Question

我正在尝试应用适合下面给出的数据（任意）集的2D曲线：

# Data
T   Z   X 1 X 2 X 3 X 4 X 5
100.000 1.000   1.000   1.478   1.304   1.162   0.805
200.000 1.500   2.000   2.314   2.168   2.086   1.801
300.000 2.250   3.000   3.246   3.114   3.058   2.798
400.000 3.375   4.000   4.211   4.087   4.044   3.780
500.000 5.063   5.000   5.189   5.070   5.035   4.780

最终目标是建立Z = f（X，T） 形式的相关性。

首先，使用二次表达式Z = a * x ^ 2 + b * x + c沿着T的常数值，即沿着每一行进行曲线拟合，这给出了如下给出的每个T的拟合参数（如一个例子）：

T   a   b   c
100.00  1.00    2.10    10.02
200.00  4.00    6.20    10.06
300.00  9.00    12.30   10.12
400.00  16.00   20.40   10.20
500.00  25.00   30.50   10.31

现在我想在T中拟合每个拟合参数，以便得到形式a = p * T ^ 2 + q * T + r，b = s * T ^ 2 + t * T + u的方程式等我尝试使用代码来应用它：

from __future__ import division
from scipy import optimize
import matplotlib.pyplot as plt
import numpy as np

data = open('data.dat', "r")
line = data.readline()
while line.startswith('#'):
    line = data.readline()
data_header = line.split("\t")
data_header[-1] = data_header[-1].strip()


_data_ = np.genfromtxt('data.dat', skiprows=2, delimiter='\t', names = data_header, dtype = None, unpack = True).transpose()
data = np.array(_data_.tolist())
m = data.shape[0]
n = data.shape[1] - 2
print m, n
y_data = np.empty(shape=(m, n))
for i in range(0, m):
    for j in range(0, n):
        y_data[i, j] = (data[i, j+2])
x = _data_['X']
z = _data_['Z']

def quadratic_fit(x, a, b, c):
    return a * x ** 2 + b * x + c

fit_a = np.empty(shape = (m, 1))
fit_b = np.empty(shape = (m, 1))
fit_c = np.empty(shape = (m, 1))
z_fit = np.empty(shape=(m, len(z)))
for j in range(m):
    x_fit = y_data[j, :]
    y_fit = z
    fit_a[j], fit_b[j], fit_c[j] = optimize.curve_fit(quadratic_fit, x_fit, y_fit)[0]
fit_a_fit_a, fit_a_fit_b, fit_a_fit_c, = optimize.curve_fit(quadratic_fit, x, fit_a)[0]
fit_b_fit_a, fit_b_fit_b, fit_b_fit_c, = optimize.curve_fit(quadratic_fit, x, fit_b)[0]
fit_c_fit_a, fit_c_fit_b, fit_c_fit_c, = optimize.curve_fit(quadratic_fit, x, fit_c)[0]
fit_a = fit_a_fit_a * x ** 2 + fit_a_fit_b * x + fit_a_fit_c
fit_b = fit_b_fit_a * x ** 2 + fit_b_fit_b * x + fit_b_fit_c
fit_c = fit_c_fit_a * x ** 2 + fit_c_fit_b * x + fit_c_fit_c
for j in range(m):              
    z_fit[j, :] = (fit_a[j] * x_fit ** 2) + (fit_b[j] * x_fit) + fit_c[j]

但它给了我以下错误：

ValueError: object too deep for desired array
Traceback (most recent call last):
    fit_a_fit_a, fit_a_fit_b, fit_a_fit_c, = optimize.curve_fit(quadratic_fit, x, fit_a)[0]
  File "scipy/optimize/minpack.py", line 533, in curve_fit
    res = leastsq(func, p0, args=args, full_output=1, **kw)
  File "scipy/optimize/minpack.py", line 378, in leastsq
    gtol, maxfev, epsfcn, factor, diag)
minpack.error: Result from function call is not a proper array of floats.

如何在Python中完成？

Answer 1

我只是玩了一下，我认为你的问题是行

fit_a = np.empty(shape = (m, 1))
fit_b = np.empty(shape = (m, 1))
fit_c = np.empty(shape = (m, 1))

应该是

fit_a = np.empty(shape = (m, ))
fit_b = np.empty(shape = (m, ))
fit_c = np.empty(shape = (m, ))

看起来形状（m，1）肯定是正确的，但它不像形状（m，）那样仅仅是一维数组。试试看，看看它是否有效。

那就是说，我不确定拟合拟合参数是解决这个问题的正确方法，至少就我理解而言......

Answer 2

我可以借此机会无耻地插上我自己的试衣包symfit吗？

我精心开发它可以使您的装配问题更容易。如果没有针对您的问题运行它，我将使用symfit来解决此问题：

from symfit import parameters, variables, Fit

Z, X, T = variables('Z, X, T')
p, q, r, s, t, u  = parameters('p, q, r, s, t, u')

a = p * T**2 + q * T + r
b = s * T**2 + t * T + u
c = ...
model = {Z: a * X ** 2 + b * X + c}

fit = Fit(model, X=_data_['X'], T=_data_['T'], Z=_data_['Z'])
fit_result = fit.execute()

print(fit_result)

有关详细信息，请查看文档:)。

如何在Python中应用2D曲线拟合？

2 个答案: