How can I multiply a vector (n*1) by each row of a matrix (m*v) to generate m (n*v) matrices?

So in my simulation I have a matrix K (1000*72) = 1000 simulations of k And a vector B (100*1).

I need 1000 matrices of Bk

I've turned to MATLAB on the advice of an engineer...

Being completely new to MATLAB (and a coding rookie) I haven't much of a clue where to start...

Please can someone break this down nice and simply for me so I can crack on with the rest of my research?!

Answer 1

[Matt Fig]

If your matrix is 1000-by-72, you cannot multiply this by a 100-by-1. None of the dimensions match up. Each row of your matrix is 1-by-72, so how do you propose to multiply this by a 100-by-1?

The only way I can see that you mean would be something like this:

M = round(rand(5,3)*10)
z = round(rand(4,1)*10)
T = cell(size(M,1),1);
for ii = 1:size(M,1)
   T{ii} = z*M(ii,:);
end

Now look at T{1}, T{2}, etc. I this what you mean?

[John]

B = (100*1)

Each row is (1*72),

Thus BK is (100*1)*(1*72) so it should... sorry i should have clarified, i want B multiplied by each row of the big matrix...

[Matt Fig]

The above is just an example for you to see if it is doing what you want by looking at the results and initial inputs. From what you are describing,

K = round(rand(1000,72)*10);
z = round(rand(100,1)*10);
T = cell(size(K,1),1);
for ii = 1:size(K,1)
   T{ii} = z*K(ii,:);
end

length(T)  % should be 1000 cells
size(T{1})  % each matrix in each cell should be 100-by-72

[John]

Yes, this is along the lines of what I need. Basically, the output I need to proceed is the 1000 matrices which are 110-by-72.

I need these as new variables, ideally named something like BK0001-BK1000,

[Sean de Wolski]

Don't do it

[John]

OK, can someone then please explain the easiest way for me to get these 1000 matrices, and in some form so that I can perform further matrix manipulations on them? Apologies for my being a NOOB. :)

[Sean de Wolski]

Sure, always willing to help a noob! Since all of the matrices are the same size stack them along the third dimension. That way you can refer to them by slice.

M = rand(110,72,1000); %random 3d matrix

Now you can reference the 462nd matrix with

M(:,:,462)

etc. How you get it into this form will depend on how its structured right now.

[Matt Fig]

You have the 1000 matrices stored very efficiently in a cell array. If you need to use them further, simply use them like you would any other matrix. For example:

M = magic(3)
J = [2;3;4]
Result = M*J

But now look what happens if the matrix is stored in a cell array instead:

G = {magic(3)} % Store in cell array G.
Result2 = G{1}*J  % You can loop, like G{ii}*J if G has many cells
isequal(Result,Result2)  % Same-same

It might help if you read up on cell arrays in MATLAB. They are very useful for doing just what you need to do! I use them all the time for my job to hold large data sets, for example.

doc cell

[John]

Thanks guys, your help is much appreciated. I'll have a bash with this and see how i get on!