text: import numpy as np
  import matplotlib.pyplot as plt
  import h5py
  import sklearn
  import sklearn.datasets
  import sklearn.linear_model
  import scipy.io
  
  
  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 load_planar_dataset(seed):
      np.random.seed(seed)
  
      m = 400  # number of examples
      N = int(m / 2)  # number of points per class
      D = 2  # dimensionality
      X = np.zeros((m, D))  # data matrix where each row is a single example
      Y = np.zeros((m, 1), dtype='uint8')  # labels vector (0 for red, 1 for blue)
      a = 4  # maximum ray of the flower
  
      for j in range(2):
          ix = range(N * j, N * (j + 1))
          t = np.linspace(j * 3.12, (j + 1) * 3.12, N) + np.random.randn(N) * 0.2  # theta
          r = a * np.sin(4 * t) + np.random.randn(N) * 0.2  # radius
          X[ix] = np.c_[r * np.sin(t), r * np.cos(t)]
          Y[ix] = j
  
      X = X.T
      Y = Y.T
  
      return X, Y
  
  
  def initialize_parameters(layer_dims):
      """
      Arguments:
      layer_dims -- python array (list) containing the dimensions of each layer in our network
      
      Returns:
      parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                      W1 -- weight matrix of shape (layer_dims[l], layer_dims[l-1])
                      b1 -- bias vector of shape (layer_dims[l], 1)
                      Wl -- weight matrix of shape (layer_dims[l-1], layer_dims[l])
                      bl -- bias vector of shape (1, layer_dims[l])
                      
      Tips:
      - For example: the layer_dims for the "Planar Data classification model" would have been [2,2,1]. 
      This means W1's shape was (2,2), b1 was (1,2), W2 was (2,1) and b2 was (1,1). Now you have to generalize it!
      - In the for loop, use parameters['W' + str(l)] to access Wl, where l is the iterative integer.
      """
  
      np.random.seed(3)
      parameters = {}
      L = len(layer_dims)  # number of layers in the network
  
      for l in range(1, L):
          parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l - 1]) / np.sqrt(layer_dims[l - 1])
          parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
  
          assert (parameters['W' + str(l)].shape == layer_dims[l], layer_dims[l - 1])
          assert (parameters['W' + str(l)].shape == layer_dims[l], 1)
  
      return parameters
  
  
  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)
      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 = 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)
      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)
      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
  
  
  def update_parameters(parameters, grads, learning_rate):
      """
      Update parameters using gradient descent
      
      Arguments:
      parameters -- python dictionary containing your parameters:
                      parameters['W' + str(i)] = Wi
                      parameters['b' + str(i)] = bi
      grads -- python dictionary containing your gradients for each parameters:
                      grads['dW' + str(i)] = dWi
                      grads['db' + str(i)] = dbi
      learning_rate -- the learning rate, scalar.
      
      Returns:
      parameters -- python dictionary containing your updated parameters 
      """
  
      n = len(parameters) // 2  # number of layers in the neural networks
  
      # Update rule for each parameter
      for k in range(n):
          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 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 ("predictions: " + str(p[0,:]))
      # print ("true labels: " + str(y[0,:]))
      print("Accuracy: " + str(np.mean((p[0, :] == y[0, :]))))
  
      return p
  
  
  def compute_cost(a3, Y):
      """
      Implement the cost function
      
      Arguments:
      a3 -- post-activation, output of forward propagation
      Y -- "true" labels vector, same shape as a3
      
      Returns:
      cost - value of the cost function
      """
      m = Y.shape[1]
  
      logprobs = np.multiply(-np.log(a3), Y) + np.multiply(-np.log(1 - a3), 1 - Y)
      cost = 1. / m * np.nansum(logprobs)
  
      return cost
  
  
  def load_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_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_planar_dataset(randomness, seed):
      np.random.seed(seed)
  
      m = 50
      N = int(m / 2)  # number of points per class
      D = 2  # dimensionality
      X = np.zeros((m, D))  # data matrix where each row is a single example
      Y = np.zeros((m, 1), dtype='uint8')  # labels vector (0 for red, 1 for blue)
      a = 2  # maximum ray of the flower
  
      for j in range(2):
  
          ix = range(N * j, N * (j + 1))
          if j == 0:
              t = np.linspace(j, 4 * 3.1415 * (j + 1), N)  # + np.random.randn(N)*randomness # theta
              r = 0.3 * np.square(t) + np.random.randn(N) * randomness  # radius
          if j == 1:
              t = np.linspace(j, 2 * 3.1415 * (j + 1), N)  # + np.random.randn(N)*randomness # theta
              r = 0.2 * np.square(t) + np.random.randn(N) * randomness  # radius
  
          X[ix] = np.c_[r * np.cos(t), r * np.sin(t)]
          Y[ix] = j
  
      X = X.T
      Y = Y.T
  
      return X, Y
  
  
  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, alpha=0.5)
      plt.ylabel('x2')
      plt.xlabel('x1')
      plt.scatter(X[0, :], X[1, :], c=y.ravel(), cmap=plt.cm.Spectral)
      plt.show()
  
  
  def load_2D_dataset():
      data = scipy.io.loadmat('datasets/data.mat')
      train_X = data['X'].T
      train_Y = data['y'].T
      test_X = data['Xval'].T
      test_Y = data['yval'].T
  
      plt.scatter(train_X[0, :], train_X[1, :], c=train_Y.ravel(), s=40, cmap=plt.cm.Spectral);
  
      return train_X, train_Y, test_X, test_Y
  