Cross Product of an Array

I have an array of size 3 x 100 and I basically want to create a new array where I take each column vector in the array and compute the cross product with the same vector each time to create another array of size 3 x 100, so in this case I take every vector and form the cross product with [0 0 1]'. What would be the easiest way of doing this?

Answer 1

[James Tursa]

M = your 3xN matrix
v = your 3x1 vector
result = cross(M,repmat(v,1,size(M,2)));

[Hollis Williams]

OK, thanks. Also I realise I have made a mistake elsewhere in the code. Say you have that that array of N column vectors in the 3 x 100 array and you want to normalise each vector in the array, so I just want to take each 3 x 1 vector and then divide it by its norm, how would I best do that?

[James Tursa]

result = M./sqrt(sum(M.*M));

Or, for older versions of MATLAB:

result = bsxfun(@rdivide,M,sqrt(sum(M.*M)));

[Hollis Williams]

Your command for cross product does not seem to work, as it seems like the two inputs for the cross product are not the same size: if M is 3x100, say, repmat(v,1,size(M,2)) is of size 3x300.

[James Tursa]

My code specifically calls out for v to be a 3x1 column vector. If your vector is a 1x3 row vector, then simply transpose it to be a column vector. Or use the colon operator to force it to a column vector in either case:

result = cross(M,repmat(v(:),1,size(M,2)));

If v is some other size, you will have to tell us what you are really working with.

[Hollis Williams]

If I try taking the transpose, I seem to get something which is of size 1 x 900 when I run repmat(v,1,size(M,2)).

[James Tursa]

What is size(v) and size(M)?

[Hollis Williams]

size(M)=3 x 100

size(v)=3x1

[James Tursa]

This is what I get:

>> M = rand(3,100);
>> v = rand(3,1);
>> size(repmat(v,1,size(M,2)))
ans =
     3   100

I have no idea why you would be getting a 3x300 result. Did you actually run the size(M) and size(v) commands at the MATLAB prompt, or are you just reporting to me what you think they are? Actually type this in and see what you get

size(M)
size(v)

[Hollis Williams]

Yes, I was using the size() command but made a typo, it is working now. I have created three 1 x 100 arrays, is it possible to put these together into one 3 x 100 array? So if A,B,C are all 1 x 100 arrays, I would need

A

B

C

[James Tursa]

result = [A;B;C];

Answer 2

[Matt J]

This way avoids repmatting, which may be desirable when N is large.

M = your 3xN matrix
v = your 3x1 vector

result=xprodmat(v)*M./vecnorm(M);

where

function A=xprodmat(a)
%Matrix representation of a cross product
%
%  A=xprodmat(a)
%
%in:
%
% a: 3D vector
%
%out:
%
% A: a matrix such that A*b=cross(a,b)



if length(a)<3, error 'Input must be a vector of length 3'; end

ax=a(1);
ay=a(2);
az=a(3);

A=zeros(3);

A(2,1)=az;  A(1,2)=-az;
A(3,1)=-ay; A(1,3)=ay;
A(3,2)=ax;  A(2,3)=-ax;

end

[Hollis Williams]

I don't think repmatting is the thing which is most computationally costly in my code but I will bear this in mind to see if I need to save time later on, thanks a lot.