Description

In this assignment we will implement the method of Least Squares fitting using a python script. For matrix routines, you may choose to use the linear algebra library routines in the numpy library, you may also use routines from this library $($which I wrote$),$ or you may wish to write your own routines. $($I like to write my own because I am too lazy to learn how to use those others have written!$)$

Your program should do the following:

take a command$-$line argument that specifies a data file containing the data to be fitted. $($Sample data file$)$

if this argument is not provided by the user, the program should prompt the user for a file

Read the data file and create the required matrices and vectors to perform the fit

Utilize matrix inversion and multiplication routines to perform the fit

Report the results including

obs$-$calc for each data point

the values of the adjustable parameters

including their uncertainties

the standard deviation of the fit.import numpy as npimport matplotlib.pyplot as pltfrom scipy.fft import fft$,$ ifft# Define single$\_$scansingle$\_$scan $=$ np$.$random.normal$(0,1,100)$  # Single scandef fourier$\_$smoothing$($data$,$ cutoff$)$: ft$\_$signal $=$ fft$($data$)$  ft$\_$signal$\_$filtered $=$ ft$\_$signal.copy$()$  ft$\_$signal$\_$filtered$[$cutoff:$]=0$  # Apply low$-$pass filter smoothed$\_$signal $=$ np$.$real$($ifft$($ft$\_$signal$\_$filtered$))$  return smoothed$\_$signalcutoff$\_$freqs $=[10,20,30]$  # Example cutoff frequenciesplt.figure$($figsize$=(10,6))$plt$.$plot$($single$\_$scan, label$=$'Original Signal'$)$for cutoff in cutoff$\_$freqs: smoothed$\_$signal $=$ fourier$\_$smoothing$($single$\_$scan, cutoff$)$  plt$.$plot$($smoothed$\_$signal, label$=$f'Cut$-$off Frequency: $\{$cutoff$\}\text{'})$plt$.$xlabel$(\text{'}$Data Points'$)$plt$.$ylabel$(\text{'}$Intensity$\text{'})$plt$.$title$(\text{'}$Fourier Transform Smoothing'$)$plt$.$legend$()$plt$.$show$()$