human
Write me a the Python program you requested given the following:
I am working on the file "2.Backpropagation.ipynb".
The first task is:
All together now ... with bias
Can you write Python program for it?
assistant
#Here is the Python program you requested.

import numpy as np

#Example dataset
N_samples_per_class = 1000
d_dimensions = 2
x = np.vstack((np.random.randn(N_samples_per_class, d_dimensions),np.random.randn(N_samples_per_class, d_dimensions)+np.array([3,3])))
y = np.vstack((-1.*np.ones((N_samples_per_class,1)),1.*np.ones((N_samples_per_class,1))))

%matplotlib inline
import matplotlib.pyplot as plt

idx = y==1
plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.1)
idx = y==-1
plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.1,color='pink')

import numpy as np
import tqdm

class loss:
    def __init__(self):
        self.y = 0    
    def evaluate(self,model,x,t):
        #Evaluates the loss function L(y,t)
        self.y = model.forward(x)
        return (t-self.y)*(t-self.y)
    def gradient(self,model,x,t):
        self.y = model.forward(x)
        return -2.*(t-self.y)
    
class reluLayer(layer): #this is a linear layer with relu activation
    def __init__(self,input_dim,n_neurons):
        self.z = np.zeros((1,n_neurons))
        self.w = np.random.randn(input_dim+1,n_neurons) 
        #self.w = self.w/np.dot(np.ones((input_dim+1,1)),np.sum(self.w*self.w,axis=0)[np.newaxis,:])
        self.y = np.zeros((1,n_neurons))
    def forward(self,x): # evaluate the layer
        self.xext = np.concatenate((x,np.ones((x.shape[0],1))),axis=1)
        self.z = np.dot(self.xext, self.w)
        self.y = np.maximum(0,self.z)
        return self.y
    def backward(self): # gradient with respect to the inputs
        dydz = np.tile(np.where(self.z>0.,1.,0.),(self.w.shape[0],1))
        tw = dydz*self.w
        return tw[:-1,:] 
    def gradient(self): # gradient with respect to the parameters
        dydz = np.where(self.z>0.,1.,0.)
        return np.dot(dydz.T,self.xext)
    
class linearLayer(layer): #this is a linear layer with relu activation
    def __init__(self,input_dim,n_neurons):
        self.w = np.random.randn(input_dim+1,n_neurons) 
        self.y = np.zeros((1,n_neurons))
    def forward(self,x): # evaluate the layer
        self.xext =...