optimization problem with piecewise curve fitting

Question

I want to fit my data with a piecewise function that I have shown below,
The whole graph is a semilogarithmic graph, and I want to fit it with two different logarithmic functions that I have shown in different colors (purple and red are drawn with my hand). The problem is that it doesn’t work, and I don’t know what I’m doing wrong. I will post the mini-code that I have summarized.


import numpy as np
from scipy.optimize import curve_fit
def func_stuck(t, a, b, c, d, e , f): # x-shifted log
    y = np.piecewise(t, [t < 100, t >= 100],
                     [lambda t:a*np.log(t + b)+c, lambda t:d*np.log(t + e)+f])
    return y

plt.semilogx(sensor_array__[0],sensor_array__[1])
popt, pcov = curve_fit(func_stuck,sensor_array__[0], sensor_array__[1],maxfev=100000000)
function_x = np.linspace(0.1 , 1200, 1200)
fitted_y = np.asarray(popt[0]*np.log(function_x + popt[1])+popt[2]+popt[3]*np.log(function_x + popt[4])+popt[5])
plt.semilogx(function_x,fitted_y)

what I get:

what I want to get:

Data

my second attempt give me this one:
But still not the one that I need.

Asked By: Ali AlCapone

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Source

Answer 1

Forget about calling the piecewise function. Slice to the segment of the array you care about, and only fit on that.

import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit


x_mid = 100


def func_stuck(t: np.ndarray, a: float, b: float, c: float, d: float, e: float) -> np.ndarray:
    # aln(x_mid + b) + c = dln(x_mid + e) + f
    f = a*np.log(x_mid + b) + c - d*np.log(x_mid + e)

    y = np.empty_like(t)
    m = mid - start
    y[:m] = a*np.log(t[:m] + b) + c
    y[m:] = d*np.log(t[m:] + e) + f
    return y


x, y = np.loadtxt('sample.csv', delimiter=',')
start = np.nonzero(x >= 0.1)[0][0]
mid = np.nonzero(x >= x_mid)[0][0]

popt, _ = curve_fit(
    func_stuck, x[start:], y[start:],
    bounds=(
        # a       b                     c        d        e
        (-np.inf, -x[start: mid].min(), -np.inf, -np.inf, -x[mid:].min()),
        (+np.inf, +np.inf,              +np.inf, +np.inf, +np.inf       ),
    ),
)
print(popt)
fitted_y = func_stuck(x, *popt)
plt.semilogx(x, y)
plt.semilogx(x[start: mid], fitted_y[start: mid], c='pink')
plt.semilogx(x[mid:],       fitted_y[mid:],       c='red')
plt.show()

[-1.31250596e+02  1.72352140e-01 -2.47615596e+02 -5.33493810e+01
 -6.92009813e+01]

Answered By: Reinderien

optimization problem with piecewise curve fitting

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