Matlab matrices dimension - matlab

Question

I am new to matlab and just wondering if you guys can help me out with this problem.
For instance, I have two matrices:
A = [X1 X2 X3 X4]
B = [Y1; Y2; Y3]
now what I really want to achieve is to multiply these two matrices in this way:
[X1Y1 X2Y1 X3Y1 X4Y1;
X1Y2 X2Y2 X3Y2 X4Y2;
X1Y3 X2Y3 X3Y3 X4Y3;
.... and so on]
I tried using A(1,:).*B(:,1) but matlab is saying that matrix dimensions must agree.
I just don't know how to manipulate this on matlab but in excel is possible.

Answer 1

This is a simple outer product. kron is not needed (although it will work.) bsxfun is wild overkill, although will yield what you have asked for. repmat is inappropriate, because while it will help you do what you wish, it replicates the arrays in memory, using more resources than are needed. (Avoid using inefficient programming styles when there are good ones immediately at your disposal.)
All you need use is the simple * operator.
A is a row vector. B a column vector.
C = B*A
will yield the result C(i,j)=B(i)*A(j), which is exactly what you are looking for. Note that this works because B is 3x1 and A is 1x4, so the "inner" dimensions of B and A do conform.
In MATLAB, IF you are unsure if something works, TRY IT!
A = [1 2 3 4];
B = [1;2;3];
C = B*A
ans =
1 2 3 4
2 4 6 8
3 6 9 12
See that kron did indeed work, although I'd bet that use of kron here is probably less efficient than is the simple outer product multiply.
C = kron(B,A)
C =
1 2 3 4
2 4 6 8
3 6 9 12
As well, bsxfun will work here too, although since we are using a general tool to do something that a basic operator will do, I'd bet it is slightly less efficient.
C = bsxfun(#times,B,A)
C =
1 2 3 4
2 4 6 8
3 6 9 12
The WORST choice is repmat. Again, since it artificially replicates the vectors in memory FIRST, it must go out and grab big chunks of memory in the case of large vectors.
C = repmat(B,1,4).*repmat(A,3,1)
C =
1 2 3 4
2 4 6 8
3 6 9 12
I suppose for completeness, you could also have used meshgrid or ndgrid. See that it is doing exactly what repmat did, but here it explicitly creates new matrices. Again, this is a poor programming style when there are good tools to do exactly what you wish.
[BB,AA] = ndgrid(B,A)
BB =
1 1 1 1
2 2 2 2
3 3 3 3
AA =
1 2 3 4
1 2 3 4
1 2 3 4
C = BB.*AA
C =
1 2 3 4
2 4 6 8
3 6 9 12
What you need to understand is exactly why each of these tools COULD have been used for the job, and why they are different.

Answer 2

In Matlab there is * and .* and they are very different.
* is normal matrix multiplication which is what you want i.e. B*A, note the B must come first as the inner dimension must match. You can multiply a column by a row but not a row by a column (unless they have the same number of elements).
.* is element by element multiplication in which case the matrices must be exactly the same size and shape so for example [1 2 3].*[4 5 6] = [1*4 2*5 3*6] = [4 10 18]

Answer 3

Do not do a ".*". You should rather do a "*".
The ".*" is for index by index multiplication and should have given you [X1Y1 X2Y2 X3Y3] were they vectors have been equal in size.
If you do the regular multiplication "*", this is actually matrix multiplication.

Answer 4

I think you just need to transpose one of the vectors. You are multiplying a column vector (A(1,:)) with a row vector (B(:,1)). This should work:
C = A(1,:).*B(:,1)';