How to multiply each row of a matrix with a second full matrix, while applying a formula

I want to multiply each row of 'a' into 'b' while applying a formula for each row of b, thus creating a new martix of size 8,4. Here is my code that's not working.

a=[3 4 5 1; 3 2 0 4]

 b=[1 2 3 4;
   2 0 2 4;
   0 4 8 2;
   2 1 0 4]

 w=1
 for s= 1:size(a,1)
    for t= 1:size(b,1)
        %updated formula%
        new(w,:)= (3*a(1,1)+b(1,1)) + (5*a(1,2)+b(1,2)) +(a(1,3)+b(1,3)) + (5*a(1,4)+b(1,4)) %a formula

 end
    w=w+size(b,1)
 end

[KSSV]

What is the formula? How you are expecting a 8X4 matrix?

Answer 1

[KSSV]

a=[3 4 5 1; 3 2 0 4] ;
b=[1 2 3 4;
    2 0 2 4;
    0 4 8 2;
    2 1 0 4] ;
M = [3 5 1 5] ;
iwant = cell(size(a,1),1) ;
for i = 1:size(a,1)
    iwant{i} = M.*a(i,:)+b ;
end
iwant = cell2mat(iwant)

[klb]

Thanks. I need it such so that the the code accomodates matrices a and b or any number of rows.

[KSSV]

The above does it...it is what you wanted?

[klb]

First, You have the formula as I intended it to be, with the "," not with the" + "as I have, which results in 8X4. Thanks ! Well the last line combining the matrices limits to 2 iterations. I was looking for a way to combine regardless of the number of rows for a and b .

[KSSV]

Okay....thanks is accepting the answer.

[klb]

:) the last bit..it limits to 2 iterations. I was looking for the code to calculate for any number of rows for a and b .. say, even a 10,000X5 for a and a 60X5 for b. can I get some help with that?

[KSSV]

Edited the answer.

[klb]

thank you!

Answer 2

[Stephen23]

In just one line, works for any number of rows of a and b:

>> a = [3,4,5,1;3,2,0,4];
>> b = [1,2,3,4;2,0,2,4;0,4,8,2;2,1,0,4];
>> M = [3,5,1,5];
>> reshape(b.'+permute(M.*a,[2,3,1]),numel(M),[]).'
ans =
   10   22    8    9
   11   20    7    9
    9   24   13    7
   11   21    5    9
   10   12    3   24
   11   10    2   24
    9   14    8   22
   11   11    0   24

For MATLAB versions prior to R2016b you will need to use bsxfun for the + and the .* operations.

[klb]

Hello Stephen. could you put this statement in spoken English. I mean, how do I read this? : reshape(b.'+permute(M.*a,[2,3,1]),numel(M),[]).'

[Stephen23]

"I mean, how do I read this?"

Break it down into its constituent parts, read the relevant documentation for those operators, and try some of their examples. It will help to print the intermediate arrays to see what values and shapes they have. You use the documentation and the examples to learn what those operators are doing, and why I combined them like that.

>> a = [3,4,5,1;3,2,0,4];
>> b = [1,2,3,4;2,0,2,4;0,4,8,2;2,1,0,4];
>> M = [3,5,1,5];
>> M.*a                  % M times a (note the scalar dimension expansion)
ans =
    9   20    5    5
    9   10    0   20
>> permute(M.*a,[2,3,1]) % rearrange dimensions [1,2,3] -> [2,3,1]
ans(:,:,1) =
    9
   20
    5
    5
ans(:,:,2) =
    9
   10
    0
   20
>> b.'                      % transpose b
ans =
   1   2   0   2
   2   0   4   1
   3   2   8   0
   4   4   2   4
>> b.'+permute(M.*a,[2,3,1]) % add (note the scalar dimension expansion)
ans(:,:,1) =
   10   11    9   11
   22   20   24   21
    8    7   13    5
    9    9    7    9
ans(:,:,2) =
   10   11    9   11
   12   10   14   11
    3    2    8    0
   24   24   22   24
>> reshape(b.'+permute(M.*a,[2,3,1]),numel(M),[]) % reshape
ans =
   10   11    9   11   10   11    9   11
   22   20   24   21   12   10   14   11
    8    7   13    5    3    2    8    0
    9    9    7    9   24   24   22   24
>> reshape(b.'+permute(M.*a,[2,3,1]),numel(M),[]).' % transpose
ans =
   10   22    8    9
   11   20    7    9
    9   24   13    7
   11   21    5    9
   10   12    3   24
   11   10    2   24
    9   14    8   22
   11   11    0   24

The documentation explains permute, reshape, times, and transpose. Try their examples to learn more about them.

Two important things to remember:

• MATLAB works columnwise, which is why I had to transpose b and the final matrix.
• For MATLAB versions R2016b+ many operators expand scalar dimensions to match the other input arguments (earlier versions will need to use bsxfun). Learn more:

https://www.mathworks.com/help/matlab/matlab_prog/compatible-array-sizes-for-basic-operations.html

https://blogs.mathworks.com/loren/2016/10/24/matlab-arithmetic-expands-in-r2016b/

[klb]

I did indeed run your code without the ; to echo the output. and then break into individual steps. The b.'+ is new syntax and I couldnt work out the logic on that. Thank you for the explantion.