How can I make the entries of a matrix be a square root of the sum of their column number squared and row number squared ?

Hello everyone, My question is: can I create a matrix of which entries are the square roots of the sum of its x and y position coordinates ( column number and row number respectively ) squared ? For example, for 3x3 matrix, it would look like: X = [ sqrt(2) sqrt(5) sqrt(10) ; sqrt(5) sqrt(8) ... ]. Is there a way of getting it in an automated way ? Thank you.

Answer 1

[Stephen23]

Method one: ndgrid:

>> Rn = 4;
>> Cn = 3;
>> [Rv,Cv] = ndgrid(1:Rn,1:Cn);
>> sqrt(Rv.^2+Cv.^2)
ans =
   1.4142   2.2361   3.1623
   2.2361   2.8284   3.6056
   3.1623   3.6056   4.2426
   4.1231   4.4721   5.0000

Method two: bsxfun:

>> fun = @(r,c)sqrt(r.^2+c.^2);
>> bsxfun(fun,(1:Rn)',1:Cn)
ans =
   1.4142   2.2361   3.1623
   2.2361   2.8284   3.6056
   3.1623   3.6056   4.2426
   4.1231   4.4721   5.0000

Method three: implicit expansion:

>> sqrt((1:Rn).'.^2 + (1:Cn).^2)
ans =
   1.4142   2.2361   3.1623
   2.2361   2.8284   3.6056
   3.1623   3.6056   4.2426
   4.1231   4.4721   5.0000

[Damian Wierzbicki]

Works perfectly ( as you know ; ) ) , thank you so much for your help !