The gradient function second argument is the uniform spacing constant (in the documentation, ‘h’, assumed to be 1 by default if not provided). Regardless of the spacing of the independent variable vector, and whether it is uniform or not, dividing the gradient of the dependent variable by the gradient of the independent variable will give the correct result for the numerical derivative of the dependent variable with respect to the independent variable.
For example, using the ‘fig.fig’ file:
F = openfig('fig.fig');
Lines = findobj(F, 'Type','Line');
for k = 1:numel(Lines)
x{k} = Lines(k).XData;
y{k} = Lines(k).YData;
dydx{k} = gradient(y{k}) ./ gradient(x{k});
end
figure
hold on
for k = 1:numel(dydx)
plot(x{k}, y{k}, '-b', x{k}, dydx{k}*10+10, '--c')
end
hold off
grid
hl = legend('Data', '$\frac{dy}{dx}$');
hl.Interpreter = 'latex';
There is only one 'Line' object in this file, however the code is written to accommodate several. (This code will require minor modifications to use with data that are not extracted from one or more figures.)
I do not know if this will result in infinite results, since I do not have the data that generated those results in the current code.
.
