (kth-object) ; inline
64 : kth-objects ( seq kths quot: ( x y -- ? ) -- elts )
66 '[ [ nth ] [ exchange ] _ ((kth-object)) ] with map ; inline
68 : kth-smallests ( seq kths -- elts ) [ < ] kth-objects-unsafe ;
70 : kth-smallest ( seq k -- elt ) [ < ] kth-object-unsafe ;
72 : kth-largests ( seq kths -- elts ) [ > ] kth-objects-unsafe ;
74 : kth-largest ( seq k -- elt ) [ > ] kth-object-unsafe ;
76 : count-relative ( seq k -- lt eq gt )
79 { +lt+ [ [ 1 + ] 2dip ] }
81 { +eq+ [ [ 1 + ] dip ] }
85 : minmax-relative ( seq k -- lt eq gt lt-max gt-min )
86 [ 0 0 0 -1/0. 1/0. ] 2dip '[
88 { +lt+ [ [ 1 + ] 5 ndip '[ _ max ] dip ] }
89 { +gt+ [ [ 1 + ] 3dip min ] }
90 { +eq+ [ [ 1 + ] 4dip drop ] }
94 : lower-median-index ( seq -- n )
96 [ length odd? [ 1 - ] unless ] bi ;
98 : lower-median ( seq -- elt )
99 [ ] [ lower-median-index ] bi kth-smallest ;
101 : upper-median ( seq -- elt )
102 dup midpoint@ kth-smallest ;
104 : medians ( seq -- lower upper )
106 [ [ lower-median-index ] [ midpoint@ ] bi 2array ]
107 bi kth-smallests first2 ;
109 : median ( seq -- x )
111 [ lower-median ] [ medians + 2 / ] if ;
113 ! quantile can be any n-tile. quartile is n = 4, percentile is n = 100
114 ! a,b,c,d parameters, N - number of samples, q is quantile (1/2 for median, 1/4 for 1st quartile)
115 ! http://mathworld.wolfram.com/Quantile.html
117 ! could subtract 1 from a
119 : quantile-x ( a b N q -- x )
120 [ + ] dip * + 1 - ; inline
124 >fraction [ /mod nip ] keep / ; inline
126 :: quantile-indices ( seq qs a b c d -- seq )
127 qs [ [ a b seq length ] dip quantile-x ] map ;
129 :: qabcd ( y-floor y-ceiling x c d -- qabcd )
130 y-floor y-ceiling y-floor - c d x frac * + * + ;
132 :: quantile-abcd ( seq qs a b c d -- quantile )
133 seq qs a b c d quantile-indices :> indices
134 indices [ [ floor ] [ ceiling ] bi 2array ] map
135 concat :> index-pairs
137 seq index-pairs kth-smallests
138 2 group indices [ [ first2 ] dip c d qabcd ] 2map ;
140 : quantile1 ( seq qs -- seq' )
141 0 0 1 0 quantile-abcd ;
143 : quantile3 ( seq qs -- seq' )
144 1/2 0 0 0 quantile-abcd ;
146 : quantile4 ( seq qs -- seq' )
147 0 0 0 1 quantile-abcd ;
149 : quantile5 ( seq qs -- seq' )
150 1/2 0 0 1 quantile-abcd ;
152 : quantile6 ( seq qs -- seq' )
153 0 1 0 1 quantile-abcd ;
155 : quantile7 ( seq qs -- seq' )
156 1 -1 0 1 quantile-abcd ;
158 : quantile8 ( seq qs -- seq' )
159 1/3 1/3 0 1 quantile-abcd ;
161 : quantile9 ( seq qs -- seq' )
162 3/8 1/4 0 1 quantile-abcd ;
164 : quartile ( seq -- seq' )
165 { 1/4 1/2 3/4 } quantile5 ;
169 : (sequence>assoc) ( seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) assoc -- assoc )
170 [ swap curry compose each ] keep ; inline
174 : sequence>assoc! ( assoc seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) -- assoc )
175 4 nrot (sequence>assoc) ; inline
177 : sequence>assoc ( seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) exemplar -- assoc )
178 clone (sequence>assoc) ; inline
180 : sequence>hashtable ( seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) -- hashtable )
181 H{ } sequence>assoc ; inline
183 : histogram! ( hashtable seq -- hashtable )
184 [ ] [ inc-at ] sequence>assoc! ;
186 : histogram-by ( seq quot: ( x -- bin ) -- hashtable )
187 [ inc-at ] sequence>hashtable ; inline
189 : histogram ( seq -- hashtable )
192 : sorted-histogram ( seq -- alist )
193 histogram sort-values ;
195 : collect-pairs ( seq quot: ( x -- v k ) -- hashtable )
196 [ push-at ] sequence>hashtable ; inline
198 : collect-by ( seq quot: ( x -- x' ) -- hashtable )
199 [ dup ] prepose collect-pairs ; inline
203 [ ] [ [ [ second ] bi@ > ] most ] map-reduce first ;
205 ERROR: empty-sequence ;
207 : minmax ( seq -- min max )
211 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] each
217 : sample-var ( seq -- x )
222 [ [ mean ] keep [ - sq ] with map-sum ]
230 [ [ mean ] keep [ - sq ] with map-sum ]
234 : std ( seq -- x ) var sqrt ;
236 : ste ( seq -- x ) [ std ] [ length ] bi sqrt / ;
238 : ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
239 ! finds sigma((xi-mean(x))(yi-mean(y))
240 0 [ [ [ pick ] dip swap - ] bi@ * + ] 2reduce 2nip ;
242 : (r) ( mean(x) mean(y) {x} {y} sx sy -- r )
243 * recip [ [ ((r)) ] keep length 1 - / ] dip * ;
245 : [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
246 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
248 : r ( {{x,y}...} -- r )
251 : r^2 ( {{x,y}...} -- r )
254 : least-squares ( {{x,y}...} -- alpha beta )
255 [r] { [ 2dup ] [ ] [ ] [ ] [ ] } spread
256 ! stack is mean(x) mean(y) mean(x) mean(y) {x} {y} sx sy
257 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
258 swap / * ! stack is mean(x) mean(y) beta
261 : cov ( {x} {y} -- cov )
262 [ dup mean v-n ] bi@ v* mean ;
264 : corr ( {x} {y} -- corr )
265 [ cov ] [ [ var ] bi@ * sqrt ] 2bi / ;
267 : cum-sum ( seq -- seq' )
268 0 swap [ + dup ] map nip ;
270 : cum-product ( seq -- seq' )
271 1 swap [ * dup ] map nip ;
273 : cum-min ( seq -- seq' )
274 [ ?first ] keep [ min dup ] map nip ;
276 : cum-max ( seq -- seq' )
277 [ ?first ] keep [ max dup ] map nip ;
279 : entropy ( seq -- n )
280 dup members [ [ = ] curry count ] with map
281 dup sum v/n dup [ log ] map v* sum neg ;
283 : binary-entropy ( p -- h )
284 [ dup log * ] [ 1 swap - dup log * ] bi + neg 2 log / ;
286 : standardize ( u -- v )
287 [ dup mean v-n ] [ std ] bi v/n ;
289 : differences ( u -- v )
290 [ 1 tail-slice ] keep [ - ] 2map ;
293 [ ] [ infimum ] [ supremum over - ] tri
294 [ v-n ] [ v/n ] bi* ;