Re: [Bug-apl] tensor product

[Louis de Forcrand]

I have no idea what you’re actually trying to do, but this (inelegant) lambda works:

tensor←{ ,[1 2] { { ,[3 4] 1 3 2 4 ⍉ ⍵} ⍣ (2 < ⍴⍴⍵) ⍵ } ⍺ ∘.× ⍵}

Basically, it conditionally executes the transpose and first ravel if the result of the outer product is of rank greater than 2.

If you don’t mind having a stray variable floating around, this is more readable:

tensor←{ ,[1 2] { ,[3 4] 1 3 2 4 ⍉ ⍵} ⍣ ( 2 < ⍴⍴T ) T ← ⍺ ∘.× ⍵}

Best regards!

Louis

On 24 Jan 2016, at 21:40, Tobia C. <address@hidden> wrote:

I'm studying tensor products[1] and I came up with these two definitions, resp. for the operation between vectors and between matrices:

tensor1←{,⍺∘.×⍵}

tensor2←{,[1 2],[3 4]1 3 2 4⍉⍺∘.×⍵}

Jay's version is more efficient, because it performs a single reshape, but it needs (⍴⍺)×⍴⍵, not (⍴⍺)+⍴⍵:

tensor2←{((⍴⍺)×⍴⍵)⍴1 3 2 4⍉⍺∘.×⍵}

It only works in Wikipedia's example because (2+2)=2×2

Can anybody suggest an idiomatic way to combine tensor1 and tensor2 into a single function? (Without using multi-statement functions or non-GNU APL syntax.)

Tobia

[1] on this very interesting book: Yanofsky, Mannucci - Quantum Computing for Computer Scientists