這門課程的作業非常值得認真完成！
由於作業的文件格式爲Jupyter Notebook，內容很多（作業指導、數學公式、圖片、代碼、執行結果、程序調試錯誤棧、音視頻等等），遠非CSDN博客所能支持。
這裏主要梳理一下作業的主要內容和思路，完整作業文件可參考:
https://github.com/pandenghuang/Andrew-Ng-Deep-Learning-notes/tree/master/assignments/C1W2
作業完整截圖，參考本文結尾：作業完整截圖。
作業指導及目標
Python Basics with Numpy (optional assignment)
Welcome to your first assignment. This exercise gives you a brief introduction to Python. Even if you've used Python before, this will help familiarize you with functions we'll need.
Instructions:
- You will be using Python 3.
- Avoid using for-loops and while-loops, unless you are explicitly told to do so.
- Do not modify the (# GRADED FUNCTION [function name]) comment in some cells. Your work would not be graded if you change this. Each cell containing that comment should only contain one function.
- After coding your function, run the cell right below it to check if your result is correct.
After this assignment you will:
- Be able to use iPython Notebooks
- Be able to use numpy functions and numpy matrix/vector operations
- Understand the concept of "broadcasting"
- Be able to vectorize code
Jupyter Notebook簡介
About iPython Notebooks
iPython Notebooks are interactive coding environments embedded in a webpage. You will be using iPython notebooks in this class. You only need to write code between the ### START CODE HERE ### and ### END CODE HERE ### comments. After writing your code, you can run the cell by either pressing "SHIFT"+"ENTER" or by clicking on "Run Cell" (denoted by a play symbol) in the upper bar of the notebook.
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重點1：
What you need to remember:
- Run your cells using SHIFT+ENTER (or "Run cell")
- Write code in the designated areas using Python 3 only
- Do not modify the code outside of the designated areas
使用numpy構造基礎函數（sigmoid、np.exp）
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()
Before using np.exp(), you will use math.exp() to implement the sigmoid function. You will then see why np.exp() is preferable to math.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−𝑥sigmoid(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().
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1.2 - Sigmoid gradient（Sigmoid函數梯度）
As you've seen in lecture, you will need to compute gradients to optimize loss functions using backpropagation. Let's code your first gradient function.
Exercise: Implement the function sigmoid_grad() to compute the gradient of the sigmoid function with respect to its input x. The formula is:
𝑠𝑖𝑔𝑚𝑜𝑖𝑑_𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒(𝑥)=𝜎′(𝑥)=𝜎(𝑥)(1−𝜎(𝑥))(2)(2)sigmoid_derivative(x)=σ′(x)=σ(x)(1−σ(x))
You often code this function in two steps:
- Set s to be the sigmoid of x. You might find your sigmoid(x) function useful.
- Compute 𝜎′(𝑥)=𝑠(1−𝑠)
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1.3 - Reshaping arrays（數組重排、變形）
Two common numpy functions used in deep learning are np.shape and np.reshape().
- X.shape is used to get the shape (dimension) of a matrix/vector X.
- X.reshape(...) is used to reshape X into some other dimension.
For example, in computer science, an image is represented by a 3D array of shape (𝑙𝑒𝑛𝑔𝑡ℎ,ℎ𝑒𝑖𝑔ℎ𝑡,𝑑𝑒𝑝𝑡ℎ=3)(length,height,depth=3). However, when you read an image as the input of an algorithm you convert it to a vector of shape (𝑙𝑒𝑛𝑔𝑡ℎ∗ℎ𝑒𝑖𝑔ℎ𝑡∗3,1)(length∗height∗3,1). In other words, you "unroll", or reshape, the 3D array into a 1D vector.
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1.4 - Normalizing rows（數據歸一化（矩陣標準化））
Another common technique we use in Machine Learning and Deep Learning is to normalize our data. It often leads to a better performance because gradient descent converges faster after normalization. Here, by normalization we mean changing x to 𝑥‖𝑥‖x‖x‖ (dividing each row vector of x by its norm).
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1.5 - Broadcasting and the softmax function（廣播機制及softmax函數）
A very important concept to understand in numpy is "broadcasting". It is very useful for performing mathematical operations between arrays of different shapes. For the full details on broadcasting, you can read the official broadcasting documentation.
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重點：
What you need to remember:
- np.exp(x) works for any np.array x and applies the exponential function to every coordinate
- the sigmoid function and its gradient
- image2vector is commonly used in deep learning
- np.reshape is widely used. In the future, you'll see that keeping your matrix/vector dimensions straight will go toward eliminating a lot of bugs.
- numpy has efficient built-in functions
- broadcasting is extremely useful
向量化
2) Vectorization
In deep learning, you deal with very large datasets. Hence, a non-computationally-optimal function can become a huge bottleneck in your algorithm and can result in a model that takes ages to run. To make sure that your code is computationally efficient, you will use vectorization. For example, try to tell the difference between the following implementations of the dot/outer/elementwise product.
2.1 Implement the L1 and L2 loss functions （L1範數和L2範數函數的實現）
Exercise: Implement the numpy vectorized version of the L1 loss. You may find the function abs(x) (absolute value of x) useful.
Reminder:
- The loss is used to evaluate the performance of your model. The bigger your loss is, the more different your predictions (𝑦̂ y^) are from the true values (𝑦y). In deep learning, you use optimization algorithms like Gradient Descent to train your model and to minimize the cost.
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重點：
What to remember:
- Vectorization is very important in deep learning. It provides computational efficiency and clarity.
- You have reviewed the L1 and L2 loss.
- You are familiar with many numpy functions such as np.sum, np.dot, np.multiply, np.maximum, etc...
作業完整截圖：
