Vectorizing a multivariate function

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Proman
Proman on 27 Aug 2021
Commented: Proman on 28 Aug 2021
Hello everyone
I have a problem to define a bivariate function using vectorization. I want to plot the function z = x1^2 + x2^2 which is a paraboloid.
I define x as:
x = [x1;x2];
z = x.' * x;
which means that z = x1^2 + x2^2 but it gives me the wrong answer. for example, for
x1 = linspace(-1,1,10);
x2 = linspace(-2,2,10);
when I define z = x.' * x the answer is wrong (however the size of z is correct and 10*10) but when I say
[X1,X2] = meshgrid(x1,x2)
z = X1.^2 + X2.^2
the answer is correct
I do not fully understand where I go wrong. I will appreciate your kindness in advance for helping me.

Accepted Answer

Chunru
Chunru on 28 Aug 2021
Define ,
x = [x1;x2];
The x here is a matrix of 2 by n:
z = x.' * x;
Here z is matrix multiplication of (x.') and x.
The result z is an nxn matrix. But it does not mean that z = x1^2 + x2^2.
When you define x1 and x2 as follows:
[X1,X2] = meshgrid(x1,x2)
,
z = X1.^2 + X2.^2
Then X1.^2 is the element-by-element square, so that
  3 Comments
Chunru
Chunru on 28 Aug 2021
Yes. It's possible use automatic array expansion.
x = (1:5); % row vector
y = (0:10:60)'; % column vector
z = x.^2 + y.^2 % vectors expanded to compatible matrices
z = 7×5
1 4 9 16 25 101 104 109 116 125 401 404 409 416 425 901 904 909 916 925 1601 1604 1609 1616 1625 2501 2504 2509 2516 2525 3601 3604 3609 3616 3625

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