## indexing by booleans

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**1**of**1**### indexing by booleans

In the recent sequence of posts (for example Addition on 1-Byte Integers), the game was to write a function g such that

where g does not use the function denoted by "symbol". Here, the game is to write a function h which does not use [;] or ⌷, so that:

⎕io←0 is assumed. ⎕io delenda est!

Rotate

Indexing ⍺ by a numeric index can be computed independently on each scalar index i (right rank 0). When i is boolean, the result is either the first (or only) major cell or the second major cell, that is, (1↓⍴⍺)⍴i⊖⍺.

Rotate with Transpose

Can we compute result on the index items in toto, all at once? Yes, we can. Dyadic transpose plays a key part in so doing.

As is often the case with dyadic transpose, the left argument is either ⍋something or ⍋⍋something; if one doesn't work, try the other☺. Seriously, the mnemonic is that an item of the left argument specifies where an argument axis goes rather than where a result axis comes from (thus allowing duplicate items and therefore diagonal sections).

Numeric Arrays

If the array to be indexed is numeric, it is possible to to use arithmetic to finesse the prohibition against using [;] and ⌷.

(x symbol y) ≡ x g y

where g does not use the function denoted by "symbol". Here, the game is to write a function h which does not use [;] or ⌷, so that:

x ← t[?3 19⍴≢t←(?3⍴0),'⍣⍟⌹ab',(⊂'asdf'),¯400+?7⍴1000]

y ← ?97 4 5⍴2

((⊂y)⌷x) ≡ x h y

1

x[y;;…;] ≡ x h y

1

⎕io←0 is assumed. ⎕io delenda est!

Rotate

ixr ← {(1↓⍴⍺)⍴⍵⊖⍺}⍤99 0

((⊂y)⌷x) ≡ x ixr y

1

x[y;] ≡ x ixr y

1

Indexing ⍺ by a numeric index can be computed independently on each scalar index i (right rank 0). When i is boolean, the result is either the first (or only) major cell or the second major cell, that is, (1↓⍴⍺)⍴i⊖⍺.

Rotate with Transpose

⍝

ixrt←{

r←≢⍴⍺

i←⍋⍋((≢⍴⍵)⍴1),r⍴0,r⍴1

((⍴⍵),1↓⍴⍺) ⍴ i ⍉ ⍵ ⊖⍤(0,r) ⊢ ((⍴⍵),2,1↓⍴⍺) ⍴ (1+1∊⍵)↑⍺

}

((⊂y)⌷x) ≡ x ixrt y

1

x[y;] ≡ x ixrt y

1

Can we compute result on the index items in toto, all at once? Yes, we can. Dyadic transpose plays a key part in so doing.

As is often the case with dyadic transpose, the left argument is either ⍋something or ⍋⍋something; if one doesn't work, try the other☺. Seriously, the mnemonic is that an item of the left argument specifies where an argument axis goes rather than where a result axis comes from (thus allowing duplicate items and therefore diagonal sections).

Numeric Arrays

⍝

ixn←{

r←≢c←1↓⍴⍺

x0←c⍴⍺ ⍝ (⊂0)⌷⍺ ←→ ⍺[0;;…;]

x1←c⍴(1∊⍵)↓⍺ ⍝ (⊂1)⌷⍺ ←→ ⍺[1;;…;], or (⊂0)⌷⍺ if ~1∊⍵

(x0 ×⍤(r,0)⊢ 0=⍵) + (x1 ×⍤(r,0)⊢ 1=⍵)

}

x←¯1e7+?3 19⍴3e7

((⊂y)⌷x) ≡ x ixn y

1

x[y;] ≡ x ixn y

1

If the array to be indexed is numeric, it is possible to to use arithmetic to finesse the prohibition against using [;] and ⌷.

- Roger|Dyalog
**Posts:**238**Joined:**Thu Jul 28, 2011 10:53 am

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