Vectorizing a multivariate function

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.

Answer 1

[Chunru]

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

[Proman]

Thank you for your kind reply.

You are absolutely correct.

But I want to see if it is possible to define the function in matrix form (rather than the meshgrid form)?

[Chunru]

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

[Proman]

Many thanks