[SciPy-User] How to optimize 2D data with leastsq in Python?

[nxkryptor nxkr]

I have data <https://drive.google.com/open?id=0BwwhEMUIYGyTQXdVR2dvLXhfZnc>
of the form given below:

X   Y1  Y2  Y3  Y4  Y5  Y61.42857 4.83    4.58    4.43    4.31    4.22
   4.141.40845 3.87    3.63    3.49    3.38    3.3 3.231.38889 3.17
2.93    2.79    2.69    2.62    2.561.36986 2.65    2.41    2.27
2.17    2.11    2.051.35135 2.27    2.02    1.88    1.78    1.72
1.67
    :     :       :       :       :        :      :1.01010 2.26    1.6
1.21    0.97    0.79    0.661.00000 2.01    1.44    1.1 0.88    0.73
 0.62

I am trying to optimize a function of the form:

[image: enter image description here]
<http://i.stack.imgur.com/xfX0Y.png> [image:
enter image description here] <http://i.stack.imgur.com/aokSR.png>

Now my y variable has 6 columns, I can optimize one column (in MWE #3)
which I have done in the MWE. How can I optimize the function to get the
parameters A, n and B for all the 6 column values? In other words how can I
get the value one value of A, n and B for all 6 values of y.

*MWE*

import numpy as npfrom scipy.signal import argrelextremaimport
scipy.interpolatefrom scipy.optimize import leastsq

with open('./exp_fit.dat', "r") as data:
    while True:
        line = data.readline()
        if not line.startswith('#'):
            break
    data_header = [i for i in line.strip().split('\t') if i]
    _data_ = np.genfromtxt(data, names = data_header, dtype = None,
delimiter = '\t')
_data_.dtype.names = [j.replace('_', ' ') for j in _data_.dtype.names]
data = np.array(_data_.tolist())

x = _data_['X']
x_interp = np.linspace(x[-1], x[0], 100)

y = np.zeros(shape = (len(x), 6))
y_interp = np.zeros(shape = (len(x_interp), 6))for i in range(6):
    y[:, i] = data[:, i + 1]
    tck = scipy.interpolate.splrep(x[::-1], y[::-1, i], s=0)
    y_interp[::-1, i] = scipy.interpolate.splev(x_interp, tck, der = 0)

def residuals(p, y, x):
    A_lt, n_lt, B_lt, A_it, n_it, B_it, A_ht, n_ht, B_ht = p
    err = y - (1 / (1 / ((A_it * (15 ** (-n_it)) * np.exp(B_it * x / 1000)) + \
        (A_lt * (15 ** (-n_lt)) * np.exp(B_lt * x / 1000))) + \
        1 / (A_ht * (15 ** (-n_ht)) * np.exp(B_ht * x / 1000))))
    return err
p1 = [2.789E-05, 1.47, 9.368E+03, 2.789E-05, 1.47, 9.368E+03,
2.789E-05, 1.47, 9.368E+03]
plsq = leastsq(residuals, p1, args=(y_interp[:, 2], x_interp))

The question is also available on SO
<http://stackoverflow.com/questions/38155014/how-to-optimize-2d-data-with-leastsq-in-python>.

nxkr
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