How can I create a matrix with the values of the elements is a function of the indices?

I am trying to create a matrix from two vectors (i.e. A = [0:2] and B = [-2:2]) where the values for each cell of the matrix is a function of the indices. I cannot see the path to get it there, any simple examples I can follow?

Thanks

[Stephen23]

The indices of the elements of vectors A and B are:

Ai = 1:numel(A)
Bi = 1:numel(B)

Is that what you want?

[Image Analyst]

What is the function? Like the sum of the squares of A and B or something? Are you aware that your A and B don't have the same number of elements so you can't do a 1-to-1 correspondence between elements?

[Benjamin Schuessler]

Hi All,

Apologies for being convoluted. Let me try to explain more.

With the vectors I gave I know it won't give an nxn matrix.

This is the matrix I get:

C =

     0     0     0     0     0
     1     1     1     1     1
     2     2     2     2     2

However, I would like to see something like

C =

     0,-2     0,-1     0,0     0,1     0,2
     1,-2     1,-1     1,0     1,1     1,2
     2,-2     2,-1     2,0     2,1     2,2

Where the values inside each element will then become inputs to a function which output the function's result in the same size matrix shown above.

I hope this can shed more light!

Thanks!

*EDIT I should say that I used C = ndgrid(A,B) to create that matrix.

Answer 1

[Cedric]

Not sure that I understand. If you wanted to create a rectangular array whose elements are a the result of some arithmetic operation between corresponding elements of A and B, you could use the fact that MATLAB expands automatically operands of such operations (from 2016b on, otherwise you have to use BSXFUN):

 >> A = 0 : 2  ;  B = -2 : 2 ;
 >> A.' .* B
 ans =
     0     0     0     0     0
    -2    -1     0     1     2
    -4    -2     0     2     4

Note that here we first make A a 3x1 column vector by transposition. Then we apply an element-wise operation ( .* ) between this transpose and B that is 1x5, and MATLAB expands automatically A.' along B and vice versa (hence building 3x5 arrays) and performs the operation.

If you needed to apply a function that is not an arithmetic operation, you could do it using BSXFUN (performing an explicit call to a function that does an implicit expansion..):

 >> result = bsxfun( @plus, A.', B )
 result =
    -2    -1     0     1     2
    -1     0     1     2     3
     0     1     2     3     4

or through an explicit expansion (using REPMAT, REPELEM, or MESHGRID):

 >> [Bx, Ax] = meshgrid( B, A )
 Bx =
    -2    -1     0     1     2
    -2    -1     0     1     2
    -2    -1     0     1     2

 Ax =
     0     0     0     0     0
     1     1     1     1     1
     2     2     2     2     2

applying whatever function to the two arrays:

 >> plus( Ax, Bx )
 ans =
    -2    -1     0     1     2
    -1     0     1     2     3
     0     1     2     3     4

[Benjamin Schuessler]

MY MAN! After reading through your answer, this is exactly what I need. Unfortunately I don't have the convenience of using R2016a however BSXFUN should work just fine!

Much appreciated!

[Cedric]

Great, well the first input of BSXFUN is a function handle so you have a lot of flexibility here; you can even adapt the interface using an anonymous function.