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Re: [Bug-apl] inner product
From: |
enztec |
Subject: |
Re: [Bug-apl] inner product |
Date: |
Fri, 17 Mar 2017 16:28:06 -0600 |
very nice work - thanks you for spending the time .. everthing here holds
when replacing +.x with +.= (which is of more interest to me)
On Fri, 17 Mar 2017 22:01:26 +0100
Nick Lobachevsky <address@hidden> wrote:
> The key to understanding inner product is that the inner dimensions of
> the arguments have to be the same. The inner dimension here is 3.
>
> a←2 3⍴⍳6
> b←3 4⍴⍳12
> a
> 0 1 2
> 3 4 5
> b
> 0 1 2 3
> 4 5 6 7
> 8 9 10 11
> a+.×b
> 20 23 26 29
> 56 68 80 92
>
> To solve this, first transpose the right argument such that the inner
> dimension goes to the back of the array and both arguments have the
> same number of columns.
>
> (¯1⌽⍳⍴⍴b)⍉b
> 0 4 8
> 1 5 9
> 2 6 10
> 3 7 11
> a
> 0 1 2
> 3 4 5
>
> Do the operations for every combination of rows in a and ⍉b. As we
> are doing +.×
> 0 1 2 × 0 4 8 is 0 4 16, +/0 4 16 is 20. First element of the result
> 0 1 2 × 1 5 9 is 0 5 18, +/0 5 18 is 23. Second element of the result
> And so on. Loop until done.
>
> Shape of the result is (¯1↓⍴a),1↓⍴b or 2 4
>
> For the vector and vector case, the lengths of both vectors have to be
> the same. The result is simply +/ a × b
>
> For higher order matrices, as before, the inner dimensions are
> important. The others less so.
> a←2 5 1 3⍴⍳30
> b←3 4 2⍴⍳12
> Here the idea is to collapse (i.e. multiply together) all but the
> inner dimensions, then compute the result as if both arguments were
> two dimensional matrices.
> a←10 3⍴⍳30
> b←3 8⍴⍳24
> And as before, the shape of the product is (¯1↓⍴a),1↓⍴b or 2 5 1 4 2
>
> See also
> http://www.dyalog.com/uploads/conference/dyalog16/presentations/U08_SIMD_Boolean_Array_Algorithms_slides.pdf
> (The part about the STAR Inner Product Algorithm)
>
> and
>
> http://www.jsoftware.com/papers/innerproduct/ip1.htm