Is there a function that returns a vector or array or list of values obtained by applying a function to margins of an array or matrix?

For example, assume x is a vector of length n, and y is a vector of length m. I would like to construct the matrix the (n x m) matrix M(i,j) = f(x(i),y(j)). Of course I do not want to use loops!

Btw, in R, there is such a function (called apply).

Answer 1

[Image Analyst]

Use meshgrid()

[X, Y] = meshgrid(x,y);
M = f(X, Y);

You might need to use reshape() after that to make M be 2D

M = reshape(M, m, n);

[Bruno Remillard]

Thank you very much. However, to get exactly what I wanted, you need to the transpose!

[James Tursa]

To avoid the transpose, simply reverse the initial indexing. E.g.,

[Y, X] = meshgrid(y,x);

[Image Analyst]

You need to be careful. meshgrid() works on x and y, while other functions, like reshape() work on rows and columns. Note, you used x and y and said x had n columns and y had m rows. However you said that M was nxm, meaning n rows and m columns, which is the reverse. So you either made the very common mistake of thinking (rows,columns) was the same as (x,y) or you intentionally thought that your "f" function would do a transpose. Either way, you just have to be careful.

Answer 2

[James Tursa]

A bit clunky, but this works and makes no assumptions about f being vectorized:

n = numel(x);
m = numel(y);
M = arrayfun(@f,repmat(x(:),1,m),repmat(y(:)',n,1));

[Bruno Remillard]

Also works! Thank you.

Answer 3

[John D'Errico]

I'm surprised nobody mentioned this.

fun = @(x,y) sin(x+y);
x = 0:5;
y = (0:2:6)';
M = bsxfun(fun,x,y)
M =
      0  0.84147   0.9093   0.14112 -0.7568  -0.95892
 0.9093  0.14112  -0.7568  -0.95892 -0.27942  0.65699
-0.7568 -0.95892  -0.27942  0.65699  0.98936  0.41212
-0.27942 0.65699   0.98936  0.41212 -0.54402 -0.99999

[James Tursa]

Good as long as fun works with column vector inputs.

[John D'Errico]

Easy enough to ensure that X and Y are always the proper shapes.

M = bsxfun(fun,x(:).',y(:));

[James Tursa]

I guess I wasn't clear. bsxfun passes column vectors to the function, so whatever the function is, it must be able to deal with column vector inputs (i.e., it must be vectorized to this extent). That was the only point I was trying to make. It is similar to the f(X,Y) used in IA's solution ... f must be vectorized for this to work.