# 👩‍💻 Python Code Snippets

## 📚 General Code Snippets in ML

### 💥 Sigmoid Function

➗ Formula
👩‍💻 Code
$sigmoid(x)=\frac{1}{1+exp(-x)}$
def sigmoid(x):
"""
Arguments:
x -- A scalar, an array or a matrix
Return:
result -- sigmoid(x)
"""
result = 1 /( 1 + np.exp(-x) )
return result

👩‍🏫 Description
➗ Formula
👩‍💻 Code
A function that computes gradients to optimize loss functions using backpropagation
$\sigma^{'}(x)=\sigma(x)(1-\sigma(x))$
def sigmoid_derivative(x):
"""
Computes the gradient (also called the slope or derivative) of the sigmoid function with respect to its input x.
Arguments:
x -- A scalar or numpy array
Return:
"""
s = 1 / (1 + np.exp(-x))
ds = s * (1 - s)
return ds

### 👩‍🔧 Reshaping Arrays (or images)

👩‍💻 Code
def arr2vec(arr, target):
"""
Argument:
image -- a numpy array of shape (length, height, depth)
Returns:
v -- a vector of shape (length*height*depth, 1)
"""
v = image.reshape(image.shape[0] * image.shape[1] * image.shape[2], 1)
return v

### 💥 Normalizing Rows

👩‍🏫 Description
➗ Formula
👩‍💻 Code
Dividing each row vector of x by its norm.
$Normalization(x)=\frac{x}{||x||}$
def normalizeRows(x):
"""
Argument:
x -- A numpy matrix of shape (n, m)
Returns:
x -- The normalized (by row) numpy matrix.
"""
# Finding norms
x_norm = np.linalg.norm(x, axis=1, keepdims=True)
# Dividing x by its norm
x = x / x_norm
return x

### 🎨 Softmax Function

👩‍🏫 Description
➗ Formula
👩‍💻 Code
A normalizing function used when the algorithm needs to classify two or more classes
$Softmax(x_i)=\frac{exp(x_i)}{\sum_{j}exp(x_j)}$
def softmax(x):
"""Calculates the softmax for each row of the input x.
Argument:
x -- A numpy matrix of shape (n,m)
Returns:
s -- A numpy matrix equal to the softmax of x, of shape (n,m)
"""
# Applying exp() element-wise to x
x_exp = np.exp(x)
# Creating a vector x_sum that sums each row of x_exp
x_sum = np.sum(x_exp, axis=1, keepdims=True)
# Computing softmax(x) by dividing x_exp by x_sum.
# numpy broadcasting will be used automatically.
s = x_exp / x_sum
return s

### 🤸‍♀️ L1 Loss Function

👩‍🏫 Description
➗ Formula
👩‍💻 Code
The loss is used to evaluate the performance of the model. The bigger the loss is, the more different that predictions ( ŷ ) are from the true values ( y ). In deep learning, we use optimization algorithms like Gradient Descent to train the model and to minimize the cos
$L_1(\hat{y},y)=\sum_{i=0}^{m}(|y^{(i)}-\hat{y}^{(i)}|)$
def L1(yhat, y):
"""
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L1 loss function defined previously
"""
loss = np.sum(np.abs(y - yhat))
return loss

### 🤸‍♂️ L2 Loss Function

👩‍🏫 Description
➗ Formula
👩‍💻 Code
The loss is used to evaluate the performance of the model. The bigger the loss is, the more different that predictions ( ŷ ) are from the true values ( y ). In deep learning, we use optimization algorithms like Gradient Descent to train the model and to minimize the cost.
$L_2(\hat{y},y)=\sum_{i=0}^{m}(y^{(i)}-\hat{y}^{(i)})^2$
def L2(yhat, y):
"""
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L2 loss function defined above
"""
loss = np.sum((y - yhat) ** 2)
return loss

### 🏃‍♀️ Propagation Function

👩‍🏫 Description
➗ Formula
👩‍💻 Code
Doing the "forward" and "backward" propagation steps for learning the parameters.
$\frac{\partial J}{\partial w}=\frac{1}{m}X(A-Y)^T$
$\frac{\partial J}{\partial b}=\frac{1}{m}\sum_{i=1}^{m}(a^{(i)}-y^{(i)})$
def propagate(w, b, X, Y):
"""
Implementation of the cost function and its gradient for the propagation
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
"""
m = X.shape[1]
# FORWARD PROPAGATION (FROM X TO COST)
# computing activation
A = sigmoid( np.dot(w.T, X) + b )
# computing cost
cost = - np.sum( Y * np.log(A) + (1-Y) * np.log(1 - A) ) / m
# BACKWARD PROPAGATION (TO FIND GRAD)
dw = (np.dot(X,(A-Y).T))/m
db = np.sum(A-Y)/m
"db": db}

👩‍🏫 Description
➗ Formula
👩‍💻 Code
The goal is to learn ω and b by minimizing the cost function J. For a parameter ω
$w=w-\alpha dw$
Where α is the learning rate
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.
"""
costs = []
for i in range(num_iterations):
grads, cost = propagate(w, b, X, Y)
# update rule
w = w - learning_rate*dw
b = b - learning_rate*db
# Record the costs
if i % 100 == 0:
costs.append(cost)
# Print the cost every 100 training iterations (optional)
if print_cost and i % 100 == 0:
print ("Cost after iteration %i: %f" %(i, cost))
params = {"w": w,
"b": b}
"db": db}

## 🕸 Basic Code Snippets for Simple NN

Functions of 2-layer NN
Input layer, 1 hidden layer and output layer

### 🚀 Parameter Initialization

👩‍🏫 Description
👩‍🏫 Code
Initializing Ws and bs, Ws must be initialized randomly in order to do symmetry-breaking, we can do zero initalization for bs
def initialize_parameters(n_x, n_h, n_y):
"""
Argument:
n_x -- size of the input layer
n_h -- size of the hidden layer
n_y -- size of the output layer
Returns:
params -- python dictionary containing your parameters:
W1 -- weight matrix of shape (n_h, n_x)
b1 -- bias vector of shape (n_h, 1)
W2 -- weight matrix of shape (n_y, n_h)
b2 -- bias vector of shape (n_y, 1)
"""
# multiplying with 0.01 to minimize values
W1 = np.random.randn(n_h,n_x) * 0.01
b1 = np.zeros((n_h,1))
W2 = np.random.randn(n_y,n_h) * 0.01
b2 = np.zeros((n_y,1))
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}
return parameters

### ⏩ Forward Propagation

👩‍🏫 Description
👩‍💻 Code
Each layer accepts the input data, processes it as per the activation function and passes to the next layer
def forward_propagation(X, parameters):
"""
Argument:
X -- input data of size (n_x, m)
parameters -- python dictionary containing your parameters (output of initialization function)
Returns:
A2 -- The sigmoid output of the second activation
cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"
"""
# Retrieving each parameter from the dictionary "parameters"
W1 = parameters['W1']
b1 = parameters['b1']
W2 = parameters['W2']
b2 = parameters['b2']
Z1 = np.dot(W1, X) + b1
A1 = np.tanh(Z1)
Z2 = np.dot(W2, A1) + b2
A2 = sigmoid(Z2)
cache = {"Z1": Z1,
"A1": A1,
"Z2": Z2,
"A2": A2}
return A2, cache

### 🚩 Cost Function

.👩‍🏫 Description
➗ Formula
👩‍💻 Code
The average of the loss functions of the entire training set due to the output layer -from A2 in our example-
$J=-\frac{1}{m}\sum_{i=1}^{m}(y^{(i)}log(a^{[2](i)}) + (1-y^{(i)}log(1-a^{[2](i)})))$
def compute_cost(A2, Y):
"""
Computes the cross-entropy cost given in the formula
Arguments:
A2 -- The sigmoid output of the second activation, of shape (1, number of examples)
Y -- "true" labels vector of shape (1, number of examples)
Returns:
cost -- cross-entropy cost given in the formula
"""
# Number of examples
m = Y.shape[1]
# Computing the cross-entropy cost
logprobs = np.multiply(np.log(A2), Y) + (1 - Y) * np.log(1 - A2)
cost = - np.sum(logprobs) / m
cost = float(np.squeeze(cost))
return cost

### ⏪ Back Propagation

👩‍🏫 Description
➗ Formula
👩‍💻 Code
Proper tuning of the weights ensures lower error rates, making the model reliable by increasing its generalization.
def backward_propagation(parameters, cache, X, Y):
"""
Implement the backward propagation using the previously given instructions.
Arguments:
parameters -- python dictionary containing our parameters
cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".
X -- input data of shape (2, number of examples)
Y -- "true" labels vector of shape (1, number of examples)
Returns:
"""
m = X.shape[1]
# Retrieving W1 and W2 from the dictionary "parameters".
W1 = parameters['W1']
W2 = parameters['W2']
# Retrieving also A1 and A2 from dictionary "cache".
A1 = cache['A1']
A2 = cache['A2']
# Backward propagation: calculating dW1, db1, dW2, db2.
dZ2 = A2 - Y
dW2 = np.dot(dZ2, A1.T) / m
db2 = np.sum(dZ2, axis = 1, keepdims = True) / m
dZ1 = np.dot(W2.T, dZ2) * (1 - A1 ** 2)
dW1 = np.dot(dZ1, X.T) / m
db1 = np.sum(dZ1, axis = 1, keepdims = True) / m
"db1": db1,
"dW2": dW2,
"db2": db2}

### 🔃 Updating Parameters

👩‍🏫 Description
➗ Formula
👩‍💻 Code
Updating the parameters due to the learning rate to complete the gradient descent
$\theta := \theta - \alpha \frac{\partial J}{\partial \theta}$
def update_parameters(parameters, grads, learning_rate = 1.2):
"""
Arguments:
parameters -- python dictionary containing your parameters
Returns:
parameters -- python dictionary containing your updated parameters
"""
# Retrieving each parameter from the dictionary "parameters"
W1 = parameters['W1']
b1 = parameters['b1']
W2 = parameters['W2']
b2 = parameters['b2']
# Updating rule for each parameter
W1 = W1 - learning_rate * dW1
b1 = b1 - learning_rate * db1
W2 = W2 - learning_rate * dW2
b2 = b2 - learning_rate * db2
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}
return parameters