在 matplotlib 中，如何将输入到 function 的辅助轴与主轴一起使用？

Question

I have a function with two arguments ( x1 , x2 ). I would like to plot the function with its result on the y axis, x1 on the x axis and x2 on the right y axis (secondary axis).

My problem is that the values of the x1 and x2 axes do not correspond together to the function point.

For example:

I want the value read on the primary y axis to match the x1 and x2 inputs of the other two axes.

Code:

x1 = np.linspace(0, 10, 10)
x2 = np.linspace(0, 5, 10)

f = lambda x1, x2: np.exp(-x1) / 10 + np.exp(-x2) / 10

resp = []
for i, j in zip(x1, x2):
    resp.append(f(i, j))
resp = np.array(resp)

fig, ax1 = plt.subplots()
ax2 = ax1.twinx()

ax1.plot(x1, resp)

ax1.set_xlabel('(x1)')
ax1.grid(True)
ax1.set_ylabel('(y)')

ax2.set_ylabel('(x2)')
ax2.set_yticks(x2)

plt.xticks(np.arange(min(x1), max(x1)))

plt.show()

Answer 1

If your input arguments are in lockstep, you do not have a function of two arguments. A function of two arguments has two independent inputs. Your inputs are dependent, so rather than writing f(x1, x2) , you have f(x, g(x)) , which is just f'(x) . In the specific example that you have x1 = np.linspace(0, 10, 10) . Rather than writing x2 = np.linspace(0, 5, 10) , you can just write x2 = 0.5 * x1 . The exponential you have can be written as

x = np.linspace(0, 10, 10)
y = np.exp(-x) / 10 + np.exp(-x / 2) / 10

Notice that you do not need a function definition or a loop to compute the y values. Using a loop defeats the entire purpose of using numpy. Your original five lines could have been reduced to y = np.exp(-x1) / 10 + np.exp(-x2) / 10 in the same way.

Now if you want to see the secondary x values in the plot of y vs x , you can take a page out of the tutorials and do something like:

fig, ax1 = plt.subplots()
ax1.plot(x, y)
ax1.set_xlabel('(x1)')
ax1.grid(True)
ax1.set_ylabel('(y)')

ax2 = ax1.secondary_xaxis('top', functions=(lambda x: x / 2, lambda x: 2 * x))
ax2.set_xlabel('(x2)')
plt.show()

The result shows "both" inputs in lockstep:

Now if you really did want to have a function of two variables, then any combination of the inputs would produce a valid y value. In this case, you would have to use a feature of numpy called broadcasting , which matches array dimensions by lining them up on the right.

Let's say you defined one of the inputs as a transpose:

x1 = np.linspace(0, 10, 10)                # Shape   (10,)
x2 = np.linspace(0, 5, 10).reshape(-1, 1)  # Shape (10, 1)

The result of an operation on these values will be a (10, 10) 2D array. Now you can meaningfully compute y as function of two independent variables:

y = np.exp(-x1) / 10 + np.exp(-x2) / 10

To plot such an array, you will need two x-axes and a y-axis, in other words a 3D plot. Here is one way to display something like that in matplotlib:

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm

fig, ax = plt.subplots(subplot_kw={'projection': '3d'})
s = ax.plot_surface(x1, x2, y, cm=cm.jet)
ax.set_xlabel('(x1)')
ax.set_ylabel('(x2)')
ax.set_zlabel('(y)')
fig.colorbar(s)

Here is the resulting plot:

It is up to you which representation of a function you want.