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

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Benjamin Schuessler on 6 Jan 2018
Commented: Cedric Wannaz on 6 Jan 2018
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
##### 3 CommentsShowHide 2 older comments
Benjamin Schuessler on 6 Jan 2018
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.

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### Accepted Answer

Cedric Wannaz on 6 Jan 2018
Edited: Cedric Wannaz on 6 Jan 2018
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
##### 2 CommentsShowHide 1 older comment
Cedric Wannaz on 6 Jan 2018
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.

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