CS231n Convolutional Neural Networks for Visual Recognition------Numpy Tutorial

源链接为：http://cs231n.github.io/python-numpy-tutorial/。

这篇指导书是由Justin Johnson编写的。

在这门课程中我们将使用Python语言完成所有变成任务！Python本身就是一种很棒的通用编程语言，但是在一些流行的库帮助下（numpy，scipy，matplotlib）它已经成为科学计算的强大环境。
我们希望你们中的许多人都有一些Python和numpy的使用经验; 对你们其他人来说，这个section将作为Python用于科学计算和使用的快速速成课程。
你们中的一些人可能已经掌握了Matlab的知识，在这种情况下我们也推荐使用numpy。

你也可以阅读由Volodymyr Kuleshov和Isaac Caswell（CS 228）编写的Notebook版笔记。

本教程使用的Python版本为Python3.

Arrays

Array indexing

Datatypes

Array math

Broadcasting

原文共分为4部分，分别介绍了Python、Numpy、Scipy和Matplotlib的使用。本次翻译为第二部分：Numpy的使用指导！

Numpy是Python中科学计算的核心库。它提供了一个高性能的多维数组对象，以及用于处理这些数组的工具。如果您已经熟悉MATLAB，那么您可能会发现本教程对Numpy入门非常有用。

Arrays

numpy数组是一个值网格，所有类型都相同，并且由非负整数元组索引。数组的形状是一个整数元组，并且给出了每个维度的数组大小。

我们可以从嵌套的Python列表初始化numpy数组，并使用方括号访问元素：

import numpy as npa = np.array([1, 2, 3])   # Create a rank 1 array
print(type(a))            # Prints "<class 'numpy.ndarray'>"
print(a.shape)            # Prints "(3,)"
print(a[0], a[1], a[2])   # Prints "1 2 3"
a[0] = 5                  # Change an element of the array
print(a)                  # Prints "[5, 2, 3]"b = np.array([[1,2,3],[4,5,6]])    # Create a rank 2 array
print(b.shape)                     # Prints "(2, 3)"
print(b[0, 0], b[0, 1], b[1, 0])   # Prints "1 2 4"

Numpy还提供了创建数组的函数：

import numpy as npa = np.zeros((2,2))   # Create an array of all zeros
print(a)              # Prints "[[ 0.  0.]#          [ 0.  0.]]"b = np.ones((1,2))    # Create an array of all ones
print(b)              # Prints "[[ 1.  1.]]"c = np.full((2,2), 7)  # Create a constant array
print(c)               # Prints "[[ 7.  7.]#          [ 7.  7.]]"d = np.eye(2)         # Create a 2x2 identity matrix
print(d)              # Prints "[[ 1.  0.]#          [ 0.  1.]]"e = np.random.random((2,2))  # Create an array filled with random values
print(e)                     # Might print "[[ 0.91940167  0.08143941]#               [ 0.68744134  0.87236687]]"

你可以在这篇文档看到更多关于创建数组的方法。

Array indexing

Numpy提供了几种索引数组的方法。

切片：与Python列表类似，可以切割numpy数组。由于数组可能是多维的，因此必须为数组的每个维指定一个切片：

import numpy as np# Create the following rank 2 array with shape (3, 4)
# [[ 1  2  3  4]
#  [ 5  6  7  8]
#  [ 9 10 11 12]]
a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])# Use slicing to pull out the subarray consisting of the first 2 rows
# and columns 1 and 2; b is the following array of shape (2, 2):
# [[2 3]
#  [6 7]]
b = a[:2, 1:3]# A slice of an array is a view into the same data, so modifying it
# will modify the original array.
print(a[0, 1])   # Prints "2"
b[0, 0] = 77     # b[0, 0] is the same piece of data as a[0, 1]
print(a[0, 1])   # Prints "77"#这里也对原始数组进行了修改

您还可以将整数索引与切片索引混合使用。但是，这样做会产生比原始数组更低级别的数组。请注意，这与MATLAB处理数组切片的方式完全不同：

import numpy as np# Create the following rank 2 array with shape (3, 4)
# [[ 1  2  3  4]
#  [ 5  6  7  8]
#  [ 9 10 11 12]]
a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])# Two ways of accessing the data in the middle row of the array.
# Mixing integer indexing with slices yields an array of lower rank,
# while using only slices yields an array of the same rank as the
# original array:
row_r1 = a[1, :]    # Rank 1 view of the second row of a
row_r2 = a[1:2, :]  # Rank 2 view of the second row of a
print(row_r1, row_r1.shape)  # Prints "[5 6 7 8] (4,)"
print(row_r2, row_r2.shape)  # Prints "[[5 6 7 8]] (1, 4)"# We can make the same distinction when accessing columns of an array:
col_r1 = a[:, 1]
col_r2 = a[:, 1:2]
print(col_r1, col_r1.shape)  # Prints "[ 2  6 10] (3,)"
print(col_r2, col_r2.shape)  # Prints "[[ 2]#          [ 6]#          [10]] (3, 1)"

整数数组索引：使用切片索引到numpy数组时，生成的数组视图将始终是原始数组的子数组。相反，整数数组索引允许您使用另一个数组中的数据构造任意数组。这是一个例子：

import numpy as npa = np.array([[1,2], [3, 4], [5, 6]])# An example of integer array indexing.
# The returned array will have shape (3,) and
print(a[[0, 1, 2], [0, 1, 0]])  # Prints "[1 4 5]"# The above example of integer array indexing is equivalent to this:
print(np.array([a[0, 0], a[1, 1], a[2, 0]]))  # Prints "[1 4 5]"# When using integer array indexing, you can reuse the same
# element from the source array:
print(a[[0, 0], [1, 1]])  # Prints "[2 2]"# Equivalent to the previous integer array indexing example
print(np.array([a[0, 1], a[0, 1]]))  # Prints "[2 2]"

整数数组索引的一个有用技巧是从矩阵的每一行中选择或改变一个元素：

import numpy as np# Create a new array from which we will select elements
a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])print(a)  # prints "array([[ 1,  2,  3],#                [ 4,  5,  6],#                [ 7,  8,  9],#                [10, 11, 12]])"# Create an array of indices
b = np.array([0, 2, 0, 1])# Select one element from each row of a using the indices in b
print(a[np.arange(4), b])  # Prints "[ 1  6  7 11]"# Mutate one element from each row of a using the indices in b
a[np.arange(4), b] += 10print(a)  # prints "array([[11,  2,  3],#                [ 4,  5, 16],#                [17,  8,  9],#                [10, 21, 12]])

布尔数组索引：布尔数组索引允许您选择数组的任意元素。通常，这种类型的索引用于选择满足某些条件的数组元素。这是一个例子：

import numpy as npa = np.array([[1,2], [3, 4], [5, 6]])bool_idx = (a > 2)   # Find the elements of a that are bigger than 2;# this returns a numpy array of Booleans of the same# shape as a, where each slot of bool_idx tells# whether that element of a is > 2.print(bool_idx)      # Prints "[[False False]#          [ True  True]#          [ True  True]]"# We use boolean array indexing to construct a rank 1 array
# consisting of the elements of a corresponding to the True values
# of bool_idx
print(a[bool_idx])  # Prints "[3 4 5 6]"# We can do all of the above in a single concise statement:
print(a[a > 2])     # Prints "[3 4 5 6]"

为简洁起见，我们遗漏了很多关于numpy数组索引的细节; 如果你想了解更多，你应该阅读文档。

Datatypes

每个numpy数组都是相同类型的元素。 Numpy提供了一组可用于构造数组的大量数值数据类型。 Numpy在创建数组时尝试猜测数据类型，但构造数组的函数通常还包含一个可选参数来显式指定数据类型。这是一个例子：

import numpy as npx = np.array([1, 2])   # Let numpy choose the datatype
print(x.dtype)         # Prints "int64"x = np.array([1.0, 2.0])   # Let numpy choose the datatype
print(x.dtype)             # Prints "float64"x = np.array([1, 2], dtype=np.int64)   # Force a particular datatype
print(x.dtype)                         # Prints "int64"

你可以在这篇文档看到更多关于数组数据类型的细节。

Array math

基本数学函数在数组上以元素方式运行，既可以作为运算符重载，也可以作为numpy模块中的函数：

import numpy as npx = np.array([[1,2],[3,4]], dtype=np.float64)
y = np.array([[5,6],[7,8]], dtype=np.float64)# Elementwise sum; both produce the array
# [[ 6.0  8.0]
#  [10.0 12.0]]
print(x + y)
print(np.add(x, y))# Elementwise difference; both produce the array
# [[-4.0 -4.0]
#  [-4.0 -4.0]]
print(x - y)
print(np.subtract(x, y))# Elementwise product; both produce the array
# [[ 5.0 12.0]
#  [21.0 32.0]]
print(x * y)
print(np.multiply(x, y))# Elementwise division; both produce the array
# [[ 0.2         0.33333333]
#  [ 0.42857143  0.5       ]]
print(x / y)
print(np.divide(x, y))# Elementwise square root; produces the array
# [[ 1.          1.41421356]
#  [ 1.73205081  2.        ]]
print(np.sqrt(x))

请注意，与MATLAB不同，*是元素乘法，而不是矩阵乘法。我们使用点函数来计算向量的内积，将向量乘以矩阵，并乘以矩阵。 dot既可以作为numpy模块中的函数使用，也可以作为数组对象的实例方法：

import numpy as npx = np.array([[1,2],[3,4]])
y = np.array([[5,6],[7,8]])v = np.array([9,10])
w = np.array([11, 12])# Inner product of vectors; both produce 219
print(v.dot(w))
print(np.dot(v, w))# Matrix / vector product; both produce the rank 1 array [29 67]
print(x.dot(v))
print(np.dot(x, v))# Matrix / matrix product; both produce the rank 2 array
# [[19 22]
#  [43 50]]
print(x.dot(y))
print(np.dot(x, y))

Numpy提供了许多用于在数组上执行计算的有用函数; 其中最有用的是sum：

import numpy as npx = np.array([[1,2],[3,4]])print(np.sum(x))  # Compute sum of all elements; prints "10"
print(np.sum(x, axis=0))  # Compute sum of each column; prints "[4 6]"
print(np.sum(x, axis=1))  # Compute sum of each row; prints "[3 7]"

您可以在文档中找到numpy提供的完整数学函数列表。

除了使用数组计算数学函数之外，我们经常需要重新整形或以其他方式操纵数组中的数据。这种操作的最简单的例子是转置矩阵; 要转置矩阵，只需使用数组对象的T属性：

import numpy as npx = np.array([[1,2], [3,4]])
print(x)    # Prints "[[1 2]#          [3 4]]"
print(x.T)  # Prints "[[1 3]#          [2 4]]"# Note that taking the transpose of a rank 1 array does nothing:
v = np.array([1,2,3])
print(v)    # Prints "[1 2 3]"
print(v.T)  # Prints "[1 2 3]"

Numpy提供了很多操作素组的方法，可以看这篇文档！

Broadcasting

广播是一种强大的机制，允许numpy在执行算术运算时使用不同形状的数组。我们经常有一个较小的数组和一个较大的数组，我们希望多次使用较小的数组来对较大的数组执行某些操作。

例如，假设我们想要向矩阵的每一行添加一个常量向量。我们可以这样做：

import numpy as np# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
y = np.empty_like(x)   # Create an empty matrix with the same shape as x# Add the vector v to each row of the matrix x with an explicit loop
for i in range(4):y[i, :] = x[i, :] + v# Now y is the following
# [[ 2  2  4]
#  [ 5  5  7]
#  [ 8  8 10]
#  [11 11 13]]
print(y)

这有效; 但是当矩阵x非常大时，在Python中计算显式循环可能会很慢。注意，将向量v添加到矩阵x的每一行等同于通过垂直堆叠v的多个副本来形成矩阵w，然后执行x和w的元素求和。我们可以像这样实现这种方法：

import numpy as np# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
vv = np.tile(v, (4, 1))   # Stack 4 copies of v on top of each other
print(vv)                 # Prints "[[1 0 1]#          [1 0 1]#          [1 0 1]#          [1 0 1]]"
y = x + vv  # Add x and vv elementwise
print(y)  # Prints "[[ 2  2  4#          [ 5  5  7]#          [ 8  8 10]#          [11 11 13]]"

Numpy广播允许我们执行此计算而不实际创建v的多个副本。考虑此版本，使用广播：

import numpy as np# We will add the vector v to each row of the matrix x,
# storing the result in the matrix y
x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
v = np.array([1, 0, 1])
y = x + v  # Add v to each row of x using broadcasting
print(y)  # Prints "[[ 2  2  4]#          [ 5  5  7]#          [ 8  8 10]#          [11 11 13]]"

支持广播的功能称为通用功能。您可以在文档中找到所有通用功能的列表。

以下是广播的一些应用：

import numpy as np# Compute outer product of vectors
v = np.array([1,2,3])  # v has shape (3,)
w = np.array([4,5])    # w has shape (2,)
# To compute an outer product, we first reshape v to be a column
# vector of shape (3, 1); we can then broadcast it against w to yield
# an output of shape (3, 2), which is the outer product of v and w:
# [[ 4  5]
#  [ 8 10]
#  [12 15]]
print(np.reshape(v, (3, 1)) * w)# Add a vector to each row of a matrix
x = np.array([[1,2,3], [4,5,6]])
# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),
# giving the following matrix:
# [[2 4 6]
#  [5 7 9]]
print(x + v)# Add a vector to each column of a matrix
# x has shape (2, 3) and w has shape (2,).
# If we transpose x then it has shape (3, 2) and can be broadcast
# against w to yield a result of shape (3, 2); transposing this result
# yields the final result of shape (2, 3) which is the matrix x with
# the vector w added to each column. Gives the following matrix:
# [[ 5  6  7]
#  [ 9 10 11]]
print((x.T + w).T)
# Another solution is to reshape w to be a column vector of shape (2, 1);
# we can then broadcast it directly against x to produce the same
# output.
print(x + np.reshape(w, (2, 1)))# Multiply a matrix by a constant:
# x has shape (2, 3). Numpy treats scalars as arrays of shape ();
# these can be broadcast together to shape (2, 3), producing the
# following array:
# [[ 2  4  6]
#  [ 8 10 12]]
print(x * 2)

广播通常会使您的代码更简洁，更快速，因此您应该尽可能地使用它。

Numpy文档
这个简短的概述涉及了许多关于numpy需要了解的重要事项，但还远未完成。查看numpy参考资料，了解有关numpy的更多信息。