Plot gradient arrows over heatmap with plt

Question

I am trying to plot arrows to visualize the gradient over a heatmap. This is the code I have until now:

import matplotlib.pyplot as plt
import numpy as np
fu         


        

Answer 1

1. It looks as though np.gradient() returns y-values before x-values
2. The colors also appeared to be incorrect because the graphing context y-values were reversed. Thus I used np.flip(result_matrix,0) during plotting
3. Finally, I noticed that there was a glitch when plotting the arrows when the stepsize did not divide the region evenly, in addition the mesh was not aligned to the center of the boxes. I have fixed both of these in the following code:

Here is the code which I used to generate the graph:

import matplotlib.pyplot as plt
import numpy as np
import math
function_to_plot = lambda x, y: x**2 + y**2
horizontal_min, horizontal_max, horizontal_stepsize = -2, 3, 0.3
vertical_min, vertical_max, vertical_stepsize = -1, 4, 0.5

horizontal_dist = horizontal_max-horizontal_min
vertical_dist = vertical_max-vertical_min

horizontal_stepsize = horizontal_dist / float(math.ceil(horizontal_dist/float(horizontal_stepsize)))
vertical_stepsize = vertical_dist / float(math.ceil(vertical_dist/float(vertical_stepsize)))

xv, yv = np.meshgrid(np.arange(horizontal_min, horizontal_max, horizontal_stepsize),
                     np.arange(vertical_min, vertical_max, vertical_stepsize))
xv+=horizontal_stepsize/2.0
yv+=vertical_stepsize/2.0

result_matrix = function_to_plot(xv, yv)
yd, xd = np.gradient(result_matrix)

def func_to_vectorize(x, y, dx, dy, scaling=0.01):
    plt.arrow(x, y, dx*scaling, dy*scaling, fc="k", ec="k", head_width=0.06, head_length=0.1)

vectorized_arrow_drawing = np.vectorize(func_to_vectorize)

plt.imshow(np.flip(result_matrix,0), extent=[horizontal_min, horizontal_max, vertical_min, vertical_max])
vectorized_arrow_drawing(xv, yv, xd, yd, 0.1)
plt.colorbar()
plt.show()