Generating gradient map of 2D array

Question

I have a 2D array that stores values of a property of each point as its element: f(x,y) = f[x][y]. Now I want to find the gradient of this array. I looked into np.gradient but it just gives two arrays as return, first with derivative in x direction and second in y direction.

I want to learn how can I use this or any other way to create a gradient map that shows the change in gradient of the 2D array.
varray is the 2D array I want to create gradient map of. Following is the only things I can think of right now. I know there should be clever way to use x gradientand y gradient generated by np.gradient() but I cannot think of it. lx and ly are x and y dimension of the 2D array.

vgrad = np.gradient(varray)
xgrad = vgrad[0]
x, y = range(0, lx), range(0,ly)
xi, yi = np.meshgrid(x, y)
rbf = scipy.interpolate.Rbf(xi, yi, xgrad)
plt.imshow(v, vmin = np.amin(xgrad), vmax=np.amax(xgrad))
plt.colorbar()
plt.show()  

I want to get basically the second image from the first image. The second image is described as σ = \alpha*grad(varray).

Using magnitude of gradient as suggested by @Mad Physicist below.

vgrad = np.gradient(varray)
fulgrad = np.sqrt(vgrad[0]**2 + vgrad[1]**2)
plt.imshow(fulgrad,cmap=plt.get_cmap('hot'), vmin = np.amin(fulgrad),vmax = np.amax(fulgrad))  
plt.colorbar()
plt.show()  

the image i get :

I am interpreting this wrong from basic understanding of the equation?

So here is my images. On left: image of the initial 2D map. On right: Image of the gradient map. @Mad Physicist do you think they are similar to above with only difference of colors?

Answer 1

If you are looking for the magnitude of the gradient, you can just do

mag = np.sqrt(vgrad[0]**2 + vgrad[1]**2)

Then plot mag instead of xgrad as above. If, you want to plot the gradient as a vector map or stream plot, do something like

plt.streamplot(xi, yi, vgrad[0], vgrad[1])

You may also be interested in the visual representation of the slope that can be obtained from just plotting the original surface in 3D:

fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(xi, yi, varray)
plt.show()

See What is the equivalent of Matlab's surf(x,y,z,c) in matplotlib? and http://matplotlib.org/examples/mplot3d/surface3d_demo.html