# max, maxs, mmax¶

## max¶

Maximum

max x    max[x]

Where x is a non-symbol sortable list, returns the maximum of its items. The maximum of an atom is itself.

Nulls are ignored, except that if the items of x are all nulls, the result is negative infinity.

q)max 2 5 7 1 3
7
q)max "genie"
"n"
q)max 0N 5 0N 1 3                  / nulls are ignored
5
q)max 0N 0N                        / negative infinity if all null
-0W
q)select max price by sym from t   / use in a select statement

max is an aggregate function. It is equivalent to |/.

domain: b g x h i j e f c s p m d z n u v t
range:  b . x h i j e f c . p m d z n u v t

## maxs¶

Maximums

maxs x    maxs[x]

Where x is a non-symbol sortable list, returns the running maximums of its prefixes.

Nulls are ignored, except that initial nulls are returned as negative infinity.

q)maxs 2 5 7 1 3
2 5 7 7 7
q)maxs "genie"
"ggnnn"
q)maxs 0N 5 0N 1 3         / initial nulls return negative infinity
-0W 5 5 5 5

maxs is a uniform function. It is equivalent to |\.

domain: b g x h i j e f c s p m d z n u v t
range:  b . x h i j e f c . p m d z n u v t

## mmax¶

Moving maximums

x mmax y    mmax[x;y]

Where

• x is a positive int atom
• y is a non-symbol sortable list

returns the x-item moving maximums of y, with nulls after the first replaced by the preceding maximum. The first x items of the result are the maximums of the items so far, and thereafter the result is the moving maximum.

q)3 mmax 2 7 1 3 5 2 8
2 7 7 7 5 5 8
q)3 mmax 0N -3 -2 0N 1 0  / initial null returns negative infinity
-0W -3 -2 -2 1 1          / remaining nulls replaced by preceding max

mmax is a uniform function.

Domain and range:

    b g x h i j e f c s p m d z n u v t
----------------------------------------
b | b g x h i j e f c s p m d z n u v t
g | . . . . . . . . . . . . . . . . . .
x | b g x h i j e f c s p m d z n u v t
h | b g x h i j e f c s p m d z n u v t
i | b g x h i j e f c s p m d z n u v t
j | b g x h i j e f c s p m d z n u v t
e | . . . . . . . . . . . . . . . . . .
f | . . . . . . . . . . . . . . . . . .
c | . . . . . . . . . . . . . . . . . .
s | . . . . . . . . . . . . . . . . . .
p | . . . . . . . . . . . . . . . . . .
m | . . . . . . . . . . . . . . . . . .
d | . . . . . . . . . . . . . . . . . .
z | . . . . . . . . . . . . . . . . . .
n | . . . . . . . . . . . . . . . . . .
u | . . . . . . . . . . . . . . . . . .
v | . . . . . . . . . . . . . . . . . .
t | . . . . . . . . . . . . . . . . . .

Range: bcdefghijmnpstuvxz

## Implicit iteration¶

max, maxs, and mmax apply to dictionaries and tables.

q)maxab!(10 21 3;4 5 6)
10 21 6
q)max flipab!(10 21 3;4 5 6)
a| 21
b| 6

q)maxsab!(10 21 3;4 5 6)
a| 10 21 3
b| 10 21 6
q)maxs flipab!(10 21 3;4 5 6)
a  b
----
10 4
21 5
21 6

q)2 mmax flipab!(10 21 3;4 5 6)
a  b
----
10 4
21 5
21 6
q)2 mmaxab!(10 21 3;4 5 6)
a| 10 21 3
b| 10 21 6

q)2 mmax ([k:abcdefghi]a:10 21 3;b:4 5 6)
k  | a  b
---| ----
abc| 10 4
def| 21 5
ghi| 21 6

## Aggregating nulls¶

avg, min, max and sum are special: they ignore nulls, in order to be similar to SQL92. But for nested x these functions preserve the nulls.

q)max (1 2;0N 4)
1 4`