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 <ibeam2...@gmail.com> 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
