如何用Python中的2D散点图数据创建热图？

Question

How can one create a heatmap from a 2D scatterplot data in Python, where for each (x,y) point in the scatterplot one has az value associated to it? The z value will be the value used to color the heatmap.

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For example, in R, I can use :

# 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))

Scatterplot (each (x,y) point in this scatterplot one has az value associated to it; the z values aren't visible in the scatterplot):

Corresponding heatmap (the color represents the z values):

Note that this question is different from Generate a heatmap in MatPlotLib using a scatter data set , where the color in the heatmap represents the density of the (x,y) points).

Answer 1

I went ahead with Gerges Dib's suggestion. Here is the code, sampling (x,y,z) points from 3D Gaussian distribution:

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()

scatterplot.png:

tricontourf.png:

heatmap_interpolation_nearest.png

heatmap_interpolation_linear.png:

heatmap_interpolation_cubic.png:

Answer 2

Here is a translation of your code into python using numpy for vector operations and matplotlib for plotting:

import numpy as np
from matplotlib import pyplot

x = np.random.uniform(size=150)
y = np.random.uniform(size=150)
z = np.concatenate([np.random.randn(100)+1, np.random.randn(50)+20])

pyplot.plot(x, y, 'ok')
pyplot.tricontourf(x, y, z)
pyplot.show()

One difference here is that I did not use interpolation to put x and y on a grid, but rather used matplotlib 's tricontourf which uses triangular tessellation. If you need to put the data onto a rectangular grid, you can use scipy.interpolate.griddata which works very similar to the interp function you have in R. Then, for plotting a regular grid, you can use pyplot.pcolormesh .