Maximum

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]
Primitive functions
	Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root
		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 ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Primitive operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Primitive operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut (J)
Quad names
	Arrays	Index origin ∙ Migration level ∙ Atomic vector
	Functions	Name class ∙ Case convert ∙ Unicode convert
	Operators	Search ∙ Replace

Maximum

Examples

External links

Documentation

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