How to plot gradients ?

Answer 1

[Star Strider]

See Contour Plot of Vector Field.

[qweasd]

thanks, I've seen this page but I still can't do it. I am new in Matlab.

[Star Strider]

This should get you started:

x = linspace(3, 4, 25);
y = linspace(5, 6, 25);
[X,Y] = meshgrid(x,y);
z = @(x,y) x.^2+y.^5+3*x+4*y;
Z = z(X,Y);

See the documentation section on Anonymous Functions to understand ‘z’.

You can also use ndgrid instead of meshgrid.

It is not a very interesting plot.

[qweasd]

Thank you, I will try it.

[Star Strider]

My pleasure!

[qweasd]

I've been working on it, but still cant do it. I'm really bad :( If you don't mind, can you share the code?

[Star Strider]

You aren’t really bad. You simply need to experiment with it.

The rest of the code is essentially what’s in the documentation example that I linked to, from the gradient call to the end of the example. You only need to make a few small changes to it.

[qweasd]

x = linspace(3, 4, 25);

y = linspace(5, 6, 25);

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

z = @(x,y) x.^2+y.^5+3*x+4*y;

Z = z(X,Y);

[px,py] = gradient(Z)

figure

contour(x,y,Z)

hold on

quiver(x,y,px,py)

hold off

Like this ?

[Star Strider]

Like that!

The code I wrote for your problem:

x = linspace(3, 4, 25);
y = linspace(5, 6, 25);
[X,Y] = meshgrid(x,y);
z = @(x,y) x.^2+y.^5+3*x+4*y;
Z = z(X,Y);
[px,py] = gradient(Z);

figure
contour(X,Y,Z)
hold on
quiver(X,Y,px,py)
hold off

They appear to match.

[qweasd]

thank you so much

[Star Strider]

As always, my pleasure!

[saurav Tiwari]

x = linspace(3, 4, 25);

y = linspace(5, 6, 25);

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

z = @(x,y) x.^2+y.^5+3*x+4*y;

Z = z(X,Y);

[px,py] = gradient(Z);

figure

contour(X,Y,Z)

hold on

quiver(X,Y,px,py)

hold off

[saurav Tiwari]

it's not working

[Star Strider]

Yes, it is!

x = linspace(3, 4, 25);
y = linspace(5, 6, 25);
[X,Y] = meshgrid(x,y);
z = @(x,y) x.^2+y.^5+3*x+4*y;
Z = z(X,Y);
[px,py] = gradient(Z);

figure
contour(X,Y,Z)
hold on
quiver(X,Y,px,py)
hold off

.

[Niklas Kurz]

I would opt to normalise the Arrows for better scaling:

Norm = sqrt(px.^2+py.^2)
quiver(X,Y,px./Norm,py./Norm,0.5)

Otherwise the code is pretty neat!