Sum of Multiplication of column values in cell array

hey i have a cell array x

    x{1,1}= {[ *3*,1,6.9,3.6,4,2.3,3,5,4.12],[ *3*,1,4,3,4,2,3.4,5,4],[ *3*,1.9,4,9.21,4,2.2,3,5,4.2],[ *2*,1.8,3.8,2,4,2.1,4,5,4.1]}
    x{2,1}= {[1,1,5,3.6,4,2.3,3,2,4.12],[3,4,4,3,4,2,8,5,4],[1,5,4,7,4,2.9,3,5,4.2],[3,1.9,4.8,2,4,2.1,5,5,6]}

and similarly other elements x{3,1} x{4,1} etc. And other array y:

       y= {[1,2,1.2,0.2];[0.32,0.42,0.4,0.07]}

I want to take each col value one by one and multiply it with the corresponding value in y and then add them all. Like this:

    (3*1) + (3*2) + (3*1.2) + (2*0.2)   [3,3,3,2 are bold values in x{1,1}]

and similarly take 2nd col of each element of x{1,1} and multiply it with corresponding values of y{1,1} and add them. When it comes to x{2,1}, it will be multiplied with y{2,1}.

Please suggest any efficient way of doing this without using multiple loops. Thank You.

[Tha saliem]

(*3*) means bold text (i think its code box so it didn't worked )

Answer 1

[Jan]

It is much easier to work with multi-dimensional arrays instead of nested cells. The cell arrays require loops for numerical operations, such that they are a bad choice, if you want to avoid loops. But you can convert the data:

Result = cell(size(x));
for k = 1:numel(x)
  Result{k} = y{k} * cat(1, x{k}{:});
end

The actual calculation is a simple matrix multiplication.

[Tha saliem]

Ok I got it. Thank You for helping.

Answer 2

[Birdman]

Additional approach to Jan's answer(I tried to eliminate the loop)

a=cell2mat(x{1,1}.');
b=cell2mat(y);

Then the rest is just a matrix calculation, as Jan said.

For instance, what you asked in the question is calculated as:

b(1,:)*a(:,1)

Hope this helps.

[Tha saliem]

A good approach. Thank You @Birdman.

[Jan]

@Birdman: Exactly. +1. If the intermediate arrays are not huge, this is the most efficient approach.

Answer 3

[Guillaume]

What is the reason for the cells of x to be themselves cell arrays? Due to your multiplication requirements each vector in these subcells must be the same length. Therefore they'd be better stored as a 2D matrix instead, i.e.:

x{1, 1} = [3,1,6.9,3.6,4,2.3,3,5,4.12;
           3,1,4,3,4,2,3.4,5,4;
           3,1.9,4,9.21,4,2.2,3,5,4.2;
           2,1.8,3.8,2,4,2.1,4,5,4.1];
x{2,1}= [1,1,5,3.6,4,2.3,3,2,4.12;
         3,4,4,3,4,2,8,5,4; 
         1,5,4,7,4,2.9,3,5,4.2;
         3,1.9,4.8,2,4,2.1,5,5,6];

You can transform your current x in the above x with

x = cellfun(@(c) vertcat(c{:}), x, 'UniformOuput', false);

With that storage, then your problem becomes a simple matrix multiplication of y cells with the x cells, which can be achieved with a single cellfun

result = cellfun(@mtimes, y, x, 'UniformOutput', false);

[Tha saliem]

Thank You for your time @Guillaume.