1 ! Copyright (C) 2008 Doug Coleman, Michael Judge, Loryn Jenkins.
2 ! See https://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 ranges math.vectors
6 sequences sequences.private sorting ;
9 : power-mean ( seq p -- x )
10 [ '[ _ ^ ] map-sum ] [ [ length / ] [ recip ^ ] bi* ] 2bi ; inline
12 ! Delta in degrees-of-freedom
13 : mean-ddof ( seq ddof -- x )
14 [ [ sum ] [ length ] bi ] dip -
15 [ drop 0 ] [ / ] if-zero ; inline
20 : meanest ( seq -- x )
21 [ mean ] keep [ - abs ] with infimum-by ;
23 GENERIC: sum-of-squares ( seq -- x )
24 M: object sum-of-squares [ sq ] map-sum ;
25 M: iota sum-of-squares
26 n>> 1 - [ ] [ 1 + ] [ 1/2 + ] tri * * 3 / ;
27 M: ranges:range sum-of-squares
28 dup { [ step>> 1 = ] [ from>> integer? ] } 1&& [
29 [ from>> ] [ length>> ] bi dupd +
30 [ <iota> sum-of-squares ] bi@ swap -
31 ] [ call-next-method ] if ;
33 GENERIC: sum-of-cubes ( seq -- x )
34 M: object sum-of-cubes [ 3 ^ ] map-sum ;
35 M: iota sum-of-cubes sum sq ;
36 M: ranges:range sum-of-cubes
37 dup { [ step>> 1 = ] [ from>> integer? ] } 1&& [
38 [ from>> ] [ length>> ] bi dupd +
39 [ <iota> sum-of-cubes ] bi@ swap -
40 ] [ call-next-method ] if ;
42 GENERIC: sum-of-quads ( seq -- x )
43 M: object sum-of-quads [ 4 ^ ] map-sum ;
54 M: ranges:range sum-of-quads
55 dup { [ step>> 1 = ] [ from>> integer? ] } 1&& [
56 [ from>> ] [ length>> ] bi dupd +
57 [ <iota> sum-of-quads ] bi@ swap -
58 ] [ call-next-method ] if ;
60 : sum-of-squared-errors ( seq -- x )
61 [ mean ] keep [ - sq ] with map-sum ; inline
63 : sum-of-absolute-errors ( seq -- x )
64 [ mean ] keep [ - ] with map-sum ; inline
66 : quadratic-mean ( seq -- x ) ! root-mean-square
67 [ sum-of-squares ] [ length ] bi / sqrt ; inline
69 : geometric-mean ( seq -- x )
70 [ [ log ] map-sum ] [ length ] bi /f e^ ; inline
72 : harmonic-mean ( seq -- x )
73 [ [ recip ] map-sum ] [ length swap / ] bi ; inline
75 : contraharmonic-mean ( seq -- x )
76 [ sum-of-squares ] [ sum ] bi / ; inline
80 : trim-points ( p seq -- from to seq )
81 [ length [ * >integer ] keep over - ] keep ;
85 : trimmed-mean ( seq p -- x )
86 swap natural-sort trim-points <slice> mean ;
88 : winsorized-mean ( seq p -- x )
89 swap natural-sort trim-points
91 [ nip dupd nth <array> ]
92 [ [ 1 - ] dip nth <array> ] 3tri
97 :: kth-object-impl ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
98 ! Wirth's method, Algorithm's + Data structues = Programs p. 84
99 k seq bounds-check 2drop
112 [ i seq nth-quot call x quot call ] [ i 1 + i! ] while
113 [ x j seq nth-quot call quot call ] [ j 1 - j! ] while
115 i j seq exchange-quot call
124 k seq nth-unsafe ; inline
126 : (kth-object) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
127 ! The algorithm modifies seq, so we clone it
128 [ >array ] 4dip kth-object-impl ; inline
130 : kth-object-unsafe ( seq k quot: ( x y -- ? ) -- elt )
131 [ [ nth-unsafe ] [ exchange-unsafe ] ] dip (kth-object) ; inline
133 : kth-objects-unsafe ( seq kths quot: ( x y -- ? ) -- elts )
134 '[ _ kth-object-unsafe ] with map ; inline
138 : kth-object ( seq k quot: ( x y -- ? ) -- elt )
139 [ [ nth ] [ exchange ] ] dip (kth-object) ; inline
141 : kth-objects ( seq kths quot: ( x y -- ? ) -- elts )
142 '[ _ kth-object ] with map ; inline
144 : kth-smallests ( seq kths -- elts ) [ < ] kth-objects-unsafe ;
146 : kth-smallest ( seq k -- elt ) [ < ] kth-object-unsafe ;
148 : kth-largests ( seq kths -- elts ) [ > ] kth-objects-unsafe ;
150 : kth-largest ( seq k -- elt ) [ > ] kth-object-unsafe ;
152 : count-relative ( seq k -- lt eq gt )
155 { +lt+ [ [ 1 + ] 2dip ] }
157 { +eq+ [ [ 1 + ] dip ] }
161 : minmax-relative ( seq k -- lt eq gt lt-max gt-min )
162 [ 0 0 0 -1/0. 1/0. ] 2dip '[
164 { +lt+ [ [ 1 + ] 5 ndip '[ _ max ] dip ] }
165 { +gt+ [ [ 1 + ] 3dip min ] }
166 { +eq+ [ [ 1 + ] 4dip drop ] }
170 : lower-median-index ( seq -- n )
172 [ length odd? [ 1 - ] unless ] bi ;
174 : lower-median ( seq -- elt )
175 [ ] [ lower-median-index ] bi kth-smallest ;
177 : upper-median ( seq -- elt )
178 dup midpoint@ kth-smallest ;
180 : medians ( seq -- lower upper )
182 [ [ lower-median-index ] [ midpoint@ ] bi 2array ]
183 bi kth-smallests first2 ;
185 : median ( seq -- x )
186 dup length odd? [ lower-median ] [ medians + 2 / ] if ;
188 ! quantile can be any n-tile. quartile is n = 4, percentile is n = 100
189 ! a,b,c,d parameters, N - number of samples, q is quantile (1/2 for median, 1/4 for 1st quartile)
190 ! https://mathworld.wolfram.com/Quantile.html
192 ! could subtract 1 from a
194 : quantile-x ( a b N q -- x )
195 [ + ] dip * + 1 - ; inline
199 >fraction [ /mod nip ] keep / ; inline
201 :: quantile-indices ( seq qs a b -- seq )
202 qs [ [ a b seq length ] dip quantile-x ] map ;
204 :: qabcd ( y-floor y-ceiling x c d -- qabcd )
205 y-floor y-ceiling y-floor - c d x frac * + * + ;
207 :: quantile-abcd ( seq qs a b c d -- quantile )
208 seq qs a b quantile-indices :> indices
209 indices [ [ floor 0 max ] [ ceiling seq length 1 - min ] bi 2array ] map
210 concat :> index-pairs
212 seq index-pairs kth-smallests
213 2 group indices [ [ first2 ] dip c d qabcd ] 2map ;
215 : quantile1 ( seq qs -- seq' )
216 0 0 1 0 quantile-abcd ;
218 : quantile3 ( seq qs -- seq' )
219 1/2 0 0 0 quantile-abcd ;
221 : quantile4 ( seq qs -- seq' )
222 0 0 0 1 quantile-abcd ;
224 : quantile5 ( seq qs -- seq' )
225 1/2 0 0 1 quantile-abcd ;
227 : quantile6 ( seq qs -- seq' )
228 0 1 0 1 quantile-abcd ;
230 : quantile7 ( seq qs -- seq' )
231 1 -1 0 1 quantile-abcd ;
233 : quantile8 ( seq qs -- seq' )
234 1/3 1/3 0 1 quantile-abcd ;
236 : quantile9 ( seq qs -- seq' )
237 3/8 1/4 0 1 quantile-abcd ;
239 : quartile ( seq -- seq' )
240 { 1/4 1/2 3/4 } quantile5 ;
242 : interquartile ( seq -- q1 q3 )
243 quartile [ first ] [ last ] bi ;
245 : interquartile-range ( seq -- n )
248 : midhinge ( seq -- n )
249 interquartile + 2 / ;
251 : trimean ( seq -- x )
252 quartile first3 [ 2 * ] dip + + 4 / ;
254 : histogram-by! ( assoc seq quot: ( x -- bin ) -- hashtable )
255 rot [ '[ @ _ inc-at ] each ] keep ; inline
257 : histogram! ( hashtable seq -- hashtable )
258 [ ] histogram-by! ; inline
260 : histogram-by ( seq quot: ( x -- bin ) -- hashtable )
261 [ H{ } clone ] 2dip histogram-by! ; inline
263 : histogram ( seq -- hashtable )
266 : sorted-histogram ( seq -- alist )
267 histogram sort-values ;
269 : normalized-histogram ( seq -- alist )
270 [ histogram ] [ length ] bi '[ _ / ] assoc-map ;
272 : equal-probabilities ( n -- array )
273 dup recip <array> ; inline
276 histogram >alist [ second ] supremum-by first ;
278 : minmax ( seq -- min max )
279 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] 1 each-from ;
284 : fivenum ( seq -- seq' )
285 [ quartile ] [ minmax ] bi [ prefix ] [ suffix ] bi* ;
287 : var-ddof ( seq n -- x )
288 2dup [ length ] dip - 0 <= [
291 [ [ sum-of-squared-errors ] [ length ] bi ] dip - /
294 : population-var ( seq -- x ) 0 var-ddof ; inline
296 : sample-var ( seq -- x ) 1 var-ddof ; inline
298 : std-ddof ( seq n -- x ) var-ddof sqrt ; inline
300 : population-std ( seq -- x ) 0 std-ddof ; inline
302 : sample-std ( seq -- x ) 1 std-ddof ; inline
304 ALIAS: std sample-std
306 : signal-to-noise ( seq -- x ) [ mean ] [ population-std ] bi / ;
308 : demean ( seq -- seq' ) dup mean v-n ;
310 : mean-dev ( seq -- x ) demean vabs mean ;
312 : demedian ( seq -- seq' ) dup median v-n ;
314 : median-dev ( seq -- x ) demedian vabs mean ;
316 : ste-ddof ( seq n -- x ) '[ _ std-ddof ] [ length ] bi sqrt / ;
318 : population-ste ( seq -- x ) 0 ste-ddof ;
320 : sample-ste ( seq -- x ) 1 ste-ddof ;
323 : r-sum-diffs ( x-mean y-mean x-seq y-seq -- (r) )
324 ! finds sigma((xi-mean(x))(yi-mean(y))
325 0 [ [ reach - ] bi@ * + ] 2reduce 2nip ;
327 : (r) ( x-mean y-mean x-seq y-seq x-std y-std -- r )
328 * recip [ [ r-sum-diffs ] keep length 1 - / ] dip * ;
330 : r-stats ( xy-pairs -- x-mean y-mean x-seq y-seq x-std y-std )
331 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ population-std ] bi@ ;
334 : pearson-r ( xy-pairs -- r ) r-stats (r) ;
336 : least-squares ( xy-pairs -- alpha beta )
337 r-stats [ 2dup ] 4dip
338 ! stack is x-mean y-mean x-mean y-mean x-seq y-seq x-std y-std
339 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
340 swap / * ! stack is mean(x) mean(y) beta
343 : cov-ddof ( x-seq y-seq ddof -- cov )
344 [ [ demean ] bi@ v* ] dip mean-ddof ;
346 : population-cov ( x-seq y-seq -- cov ) 0 cov-ddof ; inline
348 : sample-cov ( x-seq y-seq -- cov ) 1 cov-ddof ; inline
350 : corr-ddof ( x-seq y-seq n -- corr )
351 [ [ population-cov ] ] dip
352 '[ [ _ var-ddof ] bi@ * sqrt ] 2bi / ;
354 : population-corr ( x-seq y-seq -- corr ) 0 corr-ddof ; inline
356 : sample-corr ( x-seq y-seq -- corr ) 1 corr-ddof ; inline
358 : cum-sum ( seq -- seq' )
359 0 [ + ] accumulate* ;
361 : cum-sum0 ( seq -- seq' )
362 0 [ + ] accumulate nip ;
364 : cum-product ( seq -- seq' )
365 1 [ * ] accumulate* ;
367 : cum-product1 ( seq -- seq' )
368 1 [ * ] accumulate nip ;
370 : cum-mean ( seq -- seq' )
371 0 swap [ [ + dup ] dip 1 + / ] map-index nip ;
373 : cum-count ( seq quot: ( elt -- ? ) -- seq' )
374 [ 0 ] dip '[ @ [ 1 + ] when ] accumulate* ; inline
376 : cum-min ( seq -- seq' )
377 dup ?first [ min ] accumulate* ;
379 : cum-max ( seq -- seq' )
380 dup ?first [ max ] accumulate* ;
382 : entropy ( probabilities -- n )
383 dup sum '[ _ / dup log * ] map-sum neg ;
385 : maximum-entropy ( probabilities -- n )
388 : normalized-entropy ( probabilities -- n )
389 [ entropy ] [ maximum-entropy ] bi / ;
391 : binary-entropy ( p -- h )
392 [ dup log * ] [ 1 swap - dup log * ] bi + neg 2 log / ;
394 : standardize ( u -- v )
395 [ demean ] [ sample-std ] bi [ v/n ] unless-zero ;
397 : standardize-2d ( u -- v )
398 flip [ standardize ] map flip ;
400 : differences ( u -- v )
401 [ rest-slice ] keep v- ;
404 dup minmax over - [ v-n ] [ v/n ] bi* ;
406 : rankings ( histogram -- assoc )
407 sort-keys 0 swap [ rot [ + ] keep swapd ] H{ } assoc-map-as nip ;
409 : rank-values ( seq -- seq' )
410 dup histogram rankings '[ _ at ] map ;
412 : z-score ( seq -- n )
413 [ demean ] [ sample-std ] bi v/n ;
415 : dcg ( scores -- dcg )
416 dup length 1 + 2 swap [a..b] [ log 2 log /f ] map v/ sum ;
418 : ndcg ( scores -- ndcg )
423 swap natural-sort <reversed> dcg /f