import numpy as np

class Perceptron$($object$)$:

$"""$Perceptron classifier.

Parameters

$------------$

eta : float

Learning rate $($between $0\mathrm{.}0$ and $1\mathrm{.}0)$

n$\_$iter : int

Passes over the training dataset.

random$\_$state : int

Random number generator seed for random weight

initialization.

Attributes

$-----------$

w$\_$ : $1$d$-$array

Weights after fitting.

errors$\_$ : list

Number of misclassifications $($updates$)$ in each epoch.

$"""$

def $\_\_$init$\_\_($self$,$ eta$=0\mathrm{.}01,$ n$\_$iter$=50,$ random$\_$state$=1)$:

self.eta $=$ eta

self.n$\_$iter $=$ n$\_$iter

self.random$\_$state $=$ random$\_$state

def fit$($self$,$ X$,$ y$)$:

$"""$Fit training data.

Parameters

$----------$

X : $\{$array$-$like$\},$ shape $=[$n$\_$examples, n$\_$features$]$

Training vectors, where n$\_$examples is the number of examples and

n$\_$features is the number of features.

y : array$-$like, shape $=[$n$\_$examples$]$

Target values.

Returns

$-------$

self : object

$"""$

rgen $=$ np$.$random.RandomState$($self$.$random$\_$state$)$

self.w$\_=$ rgen.normal$($loc$=0\mathrm{.}0,$ scale$=0\mathrm{.}01,$ size$=1+$ X$.$shape$[1])$

self.errors$\_=[]$

for $\_$ in range$($self$.$n$\_$iter$)$:

errors $=0$

for xi$,$ target in zip$($X$,$ y$)$:

update $=$ self.eta $*($self$.$predict$($xi$)-$ target$)$

self.w$\_[1$:$]+=$ update $*$ xi

self.w$\_[0]+=$ update

errors $+=$ int$($update $!=0\mathrm{.}0)$

self.errors$\_.$append$($errors$)$

###### New code for doing nothing. $-$ MEH

this$\_$code$\_$does$\_$nothing $=$ True

######

return self

def net$\_$input$($self$,$ X$)$:

$"""$Calculate net input"""

return np$.$dot$($X$,$ self.w$\_[1$:$])+$ self.w$\_[0]$

def predict$($self$,$ X$)$:

$"""$Return class label after unit step"""

return np$.$where$($self$.$net$\_$input$($X$)>=0\mathrm{.}0,1,-1)$

There is a significant error in the above perceptron implementation. Work on the above cell and modify the code so that:

$($i$)$ The line containing the error is commented out, and a new line is added with corrected code.

$($ii$)$ The fit function stops when no more iterations are necessary.

$($iii$)$ The trained perceptron contains as an attribute not only its weights, but also the number of iterations it took for training.

$($iv$)$ The perceptron maintains a history of its weights, i$.$e$.$ the set of weights after each point is processed.

At each place where you have modified the code, please add clear comments surrounding it$,$ similarly to the $"$do$-$nothing" code. Make sure you evaluate the cell again, so that following cells will be using the modified perceptron.