Python實現(xiàn)線性擬合及繪圖的示例代碼

更新時間：2024年04月28日 14:42:20 作者：浩瀚地學

在數(shù)據(jù)處理和繪圖中,我們通常會遇到直線或曲線的擬合問題,本文主要介紹了Python實現(xiàn)線性擬合及繪圖的示例代碼,具有一定的參考價值,感興趣的可以了解一下

代碼邏輯

導入所需庫以及初步設置

# coding=gbk
# -*- coding = utf-8 -*-

import matplotlib.pyplot as plt
import numpy as np
plt.subplots_adjust(left=0.05, right=0.7, top=0.9, bottom=0.1)
plt.rcParams['font.sans-serif'] = ['SimHei']

準備數(shù)據(jù)（這里僅展示部分）

resolutions = [50, 100, 150, 200, 250]
plain = [0, 0, 1, 1, 1]
hill = [2.645751311, 7.071067812, 10.44030651, 11.48912529, 14.4222051]

這里可以改為在Excel中讀取，尤其是數(shù)據(jù)多的時候

分別繪制不同數(shù)據(jù)的趨勢線

# 繪制平原趨勢線
coefficients_plain = np.polyfit(resolutions, plain, 1)
poly_plain = np.poly1d(coefficients_plain)
plt.plot(resolutions, plain, '^', label="平原")
plt.plot(resolutions, poly_plain(resolutions), label="平原趨勢線")

# 繪制丘陵趨勢線
coefficients_hill = np.polyfit(resolutions, hill, 1)
poly_hill = np.poly1d(coefficients_hill)
plt.plot(resolutions, hill, '^', label="丘陵")
plt.plot(resolutions, poly_hill(resolutions), label="丘陵趨勢線")

使用np.polyfit函數(shù)擬合一階多項式（直線），然后使用np.poly1d構造多項式對象。繪制原始數(shù)據(jù)點（用’^'標記）和對應的擬合趨勢線。

計算指標

# 計算平原趨勢線的r值和r方
residuals_plain = plain - poly_plain(resolutions)
ss_residuals_plain = np.sum(residuals_plain**2)
ss_total_plain = np.sum((plain - np.mean(plain))**2)
r_squared_plain = 1 - (ss_residuals_plain / ss_total_plain)
r_plain = np.sqrt(r_squared_plain)

# 計算丘陵趨勢線的r值和r方
residuals_hill = hill - poly_hill(resolutions)
ss_residuals_hill = np.sum(residuals_hill**2)
ss_total_hill = np.sum((hill - np.mean(hill))**2)
r_squared_hill = 1 - (ss_residuals_hill / ss_total_hill)
r_hill = np.sqrt(r_squared_hill)

計算得到r方和r值

繪圖和打印指標

# 設置圖例和標題
plt.legend()
plt.legend(loc='center left', bbox_to_anchor=(1.05, 0.5))
plt.title("地形趨勢線")

# 設置坐標軸標題
new_ticks = np.arange(50, 251, 50)
plt.xticks(new_ticks)
plt.xlabel('分辨率（m）')
plt.ylabel('RMSE')
formula1 = "平原：{}".format(poly_plain)
plt.text(0.05, 0.95, formula1, transform=plt.gca().transAxes,
         fontsize=10, verticalalignment='top')
formula1 = "丘陵：{}".format(poly_hill)
plt.text(0.35, 0.95, formula1, transform=plt.gca().transAxes,
         fontsize=10, verticalalignment='top')

# 顯示圖形
plt.figure(figsize=(10, 10))
plt.show()

# 打印
print("平原趨勢線公式：", poly_plain)
print("丘陵趨勢線公式：", poly_hill)
print("平原趨勢線：")
print("r值：", r_plain)
print("r方：", r_squared_plain)
print()
print("丘陵趨勢線：")
print("r值：", r_hill)
print("r方：", r_squared_hill)
print()

完整代碼

# coding=gbk
# -*- coding = utf-8 -*-

import matplotlib.pyplot as plt
import numpy as np
plt.subplots_adjust(left=0.05, right=0.7, top=0.9, bottom=0.1)
plt.rcParams['font.sans-serif'] = ['SimHei']

resolutions = [50, 100, 150, 200, 250]
plain = [0, 0, 1, 1, 1]
hill = [2.645751311, 7.071067812, 10.44030651, 11.48912529, 14.4222051]

# 繪制平原趨勢線
coefficients_plain = np.polyfit(resolutions, plain, 1)
poly_plain = np.poly1d(coefficients_plain)
plt.plot(resolutions, plain, '^', label="平原")
plt.plot(resolutions, poly_plain(resolutions), label="平原趨勢線")

# 繪制丘陵趨勢線
coefficients_hill = np.polyfit(resolutions, hill, 1)
poly_hill = np.poly1d(coefficients_hill)
plt.plot(resolutions, hill, '^', label="丘陵")
plt.plot(resolutions, poly_hill(resolutions), label="丘陵趨勢線")

# 計算平原趨勢線的r值和r方
residuals_plain = plain - poly_plain(resolutions)
ss_residuals_plain = np.sum(residuals_plain**2)
ss_total_plain = np.sum((plain - np.mean(plain))**2)
r_squared_plain = 1 - (ss_residuals_plain / ss_total_plain)
r_plain = np.sqrt(r_squared_plain)

# 計算丘陵趨勢線的r值和r方
residuals_hill = hill - poly_hill(resolutions)
ss_residuals_hill = np.sum(residuals_hill**2)
ss_total_hill = np.sum((hill - np.mean(hill))**2)
r_squared_hill = 1 - (ss_residuals_hill / ss_total_hill)
r_hill = np.sqrt(r_squared_hill)

# 設置圖例和標題
plt.legend()
plt.legend(loc='center left', bbox_to_anchor=(1.05, 0.5))
plt.title("地形趨勢線")

# 設置坐標軸標題
new_ticks = np.arange(50, 251, 50)
plt.xticks(new_ticks)
plt.xlabel('分辨率（m）')
plt.ylabel('RMSE')
formula1 = "平原：{}".format(poly_plain)
plt.text(0.05, 0.95, formula1, transform=plt.gca().transAxes,
         fontsize=10, verticalalignment='top')
formula1 = "丘陵：{}".format(poly_hill)
plt.text(0.35, 0.95, formula1, transform=plt.gca().transAxes,
         fontsize=10, verticalalignment='top')

# 顯示圖形
plt.figure(figsize=(10, 10))
plt.show()

# 打印
print("平原趨勢線公式：", poly_plain)
print("丘陵趨勢線公式：", poly_hill)
print("平原趨勢線：")
print("r值：", r_plain)
print("r方：", r_squared_plain)
print()
print("丘陵趨勢線：")
print("r值：", r_hill)
print("r方：", r_squared_hill)
print()