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 : power-mean ( seq p -- x )
10 [ '[ _ ^ ] map-sum ] [ [ length / ] [ recip ^ ] bi* ] 2bi ; inline
13 [ sum ] [ length ] bi / ; inline
15 : sum-of-squares ( seq -- x )
16 [ sq ] map-sum ; inline
18 : sum-of-squared-errors ( seq -- x )
19 [ mean ] keep [ - sq ] with map-sum ; inline
21 : sum-of-absolute-errors ( seq -- x )
22 [ mean ] keep [ - ] with map-sum ; inline
24 : quadratic-mean ( seq -- x ) ! root-mean-square
25 [ sum-of-squares ] [ length ] bi / sqrt ; inline
27 : geometric-mean ( seq -- x )
28 [ length ] [ product ] bi nth-root ; inline
30 : harmonic-mean ( seq -- x )
31 [ recip ] map-sum recip ; inline
33 : contraharmonic-mean ( seq -- x )
34 [ sum-of-squares ] [ sum ] bi / ; inline
38 : trim-points ( p seq -- from to seq )
39 [ length [ * >integer ] keep over - ] keep ;
43 : trimmed-mean ( seq p -- x )
44 swap natural-sort trim-points <slice> mean ;
46 : winsorized-mean ( seq p -- x )
47 swap natural-sort trim-points
49 [ nip dupd nth <array> ]
50 [ [ 1 - ] dip nth <array> ] 3tri
55 :: ((kth-object)) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
56 #! Wirth's method, Algorithm's + Data structues = Programs p. 84
57 k seq bounds-check 2drop
70 [ i seq nth-quot call x quot call ] [ i 1 + i! ] while
71 [ x j seq nth-quot call quot call ] [ j 1 - j! ] while
73 i j seq exchange-quot call
84 : (kth-object) ( seq k nth-quot exchange-quot quot: ( x y -- ? ) -- elt )
85 #! The algorithm modifiers seq, so we clone it
86 [ clone ] 4dip ((kth-object)) ; inline
88 : kth-object-unsafe ( seq k quot: ( x y -- ? ) -- elt )
89 [ [ nth-unsafe ] [ exchange-unsafe ] ] dip (kth-object) ; inline
91 : kth-objects-unsafe ( seq kths quot: ( x y -- ? ) -- elts )
93 '[ [ nth-unsafe ] [ exchange-unsafe ] _ ((kth-object)) ] with map ; inline
97 : kth-object ( seq k quot: ( x y -- ? ) -- elt )
98 [ [ nth ] [ exchange ] ] dip (kth-object) ; inline
100 : kth-objects ( seq kths quot: ( x y -- ? ) -- elts )
102 '[ [ nth ] [ exchange ] _ ((kth-object)) ] with map ; inline
104 : kth-smallests ( seq kths -- elts ) [ < ] kth-objects-unsafe ;
106 : kth-smallest ( seq k -- elt ) [ < ] kth-object-unsafe ;
108 : kth-largests ( seq kths -- elts ) [ > ] kth-objects-unsafe ;
110 : kth-largest ( seq k -- elt ) [ > ] kth-object-unsafe ;
112 : count-relative ( seq k -- lt eq gt )
115 { +lt+ [ [ 1 + ] 2dip ] }
117 { +eq+ [ [ 1 + ] dip ] }
121 : minmax-relative ( seq k -- lt eq gt lt-max gt-min )
122 [ 0 0 0 -1/0. 1/0. ] 2dip '[
124 { +lt+ [ [ 1 + ] 5 ndip '[ _ max ] dip ] }
125 { +gt+ [ [ 1 + ] 3dip min ] }
126 { +eq+ [ [ 1 + ] 4dip drop ] }
130 : lower-median-index ( seq -- n )
132 [ length odd? [ 1 - ] unless ] bi ;
134 : lower-median ( seq -- elt )
135 [ ] [ lower-median-index ] bi kth-smallest ;
137 : upper-median ( seq -- elt )
138 dup midpoint@ kth-smallest ;
140 : medians ( seq -- lower upper )
142 [ [ lower-median-index ] [ midpoint@ ] bi 2array ]
143 bi kth-smallests first2 ;
145 : median ( seq -- x )
146 dup length odd? [ lower-median ] [ medians + 2 / ] if ;
148 ! quantile can be any n-tile. quartile is n = 4, percentile is n = 100
149 ! a,b,c,d parameters, N - number of samples, q is quantile (1/2 for median, 1/4 for 1st quartile)
150 ! http://mathworld.wolfram.com/Quantile.html
152 ! could subtract 1 from a
154 : quantile-x ( a b N q -- x )
155 [ + ] dip * + 1 - ; inline
159 >fraction [ /mod nip ] keep / ; inline
161 :: quantile-indices ( seq qs a b c d -- seq )
162 qs [ [ a b seq length ] dip quantile-x ] map ;
164 :: qabcd ( y-floor y-ceiling x c d -- qabcd )
165 y-floor y-ceiling y-floor - c d x frac * + * + ;
167 :: quantile-abcd ( seq qs a b c d -- quantile )
168 seq qs a b c d quantile-indices :> indices
169 indices [ [ floor ] [ ceiling ] bi 2array ] map
170 concat :> index-pairs
172 seq index-pairs kth-smallests
173 2 group indices [ [ first2 ] dip c d qabcd ] 2map ;
175 : quantile1 ( seq qs -- seq' )
176 0 0 1 0 quantile-abcd ;
178 : quantile3 ( seq qs -- seq' )
179 1/2 0 0 0 quantile-abcd ;
181 : quantile4 ( seq qs -- seq' )
182 0 0 0 1 quantile-abcd ;
184 : quantile5 ( seq qs -- seq' )
185 1/2 0 0 1 quantile-abcd ;
187 : quantile6 ( seq qs -- seq' )
188 0 1 0 1 quantile-abcd ;
190 : quantile7 ( seq qs -- seq' )
191 1 -1 0 1 quantile-abcd ;
193 : quantile8 ( seq qs -- seq' )
194 1/3 1/3 0 1 quantile-abcd ;
196 : quantile9 ( seq qs -- seq' )
197 3/8 1/4 0 1 quantile-abcd ;
199 : quartile ( seq -- seq' )
200 { 1/4 1/2 3/4 } quantile5 ;
204 : (sequence>assoc) ( seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) assoc -- assoc )
205 [ swap curry compose each ] keep ; inline
209 : sequence>assoc! ( assoc seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) -- assoc )
210 4 nrot (sequence>assoc) ; inline
212 : sequence>assoc ( seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) exemplar -- assoc )
213 clone (sequence>assoc) ; inline
215 : sequence>hashtable ( seq map-quot: ( x -- ..y ) insert-quot: ( ..y assoc -- ) -- hashtable )
216 H{ } sequence>assoc ; inline
218 : histogram! ( hashtable seq -- hashtable )
219 [ ] [ inc-at ] sequence>assoc! ;
221 : histogram-by ( seq quot: ( x -- bin ) -- hashtable )
222 [ inc-at ] sequence>hashtable ; inline
224 : histogram ( seq -- hashtable )
227 : sorted-histogram ( seq -- alist )
228 histogram sort-values ;
230 : normalized-histogram ( seq -- alist )
231 [ histogram ] [ length ] bi '[ _ / ] assoc-map ;
233 : collect-pairs ( seq quot: ( x -- v k ) -- hashtable )
234 [ push-at ] sequence>hashtable ; inline
236 : collect-by ( seq quot: ( x -- x' ) -- hashtable )
237 [ dup ] prepose collect-pairs ; inline
241 [ ] [ [ [ second ] bi@ > ] most ] map-reduce first ;
243 : minmax ( seq -- min max )
244 [ first dup ] keep [ [ min ] [ max ] bi-curry bi* ] each ;
249 : sample-var ( seq -- x )
250 #! normalize by N-1; unbiased
254 [ sum-of-squared-errors ] [ length 1 - ] bi /
257 : full-var ( seq -- x )
261 [ sum-of-squared-errors ] [ length ] bi /
264 ALIAS: var sample-var
266 : sample-std ( seq -- x ) sample-var sqrt ;
268 : full-std ( seq -- x ) full-var sqrt ;
270 ALIAS: std sample-std
272 : signal-to-noise ( seq -- x ) [ mean ] [ std ] bi / ;
274 : mean-dev ( seq -- x ) dup mean v-n vabs mean ;
276 : median-dev ( seq -- x ) dup median v-n vabs mean ;
278 : sample-ste ( seq -- x ) [ sample-std ] [ length ] bi sqrt / ;
280 : full-ste ( seq -- x ) [ full-std ] [ length ] bi sqrt / ;
282 ALIAS: ste sample-ste
284 : ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
285 ! finds sigma((xi-mean(x))(yi-mean(y))
286 0 [ [ [ pick ] dip swap - ] bi@ * + ] 2reduce 2nip ;
288 : (r) ( mean(x) mean(y) {x} {y} sx sy -- r )
289 * recip [ [ ((r)) ] keep length 1 - / ] dip * ;
291 : [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
292 first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
294 : r ( {{x,y}...} -- r )
297 : r^2 ( {{x,y}...} -- r )
300 : least-squares ( {{x,y}...} -- alpha beta )
301 [r] { [ 2dup ] [ ] [ ] [ ] [ ] } spread
302 ! stack is mean(x) mean(y) mean(x) mean(y) {x} {y} sx sy
303 [ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
304 swap / * ! stack is mean(x) mean(y) beta
307 : cov ( {x} {y} -- cov )
308 [ dup mean v-n ] bi@ v* mean ;
310 : sample-corr ( {x} {y} -- corr )
311 [ cov ] [ [ sample-var ] bi@ * sqrt ] 2bi / ;
313 : full-corr ( {x} {y} -- corr )
314 [ cov ] [ [ full-var ] bi@ * sqrt ] 2bi / ;
316 ALIAS: corr sample-corr
318 : cum-map ( seq identity quot -- seq' )
319 swapd [ dup ] compose map nip ; inline
321 : cum-sum ( seq -- seq' )
324 : cum-product ( seq -- seq' )
327 : cum-min ( seq -- seq' )
328 dup ?first [ min ] cum-map ;
330 : cum-max ( seq -- seq' )
331 dup ?first [ max ] cum-map ;
333 : entropy ( probabilities -- n )
334 dup sum '[ _ / dup log * ] map-sum neg ;
336 : maximum-entropy ( probabilities -- n )
339 : normalized-entropy ( probabilities -- n )
340 [ entropy ] [ maximum-entropy ] bi / ;
342 : binary-entropy ( p -- h )
343 [ dup log * ] [ 1 swap - dup log * ] bi + neg 2 log / ;
345 : standardize ( u -- v )
346 [ dup mean v-n ] [ std ] bi v/n ;
348 : differences ( u -- v )
349 [ 1 tail-slice ] keep [ - ] 2map ;
352 dup minmax over - [ v-n ] [ v/n ] bi* ;
354 : rank-values ( seq -- seq' )
356 [ ] [ length iota ] bi zip sort-keys
357 [ [ first ] bi@ = ] monotonic-split
358 [ values ] map [ 0 [ length + ] accumulate nip ] [ ] bi zip
359 ] [ length f <array> ] bi
360 [ '[ first2 [ _ set-nth ] with each ] each ] keep ;