Difference between revisions of "Indexing"

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       <td valign="top"><apll>Z←R[L]</apll>, <apll>R[L]←A</apll>, and <apll>R[L]<i>f</i>←A</apll></td>
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       <td valign="top"><apll>Z←R[L]</apll>, &nbsp;&nbsp; <apll>R[L]←A</apll>, &nbsp;&nbsp; and &nbsp;&nbsp; <apll>R[L]<i>f</i>←A</apll></td>
 
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   <td><apll>A</apll> is an arbitrary array.</td>
 
   <td><apll>A</apll> is an arbitrary array.</td>
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  <td><apll><i>f</i></apll> is an arbitrary function.</td>
 
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   <td>Both Reach and Scatter indexing may appear together within a single instance of <apll>R[L]</apll>, <apll>R[L]←A</apll>, and <apll>R[L]<i>f</i>←A</apll></td>
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   <td>Both Reach and Scatter indexing may appear together within a single instance of <apll>R[L]</apll>, &nbsp;&nbsp; <apll>R[L]←A</apll>, &nbsp;&nbsp; and &nbsp;&nbsp; <apll>R[L]<i>f</i>←A</apll></td>
 
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       <td valign="top"><apll>Z←R[L]</apll>, <apll>R[L]←A</apll>, <apll>R[L]<i>f</i>←A</apll>, <apll>L⌷R</apll>, <apll>L⍉R</apll>, and <apll>L⊃R</apll></td>
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       <td valign="top"><apll>Z←R[L]</apll>, &nbsp;&nbsp; <apll>R[L]←A</apll>, &nbsp;&nbsp; <apll>R[L]<i>f</i>←A</apll>, &nbsp;&nbsp; <apll>L⌷[X] R</apll>, &nbsp;&nbsp; <apll>L⍉R</apll>, &nbsp;&nbsp; and &nbsp;&nbsp; <apll>L⊃R</apll></td>
 
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   <td>That is, if the largest allowed value for <apll>L</apll> is <apll>N</apll>, then the previous allowable range of values was <apll>⎕IO</apll> to <apll>N</apll>, inclusive.  Now, the allowable range of values is <apll>1 ¯1[1]-N</apll> to <apll>N</apll>, inclusive.  For example, <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical for any array <apll>A</apll> in either origin.<br />Also, <apll>A</apll>, <apll>(⍳⍴⍴A)⍉A</apll>, and <apll>(⍳-⍴⍴A)⍉A</apll> are all identical for any array <apll>A</apll> in either origin.</td>
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   <td>That is, if the largest allowed value for <apll>L</apll> is <apll>N</apll>, then the previous allowable range of values was <apll>⎕IO</apll> to <apll>N</apll>, inclusive.  Now, the allowable range of values is <apll>1 ¯1[1]-N</apll> to <apll>N</apll>, inclusive.  For example, &nbsp;&nbsp; <apll>A</apll>, &nbsp;&nbsp; <apll>A[⍳⍴A]</apll>, &nbsp;&nbsp; <apll>A[⍳-⍴A]</apll>, &nbsp;&nbsp; and even &nbsp;&nbsp; <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> &nbsp;&nbsp; are all identical for any array <apll>A</apll> in either origin.<br />Also, &nbsp;&nbsp; <apll>A</apll>, &nbsp;&nbsp; <apll>(⍳⍴⍴A)⍉A</apll>, &nbsp;&nbsp; and &nbsp;&nbsp; <apll>(⍳-⍴⍴A)⍉A</apll> &nbsp;&nbsp; are all identical for any array <apll>A</apll> in either origin.</td>
 
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Latest revision as of 18:11, 30 June 2018

Z←R[L],    R[L]←A,    and    R[L]f←A are all extended to allow both Reach and Scatter indexing.
L is a nested array of integer scalars and/or vectors, suitable for indexing R.
R is an arbitrary array.
A is an arbitrary array.
f is an arbitrary function.
Reach Indexing:   If L⊃R is valid, it is equivalent to ⊃R[⊂L], and
if L⊃¨⊂R is valid, it is equivalent to R[L]
Scatter Indexing:   If L⌷R is valid, it is equivalent to R[⊃∘.,/L], and
if L⌷¨⊂R is valid, it is equivalent to ⊂¨R[⊂¨L]
Both Reach and Scatter indexing may appear together within a single instance of R[L],    R[L]←A,    and    R[L]f←A
These functions are sensitive to ⎕IO.


For example, in origin-1

      V←'123'(⊂4 5)
      V[1 (2 ⍬ 1)]
 123 4
      M←2 2⍴(10 20) (30 40 'abc') 50 60
      M[(1 1)((1 2) 3)]
 10 20  abc
Z←R[L],    R[L]←A,    R[L]f←A,    L⌷[X] R,    L⍉R,    and    L⊃R are all extended to allow negative values in L.
For all but transpose, L is a nested array of integer scalars and/or vectors, suitable for indexing R; for transpose, L is an integer scalar or vector of integers, suitable for transposing R.
That is, if the largest allowed value for L is N, then the previous allowable range of values was ⎕IO to N, inclusive. Now, the allowable range of values is 1 ¯1[1]-N to N, inclusive. For example,    A,    A[⍳⍴A],    A[⍳-⍴A],    and even    A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]    are all identical for any array A in either origin.
Also,    A,    (⍳⍴⍴A)⍉A,    and    (⍳-⍴⍴A)⍉A    are all identical for any array A in either origin.
R is an arbitrary array.
A is an arbitrary array.
These functions are sensitive to ⎕IO. Negative indexing is available only when the first element of ⎕FEATURE is set to 1.


For example, in origin-1

      ⎕FEATURE[1]←1
      V←'123'(⊂4 5)
      V[¯1 (0 ⍬ ¯1)]
 123 4