Plot 使用 matplotlib (Python) 中的颜色网格的随机轨迹偏离“真实”路径

Question

Hi I created a program that will create deviations from a real trajectory, it is complicated and I do not have a simple example unfortunately.

It calculates a path with stochastic initial conditions from the real path and does this for x iterations, the goal is to show that the deviations become larger at greater times.

The real path and the deviations are showed below.

However I want to show that the deviations become greater the longer in time we are. Ofcourse I could just calculate the variance and plot mean+var and mean-var at each time step but I was wondering if I could plot something like this, using hist2d

You see that the blocks are not as smooth as a like and this is not that great to use.

Then I went and looked at python's kde and created the following.

This is also not preferable as I think it bins more points at the minima and maxima. Also it is 'too smeared out'. Especially in the beginning, all the points are the same so I want there just to be a straight line to really show that the deviations start later on.

I guess my question is; is what I want even possible and what package/command should I use. I haven't found what I am looking for on other questions. Or has anyone a suggestion to nicely show what I want in a any other way?

Answer 1

Here is an idea plotting multiple curves with transparency on top of each other:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 10, 200)
for _ in range(1000):
    plt.plot(x, np.sin(x * np.random.normal(1, 0.1)) * np.random.normal(1, 0.1), color='r', alpha=0.02)
plt.plot(x, np.sin(x), color='b')
plt.margins(x=0)
plt.show()

Another option creates a 2d histogram:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 10, 200)
all_curves = np.array([np.sin(x * np.random.normal(1, 0.1)) * np.random.normal(1, 0.1) for _ in range(100)])
plt.hist2d(x=np.tile(x, all_curves.shape[0]), y=all_curves.ravel(), bins=(100, 100), cmap='inferno')
plt.show()

Still another approach would use fill_between (as suggested by @bramb) between confidence intervals:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 10, 200)
all_curves = np.array([np.sin(x * np.random.normal(1, 0.1)) * np.random.normal(1, 0.1) for _ in range(1000)])

confidence_interval1 = 95
confidence_interval2 = 80
confidence_interval3 = 50
for ci in [confidence_interval1, confidence_interval2, confidence_interval3]:
    low = np.percentile(all_curves, 50 - ci / 2, axis=0)
    high = np.percentile(all_curves, 50 + ci / 2, axis=0)
    plt.fill_between(x, low, high, color='r', alpha=0.2)
plt.plot(x, np.sin(x), color='b')
plt.margins(x=0)
plt.show()

Answer 2

You could use something like the matplotlib.pyplot.fill_between method. It fills everything between y1 (max) and y2 (min) for a given (common) x array. You would then be able to accentuate that the filled region keeps enlarging with increasing x value.

However, this would require you to find the minimal and maximal value of your deviations at each time point and save these to two separate arrays. The exact method of doing this will depend on how you are storing these individual runs.

In case they are separate lists / arrays, you can convert these to a numpy matrix / pandas dataframe and use the minimum / maximum methods along the relevant axis.