[SciPy-User] How to curve fit a set of fitting parameters in Python?

[nxkryptor nxkr]

Dear SciPy users,

I am trying to curve fit a data (arbitrary) set as given below:

# 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

At first it is curve fit using a quadratic expression Z = a * x ^ 2 + b * x
+ c along a constant value of T i.e. along each rows, which gives as fit
parameters for each T as given below (as an example):

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

Now I would like to fit each fit parameters along T so that I get the
equations of the form a = p * T ^ 2 + q * T + q, b = s * T + u, etc. I
tried applying this using the code:

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]

This question has already been posted on Stackoverflow
<http://stackoverflow.com/questions/29352734/how-to-curve-fit-a-set-of-fitting-parameters-in-python>
.

Thank you.

nxkr
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