Matrix Dimensions not agreeing

Hi

I am working with the following:

phi = @(ep,r1) exp(-(ep*r1).^2); 
ep = 1;
r1=0.1;  

S=linspace(0,1);
  t=linspace(0,1);

    % Randomly Select 10 points from each of S and t.

    S_rand = S(sort(randperm(numel(S), 10)));
    t_rand = t(sort(randperm(numel(t), 10)));

    [S_,t_]=meshgrid(S_rand,t_rand);
    X=[S_(:) t_(:)];
    D=phi(ep, distm(X,X));
    U=bsf(S_,t_,1,1,0.25,0.05);
    c=D\U;

I need D to be a 10 x 10 matrix (like U) and not a 100 x 100 matrix as this code is generating. I can't seem to see why this is happening. Any ideas?

Many thanks

Joe

Answer 1

[Star Strider]

Two ideas:

First, it’s best to always completely vectorise your functions unless you intend matrix operations:

phi = @(ep,r1) exp(-(ep.*r1).^2);

Second, we don’t have ‘distm’. I would break it out into its own variable for troubleshooting purposes to be certain it is not creating your (100x100) matrix:

X=[S_(:) t_(:)];
Q1 = distm(X,X)                 % See What ‘distm’ Returns
D=phi(ep, distm(X,X));

[Joe Bannen]

Hi

Thanks for your response. I have split off the variable as you suggest and vectorised the phi function.

In terms of:

   X=[S_(:) t_(:)];
   D=phi(ep, distm(X,X));

Is this not taking my new values of S_ and t_ as rows and columns so that the first point is (0th,0th) etc.? Where is the 100*100 coming from?

Sorry if I am not seeing your point!

Thanks again

Joe

[Star Strider]

My pleasure.

I am hypothesising that your ‘distm’ function (that we still have not seen) is creating the (100x100) matrix. That is the reason you need to insert the ‘Q1’ assignment between those lines:

X=[S_(:) t_(:)];
Q1 = distm(X,X)                 % See What ‘distm’ Returns
D=phi(ep, distm(X,X));

to see what ‘distm’ is returning.

[Joe Bannen]

Hi

Oops! Here it is:

function D=distm(X,Y)

    % distm is the distance matrix
    % distm(X,Y) is the matrix of the pairwise Euclidean distance
    % between the points in the rows of X and Y

    [M,s]=size(X);
    [N,s]=size(Y);
    D=repmat(sum(X.*X,2),1,N)-2*X*Y'+repmat((sum(Y.*Y,2))',M,1);
    D=sqrt(D);

Cheers

Joe

[Star Strider]

Having the ‘distm’ code solved the problem (and absolved it of blame, since it is doing exactly what you asked it to do). The problem is here:

X=[S_(:) t_(:)];

Your ‘X’ is now a (100x2) matrix, and since ‘distm’ creates pairwise distances between the rows of the argument matrices, the size of the output matrix will be (NrowsX x NrowsY), giving you the (100x100) matrix.

Consider using ‘S_rand’ and ‘t_rand’ to create ‘X’ instead, if that fits the logic of your code.

[Joe Bannen]

Thanks, that is absolutely fantastic. This is such a great place to learn more about this awesome computer program!

Cheers

Joe

[Star Strider]

As always, my pleasure! I appreciate your compliment.

It definitely is! MATLAB Answers is where I learned a lot about MATLAB, both by reading other Answers and by helping to solve problems I would never have encountered otherwise.