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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]] <source lang=apl inline>⌈/</source>, 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 <source lang=apl inline>⌈</source> 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]].
{{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:
<source lang=apl>
<syntaxhighlight lang=apl>
       2.4 ⌈ 1.9
       2.4 ⌈ 1.9
2.4
2.4
</source>
</syntaxhighlight>
Maximum [[Reduce]] finds the largest [[element]] in a [[vector]]:
Maximum [[Reduce]] finds the largest [[element]] in a [[vector]]:
<source lang=apl>
<syntaxhighlight lang=apl>
       ⌈/ 4 3 2 7 5 1 3
       ⌈/ 4 3 2 7 5 1 3
7
7
</source>
</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.
<source lang=apl>
<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
</source>
</syntaxhighlight>


Reducing over an empty axis yields the smallest representable number, as that is the identity element for Maximum. This value is usually <source lang=apl inline>¯∞</source> (for dialects that support [[infinity|infinities]]) or <source lang=apl inline>¯1.797693135E308</source> (with 64-bit [[float]]s) or <source lang=apl inline>¯1E6145</source> (with 128-bit [[decimal float]]s).
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 ===


* [http://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Maximum.htm Dyalog]
* [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]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]

Latest revision as of 21:28, 10 September 2022

This page is about the primitive function. For system limits, see LIMIT ERROR and Maximum rank.
⌈

Maximum (⌈), Max, Greater of, or Larger of is a dyadic scalar function which returns the larger of its two arguments. The name "Maximum" is sometimes also used for the Maximum Reduce ⌈/, which returns the largest element of a vector (this usage is related to the maximum of a function). Maximum is paired with Minimum, and shares the glyph ⌈ 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 tolerantly equal. As a Boolean function, Maximum is identical to Or.

Examples

See also Minimum#examples.

Maximum finds the larger of two numbers: 

      2.4 ⌈ 1.9
2.4

Maximum Reduce finds the largest element in a vector: 

      ⌈/ 4 3 2 7 5 1 3
7

The index of this element can be found with Index Of, but is also the First element of the Grade Down of the vector. 

      {⍵⍳⌈/⍵} 4 3 2 7 5 1 3
4
      ⊃⍒ 4 3 2 7 5 1 3
4

Reducing over an empty axis yields the smallest representable number, as that is the identity element for Maximum. This value is usually ¯∞ (for dialects that support infinities) or ¯1.797693135E308 (with 64-bit floats) or ¯1E6145 (with 128-bit decimal floats).

External links

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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