python - 如何从 Python 中的二维散点图数据创建热图？

Question

如何在 Python 中根据 2D 散点图数据创建热图，散点图中的每个 (x,y) 点都有一个与之关联的 z 值？ z 值将是用于为热图着色的值。

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例如，在 R 中，我可以使用:

# This example is from http://knowledge-forlife.com/r-creating-heatmap-scatterplot-data/
#I'm just setting the seed so you can see the same example on your computer
set.seed(1)

#Our X data
x <- runif(150)

#Our Y data
y <- runif(150)

#Our Z data
z <- c(rnorm(mean=1,100),rnorm(mean=20,50))

#Store the length of our data
N <- length(x)

# View the scatterplot
plot(x, y)

#Here is the interpolation to give the heatmap effect. 
#Use xo and yo to set the output grid you want to use.
#xo and yo are used to change the resolution of the interpolation
#Here, I have included a somewhat standard protocol for these parameters
s <- interp(x,y,z,xo=seq(min(x),max(x),length=N),
            yo=seq(min(x),max(x),length=N),duplicate="mean")

#Here's where the fun happens
#Note you can add your typical plotting paramaters here, such as xlab or ylab
image.plot(s,xlim=c(0,1),ylim=c(0,1),zlim=c(-2,25))

散点图(此散点图中的每个 (x,y) 点都有一个与其关联的 z 值；z 值在散点图中不可见):

对应的热图(颜色代表z值):

注意这个问题不同于Generate a heatmap in MatPlotLib using a scatter data set ，其中热图中的颜色表示 (x,y) 点的密度)。

Answer 1

我接受了 Gerges Dib 的建议。这是代码，从 3D 高斯分布中采样 (x,y,z) 点:

import numpy as np
import scipy.interpolate
from scipy.stats import multivariate_normal
import matplotlib.pyplot as plt
import seaborn as sns
sns.set()

# Sample from 3D Gaussian distribution
np.random.seed(0)
number_of_samples = 20
x = np.random.rand(number_of_samples)
y = np.random.rand(number_of_samples)
xy = np.column_stack([x.flat, y.flat]) # Create a (N, 2) array of (x, y) pairs.
mu = np.array([0.0, 0.0])
sigma = np.array([.95, 2.5])
covariance = np.diag(sigma**2)
z = multivariate_normal.pdf(xy, mean=mu, cov=covariance)

plt.scatter(x, y)
plt.savefig('scatterplot.png', dpi=300)

plt.tricontourf(x, y, z)
plt.savefig('tricontourf.png', dpi=300)

# Interpolate and generate heatmap:
grid_x, grid_y = np.mgrid[x.min():x.max():1000j, y.min():y.max():1000j]
for method in ['nearest','linear','cubic'] :
    plt.figure()
    grid_z = scipy.interpolate.griddata(xy,z,(grid_x, grid_y), method=method)
    # [pcolormesh with missing values?](https://stackoverflow.com/a/31687006/395857)
    import numpy.ma as ma
    plt.pcolormesh(grid_x, grid_y, ma.masked_invalid(grid_z), cmap='RdBu', vmin=np.nanmin(grid_z), vmax=np.nanmax(grid_z))
    plt.title('{0} interpolation'.format(method))
    plt.colorbar()
    plt.savefig('heatmap_interpolation_{0}.png'.format(method), dpi=300)
    plt.clf()
    plt.close()

散点图.png:

tricontourf.png:

heatmap_interpolation_nearest.png

heatmap_interpolation_linear.png:

heatmap_interpolation_cubic.png: