Creating a pseudo color plot with a linear and nonlinear axis and computing values based on the center of grid values

Question

I have the equation: z(x,y)=1+x^(2/3)y^(-3/4)

I would like to calculate values of z for x=[0,100] and y=[10^1,10^4]. I will do this for 100 points in each axis direction. My grid, then, will be 100x100 points. In the x-direction I want the points spaced linearly. In the y-direction I want the points space logarithmically.

Were I to need these values I could easily go through the following:

x=np.linspace(0,100,100)
y=np.logspace(1,4,100)
z=np.zeros( (len(x), len(y)) )

for i in range(len(x)):
    for j in range(len(y)):
        z[i,j]=1+x[i]**(2/3)*y[j]**(-3/4)

The problem for me comes with visualizing these results. I know that I would need to create a grid of points. I feel my options are to create a meshgrid with the values and then use pcolor.

My issue here is that the values at the center of the block do not coincide with the calculated values. In the x-direction I could fix this by shifting the x-vector by half of dx (the step between successive values). I'm not so sure how I would do this for the y-axis. Furthermore, If I wanted to compute values for each of the y-direction values, including the end points, they would not all show up.

In the final visualization I would like to have the y-axis as a log scale and the x axis as a linear scale. I would also like the tick marks to fall in the center of the cells, correlating with the correct value. Can someone point me to the correct plotting functions for this. I have to resolve the issue using pcolor or pcolormesh.

Should you require more details, please let me know.

Answer 1

In current matplotlib, you can use pcolormesh with shading='nearest', and it will center the blocks with the values:

import matplotlib.pyplot as plt

y_plot = np.log10(y)
z[5, 5] = 0  # to make it more evident
plt.pcolormesh(x, y_plot, z, shading="nearest")
plt.colorbar()
ax = plt.gca()
ax.set_xticks(x)
ax.set_yticks(y_plot)
plt.axvline(x[5])
plt.axhline(y_plot[5])

Output: