如何基于欧氏距离矩阵绘制semilogx单折线图？

DevOps 小满

2026-8-6

问题描述

尝试基于欧氏距离矩阵绘制对数正态阴影路径损耗模型的semilogx图，期望用单条折线展示路径损耗随距离的变化差异，但使用cdist生成的欧氏距离矩阵时无法实现该效果；改用distance = np.arange(0.05, 15, 0.1) ** 2生成的距离变量则能正常显示单折线。以下是原始代码，预期效果为单折线带离散点的对数坐标图。

from scipy.spatial.distance import cdist
import matplotlib.pyplot as plt
import numpy as np

# % Log-distance or Log-normal shadowing path loss model
# % Inputs: fc : Carrier frequency[Hz]
# % d : Distance between base station and mobile station[m]
# % d0 : Reference distance[m]
# % n : Path loss exponent
# % sigma : Variance[dB]
def logdist_or_norm(fc, d, d0, n, sigma):
    lamda = 3e8 / fc
    PL = -20 * np.log10(lamda / (4 * np.pi * d0)) + 10 * n * np.log10(d / d0)
    
    if sigma:
        PL = PL + sigma * np.random.randn(len(d))
    return PL

# % Channel Parameters
fc = 2.4e9 #% operation in 2.4 GHz
d0 = 0.25  #% good choice for indoor distances (microcells)
sigma = 3  #% keep the book suggestion
Gt = 1     #% No transmitter antenna gain as provided by nordic datasheet 
Gr = 1     #% No receiver antenna gain as provided by nordic datasheet 
Exp = 4    #% Mid value in the obstructed in building range (Table 1.1)

# % Distance vector also for plot
m = np.random.random((8, 2))
distance = cdist(m, m)

# % Log-normal shadowing model
y_lognorm = logdist_or_norm(fc, distance.flatten(), d0, Exp, sigma)

# % Plot Path loss versus distance
plt.semilogx(distance.flatten(), y_lognorm, 'k-o')
plt.grid(True), plt.axis([0.05, 20, 0, 110]), plt.legend('Log-normal shadowing model')
plt.title(['Log-normal Path-loss Model, f_c = ', str(fc/1e6),'MHz,', '\sigma = ', str(sigma), 'dB, n = 2'])
plt.xlabel('Distance[m]'), plt.ylabel('Path loss[dB]')

问题原因

cdist(m, m)生成的是8×8的距离矩阵，展平后包含大量重复距离值，且这些距离是无序的。semilogx会严格按照输入数据的顺序绘制点，无序的距离会导致折线来回交叉，无法形成随距离递增的单条折线。而np.arange生成的是有序递增的距离序列，因此能正常绘制符合预期的单折线。

解决方案

要实现预期效果，需要生成有序的距离序列，并为每个距离计算对应的路径损耗（含阴影衰落）。修改后的代码如下：

from scipy.spatial.distance import cdist
import matplotlib.pyplot as plt
import numpy as np

# 对数正态阴影路径损耗模型
def logdist_or_norm(fc, d, d0, n, sigma):
    lamda = 3e8 / fc
    PL = -20 * np.log10(lamda / (4 * np.pi * d0)) + 10 * n * np.log10(d / d0)
    
    if sigma:
        PL = PL + sigma * np.random.randn(len(d))
    return PL

# 信道参数
fc = 2.4e9  # 2.4GHz载波频率
d0 = 0.25   # 参考距离（室内微小区适用）
sigma = 3   # 阴影衰落方差
Exp = 4     # 路径损耗指数（室内遮挡场景中间值）

# 生成有序距离序列（替代无序的欧氏距离矩阵）
# 覆盖0.05到20m范围，步长0.1m，保证距离递增
distance = np.arange(0.05, 20, 0.1)

# 计算对数正态阴影路径损耗
y_lognorm = logdist_or_norm(fc, distance, d0, Exp, sigma)

# 绘制路径损耗vs距离
plt.semilogx(distance, y_lognorm, 'k-o')
plt.grid(True)
plt.axis([0.05, 20, 0, 110])
plt.legend(['Log-normal shadowing model'])
plt.title(f'Log-normal Path-loss Model, f_c = {fc/1e6:.0f}MHz, σ = {sigma}dB, n = {Exp}')
plt.xlabel('Distance[m]')
plt.ylabel('Path loss[dB]')
plt.show()

关键修改说明

替换cdist生成的无序距离矩阵为np.arange生成的有序递增距离序列，确保x轴数据按从小到大排列
用f-string简化标题的字符串拼接，格式更规范
修正legend参数格式，传入列表而非单个字符串
添加plt.show()确保图形正常显示

内容的提问来源于stack exchange，提问作者mmik