Calculating all combinations of vector-element multiplication

I have N vectors of varying size for which I wish to compute the product of every element.

A = [1 2 3 4]
B = [1]
C = [10 20]

Desired result = [a1*b1*c1 a1*b1*c2 a2*b1*c1 a2*b1*c2...] --> size = 1 x 8

I have found a few post for the 2 vector case in which simple vector multiplication works

D = A'*B --> this results in a matrix, but the entries align with what I am trying to achieve.

Expanding this to a 3-vector problem I had some success with bsxfun

D = bsxfun(@times,A'*B,reshape(C,1,1,numel(C))); --> this results in a 3-D matrix

How do you do this for more than 3 vectors, lets say 10, without using embedded 'for' loops???

Answer 1

[James Tursa]

I don't know how to avoid a loop of some sort for an arbitrary number of variables, even if it is hidden in the background. E.g., a function approach:

function result = timesall(varargin)
if( nargin > 0 )
    result = varargin{1};
    for k=2:nargin
        result = result(:) * reshape(varargin{k},1,[]);
    end
    result = reshape(result,1,[]);
else
    result = [];
end
end

And a sample run:

>> A = [1 2 3 4]
A =
     1     2     3     4
>> B = [1]
B =
     1
>> C = [10 20]
C =
    10    20
>> timesall(A,B,C)
ans =
    10    20    30    40    20    40    60    80

[Still Learning Matlab]

Thank you James, this is a nice neat function which does the trick. I do have 2 follow on questions: 1) How would your answer change if I know exactly the number of vectors? 2) Any recommendation for conserving space in assigning the result to an array (or cell or structure); I am experimenting on a few things but may end up need a 1*10^15 element array

[James Tursa]

1) No change, since the function takes an arbitrary number of inputs. (Unless it was exactly two inputs of course)

2) No way you can store 10^15 elements in memory, and even if you could it would take you a very long time to process it. For a double variable that is over 7 petabytes. You need to come up with a different strategy to solve your problem.

[Still Learning Matlab]

Could I use this function in conjunction with a tallarray? basically populate the tall array in batches using a function (or embed it within a for loop)

[James Tursa]

That (or similar) strategy is just an attempt to solve the memory issue, and it doesn't really solve it since you are still talking about 7 petabytes (either in memory or on disk). And it doesn't address the processing time aspect at all. Maybe you can start a new Question thread that states your problem, and people can suggest ways to approximate a solution that will fit in the memory you have and run in a reasonable amount of time.

Answer 2

[Sid Parida]

Not sure of internal tools but use the two files attached above (found on File Central) and use the following code:

a = [1 2 3 4]
b = [1]
c = [10 20]
D = prod(cartprod(a, b, c), 2)'

D should contain the desired result. It works for higher number of vectors too.

[Still Learning Matlab]

This worked okay, unless the input vector has a duplicate element (i.e. if you change a = [1 2 3 1] it throws an error).