Scalar-Vector multiplication with meshgrid (Matlab)

1
votes

I have an expression such as s=aU+bV, where a and b are scalars and U and V 3-component vectors. The output s is clearly a 3-component vector. Let's assume I want to plot the first component of s find out how this varies when I change a and b.

In order to plot I have to use surf, which takes matrices for the variables a b. So I attempt to create matrices with meshgrid:

A=0:10;
B=1:10;
[a,b]=meshgrid(A,B);

U=[1,1,0];
V=[1,0,1];

s = a*U + b*V;

This clearly doesn't work, because nor the matrix product nor the element-wise product are well defined in this case. How do I actually make the matrices which represent the grid a b multiply element-by-element the vectors U and V?

2
matlabvectorizationlinear-algebra
But if you only want to examine the first component of s, all you need to do is use the first component of U and V. Why complicate things? - Cris Luengo
@CrisLuengo I would imagine that they're just using that as an example, and will want to examine all of the components separately. - MrAzzaman
@MrAzzaman That's right! - usumdelphini

2 Answers

3
votes

You want to use element-wise multiplication (.*) because you still want to treat a and b as scalars (i.e. use each element individually).

You can make a 3D output, where each 2D slice corresponds to your meshgrid output, with one slice per component of U and V. Therefore in this example getting a 10*11*3 matrix.

To do this, just reshape the U and V vectors to be 1*1*3 in size

U = reshape( [1,1,0], 1, 1, [] ); % Or equivalently U(1,1,:) = [1,1,0]
V = reshape( [1,0,1], 1, 1, [] ); % Or equivalently U(1,1,:) = [1,0,1]

Then do element-wise multiplication

s = a.*U + b.*V;

Note: before MATLAB R2016b (when implicit expansion was introduced) you'll have to use bsxfun to get the equivalent:

s = bsxfun( @times, a, U ) + bsxfun( @times, b, V );

You can then plot the ith element of S changing with A and B by plotting s(:,:,i).

1
votes

You could do it using a 3D matrix:

[A,B] = meshgrid(0:10,1:10);
U(1,1,:) = [1,1,0];
V(1,1,:) = [1,0,1];
s = A.*U + B.*V;
% s is now a NxMx3 matrix, where N = length(A) and M = length(B)

% We can plot how s varies with a and b as follows
surf(A,B,s(:,:,1)); % first component
surf(A,B,s(:,:,2)); % second component
surf(A,B,s(:,:,3)); % third component