Vectorizing a multivariate function

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Proman 2021-8-27

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评论： Proman 2021-8-28

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.

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Answer 1

Chunru 2021-8-28

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在 MATLAB Online 中打开

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

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Chunru 2021-8-28

在 MATLAB Online 中打开

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