[ 2 ] [ { 1 2 3 } median ] unit-test
[ 5/2 ] [ { 1 2 3 4 } median ] unit-test
+{ 1 } [ { 1 2 3 4 } 0 kth-smallest ] unit-test
+{ 3 } [ { 1 2 3 4 } 2 kth-smallest ] unit-test
+
+{ 4 } [ { 1 2 3 4 } 0 kth-largest ] unit-test
+{ 2 } [ { 1 2 3 4 } 2 kth-largest ] unit-test
+
[ 1 ] [ { 1 } mode ] unit-test
[ 3 ] [ { 1 2 3 3 3 4 5 6 76 7 2 21 1 3 3 3 } mode ] unit-test
! See http://factorcode.org/license.txt for BSD license.
USING: assocs combinators generalizations kernel locals math
math.functions math.order math.vectors sequences
-sequences.private sorting ;
+sequences.private sorting fry ;
IN: math.statistics
: mean ( seq -- x )
: harmonic-mean ( seq -- x )
[ recip ] map-sum recip ;
-:: kth-smallest ( seq k -- elt )
+:: kth-object ( seq k quot: ( x y -- ? ) -- elt )
#! Wirth's method, Algorithm's + Data structues = Programs p. 84
#! The algorithm modifiers seq, so we clone it
seq clone :> seq
m j!
[ i j <= ]
[
- [ i seq nth-unsafe x < ] [ i 1 + i! ] while
- [ x j seq nth-unsafe < ] [ j 1 - j! ] while
+ [ i seq nth-unsafe x quot call ] [ i 1 + i! ] while
+ [ x j seq nth-unsafe quot call ] [ j 1 - j! ] while
i j <= [
i j seq exchange-unsafe
i 1 + i!
] while
k seq nth ; inline
+: kth-smallest ( seq k -- elt ) [ < ] kth-object ;
+
+: kth-largest ( seq k -- elt ) [ > ] kth-object ;
+
+: count-relative ( seq k -- lt eq gt )
+ [ 0 0 0 ] 2dip '[
+ _ <=> {
+ { +lt+ [ [ 1 + ] 2dip ] }
+ { +gt+ [ 1 + ] }
+ { +eq+ [ [ 1 + ] dip ] }
+ } case
+ ] each ;
+
+: minmax-relative ( seq k -- lt eq gt lt-max gt-min )
+ [ 0 0 0 -1/0. 1/0. ] 2dip '[
+ dup _ <=> {
+ { +lt+ [ [ 1 + ] 5 ndip '[ _ max ] dip ] }
+ { +gt+ [ [ 1 + ] 3dip min ] }
+ { +eq+ [ [ 1 + ] 4dip drop ] }
+ } case
+ ] each ;
+
: lower-median ( seq -- elt )
[ ] [ ] [ length odd? ] tri
[ midpoint@ ] [ midpoint@ 1 - ] if kth-smallest ;