Reverse: Difference between revisions
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{{Built-ins|Reverse|⌽|⊖}} is a [[monadic function]] which reorders [[elements]] of the argument to go in the opposite direction along a specified [[axis]]. The name Reverse is typically used for the primitive <source lang=apl inline>⌽</ | {{Built-ins|Reverse|⌽|⊖}} is a [[monadic function]] which reorders [[elements]] of the argument to go in the opposite direction along a specified [[axis]]. The name Reverse is typically used for the primitive <source lang=apl inline>⌽</syntaxhighlight>, which reverses along the last axis, while <source lang=apl inline>⊖</syntaxhighlight>, which reverses along the first axis, is called "Reverse First", "Reverse-down", or similar. In APLs with [[function axis]], either form may use a specified axis which overrides this default choice of axis. In the [[leading axis model]], specifying an axis is discouraged in favor of using <source lang=apl inline>⊖</syntaxhighlight> with the [[Rank operator]]. | ||
== Examples == | == Examples == | ||
| Line 18: | Line 18: | ||
21 22 23 24 25 26 | 21 22 23 24 25 26 | ||
11 12 13 14 15 16 | 11 12 13 14 15 16 | ||
</ | </syntaxhighlight> | ||
Since a [[vector]] only has one axis, any form of Reverse will reverse along this axis. | Since a [[vector]] only has one axis, any form of Reverse will reverse along this axis. | ||
<source lang=apl> | <source lang=apl> | ||
| Line 25: | Line 25: | ||
⊖⌽ 'Backwards text' ⍝ One reverse undoes the other | ⊖⌽ 'Backwards text' ⍝ One reverse undoes the other | ||
Backwards text | Backwards text | ||
</ | </syntaxhighlight> | ||
Reverse with a [[specified axis]] can reverse along any of the three dimensions of the array below. | Reverse with a [[specified axis]] can reverse along any of the three dimensions of the array below. | ||
<source lang=apl> | <source lang=apl> | ||
| Line 46: | Line 46: | ||
│13 14 15 16 17 18│19 20 21 22 23 24│36 35 34 33 32 31│ | │13 14 15 16 17 18│19 20 21 22 23 24│36 35 34 33 32 31│ | ||
└─────────────────┴─────────────────┴─────────────────┘ | └─────────────────┴─────────────────┴─────────────────┘ | ||
</ | </syntaxhighlight> | ||
The [[Rank operator]] can also be used to reverse along a particular axis. While Rank has no effect on Reverse (last), Reverse First with rank <source lang=apl inline>k</ | The [[Rank operator]] can also be used to reverse along a particular axis. While Rank has no effect on Reverse (last), Reverse First with rank <source lang=apl inline>k</syntaxhighlight> reverses the first axis of each <source lang=apl inline>k</syntaxhighlight>-cell, or the <source lang=apl inline>1+r-k</syntaxhighlight>'th axis of a [[rank]]-<source lang=apl inline>r</syntaxhighlight> array. | ||
<source lang=apl> | <source lang=apl> | ||
⌽⍤2⊢a ⍝ Same as ⌽ | ⌽⍤2⊢a ⍝ Same as ⌽ | ||
| Line 75: | Line 75: | ||
│13 14 15 16 17 18│19 20 21 22 23 24│36 35 34 33 32 31│ | │13 14 15 16 17 18│19 20 21 22 23 24│36 35 34 33 32 31│ | ||
└─────────────────┴─────────────────┴─────────────────┘ | └─────────────────┴─────────────────┴─────────────────┘ | ||
</ | </syntaxhighlight> | ||
Reversing a [[scalar]] has no effect: there are no axes to reverse along. | Reversing a [[scalar]] has no effect: there are no axes to reverse along. | ||
<source lang=apl> | <source lang=apl> | ||
⌽1.1 | ⌽1.1 | ||
1.1 | 1.1 | ||
</ | </syntaxhighlight> | ||
== Description == | == Description == | ||
| Line 86: | Line 86: | ||
In languages with [[function axis]], exactly one argument axis may be specified. | In languages with [[function axis]], exactly one argument axis may be specified. | ||
Reversing a [[scalar]] always yields that scalar unchanged. Otherwise, Reverse operates on a particular axis of its argument. This axis is the specified axis if one is given, and otherwise the last axis for <source lang=apl inline>⌽</ | Reversing a [[scalar]] always yields that scalar unchanged. Otherwise, Reverse operates on a particular axis of its argument. This axis is the specified axis if one is given, and otherwise the last axis for <source lang=apl inline>⌽</syntaxhighlight>, or the first axis for <source lang=apl inline>⊖</syntaxhighlight>. | ||
The result array has the same [[shape]] and [[elements]] as the argument array, but the elements go in the opposite direction along the reversal axis: the first in the argument is last in the result, and so on. Consequently if the length of this axis is 0 or 1 then reversing has no effect. | The result array has the same [[shape]] and [[elements]] as the argument array, but the elements go in the opposite direction along the reversal axis: the first in the argument is last in the result, and so on. Consequently if the length of this axis is 0 or 1 then reversing has no effect. | ||
| Line 92: | Line 92: | ||
=== APL model === | === APL model === | ||
The reverse of a vector <source lang=apl inline>x</ | The reverse of a vector <source lang=apl inline>x</syntaxhighlight> may be written in any APL, assuming <source lang=apl inline>⎕IO←0</syntaxhighlight>, as <source lang=apl inline>x[(¯1+⍴x)-⍳⍴x]</syntaxhighlight>. To reverse an arbitrary array [[Squad indexing]] with axis (or [[Rank operator|rank]]) is helpful. | ||
<source lang=apl> | <source lang=apl> | ||
ReverseAxis ← { | ReverseAxis ← { | ||
| Line 101: | Line 101: | ||
(⊂l-1+⍳l) ⌷[⍺] ⍵ ⍝ Reverse with indexing | (⊂l-1+⍳l) ⌷[⍺] ⍵ ⍝ Reverse with indexing | ||
} | } | ||
</ | </syntaxhighlight> | ||
== External links == | == External links == | ||
Revision as of 21:20, 10 September 2022
⌽ ⊖
|
Reverse (⌽, ⊖) is a monadic function which reorders elements of the argument to go in the opposite direction along a specified axis. The name Reverse is typically used for the primitive <source lang=apl inline>⌽</syntaxhighlight>, which reverses along the last axis, while <source lang=apl inline>⊖</syntaxhighlight>, which reverses along the first axis, is called "Reverse First", "Reverse-down", or similar. In APLs with function axis, either form may use a specified axis which overrides this default choice of axis. In the leading axis model, specifying an axis is discouraged in favor of using <source lang=apl inline>⊖</syntaxhighlight> with the Rank operator.
Examples
Reverse flips a matrix horizontally, changing elements to go right to left, and Reverse First flip vertically, so the elements are reordered top to bottom. <source lang=apl>
x ← 10 20 30 ∘.+ ⍳6
x
11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36
⌽x
16 15 14 13 12 11 26 25 24 23 22 21 36 35 34 33 32 31
⊖x
31 32 33 34 35 36 21 22 23 24 25 26 11 12 13 14 15 16 </syntaxhighlight> Since a vector only has one axis, any form of Reverse will reverse along this axis. <source lang=apl>
⌽ 'Backwards text'
txet sdrawkcaB
⊖⌽ 'Backwards text' ⍝ One reverse undoes the other
Backwards text </syntaxhighlight> Reverse with a specified axis can reverse along any of the three dimensions of the array below. <source lang=apl>
⎕←a←2 3 6⍴⍳36 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
(⌽[1]a)(⌽[2]a)(⌽[3]a)
┌─────────────────┬─────────────────┬─────────────────┐ │19 20 21 22 23 24│13 14 15 16 17 18│ 6 5 4 3 2 1│ │25 26 27 28 29 30│ 7 8 9 10 11 12│12 11 10 9 8 7│ │31 32 33 34 35 36│ 1 2 3 4 5 6│18 17 16 15 14 13│ │ │ │ │ │ 1 2 3 4 5 6│31 32 33 34 35 36│24 23 22 21 20 19│ │ 7 8 9 10 11 12│25 26 27 28 29 30│30 29 28 27 26 25│ │13 14 15 16 17 18│19 20 21 22 23 24│36 35 34 33 32 31│ └─────────────────┴─────────────────┴─────────────────┘ </syntaxhighlight> The Rank operator can also be used to reverse along a particular axis. While Rank has no effect on Reverse (last), Reverse First with rank <source lang=apl inline>k</syntaxhighlight> reverses the first axis of each <source lang=apl inline>k</syntaxhighlight>-cell, or the <source lang=apl inline>1+r-k</syntaxhighlight>'th axis of a rank-<source lang=apl inline>r</syntaxhighlight> array. <source lang=apl>
⌽⍤2⊢a ⍝ Same as ⌽ 5 4 3 2 1 0
11 10 9 8 7 6 17 16 15 14 13 12
23 22 21 20 19 18 29 28 27 26 25 24 35 34 33 32 31 30
⊖⍤2⊢a ⍝ Same as ⌽[2]
12 13 14 15 16 17
6 7 8 9 10 11 0 1 2 3 4 5
30 31 32 33 34 35 24 25 26 27 28 29 18 19 20 21 22 23
(⊖⍤3⊢a)(⊖⍤2⊢a)(⊖⍤1⊢a)
┌─────────────────┬─────────────────┬─────────────────┐ │19 20 21 22 23 24│13 14 15 16 17 18│ 6 5 4 3 2 1│ │25 26 27 28 29 30│ 7 8 9 10 11 12│12 11 10 9 8 7│ │31 32 33 34 35 36│ 1 2 3 4 5 6│18 17 16 15 14 13│ │ │ │ │ │ 1 2 3 4 5 6│31 32 33 34 35 36│24 23 22 21 20 19│ │ 7 8 9 10 11 12│25 26 27 28 29 30│30 29 28 27 26 25│ │13 14 15 16 17 18│19 20 21 22 23 24│36 35 34 33 32 31│ └─────────────────┴─────────────────┴─────────────────┘ </syntaxhighlight> Reversing a scalar has no effect: there are no axes to reverse along. <source lang=apl>
⌽1.1
1.1 </syntaxhighlight>
Description
In languages with function axis, exactly one argument axis may be specified.
Reversing a scalar always yields that scalar unchanged. Otherwise, Reverse operates on a particular axis of its argument. This axis is the specified axis if one is given, and otherwise the last axis for <source lang=apl inline>⌽</syntaxhighlight>, or the first axis for <source lang=apl inline>⊖</syntaxhighlight>.
The result array has the same shape and elements as the argument array, but the elements go in the opposite direction along the reversal axis: the first in the argument is last in the result, and so on. Consequently if the length of this axis is 0 or 1 then reversing has no effect.
APL model
The reverse of a vector <source lang=apl inline>x</syntaxhighlight> may be written in any APL, assuming <source lang=apl inline>⎕IO←0</syntaxhighlight>, as <source lang=apl inline>x[(¯1+⍴x)-⍳⍴x]</syntaxhighlight>. To reverse an arbitrary array Squad indexing with axis (or rank) is helpful. <source lang=apl> ReverseAxis ← {
⎕IO←0 0=≢⍴⍵: ⍵ ⍝ Return a scalar unchanged ⍺ ← ¯1+≢⍴⍵ ⍝ Assume last axis l ← ⍺ ⌷ ⍴⍵ ⍝ Length of reversed axis (⊂l-1+⍳l) ⌷[⍺] ⍵ ⍝ Reverse with indexing
} </syntaxhighlight>
External links
Lessons
Documentation
- Dyalog
- APLX
- J Dictionary, NuVoc (only first-axis reverse exists)
- BQN