深度学习：3_手写一个单层的神经网络

# *******************************
# Target：手写一个单隐层的神经网络
# Author: Magic
# Steps：1、定义网络结构（指定输出层、隐藏层、输出层的大小）
#        2、初始化模型参数
#        3、循环操作：执行前向传播/计算损失/执行后向传播/权值更新
# *******************************

import numpy as np
import tensorflow as tf

#定义网络结构
def layer_sizes(X,Y):
    n_x = X.shape[0]
    n_h = 4
    n_y = Y.shape[0]
    return (n_x,n_h,n_y)

#初始化模型参数
def initialize_parameters(n_x,n_h,n_y):
    W1 = np.random.randn(n_h,n_x)*0.01
    b1 = np.zeros((n_h,1))
    W2 = np.random.randn(n_y,n_h)*0.01
    b2 = np.zeros((n_y,1))

    assert(W1.shape == (n_h,n_x))
    assert(b1.shape == (n_h,1))
    assert(W2.shape == (n_y,n_h))
    assert(b2.shape == (n_y,1))

    parameters = {"W1":W1,
                  "b1":b1,
                  "W2":W2,
                  "b2":b2}
    return parameters


#前向传播
def forward_propagation(X,parameters):
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']

    Z1 = np.dot(W1,X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2,Z1) + b2
    A2 = tf.sigmoid(Z2)
    
    assert(A2.shape == (1,X.shape[1]))

    cache = {"Z1":Z1,
             "A1":A1,
             "Z2":Z2,
             "A2":A2}
    return A2,cache


#定义计算损失函数
def compute_coat(A2,Y,parameters):
    m = Y.shape[1]
    logprobs = np.multiply(np.log(A2),y) + np.multiply(np.log(1-A2),1 - Y)
    cost = -1/m * np.sum(logprobs)
    cost = np.squeeze(cost)

    assert(isinstance(cost,float))
    return cost

#定义反向传播函数
def backward_propagation(parameters,cache,X,Y):
    m = X.shape[1]

    W1 = parameters['W1']
    W2 = parameters['W2']
    A1 = cache['A1']
    A2 = cache['A2']

    dZ2 = A2 - Y
    dW2 = 1/m * np.dot(dZ2,A1.T)
    db2 = 1/m * np.sum(dZ2,axis = 1,keepdims = True)
    dZ1 = np.dot(W2.T,dZ2) * (1 - np.power(A1,2))
    dW1 = 1/m * np.dot(dZ1,X.T)
    db1 = 1/m * np.sum(dZ1,axis=1,keepdims = True)

    grads = {"dw1":dW1,
             "db1":db1,
             "dW2":dW2,
             "db2":db2}
    return grads

#定义权值更新函数
def update_parameters(parameters,grads,learning_rate = 1.2):
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']

    dW1 = grads['dW1']
    db1 = grads['db1']
    dW2 = grads['dW2']
    db2 = grads['db2']

    W1 -= dW1 * learning_rate
    b1 -= db1 * learning_rate
    W2 -= dW2 * learning_rate
    b2 -= db2 *learning_rate

    parameters = {"W1":W1,
                  "b1":b1,
                  "W2":W2,
                  "b2":b2}

    return parameters


#封装
def nn_model(X,Y,n_h,num_iterations = 10000,print_cost = False):
    np.random.seed(3)
    n_x = layer_sizes(X,Y)[0]
    n_y = layer_sizes(X,Y)[2]

    parameters = initialize_parameters(n_x,n_h,n_y)
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']

    for i in range(0,num_iterations):
        A2,cache = forward_propagation(X,parameters)
        cost = compute_coat(A2,Y,parameters)
        grads = backward_propagation(parameters,cache,X,Y)
        parameters = update_parameters(parameters,grads,learning_rate= 1.2)

        if print_cost and i % 1000 == 0:
            print("Cost after iteration %i:%f"%(i,cost))

    return parameters