熱圖

熱圖對於視覺化兩個變數的標量函式非常有用。它們提供二維直方圖的平面影象（例如表示某個區域的密度）。

以下原始碼說明了使用在兩個方向上均為 0 的雙變數正態分佈數字（表示 [0.0, 0.0]）和具有給定協方差矩陣的 a 的熱圖。使用 numpy 函式 numpy.random.multivariate_normal 生成資料 ; 然後將其輸入到 pyplot matplotlib.pyplot.hist2d 的 hist2d 函式中。

import numpy as np
import matplotlib
import matplotlib.pyplot as plt

# Define numbers of generated data points and bins per axis.
N_numbers = 100000
N_bins = 100

# set random seed 
np.random.seed(0)

# Generate 2D normally distributed numbers.
x, y = np.random.multivariate_normal(
        mean=[0.0, 0.0],      # mean
        cov=[[1.0, 0.4],
             [0.4, 0.25]],    # covariance matrix
        size=N_numbers
        ).T                   # transpose to get columns

# Construct 2D histogram from data using the 'plasma' colormap
plt.hist2d(x, y, bins=N_bins, normed=False, cmap='plasma')

# Plot a colorbar with label.
cb = plt.colorbar()
cb.set_label('Number of entries')

# Add title and labels to plot.
plt.title('Heatmap of 2D normally distributed data points')
plt.xlabel('x axis')
plt.ylabel('y axis')

# Show the plot.
plt.show()

這是與 3D 直方圖視覺化的相同資料（這裡我們僅使用 20 個箱來提高效率）。該程式碼基於此 matplotlib 演示 。

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib
import matplotlib.pyplot as plt

# Define numbers of generated data points and bins per axis.
N_numbers = 100000
N_bins = 20

# set random seed 
np.random.seed(0)

# Generate 2D normally distributed numbers.
x, y = np.random.multivariate_normal(
        mean=[0.0, 0.0],      # mean
        cov=[[1.0, 0.4],
             [0.4, 0.25]],    # covariance matrix
        size=N_numbers
        ).T                   # transpose to get columns

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
hist, xedges, yedges = np.histogram2d(x, y, bins=N_bins)

# Add title and labels to plot.
plt.title('3D histogram of 2D normally distributed data points')
plt.xlabel('x axis')
plt.ylabel('y axis')

# Construct arrays for the anchor positions of the bars.
# Note: np.meshgrid gives arrays in (ny, nx) so we use 'F' to flatten xpos,
# ypos in column-major order. For numpy >= 1.7, we could instead call meshgrid
# with indexing='ij'.
xpos, ypos = np.meshgrid(xedges[:-1] + 0.25, yedges[:-1] + 0.25)
xpos = xpos.flatten('F')
ypos = ypos.flatten('F')
zpos = np.zeros_like(xpos)

# Construct arrays with the dimensions for the 16 bars.
dx = 0.5 * np.ones_like(zpos)
dy = dx.copy()
dz = hist.flatten()

ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color='b', zsort='average')

# Show the plot.
plt.show()