How to remove a single point from meshgrid?

I have written this code and want to model the temperature profile. I want to exclude (0,0) from the meshgrid as the function becomes infinite there. How can I do that?

x = linspace(-3,10);
y = linspace(-3,0);
zero_x_idx = find(x == 0);
zero_y_idx = find(y == 0);
% Exclude the point (0, 0) from the arrays
x = x([1:zero_x_idx-1, zero_x_idx+1:end]);
y = y([1:zero_y_idx-1, zero_y_idx+1:end]);
[X,Y] = meshgrid(x,y);
Z=(P_l*exp(-v(sqrt((X.*10^(-3)).^2 + (Y.*10^(-3)).^2) + (X.*10^(-3)))/(2*a)))/(4*3.14*k*sqrt((X.*10^(-3)).^2 + (Y.*10^(-3)).^2))+T0;

[Matt J]

Exclude it for what purpose? If you're just plotting, it doesn't matter if you leave it in there.

Answer 1

[Star Strider]

I would use ‘logical indexing’ to simply delete that point —

x = linspace(-3,10)

x = 1×100

-3.0000 -2.8687 -2.7374 -2.6061 -2.4747 -2.3434 -2.2121 -2.0808 -1.9495 -1.8182 -1.6869 -1.5556 -1.4242 -1.2929 -1.1616 -1.0303 -0.8990 -0.7677 -0.6364 -0.5051 -0.3737 -0.2424 -0.1111 0.0202 0.1515 0.2828 0.4141 0.5455 0.6768 0.8081

y = linspace(-3,0)

y = 1×100

-3.0000 -2.9697 -2.9394 -2.9091 -2.8788 -2.8485 -2.8182 -2.7879 -2.7576 -2.7273 -2.6970 -2.6667 -2.6364 -2.6061 -2.5758 -2.5455 -2.5152 -2.4848 -2.4545 -2.4242 -2.3939 -2.3636 -2.3333 -2.3030 -2.2727 -2.2424 -2.2121 -2.1818 -2.1515 -2.1212

x = x(x~=0)

x = 1×100

-3.0000 -2.8687 -2.7374 -2.6061 -2.4747 -2.3434 -2.2121 -2.0808 -1.9495 -1.8182 -1.6869 -1.5556 -1.4242 -1.2929 -1.1616 -1.0303 -0.8990 -0.7677 -0.6364 -0.5051 -0.3737 -0.2424 -0.1111 0.0202 0.1515 0.2828 0.4141 0.5455 0.6768 0.8081

y = y(y~=0)

y = 1×99

-3.0000 -2.9697 -2.9394 -2.9091 -2.8788 -2.8485 -2.8182 -2.7879 -2.7576 -2.7273 -2.6970 -2.6667 -2.6364 -2.6061 -2.5758 -2.5455 -2.5152 -2.4848 -2.4545 -2.4242 -2.3939 -2.3636 -2.3333 -2.3030 -2.2727 -2.2424 -2.2121 -2.1818 -2.1515 -2.1212

Another option would be to replace it with something small, however not zero —

x = linspace(-3,10)

x = 1×100

-3.0000 -2.8687 -2.7374 -2.6061 -2.4747 -2.3434 -2.2121 -2.0808 -1.9495 -1.8182 -1.6869 -1.5556 -1.4242 -1.2929 -1.1616 -1.0303 -0.8990 -0.7677 -0.6364 -0.5051 -0.3737 -0.2424 -0.1111 0.0202 0.1515 0.2828 0.4141 0.5455 0.6768 0.8081

y = linspace(-3,0)

y = 1×100

-3.0000 -2.9697 -2.9394 -2.9091 -2.8788 -2.8485 -2.8182 -2.7879 -2.7576 -2.7273 -2.6970 -2.6667 -2.6364 -2.6061 -2.5758 -2.5455 -2.5152 -2.4848 -2.4545 -2.4242 -2.3939 -2.3636 -2.3333 -2.3030 -2.2727 -2.2424 -2.2121 -2.1818 -2.1515 -2.1212

x(x==0) = NaN

x = 1×100

-3.0000 -2.8687 -2.7374 -2.6061 -2.4747 -2.3434 -2.2121 -2.0808 -1.9495 -1.8182 -1.6869 -1.5556 -1.4242 -1.2929 -1.1616 -1.0303 -0.8990 -0.7677 -0.6364 -0.5051 -0.3737 -0.2424 -0.1111 0.0202 0.1515 0.2828 0.4141 0.5455 0.6768 0.8081

y(y==0) = NaN

y = 1×100

-3.0000 -2.9697 -2.9394 -2.9091 -2.8788 -2.8485 -2.8182 -2.7879 -2.7576 -2.7273 -2.6970 -2.6667 -2.6364 -2.6061 -2.5758 -2.5455 -2.5152 -2.4848 -2.4545 -2.4242 -2.3939 -2.3636 -2.3333 -2.3030 -2.2727 -2.2424 -2.2121 -2.1818 -2.1515 -2.1212

x = fillmissing(x, 'nearest')

x = 1×100

-3.0000 -2.8687 -2.7374 -2.6061 -2.4747 -2.3434 -2.2121 -2.0808 -1.9495 -1.8182 -1.6869 -1.5556 -1.4242 -1.2929 -1.1616 -1.0303 -0.8990 -0.7677 -0.6364 -0.5051 -0.3737 -0.2424 -0.1111 0.0202 0.1515 0.2828 0.4141 0.5455 0.6768 0.8081

y = fillmissing(y, 'nearest')

y = 1×100

-3.0000 -2.9697 -2.9394 -2.9091 -2.8788 -2.8485 -2.8182 -2.7879 -2.7576 -2.7273 -2.6970 -2.6667 -2.6364 -2.6061 -2.5758 -2.5455 -2.5152 -2.4848 -2.4545 -2.4242 -2.3939 -2.3636 -2.3333 -2.3030 -2.2727 -2.2424 -2.2121 -2.1818 -2.1515 -2.1212

The second approach sets the zero value equal to NaN, and then interpolates it with the nearest (most likely non-zero) value.

.

[AD]

Thanks! I am also getting this error: Array indices must be positive integers or logical values.

Error in temp_profile (line 16)

Z=(P_l*exp(-v(sqrt((X*10^(-3)).^2 + (Y*10^(-3)).^2) + (X.*10^(-3)))/(2*a)))/(4*3.14*k*sqrt((X*10^(-3)).^2 + (Y*10^(-3)).^2))+T0;

[Star Strider]

The problem is here:

Z=(P_l*exp(-v(sqrt((X*10^(-3)).^2 + (Y*10^(-3)).^2) + (X.*10^(-3)))/(2*a)))/(4*3.14*k*sqrt((X*10^(-3)).^2 + (Y*10^(-3)).^2))+T0;

↑ HERE

It needs to be:

Z=(P_l*exp(-v.*(sqrt((X.*10^(-3)).^2 + (Y.*10^(-3)).^2) + (X.*10^(-3)))./(2*a)))./(4*pi*k*sqrt((X.*10^(-3)).^2 + (Y.*10^(-3)).^2))+T0;

instead.

There is a missing operator of some type (I assume multiplication). I also did element-wise division everywhere, sincer that is usually overlooked and I assume that here you would want to do it.

x = linspace(-3,10);
y = linspace(-3,0);

x(x==0) = NaN;
y(y==0) = NaN;

x = fillmissing(x, 'nearest');
y = fillmissing(y, 'nearest');
[X,Y] = meshgrid(x,y);

P_l = randn;
v = randn;
a = randn;
k = randi(10);
T0 = randn;
Z=(P_l*exp(-v.*(sqrt((X.*10^(-3)).^2 + (Y.*10^(-3)).^2) + (X.*10^(-3)))./(2*a)))./(4*pi*k*sqrt((X.*10^(-3)).^2 + (Y.*10^(-3)).^2))+T0;

figure
contourf(X, Y, Z)

That worked correctly when I ran it.

EDIT — (31 Jul 2023 at 17:21)

Added contour plot (as contourf) since that was requested.

.

[AD]

Heyy..thanks a lot!!

[Star Strider]

My pleasure!

Answer 2

[Voss]

First, notice that zero doesn't appear in x:

x = linspace(-3,10);
zero_x_idx = find(x == 0);
zero_x_idx

zero_x_idx =

  1×0 empty double row vector

But if you used different endpoints or a different number of points in linspace, zero might appear:

x = linspace(-3,10,131);
zero_x_idx = find(x == 0);
zero_x_idx

zero_x_idx = 31

So, I'm going to go with that.

(Zero does appear in y):

y = linspace(-3,0);
zero_y_idx = find(y == 0);
zero_y_idx

zero_y_idx = 100

Second, notice that removing the 0 from x and the 0 from y before using them in meshgrid removes not only the point (0,0) but also the lines x=0 and y=0 from the X and Y matrices returned by meshgrid. In other words, you'll have the situation where X and Y don't have any points where X is 0 or Y is 0, instead of the situation where X and Y don't have any points where X is 0 and Y is 0. (I'm sure you've noticed this already but were not sure how to remove a single point instead of both lines, hence the question.)

Here's one way to remove the single point (0,0) from X and Y:

[X,Y] = meshgrid(x,y);

% note: X,Y includes (0,0) at this point in the code:
[r0,c0] = find(X == 0 & Y == 0)

r0 = 100

c0 = 31

% create a logical matrix of which points to keep:
to_keep = true(size(X));

% set the element at zero_y_idx,zero_x_idx to false:
to_keep(zero_y_idx,zero_x_idx) = false;

% only keep the points in X and Y where to_keep is true:
X = X(to_keep);
Y = Y(to_keep);

% sanity check: that (0,0) is gone
[r0,c0] = find(X == 0 & Y == 0)

r0 =

  0×1 empty double column vector


c0 =

  0×1 empty double column vector

[AD]

Thanks! I want to make a contour plot of the z function. However, I am getting only a single value of Z (300) for all values in the mesh with no countour plots. What is the error?

[Torsten]

Maybe we could tell, but - as you can imagine - it's difficult without your code :-)