使用 "vertical" 个边缘直方图创建二维数据图

Question

我如何在 python 中创建具有这样“垂直”边际直方图的双变量数据图？：

假设数据是通过以下方式生成的：

from scipy.stats import multivariate_normal
import numpy as np

mean = np.array([0, 0])
cov = np.array([[1, 0.5], [0.5, 2]])
data = multivariate_normal(mean, cov).rvs(1000)

Answer 1

下面是展示如何做到这一点的示例代码：

import math

import matplotlib.pyplot as plt
import numpy as np
from matplotlib import rc, rcParams
from numpy.linalg import eigh
from scipy.stats import multivariate_normal, norm
from mpl_toolkits.mplot3d import Axes3D

rcParams['text.latex.preamble'] = r'\boldmath'
rc('text', usetex=True)

mean = np.array([0,0])
cov = np.array([[1, 0.3], [0.3, .5]])
np.random.seed(0)
mvn_rvs = multivariate_normal(mean, cov).rvs(800)
pdf_x = norm(mean[0], np.sqrt(cov[0,0])).pdf
pdf_y = norm(mean[1], np.sqrt(cov[1,1])).pdf
rv_x = mvn_rvs[:, 0]
rv_y = mvn_rvs[:, 1]

x = np.linspace(-3, 3, 101)
y = np.linspace(-3, 3, 100)
X, Y = np.meshgrid(x, y)

fontsize = 30
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.get_proj = lambda: np.dot(Axes3D.get_proj(ax), np.diag([1.15, 1.15, 1, 1]))
ax.plot(y, pdf_y(y), zs=x.min(), zdir='x', linewidth=3, label="$\mathsf{P_y(y)}$")
ax.plot(x, pdf_x(x), zs=y.max(), zdir='y', linewidth=3, label='$\mathsf{P_x(x)}$')
leg = plt.legend(fontsize=fontsize, ncol=2, frameon=False, bbox_to_anchor=(-0.10, 1.1275),
           loc='upper left', handlelength=0.7, handletextpad=0.5, columnspacing=2.4)
grid_linewidth = 1.15
ax.xaxis._axinfo["grid"]['linewidth'] = grid_linewidth
ax.yaxis._axinfo["grid"]['linewidth'] = grid_linewidth
ax.zaxis._axinfo["grid"]['linewidth'] = grid_linewidth
ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.w_xaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
ax.w_yaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
ax.w_zaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
labelpad = -5
ax.set_xlabel("$\mathsf{x}$", fontsize=fontsize, labelpad=labelpad)
ax.set_ylabel("$\mathsf{y}$", fontsize=fontsize, labelpad=labelpad)
labelsize = 10
ax.xaxis.set_rotate_label(False)
ax.yaxis.set_rotate_label(False)
ax.set_zlim(bottom=0)
ax.set_xlim(-3, 3)
ax.set_ylim(-3, 3)
ax.xaxis.set_ticklabels([])
ax.xaxis.set_visible(False)
ax.yaxis.set_ticklabels([])
ax.zaxis.set_ticklabels([])

sx2 = cov[0, 0]
sy2 = cov[1, 1]
rho = cov[0, 1] / np.sqrt(sx2 * sy2)
Sigma = cov
target = 0.1
gamma = math.log(1 / (4*(np.pi**2)*(sx2**2)*(sy2**2)*(1 - rho**2)*(target**2)))
eigenvalues, P = eigh(np.linalg.inv(Sigma))
# Compute u and v as per link using thetas from 0 to 2pi
thetas = np.linspace(0, 2*np.pi, 10000)
uv = (np.sqrt(gamma) / np.sqrt(eigenvalues)) * np.hstack((np.cos(thetas).reshape(-1,1), np.sin(thetas).reshape(-1, 1)))

orig_coord=np.zeros((10000,2))
for i in range(len(uv)):
    orig_coord[i,0]=np.matmul(np.linalg.inv(P), uv[i,:])[0]
    orig_coord[i,1]=np.matmul(np.linalg.inv(P), uv[i,:])[1]

ax.plot(rv_x, rv_y, 0*rv_x, ' o', c='g', markersize=1.1)  # "RdBu_r")
ax.plot(orig_coord[:, 0], orig_coord[:, 1],
        0 * np.ones_like(orig_coord[:, 0]), c='r', linewidth=3)
ax.view_init(azim=-45, elev=20)

使用 "vertical" 个边缘直方图创建二维数据图

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seaborn