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• Rank (operator)
  ...rs associated with a function specifying its argument rank, see [[function rank]].'' {{Built-in|Rank|⍤}} is a [[primitive operator|primitive]] [[dyadic operator]] which applies its left [[operand]] function to [[cells]] of its arguments
  7 KB (949 words) - 23:54, 20 July 2023
• Rank operator
  #REDIRECT [[Rank (operator)]]
  29 bytes (3 words) - 15:19, 5 October 2020
• Rank Operator
  #REDIRECT [[Rank (operator)]]
  29 bytes (3 words) - 15:19, 5 October 2020

Page text matches

• Rank
  ...k]]. For the operator that applies a function at a given rank, see [[Rank (operator)]].'' ...ucture, or the length of its [[shape]]. The traditional expression for the rank of an array <syntaxhighlight lang=apl inline>A</syntaxhighlight> is <syntax
  1 KB (175 words) - 21:45, 10 September 2022
• Rank operator
  #REDIRECT [[Rank (operator)]]
  29 bytes (3 words) - 15:19, 5 October 2020
• Rank Operator
  #REDIRECT [[Rank (operator)]]
  29 bytes (3 words) - 15:19, 5 October 2020
• Function rank
  ...ines [[Close composition|"close" composition operators]] which inherit the rank of their right operand—the [[derived function]] produced by such a compos ....</ref> In [[J]] every function, primitive or user-defined, has a function rank.
  4 KB (618 words) - 18:06, 29 January 2024
• Frame
  ...duced by applying [[Enclose]] or [[Box function|Box]] with [[Rank operator|rank]] k to an array. When representing arrays as nested lists as in [[K]], this The frame is complementary to the [[cell shape]] for cells of a particular rank: while the frame occupies leading axes (and its [[shape]] is a [[prefix]] o
  1 KB (191 words) - 22:25, 10 September 2022
• Operand
  ...e|valence]] is inherent in the operator rather than determined by context. Operator valence is thus substantially different from [[function valence]] as [[mona ...operator application. Some APLs resolve this conflict by stranding before operator application while others apply operators before stranding.
  1 KB (213 words) - 15:15, 30 April 2020
• Close composition
  ...ow this pattern, while in J, both close and non-close forms (with a result rank of infinity, matching the definition in most modern APLs) are provided. ! Operator !! SHARP !! J close !! J non-close !! Modern APL
  2 KB (258 words) - 02:12, 27 August 2023
• Leading axis agreement
  ...nce all functions, including dyadic scalar functions, have [[function rank|rank]], leading axis agreement is a special case of [[frame agreement]]. ...s one step further, allowing the lower-rank array argument to have nonzero rank, as long as the leading dimensions match:
  3 KB (413 words) - 18:58, 19 July 2023
• Major cell
  ...ank <syntaxhighlight lang=apl inline>¯1</syntaxhighlight> using the [[Rank operator]]. Functions designed to follow leading axis theory often manipulate the ma ...e>A</syntaxhighlight>'s major cells using [[Enclose]] with [[Rank operator|rank]] <syntaxhighlight lang=apl inline>¯1</syntaxhighlight>:
  2 KB (306 words) - 23:27, 10 March 2024
• Terminology
  ...ll]] || a [[cell]] of an [[array]] which has [[rank]] one smaller than the rank of the array, or equal to it if the array is a [[scalar]] || Element | [[Matrix]] || an [[array]] of [[rank]] 2 || 2D array, Table
  3 KB (410 words) - 10:54, 10 August 2022
• Conformability
  ...lt shape are often considered part of conformability as well. The [[Each]] operator also checks conformability when called dyadically, and some functionality, * Otherwise, it is the shape of the argument with the largest rank (this condition is only possible with [[singleton extension]]).
  3 KB (408 words) - 03:17, 20 February 2024
• Promote
  ...ing its argument, can also be interpreted as Promote because [[depth]] and rank are equivalent in the [[list model]] of arrays. ...s this allows the axis to be placed in any other position using the [[Rank operator]].
  2 KB (244 words) - 01:22, 6 February 2024
• Fill element
  | <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> ||colspan=2| [[Rank operator]] Each operator in the table uses fills to force the results from its left operand to have
  3 KB (345 words) - 14:19, 16 May 2023
• Expand
  ...lt-ins|Expand|<nowiki>\</nowiki>|⍀}} is a [[dyadic function]] or [[monadic operator]] that copies each [[element]] of the right [[argument]] a given number of ...resolved by making Expand an operator itself, and sometimes by [[function-operator overloading]] allowing both syntactic elements to coexist.
  3 KB (353 words) - 22:11, 10 September 2022
• Atop (operator)
  {{Built-in|Atop|⍤}} is a [[primitive operator|primitive]] [[dyadic operator]] which takes two [[function]] [[operand]]s and produces a [[derived functi ...highlight lang=apl inline>f⍥g</syntaxhighlight> has the overall [[function rank]] of <syntaxhighlight lang=apl inline>g</syntaxhighlight>. J uses <code>@</
  3 KB (410 words) - 19:05, 16 March 2024
• Rank (operator)
  ...rs associated with a function specifying its argument rank, see [[function rank]].'' {{Built-in|Rank|⍤}} is a [[primitive operator|primitive]] [[dyadic operator]] which applies its left [[operand]] function to [[cells]] of its arguments
  7 KB (949 words) - 23:54, 20 July 2023
• Split
  ...t-in|Split|↓}} is a [[monadic]] [[primitive function]] which reduces the [[rank]] of its [[argument]] by converting one of its [[axis|axes]] to one level o ...ht> is <syntaxhighlight lang=apl inline>¯1+≢⍴Y</syntaxhighlight> (original rank minus 1), its [[shape]] is <syntaxhighlight lang=apl inline>(K≠⍳≢⍴Y
  4 KB (397 words) - 10:55, 11 September 2022
• Laminate
  ...ight lang=apl inline>,[⎕IO-0.5]</syntaxhighlight> case only, as the [[Rank operator]] can be used to add the axis in a later position, in accordance with [[lea ...th [[Catenate]], a scalar argument is subject to [[scalar extension]]: its rank is brought up to match that of the other argument by repeating its value.
  4 KB (527 words) - 01:30, 18 March 2024
• Depth (operator)
  :''This article is about the operator. See [[Depth]] for the number associated with every array and the function {{Built-in|Depth|⍥}} is a [[primitive operator|primitive]] [[dyadic operator]] which applies its left [[operand]] function to [[sub-array]]s of its argu
  6 KB (753 words) - 22:22, 7 February 2024
• Over
  {{Built-in|Over|⍥}} is a [[primitive operator|primitive]] [[dyadic operator]] which takes two [[function]] [[operand]]s and produces a [[derived functi ...it has the same behaviour as if the [[Beside]] or [[Atop (operator)|Atop]] operator had been used:
  3 KB (428 words) - 21:33, 28 January 2024
• Table
  :''This page is about the function that reshapes into a table. For the operator that generates a table of all combinations, see [[Outer Product]].'' For arrays of [[rank]] 1 or higher, the result is identical to applying Ravel to major cells:
  4 KB (381 words) - 15:33, 17 March 2024
• Each
  {{Built-in|Each|¨}} is a [[primitive operator|primitive]] [[monadic operator]] which applies its [[operand]] to each [[element]] of the [[argument]]s, a ...Under]] operator with [[close composition]] along with the [[Function rank|rank]]-0 function [[Disclose]] (or Unbox). In [[SHARP APL]] this is written <syn
  5 KB (488 words) - 22:16, 10 September 2022
• Scalar extension
  ...ally extending the scalar to function as though it were an array of higher rank. === Rank extension ===
  8 KB (947 words) - 03:06, 20 February 2024
• Scan
  ...can|<nowiki>\</nowiki>|⍀}} is a [[primitive operator|primitive]] [[monadic operator]] which takes a [[dyadic function]] [[operand]] and produces a [[monadic fu ...tained. That being said, unlike [[Reduce]], [[Scan]] does not reduce the [[rank]] of its argument, i.e. performing a scan over an N-dimensional [[array]] w
  1 KB (165 words) - 21:02, 10 September 2022
• Rationalized APL
  | function styles = definition operator ...introduced were later incorporated into [[J]]. It also featured the [[Rank operator]], invented by [[Arthur Whitney]] the previous year, just prior to its incl
  1 KB (170 words) - 08:49, 26 July 2021
• Leading axis theory
  ...tly using [[function rank]] or explicitly using the [[Rank (operator)|Rank operator]]. It was initially developed in [[SHARP APL]] in the early 1980s and is no ...perator is the reason to define functions on the leading axes: by applying Rank to a leading-axis function, the function can be made to work on any axis or
  10 KB (1,238 words) - 21:46, 10 September 2022
• Strand notation
  ...amming if unrelated arrays are stranded together. This issue occurs when [[operator]]s are allowed to take array [[operand]]s, and can be resolved by inserting ...APL]], [[NARS2000]], [[APL.68000]], and others, arrays are stranded before operator or function evaluation.
  3 KB (397 words) - 10:34, 11 September 2022
• Mix
  ...e same shape, or they may be extended in shape (with [[fill element]]s) or rank to fit a common shape. In all APLs Mix allows a [[simple array]] argument, ...and combine the results. Based on SHARP's definition of [[Rank (operator)|Rank]], the arrays to be combined were required to have the same [[shape]], and
  7 KB (900 words) - 18:27, 29 January 2024
• Rotate
  ...using <syntaxhighlight lang=apl inline>⊖</syntaxhighlight> with the [[Rank operator]]. ...arrays can be rotated on an arbitrary axis if [[function axis]] or [[Rank operator]] is supported:
  5 KB (626 words) - 22:15, 10 September 2022
• Axis
  ...ne dimension along which the [[element]]s of an array are organized. The [[rank]] of an array is the number of axes it has, and the [[shape]] is the list o ...ite this, the choice to make a positive operand to Rank specify a [[cell]] rank, while a negative operand specifies a [[frame]] length, weakly suggests an
  3 KB (444 words) - 22:29, 10 September 2022
• Cell
  ...ht> are called '''k-cells''' of an array. A [[major cell]] is a cell whose rank is one less than the entire array, or a 0-cell of a [[scalar]]. The k-cells of an array with [[rank]] <syntaxhighlight lang=apl inline>r</syntaxhighlight> share the last <synt
  7 KB (1,106 words) - 22:16, 10 September 2022
• Under
  ...nline>¨</syntaxhighlight>), is a [[primitive operator|primitive]] [[dyadic operator]] which takes two [[function]] [[operand]]s. It pre-processes its argument( ...highlight lang=apl inline>f¨g</syntaxhighlight> has the overall [[function rank]] of <syntaxhighlight lang=apl inline>g</syntaxhighlight>. This allows <syn
  5 KB (664 words) - 13:35, 17 February 2024
• Subarray
  ...he term sub-array may also be used to refer part of an array with lesser [[rank]] (i.e. a [[cell]]) or [[depth]].'' ...ght call such subarrays ''equal-rank'' subarrays. Otherwise a subarray has rank less than or equal to its containing array.
  3 KB (442 words) - 09:27, 14 September 2022
• Empty array
  ...using the [[Rank operator]] on an array with no [[cell]]s of the specified rank. Because the shape of each result cell might be determined by values in an ...inal result. In this case, this succeeds in finding the appropriate result rank but not the desired shape.
  5 KB (810 words) - 22:29, 10 September 2022
• Deal
  ...ng=apl inline>?⍤0</syntaxhighlight>, which uses the [[Rank (operator)|rank operator]] <syntaxhighlight lang=apl inline>⍤</syntaxhighlight>.
  4 KB (521 words) - 16:54, 8 February 2023
• Function axis
  ...cification in favor of the [[Rank operator]] because it is a fully general operator while the behavior of functions with axis must be defined for each function ...erride [[conformability]] rules: it specifies , for each axis in the lower-rank (or left, in case of a tie) argument, which axis in the other argument it i
  6 KB (878 words) - 05:12, 11 November 2022
• Ngn/apl
  * [[Rank (operator)|Rank (operator]] (<syntaxhighlight lang=apl inline>⍤</syntaxhighlight>) * the identity element operator (<syntaxhighlight lang=apl inline>⍁</syntaxhighlight>)
  5 KB (553 words) - 12:25, 31 August 2023
• Raze
  ...hape or an error results; in J, lower-rank arrays are promoted to a higher rank and arrays are padded with fills to a common major cell shape. ...rgument as singleton vectors, a convention which may be viewed as [[scalar rank extension]] or as a result of the idea that a scalar's only [[major cell]]
  6 KB (812 words) - 23:25, 29 January 2024
• Reduce
  ...uction''' or '''Insert''', is a [[primitive operator|primitive]] [[monadic operator]] which takes a [[dyadic function]] [[operand]], inserts it between the [[e ...r an axis other than the first is performed via the [[Rank (operator)|Rank operator]], which [[mix|mixes]] the results into a flat array.
  4 KB (570 words) - 19:11, 26 June 2023
• Reverse
  ...using <syntaxhighlight lang=apl inline>⊖</syntaxhighlight> with the [[Rank operator]]. ...he <syntaxhighlight lang=apl inline>1+r-k</syntaxhighlight>'th axis of a [[rank]]-<syntaxhighlight lang=apl inline>r</syntaxhighlight> array.
  6 KB (554 words) - 22:20, 10 September 2022
• Outer Product
  {{Built-in|Outer Product|<nowiki>∘.</nowiki>}}, or '''Table''' is a [[monadic operator]], which will produce a [[dyadic function]] when applied with a [[dyadic fu ...eft. For [[backwards compatibility|historical reasons]], the outer product operator is a [[bi-glyph]] denoted as <syntaxhighlight lang=apl inline>∘.</syntaxh
  8 KB (948 words) - 00:47, 19 March 2024
• Assignment
  ...th an [[array]] value. Some dialects also allow assignment of function and operator values using the assignment arrow. In [[defined function]]s, assignment is ...[rank]] arrays, the number of semicolons needed is one less than the array rank.
  4 KB (522 words) - 21:32, 9 March 2024
• ISO/IEC 13751:2001
  ...eatures not present in APL2, such as the [[Commute]] and [[Rank (operator)|Rank]] operators, the [[Identity function]]s, and [[GCD]] and [[LCM]] extending
  2 KB (308 words) - 13:04, 10 March 2024
• Tally
  ...in a higher-rank array. Tally applied to an array's [[shape]] gives its [[rank]]. ...s to count the major cells by turning each into a scalar 1 with the [[Rank operator]], then adding them up:
  3 KB (443 words) - 10:59, 11 September 2022
• Frame agreement
  ...rank (either [[Rank operator|derived]] and/or, when supported, [[function rank|native]]). The [[frame]]s must either be identical, or one must be [[empty] ...refix of the other. In J, because every function has associated [[function rank|ranks]], frame agreement generalizes [[leading axis agreement]].
  7 KB (779 words) - 14:23, 26 August 2023
• Ranking poker hands
  ...syntaxhighlight> below transforms a representation of a poker hand into a "rank" array so that the ordering of ranks under [[total array ordering]] is the ...s a single card by [[Pick|picking]] the appropriate character for suit and rank. We use the character <syntaxhighlight lang=apl inline>'T'</syntaxhighlight
  13 KB (1,398 words) - 22:22, 10 September 2022
• Function array
  .../syntaxhighlight> in the [[dfns workspace]] wraps this functionality in an operator.<ref>[[Dfns workspace]]. [https://dfns.dyalog.com/n_fnarray.htm <syntaxhigh
  2 KB (228 words) - 21:42, 2 January 2023
• Take
  ...ith the requirement that the left argument length match the right argument rank, and was extended in [[SHARP APL]] 19.0 to allow short left arguments. It i A higher-[[rank]] array can be shortened by using a left argument with one element for each
  13 KB (1,829 words) - 01:23, 2 March 2024
• SAX
  All scalar functions have rank zero. ! Glyph !! Rank !! Monadic !! Ranks !! Dyadic
  16 KB (1,327 words) - 22:20, 7 May 2024
• A+
  ...various novelties like symbols as a [[simple scalar]] type and the [[Rank operator]]. | <syntaxhighlight lang=apl inline>@</syntaxhighlight> || [[Rank operator|Rank]] ||
  9 KB (859 words) - 02:29, 5 March 2024

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