Week 2 - Python and Vectorization

Vectorization

• • 
  • if non-verctorized:
    
    Python

    Z = 0 for i in range(nx): z += W[i] * X[i] Z += b

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    Z = 0 for i in range(nx):     z += W[i] * X[i] Z += b

  • if vectorized:
    
    Python

    Z = np.dot(W,X) + b

    1	Z = np.dot(W,X) + b

  • it is much faster
    
    Python

    import numpy as np import time a = np.random.rand(1000000) b = np.random.rand(1000000) #check how much time was used tic = time.time() c = np.dot(a,b) toc = time.time() print("Vectorized version : " + str(1000*(toc-tic) + "ms") # 1.5ms c = 0 tic = time.time() for i in range(1000000): c += a[i]*b[i] toc = time.time() print("For loop version : " + str(1000*(toc-tic) + "ms") #474.2ms

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    import numpy as np import time   a = np.random.rand(1000000) b = np.random.rand(1000000)   #check how much time was used tic = time.time() c = np.dot(a,b) toc = time.time()   print("Vectorized version : " + str(1000*(toc-tic) + "ms") # 1.5ms   c = 0 tic = time.time() for i in range(1000000):     c += a[i]*b[i] toc = time.time()   print("For loop version : " + str(1000*(toc-tic) + "ms") #474.2ms

Vectorizing Logistic Regression

• • b is real number, it will be automatically changed to vector to be added each element of matrix (python broadcasting)
    
    Python

    Z = np.dot(W.T,X) + b

    1	Z = np.dot(W.T,X) + b

    

    

A note on python/numpy vectors

• to simplify code and to avoid bug, don't use rank 1 array