在Python中同時擬合N個數據集

Question

我有一個函數可以適用於許多不同的數據集，所有數據集都具有相同的點數。例如，我可能想要將多項式擬合到圖像的所有行。有沒有一種有效的，矢量化的方式來做這件事，用scipy或其他包，還是我不得不求助於一個單一的循環（或使用多處理，以加快一點）？

Answer 1

您可以使用numpy.linalg.lstsq：

import numpy as np 

# independent variable 
x = np.arange(100) 

# some sample outputs with random noise 
y1 = 3*x**2 + 2*x + 4 + np.random.randn(100) 
y2 = x**2 - 4*x + 10 + np.random.randn(100) 

# coefficient matrix, where each column corresponds to a term in your function 
# this one is simple quadratic polynomial: 1, x, x**2 
a = np.vstack((np.ones(100), x, x**2)).T 

# result matrix, where each column is one set of outputs 
b = np.vstack((y1, y2)).T 

solutions, residuals, rank, s = np.linalg.lstsq(a, b) 

# each column in solutions is the coefficients of terms 
# for the corresponding output 
for i, solution in enumerate(zip(*solutions),1): 
    print "y%d = %.1f + (%.1f)x + (%.1f)x^2" % ((i,) + solution) 


# outputs: 
# y1 = 4.4 + (2.0)x + (3.0)x^2 
# y2 = 9.8 + (-4.0)x + (1.0)x^2