Basic of Neural Networks-2

# LogisticRegression.py
import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy

from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset


# Sigmoid 函数
def sigmoid(z):
    """
    Compute the sigmoid of z

    Arguments:
    z -- A scalar or numpy array of any size.

    Return:
    s -- sigmoid(z)
    """

    s = 1 / (1 + np.exp(-z))
    return s


# 初始化 w,b
def initialize_with_zeros(dim):
    """
    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.
    
    Argument:
    dim -- size of the w vector we want (or number of parameters in this case)
    
    Returns:
    w -- initialized vector of shape (dim, 1)
    b -- initialized scalar (corresponds to the bias)
    """

    w = np.zeros((dim, 1))  # (dim, 1) 是shape参数，代表初始化一个dim*1的矩阵
    b = 0

    assert (w.shape == (dim, 1))
    assert (isinstance(b, float) or isinstance(b, int))

    return w, b


# propagate 正向与反向传播
def propagate(w, b, X, Y):
    """
    Implement the cost function and its gradient for the propagation explained above

    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)

    Return:
    cost -- negative log-likelihood cost for logistic regression
    dw -- gradient of the loss with respect to w, thus same shape as w
    db -- gradient of the loss with respect to b, thus same shape as b
    
    Tips:
    - Write your code step by step for the propagation. np.log(), np.dot()
    """

    m = X.shape[1]

    # FORWARD PROPAGATION (FROM X TO COST)
    A = sigmoid(np.dot(w.T, X) + b)  # compute activation
    cost = -1 / m * (np.dot(Y,np.log(A).T) + np.dot(1 - Y,np.log(1 - A).T))  # compute cost

    # BACKWARD PROPAGATION (TO FIND GRAD)
    dw = 1 / m * np.dot(X, (A - Y).T)
    db = 1 / m * np.sum(A - Y)

    assert (dw.shape == w.shape)
    assert (db.dtype == float)
    cost = np.squeeze(cost)  # 删除shape为1的维度，比如cost=[[1]]，则经过np.squeeze处理后cost=[1]
    assert (cost.shape == ())

    grads = {"dw": dw, "db": db}

    return grads, cost


# 梯度下降
def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost=False):
    """
    This function optimizes w and b by running a gradient descent algorithm
    
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of shape (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
    num_iterations -- number of iterations of the optimization loop
    learning_rate -- learning rate of the gradient descent update rule
    print_cost -- True to print the loss every 100 steps
    
    Returns:
    params -- dictionary containing the weights w and bias b
    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.
    
    Tips:
    You basically need to write down two steps and iterate through them:
        1) Calculate the cost and the gradient for the current parameters. Use propagate().
        2) Update the parameters using gradient descent rule for w and b.
    """

    costs = []

    for i in range(num_iterations):

        # Cost and gradient calculation
        grads, cost = propagate(w, b, X, Y)

        # Retrieve derivatives from grads
        dw = grads["dw"]
        db = grads["db"]

        # update rule
        w = w - dw * learning_rate
        b = b - db * learning_rate

        # Record the costs
        if i % 100 == 0:
            costs.append(cost)

        # Print the cost every 100 training examples
        if print_cost and i % 100 == 0:
            print("Cost after iteration %i: %f" % (i, cost))

    params = {"w": w, "b": b}

    grads = {"dw": dw, "db": db}

    return params, grads, costs


# 利用logistic regression判断Y的标签值
def predict(w, b, X):
    '''
    Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)
    
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    
    Returns:
    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X
    '''

    m = X.shape[1]
    Y_prediction = np.zeros((1, m))
    w = w.reshape(X.shape[0], 1)

    # Compute vector "A" predicting the probabilities of a cat being present in the picture
    A = sigmoid(np.dot(w.T, X) + b)  # A.shape = (1,m)

    for i in range(A.shape[1]):

        # Convert probabilities A[0,i] to actual predictions p[0,i]
        if A[0, i] > 0.5:
            Y_prediction[0, i] = 1
        else:
            Y_prediction[0, i] = 0

    assert (Y_prediction.shape == (1, m))

    return Y_prediction


# 构建整个模型
def model(X_train,
          Y_train,
          X_test,
          Y_test,
          num_iterations=2000,
          learning_rate=0.5,
          print_cost=False):
    """
    Builds the logistic regression model by calling the function you've implemented previously
    
    Arguments:
    X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)
    Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)
    X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)
    Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)
    num_iterations -- hyperparameter representing the number of iterations to optimize the parameters
    learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()
    print_cost -- Set to true to print the cost every 100 iterations
    
    Returns:
    d -- dictionary containing information about the model.
    """

    # initialize parameters with zeros
    w, b = initialize_with_zeros(X_train.shape[0])

    # Gradient descent
    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations,
                                        learning_rate, print_cost)

    # Retrieve parameters w and b from dictionary "parameters"
    w = parameters["w"]
    b = parameters["b"]

    # Predict test/train set examples
    Y_prediction_test = predict(w, b, X_test)
    Y_prediction_train = predict(w, b, X_train)

    # Print train/test Errors
    print("train accuracy: {} %".format(
        100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
    print("test accuracy: {} %".format(
        100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))

    d = {
        "costs": costs,
        "Y_prediction_test": Y_prediction_test,
        "Y_prediction_train": Y_prediction_train,
        "w": w,
        "b": b,
        "learning_rate": learning_rate,
        "num_iterations": num_iterations
    }

    return d


def main():
    train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset(
    )

    m_train = train_set_x_orig.shape[0]
    m_test = test_set_x_orig.shape[0]
    num_px = train_set_x_orig.shape[2]

    train_set_x_flatten = train_set_x_orig.reshape(m_train, -1).T
    test_set_x_flatten = test_set_x_orig.reshape(m_test, -1).T
    train_set_x = train_set_x_flatten / 255.
    test_set_x = test_set_x_flatten / 255.

    # train model
    d = model(
        train_set_x,
        train_set_y,
        test_set_x,
        test_set_y,
        num_iterations=2000,
        learning_rate=0.005,
        print_cost=True)

    # 判断单张图片是否有猫
    my_image = "a.jpg"  # change this to the name of your image file

    # We preprocess the image to fit your algorithm.
    fname = "images/" + my_image
    image = np.array(ndimage.imread(fname, flatten=False))
    my_image = scipy.misc.imresize(image, size=(num_px, num_px)).reshape((1, num_px * num_px * 3)).T
    my_predicted_image = predict(d["w"], d["b"], my_image)

    print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[
        int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.")

    plt.imshow(image)
    plt.show()


main()