I am trying to minimize a function that outputs chi-square via scipy and find the mu,sigma,normc that provide the best fit for a Gaussian overlay.
from math import exp
from math import pi
from scipy.integrate import quad
from scipy.optimize import minimize
from scipy.stats import chisquare
import numpy as np
# guess intitial values for minimized chi-square
mu, sigma = np.mean(mydata), np.std(mydata) # mydata is my data points
normc = 1/(sigma * (2*pi)**(1/2))
gauss = lambda x: normc * exp( (-1) * (x - mu)**2 / ( 2 * (sigma **2) ) ) # Gaussian Distribution
# assume I have pre-defined bin-boundaries as a list called binbound
def expvalperbin(binbound,mu,sigma,normc):
# calculates expectation value per bin
ans = []
for index in range(len(binbound)):
if index != len(binbound)-1:
ans.append( quad( gauss, binbound[index], binbound[index+1])[0] )
return ans
expvalguess = expvalperbin(binbound,mu,sig,normc)
obsval = countperbin(binbound,mydata)
arglist = [mu,sig,norm]
def chisquareopt(obslist,explist):
return chisquare(obslist,explist)[0]
chisquareguess = chisquareopt((obsval,expvalguess), expvalguess, args=arglist)
result = minimize( chisquareopt(obsval,expvalguess), chisquareguess )
print(result)
Running this code provides me with this error:
TypeError: chisquareopt() got an unexpected keyword argument 'args'
I have a few questions:
1) How can I write a function to allow arguments to be passed through to my function chisquareopt?
2) How can I tell if scipy will optimize parameters [mu, sigma, normc] that give the minimum chi-square? How could I find these parameters from the optimization?
3) It is difficult to know if I'm making progress here or not. Am I on the right track?
EDIT: If it is relevant, I have a function that inputs [mu, sigma, normc] and outputs a list of sublists, each sublist containing a possible combination of [mu, sigma, normc] (where the outer list covers all possible combinations of parameters within specified ranges).
I've simplified your problem somewhat to give you an idea on your question 2).
First, I've hard-coded your histogram obslist and the number of data points N as global variables (that simplifies the function signatures a little). Second I've hard-coded the bin boundaries in expvalperbin, assuming 9 bins with fixed width 5 and the first bin starts at 30 (so the histogram ranges from 30 to 75).
Third, I'm using optimize.fmin (Nelder-Mead) instead of optimize.minimize. The reason for using fmin instead of minimize is that the passing of additional parameters via args=(x,y) doesn't seem to work in the sense that the additional parameters are kept at the fixed values from the very first invocation. That's not what you want: you want to optimize over mu and sigma simultaneously.
Given these simplifications we have the following (surely very unpythonic) script:
from math import exp
from math import pi
from scipy.integrate import quad
from scipy.optimize import fmin
from scipy.stats import chisquare
obslist = [12, 51, 144, 268, 264, 166, 75, 18, 2] # histogram, 1000 observations
N = 1000 # no. of data points
def gauss(x, mu, sigma):
return 1/(sigma * (2*pi)**(1/2)) * exp( (-1) * (x - mu)**2 / ( 2 * (sigma **2) ) )
def expvalperbin(mu, sigma):
e = []
# hard-coded bin boundaries
for i in range(30, 75, 5):
e.append(quad(gauss, i, i + 5, args=(mu, sigma))[0] * N)
return e
def chisquareopt(args):
# args[0] = mu
# args[1] = sigma
return chisquare(obslist, expvalperbin(args[0], args[1]))[0]
# initial guesses
initial_mu = 35.5
initial_sigma = 14
result = fmin(chisquareopt, [initial_mu, initial_sigma])
print(result)
Optimization terminated successfully.
Current function value: 2.010966
Iterations: 49
Function evaluations: 95
[ 50.57590239 7.01857529]
Btw., the obslist histogram is a 1000 point random sample from a N(50.5, 7.0) normal distribution. Remember that these are my very first Python code lines, so please don't judge me on the style. I just wanted to give you an idea about the general structure of the problem.