problem doing implicit plotting

Hi, I am trying to make an implicit 3D plot in Matlab. A Matlab Help page says to use the following (as an example):

f = @(x,y,z) x.^2 + y.^2 - z.^2;
interval = [-5 5 -5 5 0 5];
fimplicit3(f,interval)

This works fine. But if I try to complicate things a bit by changing f to:

f = @(x,y,z) x.^2 + y.^2 - z.^2 + x.*y.

then I get the error message "Error: Invalid expression. Check for missing or extra characters".

Any idea what the problem is?

Thank you!

Answer 1

[Torsten]

Remove the dot at the end of the expression x.*y.

[Chris]

Thank you, Torsten, that worked! But I don't understand why the period needs to be removed because in all other reference to the variables, the period is used.

C

[Walter Roberson]

x.^2

does not mean "a reference to variable x, squared", (x.)^2 .

It means "the content of x, element-wise-power, 2"

The .^ part is a single operator, element-wise-power and it is different than the ^ operator, which is "matrix power" .

x^2

is x*x which is x matrix-multiply x.

x.^2

is element-by-element squaring of x

[Chris]

Yes, I agree that "x." means element-wise. But it sounds like you are suggesting I use:

f = @(x,y,z) x.^2 + y.^2 + x.*y (last period removed)

So my question is why do we use "." everywhere but for y in the last term "x.y"?

But maybe I am misunderstanding what you are suggesting.

Thanks again!

C

[Sam Chak]

So my question is why do we use "." everywhere but for y in the last term "x.y"?

I guess you were under the impression (learn by example) that the dots in the 1st example are all placed after the variables x, y, z.

For the 2nd example

perhaps writing as follows is clearer for you to follow:

f = @(x,y,z) (x).^2 + (y).^2 - (z).^2 + (x).*(y);

The two-character symbols ".^" (dot-power) and ".*" (dot-product) are math operators in MATLAB.

[Sam Chak]

@Chris, you can see the effect of the dot in this example and comparison.

x   = [1 2; 
       3 4];

% Case 1: element-wise product
y   = x.^2

y = 2x2

1 4 9 16

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% Case 2a: 2x2 matrix multiplication
y   = x^2 

y = 2x2

7 10 15 22

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% Case 2b: 2x2 matrix multiplication
y   = [x(1)*x(1) + x(2)*x(3), x(3)*x(1) + x(4)*x(3) 
       x(1)*x(2) + x(2)*x(4), x(3)*x(2) + x(4)*x(4)]

y = 2x2

7 10 15 22

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[Chris]

Ahhh, I see. Thank you!

C