使用Numpy生成随机相关的x和y点 [英] Generating random correlated x and y points using Numpy

问题描述

我想生成x和y坐标的相关数组，以便测试各种matplotlib绘制方法，但是我在某个地方失败了，因为无法获得numpy.random.multivariate_normal给我想要的样本.理想情况下，我希望我的x值介于-0.51和51.2之间，而我的y值介于0.33和51.6之间(尽管我认为相等的范围是可以的，因为以后可以约束该图)，但是我不确定是什么意思( 0、0?)和协方差值，我应该从函数中获取这些样本.

I'd like to generate correlated arrays of x and y coordinates, in order to test various matplotlib plotting approaches, but I'm failing somewhere, because I can't get numpy.random.multivariate_normal to give me the samples I want. Ideally, I want my x values between -0.51, and 51.2, and my y values between 0.33 and 51.6 (though I suppose equal ranges would be OK, since I can constrain the plot afterwards), but I'm not sure what mean (0, 0?) and covariance values I should be using to get these samples from the function.

推荐答案

顾名思义，numpy.random.multivariate_normal生成正态分布，这意味着在任何给定间隔之外寻找点的可能性不为零.您可以生成相关的均匀分布，但这有点复杂. 在此处中查看.

As the name implies numpy.random.multivariate_normal generates normal distributions, this means that there is a non-null probability of finding points outside of any given interval. You can generate correlated uniform distributions but this a little more convoluted. Take a look here for two possible methods.

如果要使用正态分布，可以设置sigma，以使半间隔对应3个标准差(如果需要，还可以滤除不良点).这样，您将在间隔内获得约99％的点，例如:

If you want to go with the normal distribution you can set up the sigmas so that your half-interval correspond to 3 standard deviations (you can also filter out the bad points if needed). In this way you will have ~99% of your points inside your interval, ex:

import numpy as np
from matplotlib.pyplot import scatter

xx = np.array([-0.51, 51.2])
yy = np.array([0.33, 51.6])
means = [xx.mean(), yy.mean()]  
stds = [xx.std() / 3, yy.std() / 3]
corr = 0.8         # correlation
covs = [[stds[0]**2          , stds[0]*stds[1]*corr], 
        [stds[0]*stds[1]*corr,           stds[1]**2]] 

m = np.random.multivariate_normal(means, covs, 1000).T
scatter(m[0], m[1])

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