Optimization Algorithm

optimization_algorithms/opt_utils.py

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+import numpy as np
+import matplotlib.pyplot as plt
+import h5py
+import scipy.io
+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 load_params_and_grads(seed=1):
+    np.random.seed(seed)
+    W1 = np.random.randn(2,3)
+    b1 = np.random.randn(2,1)
+    W2 = np.random.randn(3,3)
+    b2 = np.random.randn(3,1)
+
+    dW1 = np.random.randn(2,3)
+    db1 = np.random.randn(2,1)
+    dW2 = np.random.randn(3,3)
+    db2 = np.random.randn(3,1)
+
+    return W1, b1, W2, b2, dW1, db1, dW2, db2
+
+
+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(2 / 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 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.sum(logprobs)
+
+    return cost
+
+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 = 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 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 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, s=40, cmap=plt.cm.Spectral);
+
+    return train_X, train_Y, test_X, test_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)
+    plt.ylabel('x2')
+    plt.xlabel('x1')
+    plt.scatter(X[0, :], X[1, :], c=y, 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(3)
+    train_X, train_Y = sklearn.datasets.make_moons(n_samples=300, noise=.2) #300 #0.2 
+    # 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]))
+
+    return train_X, train_Y

optimization_algorithms/testCases.py

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+import numpy as np
+
+def update_parameters_with_gd_test_case():
+    np.random.seed(1)
+    learning_rate = 0.01
+    W1 = np.random.randn(2,3)
+    b1 = np.random.randn(2,1)
+    W2 = np.random.randn(3,3)
+    b2 = np.random.randn(3,1)
+
+    dW1 = np.random.randn(2,3)
+    db1 = np.random.randn(2,1)
+    dW2 = np.random.randn(3,3)
+    db2 = np.random.randn(3,1)
+
+    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
+    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}
+
+    return parameters, grads, learning_rate
+
+"""
+def update_parameters_with_sgd_checker(function, inputs, outputs):
+    if function(inputs) == outputs:
+        print("Correct")
+    else:
+        print("Incorrect")
+"""
+
+def random_mini_batches_test_case():
+    np.random.seed(1)
+    mini_batch_size = 64
+    X = np.random.randn(12288, 148)
+    Y = np.random.randn(1, 148) < 0.5
+    return X, Y, mini_batch_size
+
+def initialize_velocity_test_case():
+    np.random.seed(1)
+    W1 = np.random.randn(2,3)
+    b1 = np.random.randn(2,1)
+    W2 = np.random.randn(3,3)
+    b2 = np.random.randn(3,1)
+    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
+    return parameters
+
+def update_parameters_with_momentum_test_case():
+    np.random.seed(1)
+    W1 = np.random.randn(2,3)
+    b1 = np.random.randn(2,1)
+    W2 = np.random.randn(3,3)
+    b2 = np.random.randn(3,1)
+
+    dW1 = np.random.randn(2,3)
+    db1 = np.random.randn(2,1)
+    dW2 = np.random.randn(3,3)
+    db2 = np.random.randn(3,1)
+    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
+    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}
+    v = {'dW1': np.array([[ 0.,  0.,  0.],
+        [ 0.,  0.,  0.]]), 'dW2': np.array([[ 0.,  0.,  0.],
+        [ 0.,  0.,  0.],
+        [ 0.,  0.,  0.]]), 'db1': np.array([[ 0.],
+        [ 0.]]), 'db2': np.array([[ 0.],
+        [ 0.],
+        [ 0.]])}
+    return parameters, grads, v
+
+def initialize_adam_test_case():
+    np.random.seed(1)
+    W1 = np.random.randn(2,3)
+    b1 = np.random.randn(2,1)
+    W2 = np.random.randn(3,3)
+    b2 = np.random.randn(3,1)
+    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
+    return parameters
+
+def update_parameters_with_adam_test_case():
+    np.random.seed(1)
+    v, s = ({'dW1': np.array([[ 0.,  0.,  0.],
+         [ 0.,  0.,  0.]]), 'dW2': np.array([[ 0.,  0.,  0.],
+         [ 0.,  0.,  0.],
+         [ 0.,  0.,  0.]]), 'db1': np.array([[ 0.],
+         [ 0.]]), 'db2': np.array([[ 0.],
+         [ 0.],
+         [ 0.]])}, {'dW1': np.array([[ 0.,  0.,  0.],
+         [ 0.,  0.,  0.]]), 'dW2': np.array([[ 0.,  0.,  0.],
+         [ 0.,  0.,  0.],
+         [ 0.,  0.,  0.]]), 'db1': np.array([[ 0.],
+         [ 0.]]), 'db2': np.array([[ 0.],
+         [ 0.],
+         [ 0.]])})
+    W1 = np.random.randn(2,3)
+    b1 = np.random.randn(2,1)
+    W2 = np.random.randn(3,3)
+    b2 = np.random.randn(3,1)
+
+    dW1 = np.random.randn(2,3)
+    db1 = np.random.randn(2,1)
+    dW2 = np.random.randn(3,3)
+    db2 = np.random.randn(3,1)
+
+    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
+    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}
+
+    return parameters, grads, v, s
+