L(A, P, N) = max(||f(A) − f(P)|| 2 − ||f(A) − f(N)|| 2 + a, 0)

J(G) = aJ content (C, G) + βJ style (S, G）

# GRADED FUNCTION: triplet_loss

def triplet_loss(y_true, y_pred, alpha = 0.2):
    """
    Implementation of the triplet loss as defined by formula (3)
    
    Arguments:
    y_true -- true labels, required when you define a loss in Keras, you don't need it in this function.
    y_pred -- python list containing three objects:
            anchor -- the encodings for the anchor images, of shape (None, 128)
            positive -- the encodings for the positive images, of shape (None, 128)
            negative -- the encodings for the negative images, of shape (None, 128)
    
    Returns:
    loss -- real number, value of the loss
    """
    
    anchor, positive, negative = y_pred[0], y_pred[1], y_pred[2]
    
    ### START CODE HERE ### (≈ 4 lines)
    # Step 1: Compute the (encoding) distance between the anchor and the positive, you will need to sum over axis=-1
    pos_dist = tf.reduce_sum(tf.square(tf.subtract(anchor,positive)),axis=-1)
    # Step 2: Compute the (encoding) distance between the anchor and the negative, you will need to sum over axis=-1
    neg_dist =  tf.reduce_sum(tf.square(tf.subtract(anchor,negative)),axis=-1)
    # Step 3: subtract the two previous distances and add alpha.
    basic_loss = tf.add(alpha,tf.subtract(pos_dist,neg_dist))
    # Step 4: Take the maximum of basic_loss and 0.0. Sum over the training examples.
    loss = tf.reduce_sum(tf.maximum(basic_loss,0))
    ### END CODE HERE ###
    
    return loss

# GRADED FUNCTION: verify

def verify(image_path, identity, database, model):
    """
    Function that verifies if the person on the "image_path" image is "identity".
    
    Arguments:
    image_path -- path to an image
    identity -- string, name of the person you'd like to verify the identity. Has to be a resident of the Happy house.
    database -- python dictionary mapping names of allowed people's names (strings) to their encodings (vectors).
    model -- your Inception model instance in Keras
    
    Returns:
    dist -- distance between the image_path and the image of "identity" in the database.
    door_open -- True, if the door should open. False otherwise.
    """
    
    ### START CODE HERE ###
    
    # Step 1: Compute the encoding for the image. Use img_to_encoding() see example above. (≈ 1 line)
    encoding = img_to_encoding(image_path,model)
    
    # Step 2: Compute distance with identity's image (≈ 1 line)
    dist = np.linalg.norm(database[identity]-encoding)
    
    # Step 3: Open the door if dist < 0.7, else don't open (≈ 3 lines)
    if dist<0.7:
        print("It's " + str(identity) + ", welcome home!")
        door_open = True
    else:
        print("It's not " + str(identity) + ", please go away")
        door_open = False
        
    ### END CODE HERE ###
        
    return dist, door_open

 GRADED FUNCTION: who_is_it

def who_is_it(image_path, database, model):
    """
    Implements face recognition for the happy house by finding who is the person on the image_path image.
    
    Arguments:
    image_path -- path to an image
    database -- database containing image encodings along with the name of the person on the image
    model -- your Inception model instance in Keras
    
    Returns:
    min_dist -- the minimum distance between image_path encoding and the encodings from the database
    identity -- string, the name prediction for the person on image_path
    """
    
    ### START CODE HERE ### 
    
    ## Step 1: Compute the target "encoding" for the image. Use img_to_encoding() see example above. ## (≈ 1 line)
    encoding = img_to_encoding(image_path,model)
    
    ## Step 2: Find the closest encoding ##
    
    # Initialize "min_dist" to a large value, say 100 (≈1 line)
    min_dist = 100
    
    # Loop over the database dictionary's names and encodings.
    for (name, db_enc) in database.items():
        
        # Compute L2 distance between the target "encoding" and the current "emb" from the database. (≈ 1 line)
        dist = np.linalg.norm(db_enc-encoding)

        # If this distance is less than the min_dist, then set min_dist to dist, and identity to name. (≈ 3 lines)
        if dist<min_dist:
            min_dist = dist
            identity = name

    ### END CODE HERE ###
    
    if min_dist > 0.7:
        print("Not in the database.")
    else:
        print ("it's " + str(identity) + ", the distance is " + str(min_dist))
        
    return min_dist, identity

# GRADED FUNCTION: compute_content_cost

def compute_content_cost(a_C, a_G):
    """
    Computes the content cost
    
    Arguments:
    a_C -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing content of the image C 
    a_G -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing content of the image G
    
    Returns: 
    J_content -- scalar that you compute using equation 1 above.
    """
    
    ### START CODE HERE ###
    # Retrieve dimensions from a_G (≈1 line)
    m, n_H, n_W, n_C = a_G.get_shape().as_list()
    
    new_shape = [m,(n_H*n_W),n_C]
    
    # Reshape a_C and a_G (≈2 lines)
    a_C_unrolled = tf.reshape(a_C,shape=new_shape)
    a_G_unrolled = tf.reshape(a_G,shape=new_shape)
    
    # compute the cost with tensorflow (≈1 line)
    J_content = 1/(4*n_H*n_W*n_C)*tf.reduce_sum(tf.square(tf.subtract(a_C_unrolled,a_G_unrolled)))
    ### END CODE HERE ###
    
    return J_content

# GRADED FUNCTION: gram_matrix

def gram_matrix(A):
    """
    Argument:
    A -- matrix of shape (n_C, n_H*n_W)
    
    Returns:
    GA -- Gram matrix of A, of shape (n_C, n_C)
    """
    
    ### START CODE HERE ### (≈1 line)
    GA =  tf.matmul(A,tf.transpose(A))
    ### END CODE HERE ###
    
    return GA

# GRADED FUNCTION: compute_layer_style_cost

def compute_layer_style_cost(a_S, a_G):
    """
    Arguments:
    a_S -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing style of the image S 
    a_G -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing style of the image G
    
    Returns: 
    J_style_layer -- tensor representing a scalar value, style cost defined above by equation (2)
    """
    
    ### START CODE HERE ###
    # Retrieve dimensions from a_G (≈1 line)
    m, n_H, n_W, n_C = a_G.get_shape().as_list()
    
    new_shape = [n_H*n_W,n_C]
    # Reshape the images to have them of shape (n_C, n_H*n_W) (≈2 lines)
    a_S = tf.reshape(a_S,new_shape)
    a_S = tf.transpose(a_S)
    a_G = tf.reshape(a_G,new_shape)
    a_G = tf.transpose(a_G)
    # Computing gram_matrices for both images S and G (≈2 lines)
    GS = gram_matrix(a_S)
    GG = gram_matrix(a_G)

    # Computing the loss (≈1 line)
    J_style_layer = 1/(4*(n_H*n_W*n_C)**2)*tf.reduce_sum(tf.square(tf.subtract(GS,GG)))
    
    ### END CODE HERE ###
    
    return J_style_layer

def yolo_filter_boxes(box_confidence, boxes, box_class_probs, threshold = .6):
  """
    通过阈值来过滤对象和分类的置信度。

    参数：
        box_confidence  - tensor类型，维度为（19,19,5,1）,包含19x19单元格中每个单元格预测的5个锚框中的所有的锚框的pc （一些对象的置信概率）。
        boxes - tensor类型，维度为(19,19,5,4)，包含了所有的锚框的（px,py,ph,pw ）。
        box_class_probs - tensor类型，维度为(19,19,5,80)，包含了所有单元格中所有锚框的所有对象( c1,c2,c3，···，c80 )检测的概率。
        threshold - 实数，阈值，如果分类预测的概率高于它，那么这个分类预测的概率就会被保留。

    返回：
        scores - tensor 类型，维度为(None,)，包含了保留了的锚框的分类概率。
        boxes - tensor 类型，维度为(None,4)，包含了保留了的锚框的(b_x, b_y, b_h, b_w)
        classess - tensor 类型，维度为(None,)，包含了保留了的锚框的索引

    注意："None"是因为你不知道所选框的确切数量，因为它取决于阈值。
          比如：如果有10个锚框，scores的实际输出大小将是（10,）
    """
    """
    
    # Step 1: Compute box scores
    ### START CODE HERE ### (≈ 1 line)
    box_scores = box_confidence * box_class_probs
    ### END CODE HERE ###
    
    # Step 2: Find the box_classes thanks to the max box_scores, keep track of the corresponding score
    ### START CODE HERE ### (≈ 2 lines)
    box_classes = K.argmax(box_scores, axis = -1)
    box_class_scores = K.max(box_scores, axis = -1)
    ### END CODE HERE ###
    
    # Step 3: Create a filtering mask based on "box_class_scores" by using "threshold". The mask should have the
    # same dimension as box_class_scores, and be True for the boxes you want to keep (with probability >= threshold)
    ### START CODE HERE ### (≈ 1 line)
    filtering_mask = (box_class_scores >= threshold)
    ### END CODE HERE ###
    
    # Step 4: Apply the mask to scores, boxes and classes
    ### START CODE HERE ### (≈ 3 lines)
    scores = tf.boolean_mask(box_class_scores,filtering_mask)
    boxes = tf.boolean_mask(boxes,filtering_mask)
    classes= tf.boolean_mask(box_classes,filtering_mask)
    
    ### END CODE HERE ###
    
    return scores, boxes, classes

def yolo_non_max_suppression(scores, boxes, classes, max_boxes = 10, iou_threshold = 0.5):
    """
    Applies Non-max suppression (NMS) to set of boxes
    
    Arguments:
    scores -- tensor of shape (None,), output of yolo_filter_boxes()
    boxes -- tensor of shape (None, 4), output of yolo_filter_boxes() that have been scaled to the image size (see later)
    classes -- tensor of shape (None,), output of yolo_filter_boxes()
    max_boxes -- integer, maximum number of predicted boxes you'd like
    iou_threshold -- real value, "intersection over union" threshold used for NMS filtering
    
    Returns:
    scores -- tensor of shape (, None), predicted score for each box
    boxes -- tensor of shape (4, None), predicted box coordinates
    classes -- tensor of shape (, None), predicted class for each box
    
    Note: The "None" dimension of the output tensors has obviously to be less than max_boxes. Note also that this
    function will transpose the shapes of scores, boxes, classes. This is made for convenience.
    """
    
    max_boxes_tensor = K.variable(max_boxes, dtype='int32')     # tensor to be used in tf.image.non_max_suppression()
    K.get_session().run(tf.variables_initializer([max_boxes_tensor])) # initialize variable max_boxes_tensor
    
    # Use tf.image.non_max_suppression() to get the list of indices corresponding to boxes you keep
    ### START CODE HERE ### (≈ 1 line)
    indicesList = tf.image.non_max_suppression(
    boxes,
    scores,
    max_boxes,
    iou_threshold,
    score_threshold=float('-inf'),
    name=None
)

    ### END CODE HERE ###
        
    # Use K.gather() to select only nms_indices from scores, boxes and classes
    ### START CODE HERE ### (≈ 3 lines)
    #把在indicesList的scores gather起来
    scores = K.gather(scores,indicesList)
    boxes = K.gather(boxes,indicesList)
    classes = K.gather(classes,indicesList)
    ### END CODE HERE ###
    
    return scores, boxes, classes

def yolo_eval(yolo_outputs, image_shape = (720., 1280.), max_boxes=10, score_threshold=.6, iou_threshold=.5):
    """
    Converts the output of YOLO encoding (a lot of boxes) to your predicted boxes along with their scores, box coordinates and classes.
    
    Arguments:
    yolo_outputs -- output of the encoding model (for image_shape of (608, 608, 3)), contains 4 tensors:
                    box_confidence: tensor of shape (None, 19, 19, 5, 1)
                    box_xy: tensor of shape (None, 19, 19, 5, 2)
                    box_wh: tensor of shape (None, 19, 19, 5, 2)
                    box_class_probs: tensor of shape (None, 19, 19, 5, 80)
    image_shape -- tensor of shape (2,) containing the input shape, in this notebook we use (608., 608.) (has to be float32 dtype)
    max_boxes -- integer, maximum number of predicted boxes you'd like
    score_threshold -- real value, if [ highest class probability score < threshold], then get rid of the corresponding box
    iou_threshold -- real value, "intersection over union" threshold used for NMS filtering
    
    Returns:
    scores -- tensor of shape (None, ), predicted score for each box
    boxes -- tensor of shape (None, 4), predicted box coordinates
    classes -- tensor of shape (None,), predicted class for each box
    """
    
    ### START CODE HERE ### 
    
    # Retrieve outputs of the YOLO model (≈1 line)
    box_confidence,box_xy,box_wh,box_class_probs = yolo_outputs

    # Convert boxes to be ready for filtering functions 
    boxes = yolo_boxes_to_corners(box_xy, box_wh) 
    # Use one of the functions you've implemented to perform Score-filtering with a threshold of score_threshold (≈1 line)
    scores,boxes,classes = yolo_filter_boxes(box_confidence,boxes,box_class_probs,score_threshold)
    # Scale boxes back to original image shape.
    boxes = scale_boxes(boxes, image_shape)
    # Use one of the functions you've implemented to perform Non-max suppression with a threshold of iou_threshold (≈1 line)
    scores,boxes,classes = yolo_non_max_suppression(scores, boxes, classes,max_boxes,iou_threshold)
    ### END CODE HERE ###
    
    return scores, boxes, classes

结果参数 = 输入层 HxWx卷积核个数

总计算成本 = (结果参数28x28x32) × （卷积核大小5x5x192）

1. make
2. sudo make install
3. sudo modprobe -a 8821ce

def zero_pad(X, pad):
    """
    Pad with zeros all images of the dataset X. The padding is applied to the height and width of an image, 
    as illustrated in Figure 1.
    
    Argument:
    X -- python numpy array of shape (m, n_H, n_W, n_C) representing a batch of m images
    pad -- integer, amount of padding around each image on vertical and horizontal dimensions
    
    Returns:
    X_pad -- padded image of shape (m, n_H + 2*pad, n_W + 2*pad, n_C)
    """
    
    ### START CODE HERE ### (≈ 1 line)
    X_pad = np.pad(X, ((0, 0), (pad, pad), (pad, pad), (0, 0)), 'constant', constant_values=0)
    ### END CODE HERE ###
    
    return X_pad

def conv_single_step(a_slice_prev, W, b):
    """
    Apply one filter defined by parameters W on a single slice (a_slice_prev) of the output activation 
    of the previous layer.
    
    Arguments:
    a_slice_prev -- slice of input data of shape (f, f, n_C_prev)
    W -- Weight parameters contained in a window - matrix of shape (f, f, n_C_prev)
    b -- Bias parameters contained in a window - matrix of shape (1, 1, 1)
    
    Returns:
    Z -- a scalar value, result of convolving the sliding window (W, b) on a slice x of the input data
    """

    ### START CODE HERE ### (≈ 2 lines of code)
    # Element-wise product between a_slice and W. Add bias.
    s = np.multiply(a_slice_prev, W) + b
    # Sum over all entries of the volume s
    Z = np.sum(s)
    ### END CODE HERE ###

    return Z

def conv_forward(A_prev, W, b, hparameters):
    """
    Implements the forward propagation for a convolution function
    
    Arguments:
    A_prev -- output activations of the previous layer, numpy array of shape (m, n_H_prev, n_W_prev, n_C_prev)
    W -- Weights, numpy array of shape (f, f, n_C_prev, n_C)
    b -- Biases, numpy array of shape (1, 1, 1, n_C)
    hparameters -- python dictionary containing "stride" and "pad"
        
    Returns:
    Z -- conv output, numpy array of shape (m, n_H, n_W, n_C)
    cache -- cache of values needed for the conv_backward() function
    """
    
    ### START CODE HERE ###
    # Retrieve dimensions from A_prev's shape (≈1 line)  
    (m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
    
    # Retrieve dimensions from W's shape (≈1 line)
    (f, f, n_C_prev, n_C) = W.shape

    # Retrieve information from "hparameters" (≈2 lines)
    stride = hparameters['stride']
    pad = hparameters['pad']
    
    # Compute the dimensions of the CONV output volume using the formula given above. Hint: use int() to floor. (≈2 lines)
    n_H = int((n_H_prev - f + 2 * pad) / stride) + 1
    n_W = int((n_W_prev - f + 2 * pad) / stride) + 1
    
    # Initialize the output volume Z with zeros. (≈1 line)
    Z = np.zeros((m, n_H, n_W, n_C))
    
    # Create A_prev_pad by padding A_prev
    A_prev_pad = zero_pad(A_prev, pad)
    
    for i in range(m):                                 # loop over the batch of training examples
        a_prev_pad = A_prev_pad[i]                     # Select ith training example's padded activation
        for h in range(n_H):                           # loop over vertical axis of the output volume
            for w in range(n_W):                       # loop over horizontal axis of the output volume
                for c in range(n_C):                   # loop over channels (= #filters) of the output volume
                    # Find the corners of the current "slice" (≈4 lines)
                    vert_start = h * stride
                    vert_end = vert_start + f
                    horiz_start = w * stride
                    horiz_end = horiz_start + f
                    # Use the corners to define the (3D) slice of a_prev_pad (See Hint above the cell). (≈1 line)
                    a_slice_prev = a_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :]
                    # Convolve the (3D) slice with the correct filter W and bias b, to get back one output neuron. (≈1 line)
                    Z[i, h, w, c] = conv_single_step(a_slice_prev, W[...,c], b[...,c])
                                        
    ### END CODE HERE ###

    # Making sure your output shape is correct
    assert(Z.shape == (m, n_H, n_W, n_C))
    
    # Save information in "cache" for the backprop
    cache = (A_prev, W, b, hparameters)
    
    return Z, cache

Consequently, batch normalization adds two trainable parameters to each layer, so the normalized output is multiplied by a “standard deviation” parameter (gamma) and add a “mean” parameter (beta). In other words, batch normalization lets SGD do the denormalization by changing only these two weights for each activation, instead of losing the stability of the network by changing all the weights.

public class ThreadYield extends Thread{
  //private String name;
  public ThreadYield(String name){
      super(name);
  }

  public void run(){
    for(int i=1;i<=10;i++){
      System.out.println(this.getName()+"----"+i);
      if(i==3){
        this.yield();
      }
    }
  }

  public static void main(String[]args){

    ThreadYield thread1 = new ThreadYield("ALex");
    ThreadYield thread2 = new ThreadYield("Brecher");

    thread1.start();
    thread2.start();

  }
}

Thread t = new Athread();
t.start();
t.join();

public class Thread1 extends Thread{
  private String name;
  public Thread1(String name){
    super(name);
    this.name = name;
  }

  public void run(){
    System.out.println(Thread.currentThread().getName()+"线程开始运行");
    for(int i=0;i<5;i++){
      System.out.println("子线程"+name+"运行"+i);
      try{
        sleep((int)Math.random()*10);
      }catch(InterruptedException e){
        e.printStackTrace();
      }
    }
    System.out.println(Thread.currentThread().getName()+"线程结束运行");
  }


  public static void main(String[] args){

    System.out.println(Thread.currentThread().getName()+"主线程开始运行");
    Thread1 Athread = new Thread1("A");
    Thread1 Bthread = new Thread1("B");
    Athread.start();
    Bthread.start();
    System.out.println(Thread.currentThread().getName()+"主线程结束运行");

  }


}

public static void main(String[] args){
    System.out.println(Thread.currentThread().getName()+"主线程开始运行");
    Thread1 Athread = new Thread1("A");
    Thread1 Bthread = new Thread1("B");
    Athread.start();
    Bthread.start();
    try{
      Athread.join();
    }catch(InterruptedException e){
      e.printStackTrace();
    }

    try{
      Bthread.join();
    }catch(InterruptedException e){
      e.printStackTrace();
    }
    System.out.println(Thread.currentThread().getName()+"主线程结束运行");
  }

import java.util.concurrent.TimeUnit;

public class ThreadState {

  public static void main(String[] args){

      new Thread(new TimeWaiting(),"TimeWaitingThread").start();
      new Thread(new Waiting(),"WaitingThread").start();

      //使用两个Blocked线程，一个获取锁成功，另外一个被阻塞
      new Thread(new Blocked(),"BlockedThread-1").start();
      new Thread(new Blocked(),"BlockedTHread-2").start();
  }

  static class SleepUtils{
      public static void second(long seconds) {
        try {
          TimeUnit.SECONDS.sleep(seconds);
        } catch (InterruptedException e) {
        }
      }
  }

  //该线程不断进行睡眠
  static class TimeWaiting implements Runnable{
      public void run(){
        while(true){
          SleepUtils.second(100);
        }
      }
  }

  //在Waiting.class实例上等待
  static class Waiting implements Runnable{
    public void run(){
        while(true){
          synchronized (Waiting.class){
              try{
                  Waiting.class.wait();
              }catch(InterruptedException e){
                e.printStackTrace();
            }
          }
        }
    }
  }

  //该线程在Blocked.class 实例上加锁后，不会释放该锁
  static class Blocked implements Runnable{
    public void run(){
        synchronized (Blocked.class){
          while(true){
              SleepUtils.second(100);
          }
        }
    }
  }


}

import java.util.concurrent.TimeUnit;

public class Shutdown {

    public static void main(String[] args) throws Exception{

        Runner one = new Runner();
        Thread countThread = new Thread(one,"CountThread");
        countThread.start();
        //睡眠1s,main线程对CountThread进行中断，使得CountThread能够感知中断而结束
        TimeUnit.SECONDS.sleep(1);
        countThread.interrupt();
        Runner two = new Runner();
        countThread = new Thread(two,"CountThread");
        countThread.start();
        //睡眠1s,main线程对Runner Two进行取消，使CountThread 能够感知on 为false
        TimeUnit.SECONDS.sleep(1);
        two.cancel();

    }

    private static class Runner implements Runnable{
        private long i;
        private volatile boolean on = true;
        public void run(){
          while(on&&!Thread.currentThread().isInterrupted()){
            i++;
          }
          System.out.println("Count i = "+i);
        }
        public void cancel(){
            on = false;
        }
    }
}

public synchronized void methodAAA()

public void methodAAA(){
synchronized(this)
}

public void method3(SomeObject so){

	synchronized(so)
    
}

public class MyThreadPrint extends Thread{

    private String name;
    public MyThreadPrint(String name){
      this.name = name;
    }

    public void run(){
        System.out.println("hello"+name);
    }

    public static void main(String [] args){

      Thread thread = new MyThreadPrint("world");
      thread.start();
    }
}

public class MyThreadPrint implements Runnable{

    private String name;

    public void setName(String name){
      this.name = name;
    }

    public void run(){
        System.out.println("hello"+name);
    }

    public static void main(String [] args){

      MyThreadPrint mythread = new MyThreadPrint();
      mythread.setName("world");
      Thread thread = new Thread(mythread);
      thread.start();
    }
}

import java.util.concurrent.TimeUnit;

public class Join {
  public static void main(String[]args)throws Exception{

      Thread previous = Thread.currentThread();
      for(int i=0;i<10;i++) {
        Thread thread = new Thread(new Domino(previous), String.valueOf(i));
        thread.start();
        previous = thread;
      }
      TimeUnit.SECONDS.sleep(5);
      System.out.println(Thread.currentThread().getName()+" terminate.");

  }

  static class Domino implements Runnable{
    private Thread thread;
    public Domino(Thread thread){
        this.thread = thread;
    }
    public void run(){
        try{
          thread.join();
        }catch (InterruptedException e){
          e.printStackTrace();
        }
        System.out.println(Thread.currentThread().getName()+" terminate.");
    }

  }

}

def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):
    """
    Creates a list of random minibatches from (X, Y)
    
    Arguments:
    X -- input data, of shape (input size, number of examples)
    Y -- true "label" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)
    mini_batch_size -- size of the mini-batches, integer
    
    Returns:
    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)
    """
    
    np.random.seed(seed)            # To make your "random" minibatches the same as ours
    m = X.shape[1]                  # number of training examples
    mini_batches = []
        
    # Step 1: Shuffle (X, Y)
    permutation = list(np.random.permutation(m))
    shuffled_X = X[:, permutation]
    shuffled_Y = Y[:, permutation].reshape((1,m))

    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.
    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning
    for k in range(0, num_complete_minibatches):
        ### START CODE HERE ### (approx. 2 lines)
        mini_batch_X = shuffled_X[:,mini_batch_size*(k):mini_batch_size*(k+1)]
        mini_batch_Y = shuffled_Y[:,mini_batch_size*(k):mini_batch_size*(k+1)]
        ### END CODE HERE ###
        mini_batch = (mini_batch_X, mini_batch_Y)
        mini_batches.append(mini_batch)
    
    # Handling the end case (last mini-batch < mini_batch_size)
    if m % mini_batch_size != 0:
        ### START CODE HERE ### (approx. 2 lines)
        mini_batch_X = shuffled_X[:,mini_batch_size*(num_complete_minibatches):]
        mini_batch_Y = shuffled_Y[:,mini_batch_size*(num_complete_minibatches):]
        ### END CODE HERE ###
        mini_batch = (mini_batch_X, mini_batch_Y)
        mini_batches.append(mini_batch)
    
    return mini_batches

def initialize_velocity(parameters):
    """
    Initializes the velocity as a python dictionary with:
                - keys: "dW1", "db1", ..., "dWL", "dbL" 
                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.
    Arguments:
    parameters -- python dictionary containing your parameters.
                    parameters['W' + str(l)] = Wl
                    parameters['b' + str(l)] = bl
    
    Returns:
    v -- python dictionary containing the current velocity.
                    v['dW' + str(l)] = velocity of dWl
                    v['db' + str(l)] = velocity of dbl
    """
    
    L = len(parameters) // 2 # number of layers in the neural networks
    v = {}
    
    # Initialize velocity
    for l in range(L):
        ### START CODE HERE ### (approx. 2 lines)
        v["dW" + str(l+1)] = np.zeros(parameters['W'+str(l+1)].shape)
        v["db" + str(l+1)] = np.zeros(parameters['b'+str(l+1)].shape)
        ### END CODE HERE ###
        
    return v

def initialize_adam(parameters) :
    """
    Initializes v and s as two python dictionaries with:
                - keys: "dW1", "db1", ..., "dWL", "dbL" 
                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.
    
    Arguments:
    parameters -- python dictionary containing your parameters.
                    parameters["W" + str(l)] = Wl
                    parameters["b" + str(l)] = bl
    
    Returns: 
    v -- python dictionary that will contain the exponentially weighted average of the gradient.
                    v["dW" + str(l)] = ...
                    v["db" + str(l)] = ...
    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.
                    s["dW" + str(l)] = ...
                    s["db" + str(l)] = ...

    """
    
    L = len(parameters) // 2 # number of layers in the neural networks
    v = {}
    s = {}
    
    # Initialize v, s. Input: "parameters". Outputs: "v, s".
    for l in range(L):
    ### START CODE HERE ### (approx. 4 lines)
        v["dW" + str(l+1)] = np.zeros_like(parameters['W'+str(l+1)]) #(numpy array of zeros with the same shape as parameters["W" + str(l+1)])
        v["db" + str(l+1)] = np.zeros_like(parameters['b'+str(l+1)]) #(numpy array of zeros with the same shape as parameters["b" + str(l+1)])
        s["dW" + str(l+1)] = np.zeros_like(parameters['W'+str(l+1)]) #(numpy array of zeros with the same shape as parameters["W" + str(l+1)])
        s["db" + str(l+1)] = np.zeros_like(parameters['b'+str(l+1)]) #(numpy array of zeros with the same shape as parameters["b" + str(l+1)])


    ### END CODE HERE ###
    
    return v, s

def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate=0.01,
                                beta1=0.9, beta2=0.999, epsilon=1e-8):
    """
    Update parameters using Adam
    
    Arguments:
    parameters -- python dictionary containing your parameters:
                    parameters['W' + str(l)] = Wl
                    parameters['b' + str(l)] = bl
    grads -- python dictionary containing your gradients for each parameters:
                    grads['dW' + str(l)] = dWl
                    grads['db' + str(l)] = dbl
    v -- Adam variable, moving average of the first gradient, python dictionary
    s -- Adam variable, moving average of the squared gradient, python dictionary
    learning_rate -- the learning rate, scalar.
    beta1 -- Exponential decay hyperparameter for the first moment estimates 
    beta2 -- Exponential decay hyperparameter for the second moment estimates 
    epsilon -- hyperparameter preventing division by zero in Adam updates

    Returns:
    parameters -- python dictionary containing your updated parameters 
    v -- Adam variable, moving average of the first gradient, python dictionary
    s -- Adam variable, moving average of the squared gradient, python dictionary
    """
    
    L = len(parameters) // 2                 # number of layers in the neural networks
    v_corrected = {}                         # Initializing first moment estimate, python dictionary
    s_corrected = {}                         # Initializing second moment estimate, python dictionary
    
    # Perform Adam update on all parameters
    for l in range(L):
        # Moving average of the gradients. Inputs: "v, grads, beta1". Output: "v".
        ### START CODE HERE ### (approx. 2 lines)
        v['dW'+str(l+1)] = beta1*v['dW'+str(l+1)]+(1-beta1)*grads['dW'+str(l+1)]
        v['db'+str(l+1)] = beta1*v['db'+str(l+1)]+(1-beta1)*grads['db'+str(l+1)]
        ### END CODE HERE ###

        # Compute bias-corrected first moment estimate. Inputs: "v, beta1, t". Output: "v_corrected".
        ### START CODE HERE ### (approx. 2 lines)
        v_corrected['dW'+str(l+1)] = v['dW'+str(l+1)]/(1-np.power(beta1,t))
        v_corrected['db'+str(l+1)] = v['db'+str(l+1)]/(1-np.power(beta1,t))
        ### END CODE HERE ###

        # Moving average of the squared gradients. Inputs: "s, grads, beta2". Output: "s".
        ### START CODE HERE ### (approx. 2 lines)
        s['dW'+str(l+1)] = beta2*s['dW'+str(l+1)]+(1-beta2)*np.power(grads['dW'+str(l+1)],2)
        s['db'+str(l+1)] = beta2*s['db'+str(l+1)]+(1-beta2)*np.power(grads['db'+str(l+1)],2)
        ### END CODE HERE ###

        # Compute bias-corrected second raw moment estimate. Inputs: "s, beta2, t". Output: "s_corrected".
        ### START CODE HERE ### (approx. 2 lines)
        s_corrected['dW'+str(l+1)] = s['dW'+str(l+1)]/(1-np.power(beta2,t))
        s_corrected['db'+str(l+1)] = s['db'+str(l+1)]/(1-np.power(beta2,t))
        ### END CODE HERE ###

        # Update parameters. Inputs: "parameters, learning_rate, v_corrected, s_corrected, epsilon". Output: "parameters".
        ### START CODE HERE ### (approx. 2 lines)
        parameters['W'+str(l+1)] -= learning_rate * v_corrected['dW'+str(l+1)] /(epsilon+np.sqrt(s_corrected['dW'+str(l+1)]))
        parameters['b'+str(l+1)] -= learning_rate * v_corrected['db'+str(l+1)] /(epsilon+np.sqrt(s_corrected['db'+str(l+1)]))
        
        ### END CODE HERE ###

    return parameters, v, s

def model(X, Y, layers_dims, optimizer, learning_rate=0.0007, mini_batch_size=64, beta=0.9,
          beta1=0.9, beta2=0.999, epsilon=1e-8, num_epochs=10000, print_cost=True):
    """
    3-layer neural network model which can be run in different optimizer modes.
    
    Arguments:
    X -- input data, of shape (2, number of examples)
    Y -- true "label" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)
    layers_dims -- python list, containing the size of each layer
    learning_rate -- the learning rate, scalar.
    mini_batch_size -- the size of a mini batch
    beta -- Momentum hyperparameter
    beta1 -- Exponential decay hyperparameter for the past gradients estimates 
    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates 
    epsilon -- hyperparameter preventing division by zero in Adam updates
    num_epochs -- number of epochs
    print_cost -- True to print the cost every 1000 epochs

    Returns:
    parameters -- python dictionary containing your updated parameters 
    """

    L = len(layers_dims)             # number of layers in the neural networks
    costs = []                       # to keep track of the cost
    t = 0                            # initializing the counter required for Adam update
    seed = 10                        # For grading purposes, so that your "random" minibatches are the same as ours
    
    # Initialize parameters
    parameters = initialize_parameters(layers_dims)

    # Initialize the optimizer
    if optimizer == "gd":
        pass # no initialization required for gradient descent
    elif optimizer == "momentum":
        v = initialize_velocity(parameters)
    elif optimizer == "adam":
        v, s = initialize_adam(parameters)
    
    # Optimization loop
    for i in range(num_epochs):
        
        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch
        seed = seed + 1
        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)

        for minibatch in minibatches:

            # Select a minibatch
            (minibatch_X, minibatch_Y) = minibatch

            # Forward propagation
            a3, caches = forward_propagation(minibatch_X, parameters)

            # Compute cost
            cost = compute_cost(a3, minibatch_Y)

            # Backward propagation
            grads = backward_propagation(minibatch_X, minibatch_Y, caches)

            # Update parameters
            if optimizer == "gd":
                parameters = update_parameters_with_gd(parameters, grads, learning_rate)
            elif optimizer == "momentum":
                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)
            elif optimizer == "adam":
                t = t + 1 # Adam counter
                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,
                                                               t, learning_rate, beta1, beta2,  epsilon)
        
        # Print the cost every 1000 epoch
        if print_cost and i % 1000 == 0:
            print("Cost after epoch %i: %f" % (i, cost))
        if print_cost and i % 100 == 0:
            costs.append(cost)
                
    # plot the cost
    plt.plot(costs)
    plt.ylabel('cost')
    plt.xlabel('epochs (per 100)')
    plt.title("Learning rate = " + str(learning_rate))
    plt.show()

    return parameters

d3= np.random.rand(a3.shape[0],a3.shape[1])<keep_prob

a3 = np.multiply(a3,d3)

a3/= keep_prob

def initialize_parameters_he(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    np.random.seed(3)
    parameters = {}
    L = len(layers_dims) - 1 # integer representing the number of layers
     
    for l in range(1, L + 1):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * (np.sqrt(2. / layers_dims[l-1]))
        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
        ### END CODE HERE ###
        
    return parameters

def compute_cost_with_regularization(A3, Y, parameters, lambd):
    """
    Implement the cost function with L2 regularization. See formula (2) above.
    
    Arguments:
    A3 -- post-activation, output of forward propagation, of shape (output size, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    parameters -- python dictionary containing parameters of the model
    
    Returns:
    cost - value of the regularized loss function (formula (2))
    """
    m = Y.shape[1]
    W1 = parameters["W1"]
    W2 = parameters["W2"]
    W3 = parameters["W3"]
    
    cross_entropy_cost = compute_cost(A3, Y) # This gives you the cross-entropy part of the cost
    
    ### START CODE HERE ### (approx. 1 line)
    sumW1 = np.sum(np.square(W1))
    sumW2 = np.sum(np.square(W2))
    sumW3 = np.sum(np.square(W3))
    L2_regularization_cost = (0.5/m*lambd)*(sumW1+sumW2+sumW3)
    ### END CODER HERE ###
    
    cost = cross_entropy_cost + L2_regularization_cost
    
    return cost

def backward_propagation_with_regularization(X, Y, cache, lambd):
    """
    Implements the backward propagation of our baseline model to which we added an L2 regularization.
    
    Arguments:
    X -- input dataset, of shape (input size, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    cache -- cache output from forward_propagation()
    lambd -- regularization hyperparameter, scalar
    
    Returns:
    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables
    """
    
    m = X.shape[1]
    (Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache
    
    dZ3 = A3 - Y
    
    ### START CODE HERE ### (approx. 1 line)
    dW3 = 1./m * np.dot(dZ3, A2.T) + (lambd/m)*W3
    ### END CODE HERE ###
    db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)
    
    dA2 = np.dot(W3.T, dZ3)
    dZ2 = np.multiply(dA2, np.int64(A2 > 0))
    ### START CODE HERE ### (approx. 1 line)
    dW2 = 1./m * np.dot(dZ2, A1.T) + (lambd/m)*W2
    ### END CODE HERE ###
    db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)
    
    dA1 = np.dot(W2.T, dZ2)
    dZ1 = np.multiply(dA1, np.int64(A1 > 0))
    ### START CODE HERE ### (approx. 1 line)
    dW1 = 1./m * np.dot(dZ1, X.T) + (lambd/m)*W1
    ### END CODE HERE ###
    db1 = 1./m * np.sum(dZ1, axis=1, keepdims = True)
    
    gradients = {"dZ3": dZ3, "dW3": dW3, "db3": db3,"dA2": dA2,
                 "dZ2": dZ2, "dW2": dW2, "db2": db2, "dA1": dA1, 
                 "dZ1": dZ1, "dW1": dW1, "db1": db1}
    
    return gradients

def forward_propagation_with_dropout(X, parameters, keep_prob=0.5):
    """
    Implements the forward propagation: LINEAR -> RELU + DROPOUT -> LINEAR -> RELU + DROPOUT -> LINEAR -> SIGMOID.
    
    Arguments:
    X -- input dataset, of shape (2, number of examples)
    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
                    W1 -- weight matrix of shape (20, 2)
                    b1 -- bias vector of shape (20, 1)
                    W2 -- weight matrix of shape (3, 20)
                    b2 -- bias vector of shape (3, 1)
                    W3 -- weight matrix of shape (1, 3)
                    b3 -- bias vector of shape (1, 1)
    keep_prob - probability of keeping a neuron active during drop-out, scalar
    
    Returns:
    A3 -- last activation value, output of the forward propagation, of shape (1,1)
    cache -- tuple, information stored for computing the backward propagation
    """
    
    np.random.seed(1)
    
    # retrieve parameters
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    W3 = parameters["W3"]
    b3 = parameters["b3"]
    
    # LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID
    Z1 = np.dot(W1, X) + b1
    A1 = relu(Z1)
    ### START CODE HERE ### (approx. 4 lines)         # Steps 1-4 below correspond to the Steps 1-4 described above. 
    D1 = np.random.rand(A1.shape[0], A1.shape[1])     # Step 1: initialize matrix D1 = np.random.rand(..., ...)
    D1 = D1 < keep_prob                            # Step 2: convert entries of D1 to 0 or 1 (using keep_prob as the threshold)
    A1 = A1 * D1                                      # Step 3: shut down some neurons of A1
    A1 = A1 / keep_prob                               # Step 4: scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    Z2 = np.dot(W2, A1) + b2
    A2 = relu(Z2)
    ### START CODE HERE ### (approx. 4 lines)
    D2 = np.random.rand(A2.shape[0], A2.shape[1])     # Step 1: initialize matrix D2 = np.random.rand(..., ...)
    D2 = D2 < keep_prob                           # Step 2: convert entries of D2 to 0 or 1 (using keep_prob as the threshold)                           
    A2 = A2 * D2                                      # Step 3: shut down some neurons of A2
    A2 = A2 / keep_prob                               # Step 4: scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    Z3 = np.dot(W3, A2) + b3
    A3 = sigmoid(Z3)
    
    cache = (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3)
    
    return A3, cache

def backward_propagation_with_dropout(X, Y, cache, keep_prob):
    """
    Implements the backward propagation of our baseline model to which we added dropout.
    
    Arguments:
    X -- input dataset, of shape (2, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    cache -- cache output from forward_propagation_with_dropout()
    keep_prob - probability of keeping a neuron active during drop-out, scalar
    
    Returns:
    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables
    """
    
    m = X.shape[1]
    (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3) = cache
    
    dZ3 = A3 - Y
    dW3 = 1. / m * np.dot(dZ3, A2.T)
    db3 = 1. / m * np.sum(dZ3, axis=1, keepdims=True)
    dA2 = np.dot(W3.T, dZ3)
    ### START CODE HERE ### (≈ 2 lines of code)
    dA2 = dA2 * D2              # Step 1: Apply mask D2 to shut down the same neurons as during the forward propagation
    dA2 = dA2 / keep_prob              # Step 2: Scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    dZ2 = np.multiply(dA2, np.int64(A2 > 0))
    dW2 = 1. / m * np.dot(dZ2, A1.T)
    db2 = 1. / m * np.sum(dZ2, axis=1, keepdims=True)
    
    dA1 = np.dot(W2.T, dZ2)
    ### START CODE HERE ### (≈ 2 lines of code)
    dA1 = dA1 * D1              # Step 1: Apply mask D1 to shut down the same neurons as during the forward propagation
    dA1 = dA1 / keep_prob              # Step 2: Scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    dZ1 = np.multiply(dA1, np.int64(A1 > 0))
    dW1 = 1. / m * np.dot(dZ1, X.T)
    db1 = 1. / m * np.sum(dZ1, axis=1, keepdims=True)
    
    gradients = {"dZ3": dZ3, "dW3": dW3, "db3": db3,"dA2": dA2,
                 "dZ2": dZ2, "dW2": dW2, "db2": db2, "dA1": dA1, 
                 "dZ1": dZ1, "dW1": dW1, "db1": db1}
    
    return gradients

np.linalg.norm 是求范数的函数，默认是求二范数

def gradient_check(x, theta, epsilon = 1e-7):
    """
    Implement the backward propagation presented in Figure 1.
    
    Arguments:
    x -- a real-valued input
    theta -- our parameter, a real number as well
    epsilon -- tiny shift to the input to compute approximated gradient with formula(1)
    
    Returns:
    difference -- difference (2) between the approximated gradient and the backward propagation gradient
    """
    
    # Compute gradapprox using left side of formula (1). epsilon is small enough, you don't need to worry about the limit.
    ### START CODE HERE ### (approx. 5 lines)
    thetaPlus = theta+epsilon
    thetaMinus = theta-epsilon
    JPlus = forward_propagation(x,thetaPlus)
    JMinus = forward_propagation(x,thetaMinus)
    gradapprox = (JPlus-JMinus)/(2*epsilon)
    ### END CODE HERE ###
    
    # Check if gradapprox is close enough to the output of backward_propagation()
    ### START CODE HERE ### (approx. 1 line)
    grad = backward_propagation(x, gradapprox)
    ### END CODE HERE ###
        
    ### START CODE HERE ### (approx. 1 line)
    numerator = np.linalg.norm(grad-gradapprox)
    demurator = np.linalg.norm(grad)+np.linalg.norm(gradapprox)
    difference = numerator/demurator
    
    
    if difference < 1e-7:
        print ("The gradient is correct!")
    else:
        print ("The gradient is wrong!")
    
    return difference

def gradient_check_n(parameters, gradients, X, Y, epsilon=1e-7):
    """
    Checks if backward_propagation_n computes correctly the gradient of the cost output by forward_propagation_n
    
    Arguments:
    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
    grad -- output of backward_propagation_n, contains gradients of the cost with respect to the parameters. 
    x -- input datapoint, of shape (input size, 1)
    y -- true "label"
    epsilon -- tiny shift to the input to compute approximated gradient with formula(1)
    
    Returns:
    difference -- difference (2) between the approximated gradient and the backward propagation gradient
    """
    
    # Set-up variables
    parameters_values, _ = dictionary_to_vector(parameters)
    grad = gradients_to_vector(gradients)
    num_parameters = parameters_values.shape[0]
    J_plus = np.zeros((num_parameters, 1))
    J_minus = np.zeros((num_parameters, 1))
    gradapprox = np.zeros((num_parameters, 1))
    
    # Compute gradapprox
    for i in range(num_parameters):
        
        # Compute J_plus[i]. Inputs: "parameters_values, epsilon". Output = "J_plus[i]".
        # "_" is used because the function you have to outputs two parameters but we only care about the first one
        ### START CODE HERE ### (approx. 3 lines)
        thetaplus =  np.copy(parameters_values)                                       # Step 1
        thetaplus[i][0] = thetaplus[i][0] + epsilon                                   # Step 2
        J_plus[i], _ =  forward_propagation_n(X, Y, vector_to_dictionary(thetaplus))  # Step 3
        ### END CODE HERE ###
        
        # Compute J_minus[i]. Inputs: "parameters_values, epsilon". Output = "J_minus[i]".
        ### START CODE HERE ### (approx. 3 lines)
        thetaminus = np.copy(parameters_values)                                       # Step 1
        thetaminus[i][0] = thetaminus[i][0] - epsilon                                 # Step 2        
        J_minus[i], _ = forward_propagation_n(X, Y, vector_to_dictionary(thetaminus)) # Step 3
        ### END CODE HERE ###
        
        # Compute gradapprox[i]
        ### START CODE HERE ### (approx. 1 line)
        gradapprox[i] = (J_plus[i] - J_minus[i]) / (2 * epsilon)
        ### END CODE HERE ###
    
    # Compare gradapprox to backward propagation gradients by computing difference.
    ### START CODE HERE ### (approx. 1 line)
    numerator = np.linalg.norm(grad - gradapprox)                                     # Step 1'
    denominator = np.linalg.norm(grad) + np.linalg.norm(gradapprox)                   # Step 2'
    difference = numerator / denominator                                              # Step 3'
    ### END CODE HERE ###

    if difference > 1e-7:
        print("\033[93m" + "There is a mistake in the backward propagation! difference = " + str(difference) + "\033[0m")
    else:
        print("\033[92m" + "Your backward propagation works perfectly fine! difference = " + str(difference) + "\033[0m")
    
    return difference