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k3-notes

CREATED BY chris • LAST EDITED BY chris 5950 days AGO

Note (2007-10-07): Quite a few of the snippets listed here are known to be sub-optimal or interpretative. Use with caution. I finally worked in some improvements Attila Vrabecz sent a long while ago. Thanks again!

I'm keeping old versions for entertainment purposes.

' wonders: www.kx.com/listbox/k/msg04732.html

\ does pointer chasing, as in 0 0 1 0 2\4

& is more generic than I had thought: see &0 1 2 3 5

amend: change items in structure.

monadic amend: a[!3]-: is sugar for @[`a;!3;-;] or .[`a;,!3;-;]
dyadic amend: a[!3]-:x is sugar for @[`a;!3;-;x] or .[`a;,!3;-;x]

a:1 2 3 is sugar for a::1 2 3 (?) / only works outside of lambdas

a[;0] is a[_n;0]. _n selects all.

s[;0] eq s@'0.

{x=y}':s — pairs of equals (1 2 3 3 4 > 0 0 1 0)
=':s / attila

s:();do[1000;s,:{+/1+-2*1000_draw 2}[]] — wanderers
1_1000{+/1+-2*1000_draw 2}\0 / attila

ngrams: (x is alphabet, y is length)

{(n@*x;#x)}'=n:{y#'(!1-y-#x)_\:x} // doesn't scale
{(*x;#x)}'n@=n:{x(!1+-y-#x)+\:!y}

matrix multiplication (src): (2nd dim held in common)

{+/''x*/:\:y} / attila: incorrect?
(+/*)\: / attila, or just _mul

slice x into y parts of approximately the same size:

{n:#x;d:-':c:-1+_1+(!y)*n%y;x@c+!:'d,n-+/d}
{n:#x;x@c+!:'d,n-+/d:-':c:-1+_1+(!y)*n%y}
{(_(!y)*(#x)%y) _ x}
{(y;_%[#x]y)#x} // exact slice

slice x into parts of size y:

{x(!y)+/:&0=(!#x)!y} // exact slice
{(_%[#x]y;y)#x} // ditto

moving n-tuples (for each-n-tuple/n-gram fun):

n:{x(!1+-y-#x)+\:!y}
e.g. +/'n[1 2 3;2] is equivalent to +':1 2 3
  n["chris";3]
("chr"
 "hri"
 "ris")

(fast) moving average ("shift" approach):

{(y _ x)-(-y)_ x:0.0,+\x%y} // kx.com

set intersection:

{?y@&~{(#x)=x?y}[x;]'y}
{x@&x _in\:y}
{x@&x _lin y} / attila: faster

set union:

{?x,y}
?, / attila

multiple occurences:

{x@c[;0]@&1<#:'c:=x}
{x@*:'c@&1<#:'c:=x}

count occurrences:

{{(*x),#x}'x@=x}
{(*:;#:)@\:/:x@=x}

split:

{1_'(&x=y)_ x:y,x}

e w/ max occurrences in multiset:

{(?x)@*>#:'=x} // aw

permutations (algorithm by Roger Hui?):

{:[1<x;,/(>:'(x,x)#1,x#0)[;0,'1+_f x-1];,!x]}

(x,x)#1,x#0 is identity matrix, which can be reformulated as id:{a=\:a:!x} (slower!) or id:=\:/2#,!:, leading to:

{:[1<x;,/(>:'id x)[;0,'1+_f x-1];,!x]}

permutations (shorter but slower):

p:{:[x=1;,0;,/a,''(&:'~a=\:a:!x)@\:p x-1]}

gcd:

{:[~x%y;y;_f[y;x-y*_ x%y]]}
{:[~x;y;_f[y;x!y]]} / attila

range:

{*:'x(<x;>x)}
{*+x(<x;>x)}

www.kx.com/listbox/k/msg05537.html

10+\\10#1 // binomial coefficients/pascal diamond

subtract factors (f):

(0<){x-f@f(*&~>)\x}\

apply each left (note _n):

(#:;*:;)@\:1 2 3
(#:;*:;).\:,1 2 3
(+;-).\:1 2

hilbert matrix:

{1%(!x)+\:1+!y}

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