Cannot calculate gradient of contour plot

Hi all,

I am currently attempting to draw a quiver plot on top of a contour plot, such that I can see the gradient of the contour function. However for some reason the gradient calculation does not take place correctly as all the quivers are far from being perpendicuar to the contours. This suprises me as the task itself is pretty simple and I have managed to accomplish it with mock data, see here:

clear ; clc

% Grid matrices
x = -2:0.25:2;
y = x;
[X,Y] = meshgrid(x);

% Function Matrix
F = X.*exp(-X.^2-Y.^2);

% Calculate Gradient
[FU, FV] = gradient(F, diff(x(1:2))) ;

% Plot
figure
    hold on
    contour(X, Y, F)
    quiver(X, Y, FU, FV)
    

However, using my own data (you can find them attached its a simple 30x30 matrix), the same process does not seem to accomplish the task:

clear ; clc

% Grid matrices
 x = linspace(-0.1, 0.1, 30) ;
 y = linspace(8, 12, 30) ;
 [X, Y] = meshgrid(x, y) ;

% Function Matrix
load('my_data.mat')

% Calculate Gradient
[FU, FV] = gradient(F, diff(x(1:2)), diff(y(1:2))) ;

% Plot
figure
    hold on
    contour(X, Y, F)
    quiver(X, Y, FU, FV)
    

The weird thing is that the countour plot gets generated correctly, however something is off with the quiver. Even when I scale down the quiver vectors to say 0.2, they don't have the correct orientation relative to the contours.

Thanks for your help in advance

[KSSV]

How did you generate that F?

[KostasK]

Its a fairly complex process of generating F, that's why I have attached it as a .mat file. I assumed that it shouldn't matter how F is generated, but rather that it forms a good contour plot.

Answer 1

[Bjorn Gustavsson]

If you modify your call to gradient to:

[FU, FV] = gradient(F, diff(y(1:2)), diff(x(1:2)));

You get a more reasonable set of quivers:

contour(X, Y, F)
hold on
quiver(X(1:2:end,1:2:end), Y(1:2:end,1:2:end), FU(1:2:end,1:2:end)/2, FV(1:2:end,1:2:end)/2,0)

The zero is to turn off the automatic scaling in quiver.

HTH

[KostasK]

Yes, it appears that scaling is the issue here. Because when I use axis equal even though the contour is greately distorted and inneligible, the gradient appears to be correct. So your answer works for me.