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LorentzFit.py
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LorentzFit.py
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#To start: Please keep this script in the working directory!!
# This script does a Lorentzian fit with a constant baseline or background. It assumes that the input data are numpy arrays(float 64) having a minimum of 20 (X,Y) datapoints. If not 20 datapoints, the user should change N accordingly.
# Users can import the functions: lorentzian, initial_params, fit_lorentzian
#using the syntax given below. Please check their corresponding return variables.
#For example:
# from LorentzFit import lorentzian, initial_params, fit_lorentzian
# Yfit, params, covar, perr, r2 = fit_lorentzian(X, Y, plot=False, plot_path=None)
# If plot=True, plot_path=user_defined_path, it will plot the data and its fit and save with the name 'test.png' in the given path.
# Y_fit : Fitted Y array
# popt : fit estimates
# pcov : var-cov matrix
# perr : 1-sigma error of the fit estimates
# r2 : goodness of fit
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from typing import Callable, List, Optional, Tuple
from pathlib import Path
import warnings
from scipy.optimize import OptimizeWarning
# Configure warnings to raise exceptions
warnings.simplefilter("error", OptimizeWarning)
#import xlsxwriter
#import csv
#import os
######### moving_average : function which does the work as the name suggests :) ##################
def moving_average(n, array):
temp = []
for i in range(len(array)-n):
temp.append(np.mean(array[i:i+n]))
return np.array(temp)
################ -------------o------------------ ######################################
###### fit functions defined #############################
def lorentzian(x, k, gamma, x0, d):
return (k * ((gamma / 2)**2) / ((gamma / 2) ** 2 + (x - x0) ** 2) + d
)
##########----------o----------------##########################
##### Bounds defined for the fit function #########################
def Bounds(X):
kMin, kMax = -np.inf ,np.inf
gammaMin, gammaMax = -0.5 * (np.max(X) - np.min(X)), 0.5 * (np.max(X) - np.min(X))
x0Min, x0Max = np.min(X), np.max(X)
dMin, dMax = -np.inf, np.inf
return ([kMin, gammaMin, x0Min, dMin], [kMax, gammaMax, x0Max, dMax])
#######----------------o-------------------------########################
############ finds the true maxima or minima using moving_average and differentiating the spectrum. A set of initial guesses are passed for Lorentzian fit with constant baseline or background. #########################
def initial_params(X: np.array, Y: np.array,n_moving) -> List[float]:
print("---------Data Metrics------------")
print(f"Your input X,Y data : {type(X)}, {type(Y)}")
if type(X) is not np.ndarray or type(Y) is not np.ndarray:
print(f"Please change the input data type to numpy array of float64!!")
#Check for float type
print(f"Total no. of X,Y datapoints: {len(X)}, {len(Y)}")
if len(X) != len(Y):
print(f"The length of the input numpy arrays should be equal to work with!")
N=int(len(X)/10) #If less than 20 data points, need to modify this accordingly!
print(f"No. of datapoints in first 1/10th of data = {N}")
sigma = np.std(Y[0:N])
print(f"Standard deviation of data = {sigma} \t considering the first 1/10th of the data, supposedly with no peak or dip.\n")
'''User can modify this depending on how noisy the data is and the degree to smoothen it'''
# n_moving = 20
print(f"No. of datapoints used for smoothening = {n_moving} \t #Users can modify this number according to their need! This smoothening does not affect the final fit procedure.\n")
foo = np.diff(moving_average(n_moving,Y))
#-----Plot or save the smoothened and differentiated data----------------#
plt.plot(X[:-n_moving-1],np.diff(moving_average(n_moving,Y)))
plt.plot(X[:-n_moving-1],Y[:-n_moving-1])
# plt.show()
#plt.savefig("random.png",dpi=300)
#-------Zero-crossing index --------------------------------------------#
min_index_foo = np.argmin(foo)
max_index_foo = np.argmax(foo)
max_index = int((max_index_foo + min_index_foo)/2) # zero-crossing index
#print(X[min_index_foo], X[max_index_foo])
print(f"Value of X = {X[max_index]} \t at zero-crossing index = {max_index}")
print(f"Value of Y = {Y[max_index]} \t at zero-crossing index = {max_index}\n")
'''
Y_excluded=Y[max_index-50:max_index+50]
#print(Y_excluded)
#Y_excluded = np.delete(Y, Y_excluded)
print(Y_excluded)
mask = np.ones(Y.shape, dtype=bool)
mask[Y_excluded] = False
Y_excluded = Y[mask]
#print(Y_excluded)
sigma = np.std(Y_excluded)
#print(f"Standard deviation of data = {sigma} \t considering the first 1/5th of the data, supposedly with no peak or dip.\n")
'''
#-----------initial guesses ---------------------------#
gamma0 = np.abs(X[max_index_foo]-X[min_index_foo]) # always positive
x00 = X[max_index]
#d0 = 0.0
d0 = np.mean(Y[0:N]) #considering the first 1/10th of the data
##----True peak or dip should be greater or lesser than (30 times the sigma ---> maybe needs modification depending on quality of data) respectively----------------###
if (min_index_foo < max_index_foo) and (Y[max_index]<30.0*sigma):
print(f"Found a dip!!\n")
#k0 = np.max(Y)-np.mean(Y[0:20])
k0 = Y[max_index]-np.mean(Y[0:N])
elif (min_index_foo > max_index_foo) and (Y[max_index]>30.0*sigma):
print(f"Found a peak!!\n")
#k0 = np.max(Y)-np.mean(Y[0:20])
k0 = Y[max_index]-np.mean(Y[0:N])
else:
print("Found neither a peak nor a dip!!\n")
k0 = 0.0
p0 = [k0, gamma0,x00, d0]
print(f"Initial params [k0, gamma0, x00, d0]: {p0}")
return p0
############### fit_lorentzian: func which fits a lorentzian the peak of the spectrum ###########################
#Y_excluded=[]
#--------Fit optimisation starts here ------------------------#
def fit_lorentzian(
X: np.ndarray,
Y: np.ndarray,
plot: bool = True,
plot_path: Optional[Path] = None,n_moving=10
) -> Tuple[np.ndarray, np.ndarray, float]:
p0=initial_params(X,Y,n_moving)
bounds=Bounds(X)
print(f"Bounds[min], Bounds[max] = {Bounds(X)}\n")
try:
for temp_var in range(5): # Not important----Just to check whether it returns the same fit estimates for greater iterations!!
#print(temp_var,p0)
popt,pcov = curve_fit(f=lorentzian, xdata=X, ydata=Y, p0=p0, maxfev = 10000)
p0=popt # to ensure that at each iteration that estimates of the previous iteration is taken as initial guesses
#pass
#except OptimizeWarning as e:
# raise RuntimeError("Optimization warning occurred") from e
except:
print("Fitting fails\n")
popt = [0.0]*4
pcov = [0.0]*4
#------------ends here -------------------------------------#
#---------Checks for Bound errors!-------------------------------------#
if any(popt <= Bounds(X)[0]) == True:
print(f"WARNING: Value of the parameter estimates {popt} less than or equal to the minm bound {Bounds(X)[0]}\n")
popt[0] = 0.0
popt[1] = 0.0
popt[2] = 0.0
pcov[0] = 0.0
pcov[1] = 0.0
pcov[2] = 0.0
if any(popt >= Bounds(X)[1]) == True:
print(f"WARNING: Value of the parameter estimates {popt} greater than or equal to the maxm bound {Bounds(X)[1]}\n")
popt[0] = 0.0
popt[1] = 0.0
popt[2] = 0.0
pcov[0] = 0.0
pcov[1] = 0.0
pcov[2] = 0.0
#--------------------------o-----------------------------------------#
#--------Print the parameter estimates and goodness of fit --------------------#
[k_fit, gamma_fit, x0_fit, d_fit] = popt
#print(f"popt={popt}")
#---------1-sigma error of the estimates--------------------------#
perr = np.sqrt(np.diag(pcov))
print("1sigma-err=", perr)
# -----------calculate goodness of fit using R^2----------------#
X_fit = np.linspace(X[0],X[-1],int(1000*len(X)))
Y_fit = lorentzian(X, *popt)
# calculate R^2 , the length of X and Y arrays should be equal !
r2 = round(1.0 - (np.var(Y - Y_fit) / np.var(Y)), 3)
FWHM = np.abs(gamma_fit)
print("k_fit or fit value of amplitude:", k_fit)
print("gamma_fit or fit value of gamma:", np.abs(gamma_fit))
print("x0_fit or fit value of resonance:", x0_fit)
print("d_fit or fit value of background level:", d_fit)
Amp_fit = k_fit
print("r2:", r2)
#---------------------------o-------------------------------------------------#
#------OPTIONAL - if the Plot bool is True ------------------------------------#
Y_fit = lorentzian(X_fit, *popt)
if plot:
# plot the original data
plt.scatter(X, Y, color="black", marker=".",alpha = 0.5, label="Data")
# plot Lorentzian fit
plt.plot(
X_fit,
Y_fit,
color="red",
alpha=0.5,
label=f"Lorentzian fit \n x0={round(x0_fit,3)} \n R2={r2} \n Bkgd fit type: Constant",
)
plt.xlabel("Wavelength (nm)")
plt.ylabel("Transmitted Power(mW)")
#plt.grid(True)
plt.legend()
#plt.show()
print("Finished plotting Lorentzian")
plt.savefig(fname="test.png", dpi=300)
print("Finished saving plot\n")
#----------------------o--------------------------------------------#
return Y_fit, popt, pcov, perr, r2
############### returns the fit Y values, fitting parameters estimates, var-cov matrix, 1-sigma error of parameter estimates and goodness of fit(r2) ###########################