New answers tagged regression
1
I think that you can also solve the problem analytically.
We can write the problem as
$$\min_{a, b} f$$
with
$$f = \sum_{i = 1}^N \int\limits_{E_i}^{E_{i + 1}}(n_i - a - bE)^2 dE \, .$$
And the minimum should happen when $\nabla f = 0$ or (I would double check)
\begin{align}
&\sum_{i = 1}^N \int\limits_{E_i}^{E_{i + 1}}(n_i - a - bE) dE = 0\, ,\\
&\...
0
Edited to correct assumption on step width
If your fitting function is simply a linear relation like $a + bE$ then it's very similar to a simple linear regression (least squares) with weights. For each element (of width $w$ and centred at 0), it is simple to show that the terms in $E$ vanish so:
$$\int_{-w/2}^{w/2} \left[n(E) - a - bE\right]^2 dE = w\left(n(...
2
You could use the floor function
$$n(E) = \lfloor a + b E\rfloor\, .$$
Following is an example with $a=5$ and $b=3$.
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
def fun(x, a, b):
return a + b*x
xdata = np.linspace(-5, 5, 2001, endpoint=False)
ydata = np.floor(5 + 3*xdata)
popt, pcov = curve_fit(fun, ...
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