text: import numpy as np
  import matplotlib.pyplot as plt
  import h5py
  import sklearn
  import sklearn.datasets
  
  def sigmoid(x):
      """
      Compute the sigmoid of x
      Arguments:
      x -- A scalar or numpy array of any size.
      Return:
      s -- sigmoid(x)
      """
      s = 1/(1+np.exp(-x))
      return s
  
  def relu(x):
      """
      Compute the relu of x
      Arguments:
      x -- A scalar or numpy array of any size.
      Return:
      s -- relu(x)
      """
      s = np.maximum(0,x)
      
      return s
  
  def forward_propagation(X, parameters):
      """
      Implements the forward propagation (and computes the loss) presented in Figure 2.
      
      Arguments:
      X -- input dataset, of shape (input size, number of examples)
      Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
      parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
                      W1 -- weight matrix of shape ()
                      b1 -- bias vector of shape ()
                      W2 -- weight matrix of shape ()
                      b2 -- bias vector of shape ()
                      W3 -- weight matrix of shape ()
                      b3 -- bias vector of shape ()
      
      Returns:
      loss -- the loss function (vanilla logistic loss)
      """
          
      # 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)
      z2 = np.dot(W2, a1) + b2
      a2 = relu(z2)
      z3 = np.dot(W3, a2) + b3
      a3 = sigmoid(z3)
      
      cache = (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3)
      
      return a3, cache
  
  def backward_propagation(X, Y, cache):
      """
      Implement the backward propagation presented in figure 2.
      
      Arguments:
      X -- input dataset, of shape (input size, number of examples)
      Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
      cache -- cache output from forward_propagation()
      
      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 = 1./m * (a3 - Y)
      dW3 = np.dot(dz3, a2.T)
      db3 = np.sum(dz3, axis=1, keepdims = True)
      
      da2 = np.dot(W3.T, dz3)
      dz2 = np.multiply(da2, np.int64(a2 > 0))
      dW2 = np.dot(dz2, a1.T)
      db2 = np.sum(dz2, axis=1, keepdims = True)
      
      da1 = np.dot(W2.T, dz2)
      dz1 = np.multiply(da1, np.int64(a1 > 0))
      dW1 = np.dot(dz1, X.T)
      db1 = 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 update_parameters(parameters, grads, learning_rate):
      """
      Update parameters using gradient descent
      
      Arguments:
      parameters -- python dictionary containing your parameters 
      grads -- python dictionary containing your gradients, output of n_model_backward
      
      Returns:
      parameters -- python dictionary containing your updated parameters 
                    parameters['W' + str(i)] = ... 
                    parameters['b' + str(i)] = ...
      """
      
      L = len(parameters) // 2 # number of layers in the neural networks
  
      # Update rule for each parameter
      for k in range(L):
          parameters["W" + str(k+1)] = parameters["W" + str(k+1)] - learning_rate * grads["dW" + str(k+1)]
          parameters["b" + str(k+1)] = parameters["b" + str(k+1)] - learning_rate * grads["db" + str(k+1)]
          
      return parameters
  
  def compute_loss(a3, Y):
      
      """
      Implement the loss function
      
      Arguments:
      a3 -- post-activation, output of forward propagation
      Y -- "true" labels vector, same shape as a3
      
      Returns:
      loss - value of the loss function
      """
      
      m = Y.shape[1]
      logprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 - a3), 1 - Y)
      loss = 1./m * np.nansum(logprobs)
      
      return loss
  
  def load_cat_dataset():
      train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")
      train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features
      train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels
  
      test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")
      test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features
      test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels
  
      classes = np.array(test_dataset["list_classes"][:]) # the list of classes
      
      train_set_y = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
      test_set_y = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))
      
      train_set_x_orig = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
      test_set_x_orig = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
      
      train_set_x = train_set_x_orig/255
      test_set_x = test_set_x_orig/255
  
      return train_set_x, train_set_y, test_set_x, test_set_y, classes
  
  
  def predict(X, y, parameters):
      """
      This function is used to predict the results of a  n-layer neural network.
      
      Arguments:
      X -- data set of examples you would like to label
      parameters -- parameters of the trained model
      
      Returns:
      p -- predictions for the given dataset X
      """
      
      m = X.shape[1]
      p = np.zeros((1,m), dtype = np.int)
      
      # Forward propagation
      a3, caches = forward_propagation(X, parameters)
      
      # convert probas to 0/1 predictions
      for i in range(0, a3.shape[1]):
          if a3[0,i] > 0.5:
              p[0,i] = 1
          else:
              p[0,i] = 0
  
      # print results
      print("Accuracy: "  + str(np.mean((p[0,:] == y[0,:]))))
      
      return p
  
  def plot_decision_boundary(model, X, y):
      # Set min and max values and give it some padding
      x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
      y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
      h = 0.01
      # Generate a grid of points with distance h between them
      xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
      # Predict the function value for the whole grid
      Z = model(np.c_[xx.ravel(), yy.ravel()])
      Z = Z.reshape(xx.shape)
      # Plot the contour and training examples
      plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
      plt.ylabel('x2')
      plt.xlabel('x1')
      plt.scatter(X[0, :], X[1, :], c=y.ravel(), cmap=plt.cm.Spectral)
      plt.show()
      
  def predict_dec(parameters, X):
      """
      Used for plotting decision boundary.
      
      Arguments:
      parameters -- python dictionary containing your parameters 
      X -- input data of size (m, K)
      
      Returns
      predictions -- vector of predictions of our model (red: 0 / blue: 1)
      """
      
      # Predict using forward propagation and a classification threshold of 0.5
      a3, cache = forward_propagation(X, parameters)
      predictions = (a3>0.5)
      return predictions
  
  def load_dataset():
      np.random.seed(1)
      train_X, train_Y = sklearn.datasets.make_circles(n_samples=300, noise=.05)
      np.random.seed(2)
      test_X, test_Y = sklearn.datasets.make_circles(n_samples=100, noise=.05)
      # Visualize the data
      plt.scatter(train_X[:, 0], train_X[:, 1], c=train_Y, s=40, cmap=plt.cm.Spectral);
      train_X = train_X.T
      train_Y = train_Y.reshape((1, train_Y.shape[0]))
      test_X = test_X.T
      test_Y = test_Y.reshape((1, test_Y.shape[0]))
      return train_X, train_Y, test_X, test_Y
      