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{{Built-in|Partitioned Enclose|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the non-negative integer<ref group=note name=max>Most dialects restrict this number to a maximum of 1.</ref> left argument.
{{Built-in|Partitioned Enclose|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the left argument.


On a vector right argument, the corresponding element in the left argument indicates how many<ref group=note name=max></ref> '''divisions''' to begin there:
In the simplest case, and on a vector right argument, the corresponding element in the left argument indicates where <ref group=note name=max></ref> '''divisions''' begin:
<source lang=apl>
<source lang=apl>
       1 0 1 0 0 0 0⊂'HiEarth'
       1 0 1 0 0 0 0⊂'HiEarth'
Line 9: Line 9:
</source>
</source>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}
Empty divisions can be inserted by beginning more than 1 division at a particular index<ref group=note name=not>Most dialects do not support this.</ref>:
Almost all dialects restrict the left argument to provide only this functionality. However, the left argument can be interpreted as a count of how many partitions begin with a particular position:
<source lang=apl>
<source lang=apl>
       2 0 3 0 0 0 0⊂'HiEarth'
       2 0 3 0 0 0 0⊂'HiEarth'
Line 16: Line 16:
└┴──┴┴┴─────┘
└┴──┴┴┴─────┘
</source>
</source>
Additional trailing empty divisions are created by adding an additional division count corresponding to the index beyond the end of the right argument<ref group=note name=not></ref>:
Additional trailing empty divisions are thus created by adding an additional division count corresponding to the index beyond the end of the right argument<ref group=note name=not></ref>:
<source lang=apl>
<source lang=apl>
       1 0 1 0 0 0 0 1⊂'HiEarth'
       1 0 1 0 0 0 0 1⊂'HiEarth'
Line 23: Line 23:
└──┴─────┴┘
└──┴─────┴┘
</source>
</source>
Partitioned Enclose allows a simple definition<ref group=note>In dialects that implement the full functionality of Partitioned Enclose.</ref> of a split-into-lengths function:
This interpretation allows a simple definition of a split-into-lengths function:


[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v/ggpzMEpAjHvVuVXjU1fSod4XCo94dj3oXH1pvqKAdowCkHrVNNtQB2ff/v7GCsYKJAliTgrpHfrljUWpkfqm9OgA Try it online!]
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v/ggpzMEpAjHvVuVXjU1fSod4XCo94dj3oXH1pvqKAdowCkHrVNNtQB2ff/v7GCsYKJAliTgrpHfrljUWpkfqm9OgA Try it online!]
Line 34: Line 34:
</source>
</source>
{{Works in|[[Extended Dyalog APL]]}}
{{Works in|[[Extended Dyalog APL]]}}
==Notes==
<references group="note"/>
==External links==
==External links==
===Tutorials===
===Tutorials===

Revision as of 13:00, 27 January 2020

⊂

Partitioned Enclose (⊂) is a dyadic function which splits its right argument into differently sized pieces as determined by the left argument.

In the simplest case, and on a vector right argument, the corresponding element in the left argument indicates where [note 1] divisions begin: 

      1 0 1 0 0 0 0⊂'HiEarth'
┌──┬─────┐
│Hi│Earth│
└──┴─────┘
Works in: Dyalog APL

Almost all dialects restrict the left argument to provide only this functionality. However, the left argument can be interpreted as a count of how many partitions begin with a particular position: 

      2 0 3 0 0 0 0⊂'HiEarth'
┌┬──┬┬┬─────┐
││Hi│││Earth│
└┴──┴┴┴─────┘

Additional trailing empty divisions are thus created by adding an additional division count corresponding to the index beyond the end of the right argument[note 2]: 

      1 0 1 0 0 0 0 1⊂'HiEarth'
┌──┬─────┬┐
│Hi│Earth││
└──┴─────┴┘

This interpretation allows a simple definition of a split-into-lengths function:

Try it online! 

      Split←{⍵ ⊂⍨ ⍸⍣¯1 +\ ¯1↓1,⍺}
      3 3 4 Split 'HowAreYou?'
┌───┬───┬────┐
│How│Are│You?│
└───┴───┴────┘
Works in: Extended Dyalog APL

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
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
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector


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