Partition: Difference between revisions

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{{Built-ins|Partition|⊆|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the non-negative integer left argument. This article uses <source lang=apl inline>⊆</source> to distinguish Partition from [[Partitioned Enclose]] (which is always <source lang=apl inline>⊂</source>), but the actual [[glyph]] used [[Migration level|varies by dialect]].
{{Built-ins|Partition|⊆|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the non-negative integer left argument. This article uses <syntaxhighlight lang=apl inline>⊆</syntaxhighlight> to distinguish Partition from [[Partitioned Enclose]] (which is always <syntaxhighlight lang=apl inline>⊂</syntaxhighlight>), but the actual [[glyph]] used [[Migration level|varies by dialect]].


On a vector right argument, the arguments must have the same length with each element in the left argument corresponding to an element in the right argument. Partition begins a new '''division''' of its right argument whenever a left argument element is greater than its neighbour on the left (with a 0 assumed to the left of the first element):
On a vector right argument, the arguments must have the same length with each element in the left argument corresponding to an element in the right argument. Partition begins a new '''division''' of its right argument whenever a left argument element is greater than its neighbour on the left (with a 0 assumed to the left of the first element):
<source lang=apl>
 
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v///w0VDBWMYPBRV5u6R6ZrYlFJhjoA Try it online!]
<syntaxhighlight lang=apl>
       1 1 2 2 2 2 2⊆'HiEarth'
       1 1 2 2 2 2 2⊆'HiEarth'
┌──┬─────┐
┌──┬─────┐
│Hi│Earth│
│Hi│Earth│
└──┴─────┘
└──┴─────┘
</source>
</syntaxhighlight>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}
Right argument elements can be skipped by having their corresponding left argument element be 0:
Right argument elements can be skipped by having their corresponding left argument element be 0:
<source lang=apl>
<syntaxhighlight lang=apl>
       1 1 2 2 2 0 0⊆'HiEarth'
       1 1 2 2 2 0 0⊆'HiEarth'
┌──┬───┐
┌──┬───┐
│Hi│Ear│
│Hi│Ear│
└──┴───┘
└──┴───┘
</source>
</syntaxhighlight>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}
In the case where the left argument is [[Boolean]], Partition splits its right argument on runs of 0s in the left argument, allowing a very short split-on-delimiter function:
In the case where the left argument is [[Boolean]], Partition splits its right argument on runs of 0s in the left argument, allowing a very short split-on-delimiter function:
<source lang=apl>
 
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v///w0VQNBAAZU2fNTVpu6RX66QWJSqUJlfaq/OBTRF41HnAqDEo65FmqiSAA Try it online!]
<syntaxhighlight lang=apl>
       1 1 1 0 1 1 1 0 1 1 1 1⊆'How are you?'
       1 1 1 0 1 1 1 0 1 1 1 1⊆'How are you?'
┌───┬───┬────┐
┌───┬───┬────┐
Line 27: Line 31:
│How│are│you?│
│How│are│you?│
└───┴───┴────┘
└───┴───┴────┘
</source>
</syntaxhighlight>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}
{{APL built-ins}}
== See also ==
* [[Partitioned Enclose]]
* [[Cut (K)]]
* [[Partition representations]]
 
==External links==
===Tutorials===
* [https://chat.stackexchange.com/rooms/52405/conversation/lesson-7-apl-functions-#41436171 APL Cultivation]
===Documentation===
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Partition.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_590.htm APLX]
{{APL built-ins}}[[Category:Primitive functions]]

Latest revision as of 22:18, 10 September 2022

⊆ ⊂

Partition (⊆, ⊂) is a dyadic function which splits its right argument into differently sized pieces as determined by the non-negative integer left argument. This article uses ⊆ to distinguish Partition from Partitioned Enclose (which is always ⊂), but the actual glyph used varies by dialect.

On a vector right argument, the arguments must have the same length with each element in the left argument corresponding to an element in the right argument. Partition begins a new division of its right argument whenever a left argument element is greater than its neighbour on the left (with a 0 assumed to the left of the first element):

Try it online! 

      1 1 2 2 2 2 2⊆'HiEarth'
┌──┬─────┐
│Hi│Earth│
└──┴─────┘
Works in: Dyalog APL

Right argument elements can be skipped by having their corresponding left argument element be 0: 

      1 1 2 2 2 0 0⊆'HiEarth'
┌──┬───┐
│Hi│Ear│
└──┴───┘
Works in: Dyalog APL

In the case where the left argument is Boolean, Partition splits its right argument on runs of 0s in the left argument, allowing a very short split-on-delimiter function:

Try it online! 

      1 1 1 0 1 1 1 0 1 1 1 1⊆'How are you?'
┌───┬───┬────┐
│How│are│you?│
└───┴───┴────┘
      ' '(≠⊆⊢)'How are you?'
┌───┬───┬────┐
│How│are│you?│
└───┴───┴────┘
Works in: Dyalog APL

See also

External links

Tutorials

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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