#ANSQ3
def sse(output, target):
    return 0.5 * (output - target) ** 2;

def gradSse(output, target):
    return output - target;

def neuron(weights, inputs):
    return sigma(np.dot(weights,inputs))

def gradNeuron(weights, inputs):
    return neuron(weights, inputs) * (1 - neuron(weights, inputs)) * inputs


#/ANSQ3


#################################################################################
#ANSQ4

delta = 1e-5
for i in range(10):
    w = np.random.randn(5)
    x = np.random.randn(5)

    gw = 0.
    # Your code comes here...
    FDlist = []

    for j in range(5):
        wd1 = w.copy(); wd1[j] = wd1[j]+delta/2
        wd2 = w.copy(); wd2[j] = wd2[j]-delta/2

        FDlist.append((neuron(wd1,x)-neuron(wd2,x))/delta)



    analytical = gradNeuron(w,x)
    print ("FD:       ", np.round(FDlist, 8))
    print ("Analytical", analytical)
    print (" -- DIFF  ", FDlist - analytical)

#/ANSQ4

##############
#ANSQ5

# Start by augmenting the data with a 1 so that w[0] is the bias
X = np.ones((train.shape[0],2))
X[:,1] = train[:,0]

def errorFun(w):
	err_sum = 0
	for n in range(len(traint)):
    	out_n = neuron(w,X[n])
    	err_n = sse(out_n, traint[n])
    	err_sum += err_n
	return err_sum

def gradFun(w):
	grad_sum = 0
	for n in range(len(traint)):
    	out_n = neuron(w,X[n])
    	grad_sum += gradSse(out_n,traint[n])*gradNeuron(w,X[n])
	return grad_sum

w = np.zeros(2)
w_fit, err, times = gradDesc(w,errorFun,gradFun,verbose=False)

fitline = np.zeros(len(traint))
for n in range(len(traint)):
	fitline[n] = neuron(w_fit,X[n,:])

print(err)
plt.figure(1)
plt.plot(err)

plt.figure(2)
plt.plot(train, traint, 'bo', train, fitline);


#/ANSQ5
########################