轉載於：http://blog.csdn.net/Koala_Tree/article/details/78057033

吳恩達Coursera課程 DeepLearning.ai 程式設計作業系列，本文為《神經網路與深度學習》部分的第二週“神經網路基礎”的課程作業（做了無用部分的刪減）。

Part 1：Python Basics with Numpy (optional assignment)

1 - Building basic functions with numpy

Numpy is the main package for scientific computing in Python. It is maintained by a large community (www.numpy.org). In this exercise you will learn several key numpy functions such as np.exp, np.log, and np.reshape. You will need to know how to use these functions for future assignments.

1.1 - sigmoid function, np.exp()

Exercise: Build a function that returns the sigmoid of a real number x. Use math.exp(x) for the exponential function.

Reminder: 
sigmoid(x)=11+e−x is sometimes also known as the logistic function. It is a non-linear function used not only in Machine Learning (Logistic Regression), but also in Deep Learning.

To refer to a function belonging to a specific package you could call it using package_name.function(). Run the code below to see an example with math.exp().

# GRADED FUNCTION: basic_sigmoid

import math

def basic_sigmoid(x):
    """
    Compute sigmoid of x.

    Arguments:
    x -- A scalar

    Return:
    s -- sigmoid(x)
    """
 


    ### START CODE HERE ### (≈ 1 line of code)
    s = 1.0 / (1 + 1/ math.exp(x))
    ### END CODE HERE ###

    return s

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basic_sigmoid(3)

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0.9525741268224334

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Actually, we rarely use the “math” library in deep learning because the inputs of the functions are real numbers. In deep learning we mostly use matrices and vectors. This is why numpy is more useful.

### One reason why we use "numpy" instead of "math" in Deep Learning ###
x = [1, 2, 3]
basic_sigmoid(x) # you will see this give an error when you run it, because x is a vector.

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---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-3-2e11097d6860> in <module>()
      1 ### One reason why we use "numpy" instead of "math" in Deep Learning ###
      2 x = [1, 2, 3]
----> 3 basic_sigmoid(x) # you will see this give an error when you run it, because x is a vector.


<ipython-input-1-65a96864f65f> in basic_sigmoid(x)
     15 
     16     ### START CODE HERE ### (≈ 1 line of code)
---> 17     s = 1.0 / (1 + 1/ math.exp(x))
     18     ### END CODE HERE ###
     19 


TypeError: a float is required

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In fact, if x=(x1,x2,...,xn) is a row vector then np.exp(x) will apply the exponential function to every element of x. The output will thus be: np.exp(x)=(ex1,ex2,...,exn)

import numpy as np

# example of np.exp
x = np.array([1, 2, 3])
print(np.exp(x)) # result is (exp(1), exp(2), exp(3))

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[  2.71828183   7.3890561   20.08553692]

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Furthermore, if x is a vector, then a Python operation such as s=x+3 or s=1x will output s as a vector of the same size as x.

# example of vector operation
x = np.array([1, 2, 3])
print (x + 3)

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[4 5 6]

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Exercise: Implement the sigmoid function using numpy.

Instructions: x could now be either a real number, a vector, or a matrix. The data structures we use in numpy to represent these shapes (vectors, matrices…) are called numpy arrays. You don’t need to know more for now.