Compute the partial derivative numerically

F.O

2017 12 21

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Hi, I want to compute the first and second partial derivative with respect to x, y for this function

x0=0
y0=0
x=[-1:0.1:1];
y=[-2:0.1:2];
v=x+exp(-((x-x0).^2+(y-y0).^2))

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Star Strider 2017-12-21

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See if the gradient (link) function will do what you want:

Example —

x0=0;
y0=0;
x=[-1:0.1:1];
y=[-2:0.1:2];
[X,Y] = meshgrid(x, y);
v = @(x,y) x+exp(-((x-x0).^2+(y-y0).^2));
[dX,dY] = gradient(v(X,Y));
figure(1)
surf(X, Y, v(X,Y), 'FaceAlpha',0.5, 'EdgeColor',[0.3 0.3 0.7])
hold on
surf(X, Y, dX, 'EdgeColor','g')
surf(X, Y, dY, 'EdgeColor','r')
hold off
grid on
legend('v(x,y)', 'dX', 'dY')
xlabel('\bfX')
ylabel('\bfY')
view(40, 20)
figure(2)
contour(X, Y, v(X,Y))
hold on
quiver(X, Y, dX, dY)
hold off
legend('v(x,y)', 'Gradient')