1 ! Copyright (C) 2008 Doug Coleman, Michael Judge, Loryn Jenkins.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: accessors arrays assocs combinators
4 combinators.short-circuit fry generalizations grouping kernel
5 locals math math.functions math.order math.ranges math.vectors
6 sequences sequences.private sorting ;
7 FROM: math.ranges => [a,b] ;
10 : power-mean ( seq p -- x )
11 [ '[ _ ^ ] map-sum ] [ [ length / ] [ recip ^ ] bi* ] 2bi ; inline
13 ! Delta in degrees-of-freedom
14 : mean-ddof ( seq ddof -- x )
15 [ [ sum ] [ length ] bi ] dip -
16 [ drop 0 ] [ / ] if-zero ; inline
21 : meanest ( seq -- x )
22 [ mean ] keep [ - abs ] with infimum-by ;
24 GENERIC: sum-of-squares ( seq -- x )
25 M: object sum-of-squares [ sq ] map-sum ;
26 M: iota sum-of-squares
27 n>> 1 - [ ] [ 1 + ] [ 1/2 + ] tri * * 3 / ;
28 M: math.ranges:range sum-of-squares
29 dup { [ step>> 1 = ] [ from>> integer? ] } 1&& [
30 [ from>> ] [ length>> ] bi dupd +
31 [ <iota> sum-of-squares ] bi@ swap -
32 ] [ call-next-method ] if ;
34 GENERIC: sum-of-cubes ( seq -- x )
35 M: object sum-of-cubes [ 3 ^ ] map-sum ;
36 M: iota sum-of-cubes sum sq ;
37 M: math.ranges:range sum-of-cubes
38 dup { [ step>> 1 = ] [ from>> integer? ] } 1&& [
39 [ from>> ] [ length>> ] bi dupd +
40 [ <iota> sum-of-cubes ] bi@ swap -
41 ] [ call-next-method ] if ;
43 GENERIC: sum-of-quads ( seq -- x )
44 M: object sum-of-quads [ 4 ^ ] map-sum ;
55 M: math.ranges:range sum-of-quads
56 dup { [ step>> 1 = ] [ from>> integer? ] } 1&& [
57 [ from>> ] [ length>> ] bi dupd +
58 [ <iota> sum-of-quads ] bi@ swap -
59 ] [ call-next-method ] if ;
61 : sum-of-squared-errors ( seq -- x )
62 [ mean ] keep [ - sq ] with map-sum ; inline
64 : sum-of-absolute-errors ( seq -- x )
65 [ mean ] keep [ - ] with map-sum ; inline
67 : quadratic-mean ( seq -- x ) ! root-mean-square
68 [ sum-of-squares ] [ length ] bi / sqrt ; inline
70 : geometric-mean ( seq -- x )
71 [ [ log ] map-sum ] [ length ] bi /f e^ ; inline
73 : harmonic-mean ( seq -- x )
74 [ [ recip ] map-sum ] [ length swap / ] bi ; inline
76 : contraharmonic-mean ( seq -- x )
77 [ sum-of-squares ] [ sum ] bi / ; inline
81 : trim-points ( p seq -- from to seq )
82 [ length [ * >integer ] keep over - ] keep ;
86 : trimmed-mean ( seq p -- x )
87 swap natural-sort trim-points <slice> mean ;
89 : winsorized-mean ( seq p -- x )
90 swap natural-sort trim-points
92 [ nip dupd nth <array> ]
93 [ [ 1 - ] dip nth <array> ] 3tri
98 :: kth-object-impl ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
99 ! Wirth's method, Algorithm's + Data structues = Programs p. 84
100 k seq bounds-check 2drop
113 [ i seq nth-quot call x quot call ] [ i 1 + i! ] while
114 [ x j seq nth-quot call quot call ] [ j 1 - j! ] while
116 i j seq exchange-quot call
125 k seq nth-unsafe ; inline
127 : (kth-object) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
128 ! The algorithm modifiers seq, so we clone it
129 [ >array ] 4dip kth-object-impl ; inline
131 : kth-object-unsafe ( seq k quot: ( x y -- ? ) -- elt )
132 [ [ nth-unsafe ] [ exchange-unsafe ] ] dip (kth-object) ; inline
134 : kth-objects-unsafe ( seq kths quot: ( x y -- ? ) -- elts )
135 '[ _ kth-object-unsafe ] with map ; inline
139 : kth-object ( seq k quot: ( x y -- ? ) -- elt )
140 [ [ nth ] [ exchange ] ] dip (kth-object) ; inline
142 : kth-objects ( seq kths quot: ( x y -- ? ) -- elts )
143 '[ _ kth-object ] with map ; inline
145 : kth-smallests ( seq kths -- elts ) [ < ] kth-objects-unsafe ;
147 : kth-smallest ( seq k -- elt ) [ < ] kth-object-unsafe ;
149 : kth-largests ( seq kths -- elts ) [ > ] kth-objects-unsafe ;
151 : kth-largest ( seq k -- elt ) [ > ] kth-object-unsafe ;
153 : count-relative ( seq k -- lt eq gt )
156 { +lt+ [ [ 1 + ] 2dip ] }
158 { +eq+ [ [ 1 + ] dip ] }
162 : minmax-relative ( seq k -- lt eq gt lt-max gt-min )
163 [ 0 0 0 -1/0. 1/0. ] 2dip '[
165 { +lt+ [ [ 1 + ] 5 ndip '[ _ max ] dip ] }
166 { +gt+ [ [ 1 + ] 3dip min ] }
167 { +eq+ [ [ 1 + ] 4dip drop ] }
171 : lower-median-index ( seq -- n )
173 [ length odd? [ 1 - ] unless ] bi ;
175 : lower-median ( seq -- elt )
176 [ ] [ lower-median-index ] bi kth-smallest ;
178 : upper-median ( seq -- elt )
179 dup midpoint@ kth-smallest ;
181 : medians ( seq -- lower upper )
183 [ [ lower-median-index ] [ midpoint@ ] bi 2array ]
184 bi kth-smallests first2 ;
186 : median ( seq -- x )
187 dup length odd? [ lower-median ] [ medians + 2 / ] if ;
189 ! quantile can be any n-tile. quartile is n = 4, percentile is n = 100
190 ! a,b,c,d parameters, N - number of samples, q is quantile (1/2 for median, 1/4 for 1st quartile)
191 ! http://mathworld.wolfram.com/Quantile.html
193 ! could subtract 1 from a
195 : quantile-x ( a b N q -- x )
196 [ + ] dip * + 1 - ; inline
200 >fraction [ /mod nip ] keep / ; inline
202 :: quantile-indices ( seq qs a b -- seq )
203 qs [ [ a b seq length ] dip quantile-x ] map ;
205 :: qabcd ( y-floor y-ceiling x c d -- qabcd )
206 y-floor y-ceiling y-floor - c d x frac * + * + ;
208 :: quantile-abcd ( seq qs a b c d -- quantile )
209 seq qs a b quantile-indices :> indices
210 indices [ [ floor 0 max ] [ ceiling seq length 1 - min ] bi 2array ] map
211 concat :> index-pairs
213 seq index-pairs kth-smallests
214 2 group indices [ [ first2 ] dip c d qabcd ] 2map ;
216 : quantile1 ( seq qs -- seq' )
217 0 0 1 0 quantile-abcd ;
219 : quantile3 ( seq qs -- seq' )
220 1/2 0 0 0 quantile-abcd ;
222 : quantile4 ( seq qs -- seq' )
223 0 0 0 1 quantile-abcd ;
225 : quantile5 ( seq qs -- seq' )
226 1/2 0 0 1 quantile-abcd ;
228 : quantile6 ( seq qs -- seq' )
229 0 1 0 1 quantile-abcd ;
231 : quantile7 ( seq qs -- seq' )
232 1 -1 0 1 quantile-abcd ;
234 : quantile8 ( seq qs -- seq' )
235 1/3 1/3 0 1 quantile-abcd ;
237 : quantile9 ( seq qs -- seq' )
238 3/8 1/4 0 1 quantile-abcd ;
240 : quartile ( seq -- seq' )
241 { 1/4 1/2 3/4 } quantile5 ;
243 : interquartile ( seq -- q1 q3 )
244 quartile [ first ] [ last ] bi ;
246 : interquartile-range ( seq -- n )
249 : midhinge ( seq -- n )
250 interquartile + 2 / ;
252 : trimean ( seq -- x )
253 quartile first3 [ 2 * ] dip + + 4 / ;
255 : histogram! ( hashtable seq -- hashtable )
256 over '[ _ inc-at ] each ;
258 : histogram-by ( seq quot: ( x -- bin ) -- hashtable )
259 H{ } clone [ '[ @ _ inc-at ] each ] keep ; inline
261 : histogram ( seq -- hashtable )
264 : sorted-histogram ( seq -- alist )
265 histogram sort-values ;
267 : normalized-histogram ( seq -- alist )
268 [ histogram ] [ length ] bi '[ _ / ] assoc-map ;
270 : equal-probabilities ( n -- array )
271 dup recip <array> ; inline
274 histogram >alist [ second ] supremum-by first ;
276 : minmax ( seq -- min max )
277 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] 1 each-from ;
282 : fivenum ( seq -- seq' )
283 [ quartile ] [ minmax ] bi [ prefix ] [ suffix ] bi* ;
285 : var-ddof ( seq n -- x )
286 2dup [ length ] dip - 0 <= [
289 [ [ sum-of-squared-errors ] [ length ] bi ] dip - /
292 : population-var ( seq -- x ) 0 var-ddof ; inline
294 : sample-var ( seq -- x ) 1 var-ddof ; inline
296 : std-ddof ( seq n -- x ) var-ddof sqrt ; inline
298 : population-std ( seq -- x ) 0 std-ddof ; inline
300 : sample-std ( seq -- x ) 1 std-ddof ; inline
302 ALIAS: std sample-std
304 : signal-to-noise ( seq -- x ) [ mean ] [ population-std ] bi / ;
306 : demean ( seq -- seq' ) dup mean v-n ;
308 : mean-dev ( seq -- x ) demean vabs mean ;
310 : demedian ( seq -- seq' ) dup median v-n ;
312 : median-dev ( seq -- x ) demedian vabs mean ;
314 : ste-ddof ( seq n -- x ) '[ _ std-ddof ] [ length ] bi sqrt / ;
316 : population-ste ( seq -- x ) 0 ste-ddof ;
318 : sample-ste ( seq -- x ) 1 ste-ddof ;
321 : r-sum-diffs ( x-mean y-mean x-seq y-seq -- (r) )
322 ! finds sigma((xi-mean(x))(yi-mean(y))
323 0 [ [ reach - ] bi@ * + ] 2reduce 2nip ;
325 : (r) ( x-mean y-mean x-seq y-seq x-std y-std -- r )
326 * recip [ [ r-sum-diffs ] keep length 1 - / ] dip * ;
328 : r-stats ( xy-pairs -- x-mean y-mean x-seq y-seq x-std y-std )
329 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ population-std ] bi@ ;
332 : pearson-r ( xy-pairs -- r ) r-stats (r) ;
334 : least-squares ( xy-pairs -- alpha beta )
335 r-stats [ 2dup ] 4dip
336 ! stack is x-mean y-mean x-mean y-mean x-seq y-seq x-std y-std
337 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
338 swap / * ! stack is mean(x) mean(y) beta
341 : cov-ddof ( x-seq y-seq ddof -- cov )
342 [ [ demean ] bi@ v* ] dip mean-ddof ;
344 : population-cov ( x-seq y-seq -- cov ) 0 cov-ddof ; inline
346 : sample-cov ( x-seq y-seq -- cov ) 1 cov-ddof ; inline
348 : corr-ddof ( x-seq y-seq n -- corr )
349 [ [ population-cov ] ] dip
350 '[ [ _ var-ddof ] bi@ * sqrt ] 2bi / ;
352 : population-corr ( x-seq y-seq -- corr ) 0 corr-ddof ; inline
354 : sample-corr ( x-seq y-seq -- corr ) 1 corr-ddof ; inline
356 : cum-sum ( seq -- seq' )
357 0 [ + ] accumulate* ;
359 : cum-sum0 ( seq -- seq' )
360 0 [ + ] accumulate nip ;
362 : cum-product ( seq -- seq' )
363 1 [ * ] accumulate* ;
365 : cum-product1 ( seq -- seq' )
366 1 [ * ] accumulate nip ;
368 : cum-mean ( seq -- seq' )
369 0 swap [ [ + dup ] dip 1 + / ] map-index nip ;
371 : cum-count ( seq quot: ( elt -- ? ) -- seq' )
372 [ 0 ] dip '[ @ [ 1 + ] when ] accumulate* ; inline
374 : cum-min ( seq -- seq' )
375 dup ?first [ min ] accumulate* ;
377 : cum-max ( seq -- seq' )
378 dup ?first [ max ] accumulate* ;
380 : entropy ( probabilities -- n )
381 dup sum '[ _ / dup log * ] map-sum neg ;
383 : maximum-entropy ( probabilities -- n )
386 : normalized-entropy ( probabilities -- n )
387 [ entropy ] [ maximum-entropy ] bi / ;
389 : binary-entropy ( p -- h )
390 [ dup log * ] [ 1 swap - dup log * ] bi + neg 2 log / ;
392 : standardize ( u -- v )
393 [ demean ] [ sample-std ] bi [ v/n ] unless-zero ;
395 : standardize-2d ( u -- v )
396 flip [ standardize ] map flip ;
398 : differences ( u -- v )
399 [ rest-slice ] keep v- ;
402 dup minmax over - [ v-n ] [ v/n ] bi* ;
404 : rankings ( histogram -- assoc )
405 sort-keys 0 swap [ rot [ + ] keep swapd ] H{ } assoc-map-as nip ;
407 : rank-values ( seq -- seq' )
408 dup histogram rankings '[ _ at ] map ;
410 : z-score ( seq -- n )
411 [ demean ] [ sample-std ] bi v/n ;
413 : dcg ( scores -- dcg )
414 dup length 1 + 2 swap [a,b] [ log 2 log /f ] map v/ sum ;
416 : ndcg ( scores -- ndcg )
421 swap natural-sort <reversed> dcg /f