Forcing specific intercepts using scipy.curve_fit

Question

I am currently trying several methods to fit and afterwards transform some data using a 2nd degree polynomial function. I have been using the following code to that end:

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

def fitFunc(self, x,a,b,c):
    return a*x**2 + b*x + c

def calcQuadratic(self,data):
    """ This function fits the specified function in 'fitFunc'
    to the data, using the curve_fit package from scipy.optimize.

    INPUT: A list of (m/z,int) tuples
    OUTPUT: The parameters for the fitted function
    """
    expected = []
    observed = []
    for i in data:
        expected.append(i[0])
        observed.append(i[1])
    z = curve_fit(self.fitFunc, observed, expected)
    #############
    # Plot Code #
    #############
    newX = numpy.linspace(0,400,2500)
    yNew = self.fitFunc(newX,*z[0])
    fig =  plt.figure()
    ax = fig.add_subplot(111)
    plt.scatter(expected,observed,label='raw')
    plt.plot(newX,yNew,label='obs-exp')
    plt.legend()
    plt.show()
    ###############
    # end of plot #
    ###############
    return z[0]

Subsequently I transform the data by doing basically:

   new = []
   for i in data:
      new.append((fitFunc(i[0],*z[0]),i[1]))

Problem

The above transformation can result in my Y-intercept having a positive X-value. The result of that is that after the transformation, I have data that is now found at the same value (see the picture below)

The data points connected by the purple line are examples of problem cases, data observed at ~5 seconds and ~110 seconds would be forced to a time of ~100 seconds after transformation.

Question

Therefore, I would like to know if there is a way to force the function maximum (or minimum) to X = 0? I am also open to other suggestions to bypass this problem (currently, I am ignoring the left half of the polynomial as a temporary dirty hack/fix).

Additional information

Removing the b*x part of the fit function is not a possibility as this function should be able to return a (near) linear fit as well, see the below plot

If "near-linear" and quadratic results are both legitimate possibilities, I suspect you are looking for some sort of empirical fit. Perhaps a power law would be a better model: `a*x**b + c`. This includes the possibilities of a parabola (`b` is 2), and a line (`b` is 1). — Warren Weckesser, Aug 10 '15 at 15:01
You do not pass the parameter c to fitFunc; is that on purpose? You can add the point (0,0) to your data and then use a high weight for this point. I show something similar for R [here.](http://stackoverflow.com/questions/31837610/forcing-nls-to-fit-a-curve-passing-through-a-specified-point/31888068#31888068) If you provide all your data, I could try to do this for Python as well which should not be too difficult; you then pass 'sigma' in the curve_fit function: [doc](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.curve_fit.html). — Cleb, Aug 10 '15 at 16:12
Possible duplicate of http://stackoverflow.com/questions/16541171/how-do-i-put-a-constraint-on-scipy-curve-fit — Daniel Renshaw, Aug 10 '15 at 16:28
@Cleb The omission of `c` is an error on mine part when writing the question here. Furthermore, I will attach the coordinates that I used in both example segments. — Bas Jansen, Aug 10 '15 at 16:41
@WarrenWeckesser I will accept your answer on using power law if you write one, that indeed achieved everything that I wanted. — Bas Jansen, Aug 10 '15 at 17:09

score 1 · Accepted Answer · answered Aug 10 '15 at 17:57

If "near-linear" and quadratic results are both legitimate possibilities, I suspect you are looking for some sort of empirical fit. Perhaps a power law would be a better model: a*x**b + c. This includes the possibilities of a parabola (b is 2), and a line (b is 1)

Forcing specific intercepts using scipy.curve_fit

1 Answers1