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{{Built-in|Minimum|⌊}}, '''Min''', or '''Lesser of''' is a [[dyadic]] [[scalar function]] which returns the [[Less than|smaller]] of its two [[argument]]s. The name "Minimum" is sometimes also used for the Minimum [[Reduce]] <source lang=apl inline>⌊/</source>, which returns the smallest element of a [[vector]] (this usage is related to the [[wikipedia:minimum|minimum]] of a function). Minimum is paired with [[Maximum]], which returns the greater argument rather than the smaller, and shares the glyph <source lang=apl inline>⌊</source> with the [[Floor]] 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 | {{Built-in|Minimum|⌊}}, '''Min''', or '''Lesser of''' is a [[dyadic]] [[scalar function]] which returns the [[Less than|smaller]] of its two [[argument]]s. The name "Minimum" is sometimes also used for the Minimum [[Reduce]] <source lang=apl inline>⌊/</source>, which returns the smallest element of a [[vector]] (this usage is related to the [[wikipedia:minimum|minimum]] of a function). Minimum is paired with [[Maximum]], which returns the greater argument rather than the smaller, and shares the glyph <source lang=apl inline>⌊</source> with the [[Floor]] 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 larger argument even if the two arguments are [[tolerant comparison|tolerantly]] equal. As a [[Boolean function]], Minimum is identical to [[And]]. | ||
== Examples == | == Examples == | ||
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</source> | </source> | ||
The two solutions may differ when [[comparison tolerance]] is not zero, because Index Of uses tolerant comparison but Grade does not. The first solution will return a smaller index if an element that is tolerantly but not exactly equal to the minimum is found at that index. | The two solutions may differ when [[comparison tolerance]] is not zero, because Index Of uses tolerant comparison but Grade does not. The first solution will return a smaller index if an element that is tolerantly but not exactly equal to the minimum is found at that index. | ||
Reducing over an empty axis yields the largest representable number, as that is the identity element for Minimum. 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). | |||
== External links == | == External links == | ||
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=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Minimum.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_120.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_120.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d011.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ltdot#dyadic NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d011.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ltdot#dyadic NuVoc] | ||
{{APL built-ins}} | {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] | ||