def node_activation(weighted_sum):
return 1.0 / (1.0 + np.exp(-1 * weighted_sum))
def forward_propagate(network, inputs):
layer_inputs = list(inputs) # start with the input layer as the input to the first hidden layer
for layer in network:
layer_data = network[layer]
layer_outputs = []
for layer_node in layer_data:
node_data = layer_data[layer_node]
# compute the weighted sum and the output of each node at the same time
node_output = node_activation(compute_weighted_sum(layer_inputs, node_data['weights'], node_data['bias']))
layer_outputs.append(np.around(node_output[0], decimals=4))
if layer != 'output':
print('The outputs of the nodes in hidden layer number {} is {}'.format(layer.split('_')[1], layer_outputs))
layer_inputs = layer_outputs # set the output of this layer to be the input to next layer
network_predictions = layer_outputs
return network_predictions
plt.figure(facecolor='w')
plt.plot(xx, tempinf, label="Temps inf")
plt.xlabel("Abscisse x de la barre (m)")
plt.ylabel("Température (K)")
plt.title("Diffusion de la chaleur dans une barre")
n1, n2 = 5, 8
theta1, theta2 = 50, 100
temp1 = np.sin(2*pi*n1*(xx+a)/2/(b+a))
temp2 = np.sin(2*pi*n2*(xx+a)/2/(b+a))
temp0 = tempinf + theta1*temp1 + theta2*temp2
plt.plot(xx, temp0, label="Temps 0")
T = 60
temp1 *= np.exp(-(pi*n1/(b+a))**2*sigma**2*T/2)
temp2 *= np.exp(-(pi*n2/(b+a))**2*sigma**2*T/2)
tempT = tempinf + theta1*temp1 + theta2*temp2
plt.plot(xx, tempT, label="Temps T = "+'{}'.format(T)+' s')
plt.legend(loc="best")
#%%
# calcul de la température au point x en date t
# choix du point x
x = 0
#temperature exacte en point x
temp1 = np.sin(2*pi*n1*(x+a)/2/(b+a))
temp2 = np.sin(2*pi*n2*(x+a)/2/(b+a))
temp1 *= np.exp(-(pi*n1/(b+a))**2*sigma**2*T/2)
temp2 *= np.exp(-(pi*n2/(b+a))**2*sigma**2*T/2)