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