Why does decode of a matrix work by column and not row

[jmosk]

I have matrix ← 4 3 ⍴ 0 0 0 1 1 0 0 1 1 1 1 1

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0 0 0
1 1 0
0 1 1
1 1 1


I wish to convert each row from binary to decimal with the ⊥ primitive. The result is

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2⊥ matrix
5 7 3


I thought/expected to get 0 6 3 7. I had to transpose the matrix to get what I thought.

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2⊥⍉matrix
0 6 3 7


Yet if I sum reduce the matrix, it operates by rows

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+/matrix
0 2 2 3


So why does the ⊥ seem to function on rank 2, while the / functions on rank 1? There is a separate ⌿ function to operate on rank 2.

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+⌿matrix
2 3 2


This seems inconsistent between the two primitives with one operating column-wise and the other row-wise.

[Phil Last]

In fact decode works not on rank 2 but on the first dimension. The fact that reduction works on the last dimension is a mistake or oversight made in the earliest impementations and only corrected by Ken and Roger when they implemented J.

So the why is history.

[yaemmanuelli]

Hello,
Decode syntax is derived from internal product syntax which operates on last dimension of left argument and first dimension of right argument.
Regards.
--
Yves-Antoine Emmanuelli

[Adam|Dyalog]

To summarise previous posts:

1. Regard ⌿ as the primary form and works along the leading axis, and / is convenient name for ⌿⍤1 which works along the trailing axis
   
2. ⊥ is a convenient wrapper on +.× namely {⍵+.×⍨⌽×\1,⍺⍴⍨¯1+≢⍵} making it work along the leading axis

And to fix your issue:

1. As with ⌿ you can make ⊥ work along the trailing axis with ⍤1:
   

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         2(⊥⍤1)matrix
0 6 3 7