我正在探索一些numpy / scipy函数,并且我注意到scipy.optimize.fmin_bfgs要求对被调用的函数进行更改以提供与直接函数调用相比正确的结果。我对fnRSS
函数的第一个定义在调用函数时返回了正确的值,但拒绝进行优化。我的第二个定义在调用函数时给出了错误的结果,但在运行优化时给出了正确的结果。有人可以告诉我,为vY
优化而调换参数有何关键?它应该已经是164x1。
import numpy as np
import scipy as sp
import pandas as pd
from scipy import optimize
if __name__ == "__main__":
urlSheatherData = "http://www.stat.tamu.edu/~sheather/book/docs/datasets/MichelinNY.csv"
data = pd.read_csv(urlSheatherData)
Xs = np.vstack(data[['Service','Decor', 'Food', 'Price']].values)
Xs = np.concatenate((np.vstack(np.ones(Xs.shape[0])),Xs), axis=1)
Ys = np.vstack(data[['InMichelin']].values)
# optimal solution (given)
vBeta = np.array([-1.49209249, -0.01117662, 0.044193, 0.05773374, 0.00179794]).reshape(5,1)
print Ys.shape, Xs.shape, vBeta.shape
# first definition of function
def fnRSS(vBeta, vY, mX):
return np.sum((vY - np.dot(mX, vBeta))**2)
print fnRSS(vBeta, Ys, Xs) # correct value
print np.linalg.lstsq(Xs, Ys)[1] # confirm correct value
print sp.optimize.fmin_bfgs(fnRSS, x0=vBeta, args=(Ys,Xs)) # wrong value
# second definition
def fnRSS(vBeta, vY, mX):
return np.sum((vY.T - np.dot(mX, vBeta))**2)
print fnRSS(vBeta, Ys, Xs) # incorrect value
print sp.optimize.fmin_bfgs(fnRSS, x0=vBeta, args=(Ys,Xs)) # correct convergence but simple call gives different value
我的输出:
(164, 1) (164, 5) (5, 1)
26.3239061505
[ 26.32390615]
Warning: Desired error not necessarily achieved due to precision loss.
Current function value: 6660.000000
Iterations: 39
Function evaluations: 3558
Gradient evaluations: 480
[ 4.51220111e-01 1.32711255e-07 8.09143368e-08 -1.06633003e-07
-5.18448332e-08]
9002.87916028
Warning: Desired error not necessarily achieved due to precision loss.
Current function value: 26.323906
Iterations: 29
Function evaluations: 1954
Gradient evaluations: 260
[-1.49209095 -0.0111764 0.04419313 0.05773347 0.00179789]
它不是关于vY.T
,而是vBeta
,即作为2d向量而不是1d数组x
传递fmin_bfgs
给fnRSS
。因此,尽管您确实尝试明确指定x0=vBeta
为形状(5,1)的数组,但仍会在内部将其转换为形状(5,)的1d数组,最后按原样返回。
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我来说两句