在图形上进行多线拟合并计算线交点的位置

Question

使用输入数据集，我绘制了一个类似于下图的图表： 我想要拟合多行，如下所示： 然后计算这条线的交点的位置。我通过这个Python代码检查了它，但这不起作用，请帮助我。

dfn=pd.read_csv('input.csv')
x=dfn['X']
y=dfn['Y']
plt.scatter(np.log(x),np.log(y))
num_lines=3
for i in range(num_lines):
    coef=np.polyfit(np.log(x),np.log(y),1)
    poly1d_fn=np.poly1d(coef)
    plt.plot(np.log(x),poly1d_fn(np.log(x)),'r--')
intersection_points=[]
for i in range(num_lines):
    for j in range(i+1, num_lines):
        coef1=np.polyfit(np.log(x),np.log(y),1)
        coef2=np.polyfit(np.log(x),np.log(y),1)
        poly1d_fn1=np.poly1d(coef1)
        poly1d_fn2=np.poly1d(coef2)
        intersection_point=(np.exp((poly1d_fn2-poly1d_fn1).roots),np.exp(poly1d_fn1((poly1d_fn2-poly1d_fn1).roots)))
        intersection_points.append(intersection_point)
intersection_df=pd.DataFrame(intersection_points,columns=['X','Y'])
intersection_df.to_csv('intersection_points.csv',index=False)
plt.show()

Answer 1

下面的示例代码标识了线条相交的位置。您需要指定

x

、

y

和

n_lines

。代码解决了剩下的问题。

import numpy as np
import matplotlib.pyplot as plt

#
# Synthetic data
#
x = np.linspace(1e-3, 1, 150)
y = np.cos(2 * np.pi * x**2/3)

#Plot the data
f, ax = plt.subplots(figsize=(8, 3))
ax.scatter(x, y, marker='|', s=90)
ax_lims = ax.axis()

#
# Fit lines
#
n_lines = 3

#Divide the x range into n_lines segments
points_per_line = len(x) // n_lines

coefs_per_line = []
for index in range(n_lines):
    start = points_per_line * index
    end = start + points_per_line
    
    #If this is the last line,
    # Use up all the remaining points
    is_last_line = (index == n_lines - 1)
    if is_last_line:
        end = len(x)
        
    x_segment = x[start:end]
    y_segment = y[start:end]
    
    #Fit line, and store coefficients
    slope, intercept = np.polyfit(x_segment, y_segment, deg=1)
    coefs_per_line.append((slope, intercept))
    
    #Plot longer lines to show them intersecting
    pad = 10
    x_longer = x[start - pad if is_last_line else start : end if is_last_line else end + pad]
    ax.plot(x_longer, slope * x_longer + intercept, 'r-', linewidth=2)
    
    if index == 0:
        ax.legend(['data', 'linear fits'])

#
# Now, try to find where adjacent lines intersect
#
intersections = []
for index in range(n_lines - 1):
    #Get the coefficients for a line, and the line next to it
    slope_a, intercept_a = coefs_per_line[index]
    slope_b, intercept_b = coefs_per_line[index + 1]
    
    #Solve for the x where line_a = line_b
    #No solution when they're parallell (slope_a = slope_b)
    if slope_a == slope_b:
        intersection_x = np.nan
    else:
        intersection_x = (intercept_a - intercept_b) / (slope_b - slope_a)
    intersections.append(intersection_x)

#
# Finally, add lines showing the locations of the intersections
#

for intersection in intersections:
    ax.vlines(intersection, ymin=y.min() - 1, ymax=y.max() + 1, color='k', linestyle=':')
    
ax.axis(ax_lims)