Question

我一直在努力拟合本文http://arxiv.org/ftp/arxiv/papers/1202/1202.4380.pdf中公式21给出的傅立叶级数解。但是代码并没有正确地最小化chi_squared函数。我查看了scipy.optimize的文档，并设法最小化其他功能。你能否为我的代码建议修改或建议替代方案。

from __future__ import division
import numpy
import scipy.optimize

Z            = 0.0314 #m length between the thermocouples
T1_data      = numpy.array(       [20.0,20.1,20.4,21.0,21.8,22.4,23.1,23.8,25.5,25.2,26.0,26.7,27.3,28.0,28.7,29.3,29.9,30.6,31.2])
T_Theory     = numpy.array( [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
T2_data      = numpy.array( [20.0,20.6,21.7,22.6,23.6,24.4,25.0,25.7,26.5,27.2,27.9,28.6,29.3,30.0,30.7,31.3,31.9,32.6,33.2])
time_diff    = 10
f            = 100

T1_max       = T1_data.max()
T1_data      = T1_data/T1_max

T2_max       = T2_data.max()
T2_data      = T2_data/T2_max


def omega_n(n):
    return ((2*n)+1)*numpy.pi / (2*Z)

def phi_n(n):
    return numpy.sin(omega_n(n)*Z)

def F_n(n):
    return 2/ (Z*omega_n(n))

def theoretical2(dif):
    T_Theory[0]=T1_data[0]
    for d in range(1,len(T1_data)): # Calculate the theoretical data 
        for n in range((f+1)): # n is the power of the fourier co-efficient go up to
            for p in range(1, d+1):
                exp_pow3 = -1 * dif * time_diff * (d-p)* (omega_n(n))**2        
                T_Theory[d] = T_Theory[d-1] + (T1_data[(p-1)] -    T1_data[p])*F_n(n)*phi_n(n)*numpy.exp(exp_pow3)


def chi_squared(dif):
    theoretical2(dif)
    chi_sum = 0
    for c in range ( len(T2_data)):
        chi_sum = chi_sum + (T_Theory[c] - T1_data[c])**2
    return chi_sum

if __name__ == "__main__":
    x0 = 0.0075

    diff = scipy.optimize.minimize(chi_squared,x0)
    print diff

感谢您查看我的代码。任何帮助将不胜感激。

谢谢你，Alex

Python-Chi平方最小化问题

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