线性拟合与交点计算

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k1 = 62720.19103
b1 = 37.35983
k2 = 40893.51285
b2 = 177.4847

x_intersect = (b2 - b1) / (k1 - k2)
y_intersect = k1 * x_intersect + b1
print(x_intersect, y_intersect)

1

0.0064198898634240074 440.01654862551436

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import numpy as np
import matplotlib.pyplot as plt
import os
os.chdir(os.path.split(os.path.realpath(__file__))[0])
plt.rcParams['font.sans-serif'] = ['LXGW ZhenKai']

# 数据
x1 = np.array([0.002, 0.0024, 0.0036, 0.005, 0.0062, 0.0071])
y1 = np.array([159.3, 181.4, 271, 361, 426, 475])

x2 = np.array([0.01, 0.0114, 0.0126, 0.0136, 0.0146])
y2 = np.array([588, 638, 698, 734, 773])

# 线性拟合
coef1 = np.polyfit(x1, y1, 1)
coef2 = np.polyfit(x2, y2, 1)

# 直线方程
f1 = np.poly1d(coef1)
f2 = np.poly1d(coef2)

# 计算交点
A = np.array([[coef1[0], -1], [coef2[0], -1]])
b = np.array([-coef1[1], -coef2[1]])
intersect_x, intersect_y = np.linalg.solve(A, b)

# 生成拟合曲线数据
x_fit = np.linspace(min(x1.min(), x2.min()), max(x1.max(), x2.max()), 100)
y_fit1 = f1(x_fit)
y_fit2 = f2(x_fit)

# 绘图
plt.figure(figsize=(6, 4), dpi=300)
plt.plot(x1, y1, 'o', label='Data 1', color='tab:blue')
plt.plot(x2, y2, 'o', label='Data 2', color='tab:orange')
plt.plot(x_fit, y_fit1, '-', label=f'Fit 1: y={coef1[0]:.2f}x+{coef1[1]:.2f}', color='tab:blue')
plt.plot(x_fit, y_fit2, '-', label=f'Fit 2: y={coef2[0]:.2f}x+{coef2[1]:.2f}', color='tab:orange')
plt.scatter(intersect_x, intersect_y, color='red', zorder=3, label=f'Intersection ({intersect_x:.4f}, {intersect_y:.1f})')

# 轴标签与图例
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.grid(True)
plt.tight_layout()

# 保存图像
plt.savefig('intersection_python_plot.jpg', dpi=300)
plt.show()

# 输出交点坐标
(intersect_x, intersect_y)

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% 数据
x1 = [0.002, 0.0024, 0.0036, 0.005, 0.0062, 0.0071];
y1 = [159.3, 181.4, 271, 361, 426, 475];

x2 = [0.01, 0.0114, 0.0126, 0.0136, 0.0146];
y2 = [588, 638, 698, 734, 773];

% 线性拟合
p1 = polyfit(x1, y1, 1);
p2 = polyfit(x2, y2, 1);

% 直线方程
f1 = @(x) p1(1)*x + p1(2);
f2 = @(x) p2(1)*x + p2(2);

% 计算交点
A = [p1(1), -1; p2(1), -1];
b = [-p1(2); -p2(2)];
intersect = A\b;

intersect_x = intersect(1);
intersect_y = intersect(2);

% 生成拟合曲线数据
x_fit = linspace(min([x1, x2]), max([x1, x2]), 100);
y_fit1 = f1(x_fit);
y_fit2 = f2(x_fit);

% 颜色设定
color1 = [0.1216, 0.4667, 0.7059];  % tab:blue
color2 = [1.0000, 0.4980, 0.0549];  % tab:orange
intersect_color = [0.8353, 0.0588, 0.1569]; % red

% 绘图
figure('Position', [100, 100, 800, 600], 'Color', 'w'); % 增大图片尺寸
hold on;
plot(x1, y1, 'o', 'MarkerSize', 8, 'DisplayName', 'Data 1', 'Color', color1, 'LineWidth', 1.5);
plot(x2, y2, 'o', 'MarkerSize', 8, 'DisplayName', 'Data 2', 'Color', color2, 'LineWidth', 1.5);
plot(x_fit, y_fit1, '-', 'DisplayName', sprintf('Fit 1: y=%.2fx+%.2f', p1(1), p1(2)), 'Color', color1, 'LineWidth', 2);
plot(x_fit, y_fit2, '-', 'DisplayName', sprintf('Fit 2: y=%.2fx+%.2f', p2(1), p2(2)), 'Color', color2, 'LineWidth', 2);
scatter(intersect_x, intersect_y, 100, 'filled', 'MarkerFaceColor', intersect_color, 'DisplayName', ...
    sprintf('Intersection (%.4f, %.1f)', intersect_x, intersect_y));

% 轴标签与图例
xlabel('x', 'FontName', 'LXGW ZhenKai', 'FontSize', 16, 'FontWeight', 'bold');
ylabel('y', 'FontName', 'LXGW ZhenKai', 'FontSize', 16, 'FontWeight', 'bold');
title('线性拟合交点计算', 'FontName', 'LXGW ZhenKai', 'FontSize', 18, 'FontWeight', 'bold');
legend('show', 'FontName', 'LXGW ZhenKai', 'FontSize', 14);
grid on;

% 自动调整布局
set(gca, 'FontName', 'LXGW ZhenKai', 'FontSize', 14, 'LineWidth', 1.2);
set(gca, 'Box', 'on');

% 获取当前脚本所在目录
script_path = fileparts(mfilename('fullpath'));
save_path = fullfile(script_path, 'intersection_matlab_plot.jpg');

% 保存图像
print(gcf, save_path, '-djpeg', '-r300');  % 300dpi JPG
disp(['图像已保存至: ', save_path]);

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In[188]:= (*数据*)
data1 = {{0.002, 159.3}, {0.0024, 181.4}, {0.0036, 271}, {0.005, 
    361}, {0.0062, 426}, {0.0071, 475}};
data2 = {{0.01, 588}, {0.0114, 638}, {0.0126, 698}, {0.0136, 
    734}, {0.0146, 773}};

(*线性拟合*)
fit1 = Fit[data1, {1, x}, x];
fit2 = Fit[data2, {1, x}, x];

(*计算交点*)
solve = Solve[fit1 == fit2, x];
intersection = {x /. solve[[1]], fit1 /. solve[[1]]};

(*生成拟合曲线数据*)
xRange = {Min[Join[data1[[All, 1]], data2[[All, 1]]]], 
   Max[Join[data1[[All, 1]], data2[[All, 1]]]]};
fitLine1 = 
  Plot[fit1, {x, xRange[[1]], xRange[[2]]}, 
   PlotStyle -> {Thick, color1}];
fitLine2 = 
  Plot[fit2, {x, xRange[[1]], xRange[[2]]}, 
   PlotStyle -> {Thick, color2}];

(*颜色设定*)
color1 = RGBColor[31/255, 119/255, 180/255];(*tab:blue*)color2 = 
 RGBColor[255/255, 127/255, 14/255];(*tab:orange*)intersectColor = 
 RGBColor[214/255, 39/255, 40/255];(*red*)(*绘制图形*)plot = 
 Show[ListPlot[{data1, data2}, 
   PlotStyle -> {PointSize[0.02], {color1, color2}}, 
   PlotMarkers -> Automatic, Joined -> False], fitLine1, fitLine2, 
  Graphics[{intersectColor, PointSize[0.03], Point[intersection]}], 
  Frame -> True, GridLines -> Automatic, FrameLabel -> {"x", "y"}, 
  LabelStyle -> {FontFamily -> "LXGW ZhenKai", FontSize -> 12, Bold}, 
  PlotLabel -> 
   Style["线性拟合交点计算", FontFamily -> "LXGW ZhenKai", FontSize -> 12, 
    Bold], PlotLegends -> 
   Placed[{"Data 1", "Data 2", StringForm["Fit 1: ``", fit1], 
     StringForm["Fit 2: ``", fit2], 
     StringForm["Intersection: (`` , ``)", intersection[[1]], 
      intersection[[2]]]}, Above]];

(*保存为 300 dpi JPG*)
Export["C:\\Users\\lenovo\\Desktop\\intersection_mathematica_plot.\
jpg", plot, "JPEG", ImageResolution -> 300];

(*输出交点坐标*)
intersection