1 ! Copyright (C) 2008 Doug Coleman, Michael Judge, Loryn Jenkins.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: arrays assocs combinators fry generalizations grouping
4 kernel locals math math.functions math.order math.vectors
5 sequences sequences.private sorting ;
8 : power-mean ( seq p -- x )
9 [ '[ _ ^ ] map-sum ] [ [ length / ] [ recip ^ ] bi* ] 2bi ; inline
11 ! Delta in degrees-of-freedom
12 : mean-ddof ( seq ddof -- x )
13 [ [ sum ] [ length ] bi ] dip -
14 [ drop 0 ] [ / ] if-zero ; inline
19 : sum-of-squares ( seq -- x )
20 [ sq ] map-sum ; inline
22 : sum-of-squared-errors ( seq -- x )
23 [ mean ] keep [ - sq ] with map-sum ; inline
25 : sum-of-absolute-errors ( seq -- x )
26 [ mean ] keep [ - ] with map-sum ; inline
28 : quadratic-mean ( seq -- x ) ! root-mean-square
29 [ sum-of-squares ] [ length ] bi / sqrt ; inline
31 : geometric-mean ( seq -- x )
32 [ [ log ] map-sum ] [ length ] bi /f e^ ; inline
34 : harmonic-mean ( seq -- x )
35 [ [ recip ] map-sum ] [ length swap / ] bi ; inline
37 : contraharmonic-mean ( seq -- x )
38 [ sum-of-squares ] [ sum ] bi / ; inline
42 : trim-points ( p seq -- from to seq )
43 [ length [ * >integer ] keep over - ] keep ;
47 : trimmed-mean ( seq p -- x )
48 swap natural-sort trim-points <slice> mean ;
50 : winsorized-mean ( seq p -- x )
51 swap natural-sort trim-points
53 [ nip dupd nth <array> ]
54 [ [ 1 - ] dip nth <array> ] 3tri
59 :: kth-object-impl ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
60 ! Wirth's method, Algorithm's + Data structues = Programs p. 84
61 k seq bounds-check 2drop
74 [ i seq nth-quot call x quot call ] [ i 1 + i! ] while
75 [ x j seq nth-quot call quot call ] [ j 1 - j! ] while
77 i j seq exchange-quot call
86 k seq nth-unsafe ; inline
88 : (kth-object) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
89 ! The algorithm modifiers seq, so we clone it
90 [ >array ] 4dip kth-object-impl ; inline
92 : kth-object-unsafe ( seq k quot: ( x y -- ? ) -- elt )
93 [ [ nth-unsafe ] [ exchange-unsafe ] ] dip (kth-object) ; inline
95 : kth-objects-unsafe ( seq kths quot: ( x y -- ? ) -- elts )
96 '[ _ kth-object-unsafe ] with map ; inline
100 : kth-object ( seq k quot: ( x y -- ? ) -- elt )
101 [ [ nth ] [ exchange ] ] dip (kth-object) ; inline
103 : kth-objects ( seq kths quot: ( x y -- ? ) -- elts )
104 '[ _ kth-object ] with map ; inline
106 : kth-smallests ( seq kths -- elts ) [ < ] kth-objects-unsafe ;
108 : kth-smallest ( seq k -- elt ) [ < ] kth-object-unsafe ;
110 : kth-largests ( seq kths -- elts ) [ > ] kth-objects-unsafe ;
112 : kth-largest ( seq k -- elt ) [ > ] kth-object-unsafe ;
114 : count-relative ( seq k -- lt eq gt )
117 { +lt+ [ [ 1 + ] 2dip ] }
119 { +eq+ [ [ 1 + ] dip ] }
123 : minmax-relative ( seq k -- lt eq gt lt-max gt-min )
124 [ 0 0 0 -1/0. 1/0. ] 2dip '[
126 { +lt+ [ [ 1 + ] 5 ndip '[ _ max ] dip ] }
127 { +gt+ [ [ 1 + ] 3dip min ] }
128 { +eq+ [ [ 1 + ] 4dip drop ] }
132 : lower-median-index ( seq -- n )
134 [ length odd? [ 1 - ] unless ] bi ;
136 : lower-median ( seq -- elt )
137 [ ] [ lower-median-index ] bi kth-smallest ;
139 : upper-median ( seq -- elt )
140 dup midpoint@ kth-smallest ;
142 : medians ( seq -- lower upper )
144 [ [ lower-median-index ] [ midpoint@ ] bi 2array ]
145 bi kth-smallests first2 ;
147 : median ( seq -- x )
148 dup length odd? [ lower-median ] [ medians + 2 / ] if ;
150 ! quantile can be any n-tile. quartile is n = 4, percentile is n = 100
151 ! a,b,c,d parameters, N - number of samples, q is quantile (1/2 for median, 1/4 for 1st quartile)
152 ! http://mathworld.wolfram.com/Quantile.html
154 ! could subtract 1 from a
156 : quantile-x ( a b N q -- x )
157 [ + ] dip * + 1 - ; inline
161 >fraction [ /mod nip ] keep / ; inline
163 :: quantile-indices ( seq qs a b -- seq )
164 qs [ [ a b seq length ] dip quantile-x ] map ;
166 :: qabcd ( y-floor y-ceiling x c d -- qabcd )
167 y-floor y-ceiling y-floor - c d x frac * + * + ;
169 :: quantile-abcd ( seq qs a b c d -- quantile )
170 seq qs a b quantile-indices :> indices
171 indices [ [ floor 0 max ] [ ceiling seq length 1 - min ] bi 2array ] map
172 concat :> index-pairs
174 seq index-pairs kth-smallests
175 2 group indices [ [ first2 ] dip c d qabcd ] 2map ;
177 : quantile1 ( seq qs -- seq' )
178 0 0 1 0 quantile-abcd ;
180 : quantile3 ( seq qs -- seq' )
181 1/2 0 0 0 quantile-abcd ;
183 : quantile4 ( seq qs -- seq' )
184 0 0 0 1 quantile-abcd ;
186 : quantile5 ( seq qs -- seq' )
187 1/2 0 0 1 quantile-abcd ;
189 : quantile6 ( seq qs -- seq' )
190 0 1 0 1 quantile-abcd ;
192 : quantile7 ( seq qs -- seq' )
193 1 -1 0 1 quantile-abcd ;
195 : quantile8 ( seq qs -- seq' )
196 1/3 1/3 0 1 quantile-abcd ;
198 : quantile9 ( seq qs -- seq' )
199 3/8 1/4 0 1 quantile-abcd ;
201 : quartile ( seq -- seq' )
202 { 1/4 1/2 3/4 } quantile5 ;
204 : interquartile ( seq -- q1 q3 )
205 quartile [ first ] [ last ] bi ;
207 : interquartile-range ( seq -- n )
210 : midhinge ( seq -- n )
211 interquartile + 2 / ;
213 : trimean ( seq -- x )
214 quartile first3 [ 2 * ] dip + + 4 / ;
216 : histogram! ( hashtable seq -- hashtable )
217 over '[ _ inc-at ] each ;
219 : histogram-by ( seq quot: ( x -- bin ) -- hashtable )
220 H{ } clone [ '[ @ _ inc-at ] each ] keep ; inline
222 : histogram ( seq -- hashtable )
225 : sorted-histogram ( seq -- alist )
226 histogram sort-values ;
228 : normalized-histogram ( seq -- alist )
229 [ histogram ] [ length ] bi '[ _ / ] assoc-map ;
231 : equal-probabilities ( n -- array )
232 dup recip <array> ; inline
235 histogram >alist [ second ] supremum-by first ;
237 : minmax ( seq -- min max )
238 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] 1 each-from ;
243 : fivenum ( seq -- seq' )
244 [ quartile ] [ minmax ] bi [ prefix ] [ suffix ] bi* ;
246 : var-ddof ( seq n -- x )
247 2dup [ length ] dip - 0 <= [
250 [ [ sum-of-squared-errors ] [ length ] bi ] dip - /
253 : population-var ( seq -- x ) 0 var-ddof ; inline
255 : sample-var ( seq -- x ) 1 var-ddof ; inline
257 : std-ddof ( seq n -- x ) var-ddof sqrt ; inline
259 : population-std ( seq -- x ) 0 std-ddof ; inline
261 : sample-std ( seq -- x ) 1 std-ddof ; inline
263 ALIAS: std sample-std
265 : signal-to-noise ( seq -- x ) [ mean ] [ population-std ] bi / ;
267 : demean ( seq -- seq' ) dup mean v-n ;
269 : mean-dev ( seq -- x ) demean vabs mean ;
271 : demedian ( seq -- seq' ) dup median v-n ;
273 : median-dev ( seq -- x ) demedian vabs mean ;
275 : ste-ddof ( seq n -- x ) '[ _ std-ddof ] [ length ] bi sqrt / ;
277 : population-ste ( seq -- x ) 0 ste-ddof ;
279 : sample-ste ( seq -- x ) 1 ste-ddof ;
282 : r-sum-diffs ( x-mean y-mean x-seq y-seq -- (r) )
283 ! finds sigma((xi-mean(x))(yi-mean(y))
284 0 [ [ reach - ] bi@ * + ] 2reduce 2nip ;
286 : (r) ( x-mean y-mean x-seq y-seq x-std y-std -- r )
287 * recip [ [ r-sum-diffs ] keep length 1 - / ] dip * ;
289 : r-stats ( xy-pairs -- x-mean y-mean x-seq y-seq x-std y-std )
290 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ population-std ] bi@ ;
293 : pearson-r ( xy-pairs -- r ) r-stats (r) ;
295 : least-squares ( xy-pairs -- alpha beta )
296 r-stats [ 2dup ] 4dip
297 ! stack is x-mean y-mean x-mean y-mean x-seq y-seq x-std y-std
298 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
299 swap / * ! stack is mean(x) mean(y) beta
302 : cov-ddof ( x-seq y-seq ddof -- cov )
303 [ [ demean ] bi@ v* ] dip mean-ddof ;
305 : population-cov ( x-seq y-seq -- cov ) 0 cov-ddof ; inline
307 : sample-cov ( x-seq y-seq -- cov ) 1 cov-ddof ; inline
309 : corr-ddof ( x-seq y-seq n -- corr )
310 [ [ population-cov ] ] dip
311 '[ [ _ var-ddof ] bi@ * sqrt ] 2bi / ;
313 : population-corr ( x-seq y-seq -- corr ) 0 corr-ddof ; inline
315 : sample-corr ( x-seq y-seq -- corr ) 1 corr-ddof ; inline
317 : cum-sum ( seq -- seq' )
318 0 [ + ] accumulate* ;
320 : cum-sum0 ( seq -- seq' )
321 0 [ + ] accumulate nip ;
323 : cum-product ( seq -- seq' )
324 1 [ * ] accumulate* ;
326 : cum-product1 ( seq -- seq' )
327 1 [ * ] accumulate nip ;
329 : cum-mean ( seq -- seq' )
330 0 swap [ [ + dup ] dip 1 + / ] map-index nip ;
332 : cum-count ( seq quot: ( elt -- ? ) -- seq' )
333 [ 0 ] dip '[ @ [ 1 + ] when ] accumulate* ; inline
335 : cum-min ( seq -- seq' )
336 dup ?first [ min ] accumulate* ;
338 : cum-max ( seq -- seq' )
339 dup ?first [ max ] accumulate* ;
341 : entropy ( probabilities -- n )
342 dup sum '[ _ / dup log * ] map-sum neg ;
344 : maximum-entropy ( probabilities -- n )
347 : normalized-entropy ( probabilities -- n )
348 [ entropy ] [ maximum-entropy ] bi / ;
350 : binary-entropy ( p -- h )
351 [ dup log * ] [ 1 swap - dup log * ] bi + neg 2 log / ;
353 : standardize ( u -- v )
354 [ demean ] [ sample-std ] bi [ v/n ] unless-zero ;
356 : standardize-2d ( u -- v )
357 flip [ standardize ] map flip ;
359 : differences ( u -- v )
360 [ rest-slice ] keep v- ;
363 dup minmax over - [ v-n ] [ v/n ] bi* ;
365 : rankings ( histogram -- assoc )
366 sort-keys 0 swap [ rot [ + ] keep swapd ] H{ } assoc-map-as nip ;
368 : rank-values ( seq -- seq' )
369 dup histogram rankings '[ _ at ] map ;
371 : z-score ( seq -- n )
372 [ demean ] [ sample-std ] bi v/n ;