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:''This page is about the primitive function. For system limits, see [[LIMIT ERROR]] and [[Maximum rank]].'' | :''This page is about the primitive function. For system limits, see [[LIMIT ERROR]] and [[Maximum rank]].'' | ||
{{Built-in|Maximum|⌈}}, '''Max''', '''Greater of''', or '''Larger of''' is a [[dyadic]] [[scalar function]] which returns the [[Greater than|larger]] of its two [[argument]]s. The name "Maximum" is sometimes also used for the Maximum [[Reduce]] < | {{Built-in|Maximum|⌈}}, '''Max''', '''Greater of''', or '''Larger of''' is a [[dyadic]] [[scalar function]] which returns the [[Greater than|larger]] of its two [[argument]]s. The name "Maximum" is sometimes also used for the Maximum [[Reduce]] <syntaxhighlight lang=apl inline>⌈/</syntaxhighlight>, which returns the largest element of a [[vector]] (this usage is related to the [[wikipedia:maximum|maximum]] of a function). Maximum is paired with [[Minimum]], and shares the glyph <syntaxhighlight lang=apl inline>⌈</syntaxhighlight> with the [[Ceiling]] function. It is not subject to [[comparison tolerance]], since the result will be exactly equal to one argument, and there is no reason to choose a smaller argument even if the two arguments are [[tolerant comparison|tolerantly]] equal. As a [[Boolean function]], Maximum is identical to [[Or]]. | ||
== Examples == | == Examples == | ||
| Line 7: | Line 7: | ||
Maximum finds the larger of two numbers: | Maximum finds the larger of two numbers: | ||
< | <syntaxhighlight lang=apl> | ||
2.4 ⌈ 1.9 | 2.4 ⌈ 1.9 | ||
2.4 | 2.4 | ||
</ | </syntaxhighlight> | ||
Maximum [[Reduce]] finds the largest [[element]] in a [[vector]]: | Maximum [[Reduce]] finds the largest [[element]] in a [[vector]]: | ||
< | <syntaxhighlight lang=apl> | ||
⌈/ 4 3 2 7 5 1 3 | ⌈/ 4 3 2 7 5 1 3 | ||
7 | 7 | ||
</ | </syntaxhighlight> | ||
The [[index]] of this element can be found with [[Index Of]], but is also the [[First]] element of the [[Grade Down]] of the vector. | The [[index]] of this element can be found with [[Index Of]], but is also the [[First]] element of the [[Grade Down]] of the vector. | ||
< | <syntaxhighlight lang=apl> | ||
{⍵⍳⌈/⍵} 4 3 2 7 5 1 3 | {⍵⍳⌈/⍵} 4 3 2 7 5 1 3 | ||
4 | 4 | ||
⊃⍒ 4 3 2 7 5 1 3 | ⊃⍒ 4 3 2 7 5 1 3 | ||
4 | 4 | ||
</ | </syntaxhighlight> | ||
Reducing over an empty axis yields the smallest representable number, as that is the identity element for Maximum. This value is usually < | Reducing over an empty axis yields the smallest representable number, as that is the identity element for Maximum. This value is usually <syntaxhighlight lang=apl inline>¯∞</syntaxhighlight> (for dialects that support [[infinity|infinities]]) or <syntaxhighlight lang=apl inline>¯1.797693135E308</syntaxhighlight> (with 64-bit [[float]]s) or <syntaxhighlight lang=apl inline>¯1E6145</syntaxhighlight> (with 128-bit [[decimal float]]s). | ||
== External links == | == External links == | ||
| Line 30: | Line 30: | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Maximum.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_100.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_100.htm APLX] | ||
* J [http://www.jsoftware.com/help/dictionary/d021.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/gtdot#dyadic NuVoc] | * J [http://www.jsoftware.com/help/dictionary/d021.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/gtdot#dyadic NuVoc] | ||
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#additional-arithmetic BQN] | |||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] | {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] | ||