# Q by examples¶

## Simple arithmetic¶

q)2+2           / comment is ' /': left of /: whitespace or nothing
4

q)2-3           / negative numbers
-1

q)2*3+4         / no precedence, right to left
14

q)(2*3)+4       / parentheses change order
10

q)3%4           / division
0.75

q){x*x}4        / square
16

q)sqrt 4        / square root
2.0

q)reciprocal 4  / 1/x
0.25

## Operations using lists¶

q)2*1 2 3      / numeric list with space separators
2 4 6

q)1 2 3%2 4 6  / list-to-list operations, same size
0.5 0.5 0.5

q)count 1 2 3  / items in a list
3

q)3#1          / generate sequence of same numbers
1 1 1

q)5#1 2        / or from a list of given items
1 2 1 2 1

## List items¶

q)first 1 2 3     / first item
1

q)last 1 2 3      / last item
3

q)1_1 2 3         / rest without first item
2 3

q)-1_1 2 3        / rest without last item
1 2

q)reverse 1 2 3   / reverse
3 2 1

## Indexing and sorting¶

q)1 2 3@1       / indexing is zero-based
2

q)1 2 3@1 0     / index can be vector too
2 1

q)til 3         / generate zero-based sequence
0 1 2

q)2 4 6?4       / index of given item/s
1

q)iasc 2 1 6    / indexes of sorted order
1 0 2

q)asc 2 1 6     / sort vector
s#1 2 6

## List aggregation¶

q)1 2 3,10 20         / join lists
1 2 3 10 20

q)1+2+3               / sum of items
6

q)sum 1 2 3           / insert '+' between items
6

q)sums 1 2 3          / running sum of items
1 3 6

q)1,(1+2),(1+2+3)     / same as this
1 3 6

q){1_x+prev x}til 5   / sum running pairs
1 3 5 7

q)sum each{(2*til ceiling .5*count x)_x}1 2 3 4 5 / non-intersecting pairs
3 7 5

q)(1 2;3 4 6;7 6)     / list
(1 2;3 4 6;7 6)

q)first(3 4 6;7 6)    / first item in the list
3 4 6

## Function combinations¶

q){x+x*x}4              / a + a^2
20

q)(sqrt;{x*x})@\:4      / [sqrt(a), a^2]
(2f;16)

q){x*x}sum 2 3          / (a +b)^2
25

q)sum{x*x}2 3           / a^2 + b^2
13

q){sum(x*x),2*/x}2 3    / (a + b)^2 = a^2 + b^2 + 2ab
25

q)sqrt sum{x*x}3 4      / sqrt(a^2 + b^2)
5f

## User-defined functions and arguments¶

q)d1:-                  / binary projection
q)d2:{x-y}              / explicit binary
q)m1:neg                / unary projection
q)m2:0-                 / unary projection
q)m3:{neg x}            / explicit unary

q)(m1;m2;m3)@\:4        / unary functions
-4 -4 -4

q)(d1;d2).\:3 4         / binary functions
-1 -1

## Exponent and logarithm¶

q)(e;2*e;e*e:exp 1)    / e, 2e, e squared
2.718282 5.436564 7.389056

q)exp 2               / exponent, e^2
7.389056

q)2 xexp 16           / exponent base 2, 2^16
65536.0

q)log exp 2           / logarithm, ln e^2
2.0

q)2 xlog 65536        / logarithm base 2, log2 65536
16.0

## Trigonometry¶

q)a:(pi;2*pi;pi*pi:acos -1)     / pi, 2 pi, pi squared
3.141593 6.283185 9.869604

q)cos pi                        / cosine of pi
-1.0

q)(t:sum{x*x}@(cos;sin)@\:)pi   / theorem of trigonometry
1.0

q)t a                           / test theorem at angles
1 1 1.0

## Matrixes¶

q)1 2 3*/:1 2 3                 / outer product: multiplication table
(1 2 3;2 4 6;3 6 9)

q){x=/:x}@til 3                 / identity matrix
(100b;010b;001b)

q)2 3#til 6                     / generate matrix
(0 1 2;3 4 5)

q)2 2#0 1 1 1                   / reshape vector to matrix
(0 1;1 1)

## Structural transforms¶

q)show N:0 3_/:2 6#til 12                            / list of atoms
0 1 2   3 4 5
6 7  8  9 10 11
q)raze/[N]                                           / ravel
0 1 2 3 4 5 6 7 8 9 10 11

q)raze each N                                        / ravel each sub-matrix
(0 1 2 3 4 5;6 7 8 9 10 11)

q)show M:3 3#"ABC123!@#"                             / character matrix
"ABC"
"123"
"!@#"
q)(::;flip;reverse;reverse each;1 rotate)@\:M
"ABC" "123" "!@#"
"A1!" "B2@" "C3#"
"!@#" "123" "ABC"
"CBA" "321" "#@!"
"123" "!@#" "ABC"

q)M ./:/:f value group sum each f:n cross n:til 3    / secondary diagonals
,"A"
"B1"
"C2!"
"3@"
,"#"

q)M ./:a,'a:til count M                              / main diagonal
"A2#"

## Selection¶

q)N:((0 1 2;3 4 5);(6 7 8;9 10 11))
q)((N 1) 1) 1           / repetitive selection of items From list
10

q)3@[;1]/N              / apply select 3 times
10

q)N[1;1;1]              / cross sectional select
10

q)N . 1 1 1             / cross sectional select too
10

## Factorial and binomial¶

q)each[f:{$[x<0;0;prd 1.+til x]}]1+til 5 / factorial 1 2 6 24 120.0 q)prds 1+til 5 / running product 1 2 6 24 120 q)(b:{til[x]{$[x<y;0;floor f[x]%f[y]*f x-y]}\:/:til x})5    / binomial coeff.
(1 1 1 1 1;0 1 2 3 4;0 0 1 3 6;0 0 0 1 4;0 0 0 0 1)

q)/ fibonacci: sum of second diagonal of binomial matrix
q)1_{sum b[x]./:flip(til x;reverse til x)}each til 16
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610

## Dot product¶

q)1 2 3 wsum 1 2 3       / dot product wsum=+/* (optimized)
14f

q)1 2 3.$1 2 3. / also 14f q)M:(0 1.;1 1.) / assignment q)M$M                    / matrix squared (optimized)
(1 1.;1 2.)

q)15$[M]/M / matrix to the power of 15, also fibonacci (610 987.;987 1597.) q)(14$[M]\M)[;0;1]
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610f

## Randomness and probability¶

q)A:5?1.;A                 / 5 random floats from 0..1
0.03505812 0.7834427 0.7999031 0.9046515 0.2232866

q)B:10?2;B                 / coin toss
1 1 1 0 1 0 1 1 0 0

q)B1:10?0b;B1              / with booleans
11110010101b

q)C:-3?3;C                 / deal 3 unique cards out of 3
1 0 2

q)(min;max)@\:A            / min and max over the list
0.03505812 0.9046515

q)B?0                      / first zero
3

q)avg C~/:1_10000{-3?3}\() / method monte carlo
0.1643836

q)reciprocal f 3           / exact probability of 3 cards in given order
0.1666667

## Unique elements¶

q)D:distinct S:"mississippi"                / distinct items
"misp"

q)K:D?S;K                                   / find (?) indexes
0 1 2 2 1 2 2 1 3 3 1

q)S value group K                           / group by key
(enlist"m";"iiii";"ssss";"pp")

q)count each group S                        / frequencies
"misp"!1 4 4 2

q)I:(til count S)in first each group S;I    / sieve of nub where D is in S
11100000100b

q)S where I                                 / filter by sieve to get D
"misp"

q)sum D=/:S                                 / where items of D are in S
1 4 4 2`

## Source¶

Source code kxcontrib/avrabecz/qybeg.q

Based on J by Example 06/11/2005 © Oleg Kobchenko