why the output of curve fitting is not true?

Question

I am trying to fit a curve into my data. my function is polynomial order 3 as bellow:

def objective3(x, a, b, c,d):
    return a * x + b * x**2 + c * x**3 +d
y=center_1080[itr,:]
x=[1000 ,2000, 3000, 4000, 5000, 6000, 8000, 10000, 12000]
popt, pcov,info,msg, ier= curve_fit(objective3, x, y,full_output=True)
a, b, c ,d= popt

y has the same shape as x. after that I used the following code to find the new values based on this curve for y:

x_line4 = arange(min(x), max(x), 1)
# calculate the output for the range
y_line4 = objective3(x_line4, a, b, c,d)

suppose x_line4 value is as follows (shape (5,):

when I use objective3(x_line4,a,b,c,d) the output is:

but when I use each element of x_line4 separately as input the output is different. for example objective3(11999,a,b,c,d)=81.11075844620781but objective3(x_line4[4],a,b,c,d)=66.4773!!!! what is the problem? a=0.003184157353698613,b=-2.2820353448818053e-07,c=8.475420387015893e-12,d=61.11802131658904

Asked By: david

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Answer 1

What you are experiencing is an int-overflow:
The type of x_line4[4] is int32 which is limited to 2,147,483,648. If you plug in 11999 instead, you still have an int that is in principle limited to the same range, but Python seems to perform automated adjustment of the int from a int32 to an int64 or something alike under the hood (not sure here).

For the individual numbers, the easiest thing to do is to add x = float(x) in the first row of your function objective3. If you expect your function to handle both single numbers as well as numpy arrays, you will have to check whether it is an numpy array using something like this:

import numpy as np

def objective3(x, a, b, c,d):
    if isinstance(x, np.ndarray):
        x.astype(float)
    else:
        x = float(x)
    return a * x + b * x**2 + c * x**3 +d

Alternatively, you could also ensure that all numpy arrays are float arrays instead.

Edit: Just for clarification: The part where the error occurs is the x**3 since that value is above the maximum value an int32 can hold.

Answered By: C Hecht

why the output of curve fitting is not true?

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