4,创建和操控张量

矢量加法
您可以对张量执行很多典型数学运算 (TF API)。以下代码会创建和操控两个矢量(一维张量),每个矢量正好六个元素:
[cceN_python]

import tensorflow as tf

with tf.Graph().as_default():
# Create a six-element vector (1-D tensor).
primes = tf.constant([2, 3, 5, 7, 11, 13], dtype=tf.int32)

# Create another six-element vector. Each element in the vector will be
# initialized to 1. The first argument is the shape of the tensor (more
# on shapes below).
ones = tf.ones([6], dtype=tf.int32)

# Add the two vectors. The resulting tensor is a six-element vector.
just_beyond_primes = tf.add(primes, ones)

# Create a session to run the default graph.
with tf.Session() as sess:
print just_beyond_primes.eval()

[/cceN_python]

 

张量形状

形状用于描述张量维度的大小和数量。张量的形状表示为列表,其中第 i 个元素表示维度 i 的大小。列表的长度表示张量的阶(即维数)。

有关详情,请参阅 TensorFlow 文档

以下是一些基本示例:

形状

张量的形状是每个维度中元素的数量。TensorFlow 在图的构建过程中自动推理形状。这些推理的形状可能具有已知或未知的阶。如果阶已知,则每个维度的大小可能已知或未知。

TensorFlow 文件编制中通过三种符号约定来描述张量维度:阶,形状和维数。下表阐述了三者如何相互关联:

形状 维数 示例
0 [] 0-D 0 维张量。标量。
1 [D0] 1-D 形状为 [5] 的 1 维张量。
2 [D0, D1] 2-D 形状为 [3, 4] 的 2 维张量。
3 [D0, D1, D2] 3-D 形状为 [1, 4, 3] 的 3 维张量。
n [D0, D1, … Dn-1] n-D 形状为 [D0, D1, … Dn-1] 的张量。

形状可以通过 Python 的整数列表或元祖来进行表示,也可以用 tf.TensorShape
:[cceN_python]
with tf.Graph().as_default():
# A scalar (0-D tensor).
scalar = tf.zeros([])

# A vector with 3 elements.
vector = tf.zeros([3])

# A matrix with 2 rows and 3 columns.
matrix = tf.zeros([2, 3])

with tf.Session() as sess:
print ‘scalar has shape’, scalar.get_shape(), ‘and value:\n’, scalar.eval()
print ‘vector has shape’, vector.get_shape(), ‘and value:\n’, vector.eval()
print ‘matrix has shape’, matrix.get_shape(), ‘and value:\n’, matrix.eval()
[/cceN_python]广播
在数学中,您只能对形状相同的张量执行元素级运算(例如,相加和等于)。不过,在 TensorFlow 中,您可以对张量执行传统意义上不可行的运算。TensorFlow 支持广播(一种借鉴自 Numpy 的概念)。利用广播,元素级运算中的较小数组会增大到与较大数组具有相同的形状。例如,通过广播:
如果指令需要大小为 [6] 的张量,则大小为 [1] 或 [] 的张量可以作为运算数。
如果指令需要大小为 [4, 6] 的张量,则以下任何大小的张量都可以作为运算数。
[1, 6]
[6]
[]
如果指令需要大小为 [3, 5, 6] 的张量,则以下任何大小的张量都可以作为运算数。
[1, 5, 6]
[3, 1, 6]
[3, 5, 1]
[1, 1, 1]
[5, 6]
[1, 6]
[6]
[1]
[]
注意:当张量被广播时,从概念上来说,系统会复制其条目(出于性能考虑,实际并不复制。广播专为实现性能优化而设计)。
有关完整的广播规则集,请参阅简单易懂的 Numpy 广播文档。
以下代码执行了与之前一样的张量加法,不过使用的是广播:

with tf.Graph().as_default():
# Create a six-element vector (1-D tensor).
primes = tf.constant([2, 3, 5, 7, 11, 13], dtype=tf.int32)
​
# Create a constant scalar with value 1.
ones = tf.constant(1, dtype=tf.int32)
​
# Add the two tensors. The resulting tensor is a six-element vector.
just_beyond_primes = tf.add(primes, ones)
​
with tf.Session() as sess:
print just_beyond_primes.eval()

矩阵乘法
在线性代数中,当两个矩阵相乘时,第一个矩阵的列数必须等于第二个矩阵的行数。
3×4 矩阵乘以 4×2 矩阵是有效的,可以得出一个 3×2 矩阵。
4×2 矩阵乘以 3×4 矩阵是无效的。

with tf.Graph().as_default():
# Create a matrix (2-d tensor) with 3 rows and 4 columns.
x = tf.constant([[5, 2, 4, 3], [5, 1, 6, -2], [-1, 3, -1, -2]],
dtype=tf.int32)

# Create a matrix with 4 rows and 2 columns.
y = tf.constant([[2, 2], [3, 5], [4, 5], [1, 6]], dtype=tf.int32)

# Multiply `x` by `y`.
# The resulting matrix will have 3 rows and 2 columns.
matrix_multiply_result = tf.matmul(x, y)

with tf.Session() as sess:
print matrix_multiply_result.eval()

张量变形

由于张量加法和矩阵乘法均对运算数施加了限制条件,TensorFlow 编程者肯定会频繁改变张量的形状。

您可以使用 tf.reshape 方法改变张量的形状。 例如,您可以将 8×2 张量变形为 2×8 张量或 4×4 张量:

with tf.Graph().as_default():
# Create an 8×2 matrix (2-D tensor).
matrix = tf.constant([[1,2], [3,4], [5,6], [7,8],
[9,10], [11,12], [13, 14], [15,16]], dtype=tf.int32)

# Reshape the 8×2 matrix into a 2×8 matrix.
reshaped_2x8_matrix = tf.reshape(matrix, [2,8])

# Reshape the 8×2 matrix into a 4×4 matrix
reshaped_4x4_matrix = tf.reshape(matrix, [4,4])

with tf.Session() as sess:
print “Original matrix (8×2):”
print matrix.eval()
print “Reshaped matrix (2×8):”
print reshaped_2x8_matrix.eval()
print “Reshaped matrix (4×4):”
print reshaped_4x4_matrix.eval()

此外,您还可以使用 tf.reshape 更改张量的维数(\’阶\’)。 例如,您可以将 8×2 张量变形为三维 2x2x4 张量或一维 16 元素张量。

with tf.Graph().as_default():
# Create an 8×2 matrix (2-D tensor).
matrix = tf.constant([[1,2], [3,4], [5,6], [7,8],
[9,10], [11,12], [13, 14], [15,16]], dtype=tf.int32)

# Reshape the 8×2 matrix into a 3-D 2x2x4 tensor.
reshaped_2x2x4_tensor = tf.reshape(matrix, [2,2,4])

# Reshape the 8×2 matrix into a 1-D 16-element tensor.
one_dimensional_vector = tf.reshape(matrix, [16])

with tf.Session() as sess:
print “Original matrix (8×2):”
print matrix.eval()
print “Reshaped 3-D tensor (2x2x4):”
print reshaped_2x2x4_tensor.eval()
print “1-D vector:”
print one_dimensional_vector.eval()

 

变量、初始化和赋值

到目前为止,我们执行的所有运算都是针对静态值 (tf.constant) 进行的;调用 eval() 始终返回同一结果。在 TensorFlow 中可以定义 Variable 对象,它的值是可以更改的。

创建变量时,您可以明确设置一个初始值,也可以使用初始化程序(例如分布):

g = tf.Graph()
with g.as_default():
# Create a variable with the initial value 3.
v = tf.Variable([3])

# Create a variable of shape [1], with a random initial value,
# sampled from a normal distribution with mean 1 and standard deviation 0.35.
w = tf.Variable(tf.random_normal([1], mean=1.0, stddev=0.35))

 

要初始化变量,最简单的方式是调用 global_variables_initializer。请注意 Session.run() 的用法(与 eval() 的用法大致相同)。

with g.as_default():
with tf.Session() as sess:
initialization = tf.global_variables_initializer()
sess.run(initialization)
# Now, variables can be accessed normally, and have values assigned to them.
print v.eval()
print w.eval()

初始化后,变量的值保留在同一会话中(不过,当您启动新会话时,需要重新初始化它们):

要更改变量的值,请使用 assign 指令。请注意,仅创建 assign 指令不会起到任何作用。和初始化一样,您必须运行赋值指令才能更新变量值:

with g.as_default():
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
# This should print the variable’s initial value.
print v.eval()

assignment = tf.assign(v, [7])
# The variable has not been changed yet!
print v.eval()

# Execute the assignment op.
sess.run(assignment)
# Now the variable is updated.
print v.eval()

3,TensorFlow 编程概念

学习目标:
学习 TensorFlow 编程模型的基础知识,重点了解以下概念:
*张量
*指令
*图
*会话
构建一个简单的 TensorFlow 程序,使用该程序绘制一个默认图并创建一个运行该图的会话

 

概念概览

TensorFlow 的名称源自张量,张量是任意维度的数组。借助 TensorFlow,您可以操控具有大量维度的张量。即便如此,在大多数情况下,您会使用以下一个或多个低维张量:

  • 标量是零维数组(零阶张量)。例如,\'Howdy\'5
  • 矢量是一维数组(一阶张量)。例如,[2, 3, 5, 7, 11][5]
  • 矩阵是二维数组(二阶张量)。例如,[[3.1, 8.2, 5.9][4.3, -2.7, 6.5]]

TensorFlow 指令会创建、销毁和操控张量。典型 TensorFlow 程序中的大多数代码行都是指令。

TensorFlow (也称为计算图数据流图)是一种图数据结构。很多 TensorFlow 程序由单个图构成,但是 TensorFlow 程序可以选择创建多个图。图的节点是指令;图的边是张量。张量流经图,在每个节点由一个指令操控。一个指令的输出张量通常会变成后续指令的输入张量。TensorFlow 会实现延迟执行模型,意味着系统仅会根据相关节点的需求在需要时计算节点。

张量可以作为常量变量存储在图中。您可能已经猜到,常量存储的是值不会发生更改的张量,而变量存储的是值会发生更改的张量。不过,您可能没有猜到的是,常量和变量都只是图中的一种指令。常量是始终会返回同一张量值的指令。变量是会返回分配给它的任何张量的指令。

要定义常量,请使用 tf.constant 指令,并传入它的值。例如:

  x = tf.constant([5.2])

同样,您可以创建如下变量:

  y = tf.Variable([5])

或者,您也可以先创建变量,然后再如下所示地分配一个值(注意:您始终需要指定一个默认值):

  y = tf.Variable([0])
  y = y.assign([5])

定义一些常量或变量后,您可以将它们与其他指令(如 tf.add)结合使用。在评估 tf.add 指令时,它会调用您的 tf.constanttf.Variable 指令,以获取它们的值,然后返回一个包含这些值之和的新张量。

图必须在 TensorFlow 会话中运行,会话存储了它所运行的图的状态:

将 tf.Session() 作为会话:
  initialization = tf.global_variables_initializer()
  print y.eval()

在使用 tf.Variable 时,您必须在会话开始时调用 tf.global_variables_initializer,以明确初始化这些变量,如上所示。

注意:会话可以将图分发到多个机器上执行(假设程序在某个分布式计算框架上运行)。有关详情,请参阅分布式 TensorFlow

总结

TensorFlow 编程本质上是一个两步流程:

  1. 将常量、变量和指令整合到一个图中。
  2. 在一个会话中评估这些常量、变量和指令。

创建一个简单的 TensorFlow 程序

我们来看看如何编写一个将两个常量相加的简单 TensorFlow 程序。

添加 import 语句

与几乎所有 Python 程序一样,您首先要添加一些 import 语句。 当然,运行 TensorFlow 程序所需的 import 语句组合取决于您的程序将要访问的功能。至少,您必须在所有 TensorFlow 程序中添加 import tensorflow 语句:

Pandas 简介

import pandas as pd
pd.__version__

pandas 中的主要数据结构被实现为以下两类:
DataFrame,您可以将它想象成一个关系型数据表格,其中包含多个行和已命名的列。
Series,它是单一列。DataFrame 中包含一个或多个 Series,每个 Series 均有一个名称。
数据框架是用于数据操控的一种常用抽象实现形式。Spark 和 R 中也有类似的实现。

创建 Series 的一种方法是构建 Series 对象。例如:

pd.Series(['San Francisco', 'San Jose', 'Sacramento'])

您可以将映射 string 列名称的 dict 传递到它们各自的 Series,从而创建DataFrame对象。如果 Series 在长度上不一致,系统会用特殊的 NA/NaN 值填充缺失的值。例如:

[ccen theme="default"]
city_names = pd.Series(['San Francisco', 'San Jose', 'Sacramento'])
population = pd.Series([852469, 1015785, 485199])
pd.DataFrame({ 'City name': city_names, 'Population': population })
[/ccen]

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