本文用吴恩达deeplearning.ai里的数据进行训练，相应的习题如下，写出一个n层的deeplearning程序，相应程序结构如图片所示： 
相应代码实现如下：
import numpy as np
import matplotlib.pyplot as plt
import h5py
#%matplotlib inline
def load_data():
x_train_set = h5py.File('datasets/train_catvnoncat.h5','r')
x_train = np.array(x_train_set['train_set_x'][:])
y_train = np.array(x_train_set['train_set_y'][:])
x_test_set = h5py.File('datasets/test_catvnoncat.h5','r')
x_test = np.array(x_test_set['test_set_x'][:])
y_test = np.array(x_test_set['test_set_y'][:])
num_px = x_train.shape[1]
x_train = x_train.reshape(-1,num_px*num_px*3).T
x_test = x_train.reshape(-1,num_px*num_px*3).T
y_train = y_train.reshape(1,-1)
y_test = y_test.reshape(1,-1)
label_names = np.array(x_test_set['list_classes'][:])
x_train = x_train / 255.0
x_test = x_test / 255.0
return x_train,x_test,y_train,y_test,label_names
x_train, x_test,y_train,y_test,label_names = load_data()
units_list = [x_train.shape[0],100,20,7,1]
activation_list = ['None','relu','relu','relu','sigmoid']
learning_rate = 0.0055
def sigmoid_forward(Z):
'''
sigmoid function do calc of z =1.0/(1+exp(-x))
return z
'''
A = 1.0/(1.0 + np.exp(-Z))
assert(Z.shape == A.shape)
return A
def sigmoid_backward(dA,Z):
'''
Inputs:
dA: the backprop derivations of A
Z: in forwardprop A = g(Z)
return:
dZ: the gradient of Z
'''
temp_A = sigmoid_forward(Z)
# dZ = dA*A(1-A)
dZ = np.multiply(dA,np.multiply(temp_A,(1.0-temp_A)))
assert(dA.shape == dZ.shape)
return dZ
def relu_forward(Z):
'''
relu calc
'''
A = np.maximum(0,Z)
assert(A.shape == Z.shape)
return A
def relu_backward(dA,Z):
'''
relu backprop calc
'''
dZ = np.copy(dA)
dZ[Z<0] = 0.0
assert(dA.shape == dZ.shape)
return dZ
def init(X,units_list):
'''
function used to init variables about to use
Inputs:
X: inputs values used to train model
units_list: list structure ,length is layer number, values represents units names(inputs as the 0 layers as first layers)
Outputs:
parameters : W,b in every layers
caches: Z,A in every layers
gradients : dZ,dA,dW,db in every layers
'''
np.random.seed(1)
n_layers = len(units_list)
m_samples = X.shape[1]
parameters = []
caches = []
gradients = []
for i in range(n_layers):
param_temp = {}
cache_temp = {}
grad_temp = {}
if (i==0):
param_temp['W'] = np.random.randn(units_list[i],units_list[i])*0.01 # will not used
param_temp['b'] = np.random.randn(units_list[i],1)*0.01 # will not used
cache_temp['Z'] = X # will not be used
cache_temp['A'] = X #!!!!!! trainning values important
grad_temp['dW'] = np.random.randn(units_list[i],units_list[i])*0.01 # will not used
grad_temp['db'] = np.random.randn(units_list[i])*0.01 # will not used
grad_temp['dA'] = np.random.randn(X.shape[0],X.shape[1])*0.01 # will not used
grad_temp['dZ'] = np.random.randn(X.shape[0],X.shape[1])*0.01 # will not used
parameters.append(param_temp)
caches.append(cache_temp)
gradients.append(grad_temp)
else:
param_temp['W'] = np.random.randn(units_list[i],units_list[i-1])*0.01
param_temp['b'] = np.random.randn(units_list[i],1)*0.01
cache_temp['Z'] = np.random.randn(units_list[i],m_samples)*0.01
cache_temp['A'] = np.random.randn(units_list[i],m_samples)*0.01
grad_temp['dW'] = np.random.randn(units_list[i],units_list[i-1])*0.01
grad_temp['db'] = np.random.randn(units_list[i],1)*0.01
grad_temp['dA'] = np.random.randn(units_list[i],m_samples)*0.01
grad_temp['dZ'] = np.random.randn(units_list[i],m_samples)*0.01
parameters.append(param_temp)
caches.append(cache_temp)
gradients.append(grad_temp)
return parameters, caches, gradients
# para,cach,grad = init(x_train,units_list)
# for i in range(len(units_list)):
# print('out in:',i,'layers, w,b,, z,a, dw,db,dz,dz shapes')
# print(para[i]['W'].shape,para[i]['b'].shape)
# print(cach[i]['Z'].shape,cach[i]['A'].shape)
# print(grad[i]['dW'].shape,grad[i]['db'].shape,grad[i]['dA'].shape,grad[i]['dZ'].shape)
def linear_forward(X,W,b):
'''
calc the preocess w*x + b
'''
Z = np.dot(W,X) + b
assert(Z.shape[0] == W.shape[0])
assert(Z.shape[1] == X.shape[1])
return Z
def linear_activation_forward(A_prev,W,b,activation='None'):
'''
function is a single layer calc
return cache parameters
outputs cache values of Z,A
'''
Z = linear_forward(A_prev,W,b)
if(activation == 'relu'):
A = relu_forward(Z)
elif(activation == 'sigmoid'):
A = sigmoid_forward(Z)
else:
A = Z
print('wrong in activation function!!!')
assert(Z.shape == A.shape)
return Z,A
def n_layers_forward(parameters,caches,activation_list):
'''
this function calc the caches use w,b and Aprev
'''
n_layers = len(activation_list)
for i in range(1,n_layers):
A_prev = caches[i-1]['A']
W = parameters[i]['W']
b = parameters[i]['b']
activation = activation_list[i]
caches[i]['Z'], caches[i]['A'] = linear_activation_forward(A_prev,W,b,activation)
return caches
def linear_backward(dZ,Aprev):
'''
single layers in linear calc backprop calc
Inputs:
dZ: gradients of loss to ith layers' Z
Aprev: cache values in (i-1) layers' matrix A
Outputs:
dW: gradients of loss to ith layers' W
db: gradients of loss to ith layers' b
'''
m_samples = dZ.shape[1]
dW = np.dot(dZ, Aprev.T)/np.float(m_samples)
db = np.sum(dZ,axis=1,keepdims=True)/np.float(m_samples)
return dW, db
def linear_activation_backward(Z,Aprev,Wplus,dZplus,activation):
'''
used to calc single layer's dZ,dA,dW,db
Inputs:
Z : matrix of i th layers
Aprev: matrix of previous layers
Wplus: parameters of W of i+1 th layers
dZplus: dz gradients of (i+1)th layers
activation: activation function
Outputs:
dA: dA gradients of i th layers
dZ: dZ gradients of i th layers
dW: dW gradients of i th layers
db: db gradients of i th layers
'''
dA = np.dot(Wplus.T,dZplus)
if (activation == 'sigmoid'):
dZ = sigmoid_backward(dA,Z)
elif(activation == 'relu'):
dZ = relu_backward(dA,Z)
else:
dZ = dA
print('Wrong in calc dz,da,dw,db')
dW,db = linear_backward(dZ,Aprev)
return dZ,dA,dW,db
def n_layers_backward(Y,parameters,caches,gradients, activation_list):
'''
used to calc the n_layers gradients
Inputs:
parameters: w,b every layer model to learn
caches: Z,A every layers
gradients: used as inputs
activation_list: every layers activation_function
Outputs:
gradients: cost function gradients to every in dA,dZ,dW,db
'''
n_layers = len(activation_list)
for i in range(n_layers-1,0,-1):
activation = activation_list[i]
Z = caches[i]['Z']
A = caches[i]['A']
Aprev = caches[i-1]['A']
if (i == n_layers -1):
gradients[i]['dA'] = -np.divide(Y,A) + np.divide((1.0-Y),(1.0-A))
dA = gradients[i]['dA']
gradients[i]['dZ'] = sigmoid_backward(dA,Z)
dZ = gradients[i]['dZ']
gradients[i]['dW'],gradients[i]['db'] = linear_backward(dZ,Aprev)
else:
Wplus = parameters[i+1]['W']
dZplus = gradients[i+1]['dZ']
gradients[i]['dZ'],gradients[i]['dA'],gradients[i]['dW'],gradients[i]['db'] = \
linear_activation_backward(Z,Aprev,Wplus,dZplus,activation)
return gradients
def update_parameters(parameters,gradients,learning_rate):
'''
function used to update parameters w,b
Inputs:
parameters,gradients,learning_rate
Outputs:
parameters: updated parameters
'''
n_layers = len(parameters)
#print('shape of learning_rate',learning_rate)
for i in range(1,n_layers):
assert(parameters[i]['W'].shape == gradients[i]['dW'].shape)
assert(parameters[i]['b'].shape == gradients[i]['db'].shape)
parameters[i]['W'] += -learning_rate*gradients[i]['dW']
parameters[i]['b'] += -learning_rate*gradients[i]['db']
return parameters
def cost_function(AL,Y):
'''
function to calc cost values
Inputs: AL last layers' cache matrix A
Y: labeled samples targets
Outputs:
loss: total cost function values
'''
m_samples = Y.shape[1]
AL.reshape(-1,1)
Y.reshape(-1,1)
loss = np.dot(Y.T,np.log(AL)) + np.dot((1.0-Y).T,np.log(1.0-AL))
loss = -loss / np.float(m_samples)
loss = loss.reshape(-1,1)
loss = loss[0]
return loss
def predict(AL,Y):
'''
function use learned parameters to predict
Inputs:
AL: last layer cache matrix
Y: labeled datas
Outputs:
accuracy: the predict accuracy real number
'''
AL = AL.reshape(-1,1)
Y = Y.reshape(-1,1)
m_samples = Y.shape[0]
counts = 0.0
for i in range(m_samples):
if AL[i] >=0.5:
AL[i] = 1.0
else:
AL[i] = 0.0
accuracy = np.sum(AL == Y)/np.float(m_samples)
return accuracy
def learning_process(X,Y,units_list,activation_list,learning_rate = 0.0075):
'''
function used to learn model
Inputs:
X: inputs data including features
Y: labeled data
learning_rate: learning_rate
units_list : layers length and layers units number
activation_list: activations in each layer
Outputs:
parameters: learned W b in all layers
loss: total cost function in convergence
'''
n_layers = len(units_list)
num_epoch = 200000
loss_list = []
accuracy_list = []
steps = []
plt.ion()
plt.figure(1)
plt.figure(2)
loss_temp = 0.0
parameters, caches, gradients = init(X,units_list)
for i in range(num_epoch):
caches = n_layers_forward(parameters,caches,activation_list)
loss = cost_function(caches[n_layers-1]['A'],Y)
dloss = np.abs(loss-loss_temp)/(np.abs(loss)+1.0e-15)
loss_temp = loss
gradients = n_layers_backward(Y,parameters,caches,gradients,activation_list)
parameters = update_parameters(parameters,gradients,learning_rate)
if(i%200 == 0):
steps.append(i)
loss_list.append(loss)
accuracy_list.append(predict(caches[n_layers-1]['A'],Y))
print('The trainning steps is {0} total loss is: {1} residual is:{2}'.format(i,loss,dloss))
print('The trainning accuracy is {0}'.format(accuracy_list[-1]))
plt.figure(1)
line1,=plt.plot(steps,loss_list,'r',linewidth=1.5)
plt.xlabel('Trainning steps')
plt.ylabel('Total loss values')
plt.legend([line1],['total loss'],loc = 'best')
plt.figure(2)
line2, = plt.plot(steps,accuracy_list,'g',linewidth=1.5)
plt.xlabel('Trainning steps')
plt.ylabel('Trainning Accuracy')
plt.legend([line2],['Trainning Accuracy'],loc='best')
plt.pause(0.01)
return parameters, loss
parameters,loss = learning_process(x_train,y_train,units_list,activation_list,learning_rate)
print('final loss is:',loss)
相应输出如下： 
