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week1/betaversion/lab_utils_common.py

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+""" 
+lab_utils_common.py
+    functions common to all optional labs, Course 1, Week 2 
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+plt.style.use('./deeplearning.mplstyle')
+dlblue = '#0096ff'; dlorange = '#FF9300'; dldarkred='#C00000'; dlmagenta='#FF40FF'; dlpurple='#7030A0';
+dlcolors = [dlblue, dlorange, dldarkred, dlmagenta, dlpurple]
+dlc = dict(dlblue = '#0096ff', dlorange = '#FF9300', dldarkred='#C00000', dlmagenta='#FF40FF', dlpurple='#7030A0')
+
+
+##########################################################
+# Regression Routines
+##########################################################
+
+#Function to calculate the cost
+def compute_cost_matrix(X, y, w, b, verbose=False):
+    """
+    Computes the gradient for linear regression
+     Args:
+      X (ndarray (m,n)): Data, m examples with n features
+      y (ndarray (m,)) : target values
+      w (ndarray (n,)) : model parameters  
+      b (scalar)       : model parameter
+      verbose : (Boolean) If true, print out intermediate value f_wb
+    Returns
+      cost: (scalar)
+    """
+    m = X.shape[0]
+
+    # calculate f_wb for all examples.
+    f_wb = X @ w + b
+    # calculate cost
+    total_cost = (1/(2*m)) * np.sum((f_wb-y)**2)
+
+    if verbose: print("f_wb:")
+    if verbose: print(f_wb)
+
+    return total_cost
+
+def compute_gradient_matrix(X, y, w, b):
+    """
+    Computes the gradient for linear regression
+
+    Args:
+      X (ndarray (m,n)): Data, m examples with n features
+      y (ndarray (m,)) : target values
+      w (ndarray (n,)) : model parameters  
+      b (scalar)       : model parameter
+    Returns
+      dj_dw (ndarray (n,1)): The gradient of the cost w.r.t. the parameters w.
+      dj_db (scalar):        The gradient of the cost w.r.t. the parameter b.
+
+    """
+    m,n = X.shape
+    f_wb = X @ w + b
+    e   = f_wb - y
+    dj_dw  = (1/m) * (X.T @ e)
+    dj_db  = (1/m) * np.sum(e)
+
+    return dj_db,dj_dw
+
+
+# Loop version of multi-variable compute_cost
+def compute_cost(X, y, w, b):
+    """
+    compute cost
+    Args:
+      X (ndarray (m,n)): Data, m examples with n features
+      y (ndarray (m,)) : target values
+      w (ndarray (n,)) : model parameters  
+      b (scalar)       : model parameter
+    Returns
+      cost (scalar)    : cost
+    """
+    m = X.shape[0]
+    cost = 0.0
+    for i in range(m):
+        f_wb_i = np.dot(X[i],w) + b           #(n,)(n,)=scalar
+        cost = cost + (f_wb_i - y[i])**2
+    cost = cost/(2*m)
+    return cost 
+
+def compute_gradient(X, y, w, b):
+    """
+    Computes the gradient for linear regression
+    Args:
+      X (ndarray (m,n)): Data, m examples with n features
+      y (ndarray (m,)) : target values
+      w (ndarray (n,)) : model parameters  
+      b (scalar)       : model parameter
+    Returns
+      dj_dw (ndarray Shape (n,)): The gradient of the cost w.r.t. the parameters w.
+      dj_db (scalar):             The gradient of the cost w.r.t. the parameter b.
+    """
+    m,n = X.shape           #(number of examples, number of features)
+    dj_dw = np.zeros((n,))
+    dj_db = 0.
+
+    for i in range(m):
+        err = (np.dot(X[i], w) + b) - y[i]
+        for j in range(n):
+            dj_dw[j] = dj_dw[j] + err * X[i,j]
+        dj_db = dj_db + err
+    dj_dw = dj_dw/m
+    dj_db = dj_db/m
+
+    return dj_db,dj_dw
+