3、TensorFlow 的数据模型-----张量(Tensor)

一、Tensor 类简介

tf.Session

数据

n 维的数组

batch*height*width*channel

tf.Tensor

tf.Variable

numpy.ndarray

list (and lists of tensor-like objects)

Scalar Python types: bool, float, int, str

tf.Tensor

常量 tensor

tensor-like 对象

tensor-like 对象

handle for feeding a value

二、Tensor 创建

TF op

单个数值

数值列表

列表构成的列表

1、常量 Tensor 的创建

Constant Value Tensors

# 产生全 0 的张量
tf.zeros(shape, dtype=tf.float32, name=None)
tf.zeros_like(tensor, dtype=None, name=None)

# 产生全 1 的张量
tf.ones(shape, dtype=tf.float32, name=None)
tf.ones_like(tensor, dtype=None, name=None)

# Creates a tensor of shape  and fills it with value
tf.fill(shape, value, name=None)
tf.fill([2, 3], 9) ==> [[9, 9, 9]
[9, 9, 9]]

# 产生常量 Tensor, value 值可为 python 标准数据类型、Numpy 等
tf.constant(value, dtype=None, shape=None, name='Const')
tf.constant(-1.0, shape=[2, 3]) => [[-1., -1., -1.]  # Note: 注意 shape 的用法(广播机制)
[-1., -1., -1.]]
tf.constant([1,2,3,4,5,6], shape=[2,3]) => [[1, 2, 3]
[4, 5, 6]]

Sequences

# 产生 N 个等距分布在[start, stop]间元素组成的数组，包括start & stop
tf.linspace(start, stop, N, name=None)

# []为可选参数，步长默认为1，stop 的值取不到，它产生一个数字序列
tf.range([start], stop, [step=1], name='range')

Random Tensors

# 正态分布，默认均值为0，标准差为1.0，数据类型为float32
tf.random_normal(shape, mean=0.0, stddev=1.0, dtype=tf.float32, seed=None, name=None)

# 正态分布，但那些到均值的距离超过2倍标准差的随机数将被丢弃，然后重新抽取，直到取得足够数量的随机数为止, 随机数 x
# 的取值范围是$[mean - 2*stddev, mean + 2*stddev]$, 从而可以防止有元素与该张量中的其他元素显著不同的情况出现
tf.truncated_normal(shape, mean=0.0, stddev=1.0, dtype=tf.float32, seed=None, name=None)

# 产生在[minval, maxval)之间形状为 shape 的均匀分布, 默认是[0, 1)之间形状为 shape 的均匀分布
tf.random_uniform(shape, minval=0.0, maxval=1, dtype=tf.float32, seed=None, name=None)

# Randomly shuffles a tensor along its first dimension
tf.random_shuffle(value, seed=None, name=None)

# Randomly crops a tensor to a given size
tf.random_crop(value, size, seed=None, name=None)
# Note：If a dimension should not be cropped, pass the full size of that dimension.
# For example, RGB images can be cropped with size = [crop_height, crop_width, 3]

# Sets the graph-level random seed
tf.set_random_seed(seed)
# 1. To generate the same repeatable sequence for an op across sessions
# set the seed for the op, a = tf.random_uniform([1], seed=1)
# 2. To make the random sequences generated by all ops be repeatable across sessions
# set a graph-level seed, tf.set_random_seed(1234)

# 其它
tf.multinomial(logits, num_samples, seed=None, name=None)
tf.random_gamma(shape,alpha,beta=None,dtype=tf.float32,seed=None,name=None)

2、变量 Tensor 的创建

I、Class tf.Variable()

dtype、shape、name

initializer

initial_value

eval(session=None)

get_shape()

set_shape(shape)

initialized_value()

read_value()

assign(value, use_locking=False)

assign_add(delta, use_locking=False)

assign_sub(delta, use_locking=False)

# tf.constant 是 op，而 tf.Variable() 是一个类，初始化的对象有多个op
var_obj = tf.Variable(
initial_value,
dtype=None,
name=None,
trainable=True,
collections=None,
validate_shape=True
)

# 初始化参数
initial_value：可由 Python 内置数据类型提供，也可由常量 Tensor 的内置 op 来快速构建，但所有这些 op 都需要提供 shape

trainable：指明了该变量是否可训练, 会加入 `GraphKeys.TRAINABLE_VARIABLES` collection 中去。

collections: List of graph collections keys. The new variable is added to these collections. Defaults to [GraphKeys.GLOBAL_VARIABLES].

validate_shape: If False, allows the variable to be initialized with a value of unknown shape. If True, the default, the shape of initial_value must be known.

# 返回值
变量实例对象(Tensor-like)

II、tf.get_variable()

# Gets an existing variable with these parameters or create a new one
tf.get_variable(
name,
shape=None,
dtype=None,
initializer=None,
trainable=True,
regularizer=None,
collections=None,
caching_device=None,
partitioner=None,
validate_shape=True,
use_resource=None,
custom_getter=None
)

# 初始化参数
name: The name of the new or existing variable.
shape: Shape of the new or existing variable.
dtype: Type of the new or existing variable (defaults to DT_FLOAT).
initializer: Initializer for the variable if one is created.

trainable: If True also add the variable to the graph collection tf.GraphKeys.TRAINABLE_VARIABLES.

regularizer: A (Tensor -> Tensor or None) function; the result of applying it on a newly created variable will be added to the collection tf.GraphKeys.REGULARIZATION_LOSSES and can be used for regularization.

collections: List of graph collections keys to add the Variable to. Defaults to [GraphKeys.GLOBAL_VARIABLES] (see tf.Variable).

# 返回值
The created or existing Variable, 拥有变量类的所有属性和方法。

# Note:
>>> name 参数必须要指定，如果仅给出 shape 参数而未指定 initializer，那么它的值将由 tf.glorot_uniform_initializer 随机产生，数据类型为tf.float32;
>>> 另外，initializer 可以为一个张量，这种情况下，变量的值和形状即为此张量的值和形状(就不必指定shape 了)。
>>> 此函数经常和 tf.variable_scope() 一起使用，产生共享变量

III、initializer 参数的初始化

tf.get_variable()

shape

initializer

tf.constant_initializer()、tf.zeros_initializer()、tf.ones_initializer()

tf.constant_initializer(
value=0,
dtype=dtypes.float32,
verify_shape=False
)

# 通常偏置项就是用它初始化的。由它衍生出的两个初始化方法：
I、tf.zeros_initializer()
II、tf.ones_initializer()

init = tf.constant_initializer()
x = tf.get_variable('x', shape=[2, 3], initializer=init) # 必须指定shape
sess.run(x.initializer)
sess.run(x)
>>> array([[ 0.,  0.,  0.],
[ 0.,  0.,  0.]], dtype=float32)

tf.truncated_normal_initializer()、tf.random_normal_initializer()

# 生成截断正态分布的随机数，方差一般选0.01等比较小的数
tf.truncated_normal_initializer(
mean=0.0,
stddev=1.0,
seed=None,
dtype=tf.float32
)

# 生成标准正态分布的随机数，方差一般选0.01等比较小的数
tf.random_normal_initializer(
mean=0.0,
stddev=1.0,
seed=None,
dtype=tf.float32
)

tf.random_uniform_initializer()、tf.uniform_unit_scaling_initializer()

# 生成均匀分布的随机数
tf.random_uniform_initializer(
minval=0,
maxval=None,
seed=None,
dtype=tf.float32
)

# 和均匀分布差不多，只是这个初始化方法不需要指定最小最大值，是通过计算出来的
# 它的分布区间为[-max_val, max_val]
tf.uniform_unit_scaling_initializer(
factor=1.0,
seed=None,
dtype=tf.float32
)

max_val = math.sqrt(3 / input_size) * self.factor
# input size is obtained by multiplying W's all dimensions but the last one
# for a linear layer factor is 1.0, relu: ~1.43, tanh: ~1.15

tf.variance_scaling_initializer()

tf.variance_scaling_initializer(
scale=1.0,
mode='fan_in',
distribution='normal',
seed=None,
dtype=tf.float32
)

# 初始化参数
scale: Scaling factor (positive float).
mode: One of "fan_in", "fan_out", "fan_avg".
distribution: Random distribution to use. One of "normal", "uniform".

# 1、当 distribution="normal" 的时候：
生成 truncated normal distribution（截断正态分布）的随机数，其中mean = 0, stddev = sqrt(scale / n)，
n 的计算与 mode 参数有关：
如果mode = "fan_in"， n 为输入单元的结点数
如果mode = "fan_out"，n 为输出单元的结点数
如果mode = "fan_avg",n 为输入和输出单元结点数的平均值

# 2、当distribution="uniform”的时候：
生成均匀分布的随机数，假设分布区间为[-limit, limit]，则limit = sqrt(3 * scale / n)

tf.glorot_uniform_initializer()、tf.glorot_normal_initializer()

# 又称 Xavier uniform initializer
tf.glorot_uniform_initializer(
seed=None,
dtype=tf.float32
)

# It draws samples from a uniform distribution within [a=-limit, b=limit]
limit： sqrt(6 / (fan_in + fan_out))
fan_in：the number of input units in the weight tensor
fan_out：the number of output units in the weight tensor
mean = (b + a) / 2
stddev = (b - a)**2 /12

# 又称 Xavier normal initializer
tf.glorot_normal_initializer(
seed=None,
dtype=tf.float32
)

# It draws samples from a truncated normal distribution centered on 0 with
# stddev = sqrt(2 / (fan_in + fan_out))
fan_in：the number of input units in the weight tensor
fan_out：the number of output units in the weight tensor

三、 Tensor 初始化及访问

1、Constants 初始化

call tf.constant

2、Variables 初始化

call a special operation

# 变量使用前一定要初始化
init = tf.global_variables_initializer() # 初始化全部变量
sess.run(init)

# 使用变量的 initializer 属性初始化
sess.run(v.initializer)

用另一个变量的初始化值给当前变量初始化

tf.global_variables_initializer()

initialized_value()

# Create a variable with a random value.
weights = tf.Variable(tf.random_normal([784, 200], stddev=0.35), name="weights")

# Create another variable with the same value as 'weights'.
w2 = tf.Variable(weights.initialized_value(), name="w2")

# Create another variable with twice the value of 'weights'
w_twice = tf.Variable(weights.initialized_value() * 0.2, name="w_twice")

update = tf.assign(old_variable, new_value)

v.assign(new_value)

3、Tensor 的访问

(可以逆序索引(arr[ : : -1])和负索引arr[-3])

arr[i, j] == arr[i][j]

ndarray

arr[conditon] # conditon 可以使用 & | 进行多条件组合

arr[r1:r2, c1:c2:step] # 也可指定 step 进行切片

四、Tensor 常用属性

tf.float32/64、tf.int8/16/32/64

tf.string、tf.bool、tf.complex64、tf.qint8

tf.int32

tf.float32

tf.cast(x, dtype, name=None)

tf.rank(tensor)

shape 属性

get_shape() 方法

tf.shape()函数

batch_size = tf.shape(input)[0]

tf.reshape(tensor, shape, name=None)

-1

Tensor.set_shape()

unknown dimensions

additional information

Tensor.set_shape()

eg: w1 = tf.Variable(tf.random_normal([2, 3], stddev=1), name='weight1')

w1

name='weight1'

w1

name='weight1'

五、Tensor 常用方法

eval(feed_dict=None, session=None)

get_shape()

set_shape(shape)

_, image_data = tf.TFRecordReader(...).read(...)
image = tf.image.decode_png(image_data, channels=3)

# The height and width dimensions of `image` are data dependent, and
# cannot be computed without executing the op.
print(image.shape)
==> TensorShape([Dimension(None), Dimension(None), Dimension(3)])

# We know that each image in this dataset is 28 x 28 pixels.
image.set_shape([28, 28, 3])
print(image.shape)
==> TensorShape([Dimension(28), Dimension(28), Dimension(3)])

六、Tensor 变换常用方法

1.Casting：数据类型转换

tf.string_to_number(string_tensor, out_type=None, name=None)
tf.to_double(x, name='ToDouble')
tf.to_float(x, name='ToFloat')
tf.to_int32(x, name='ToInt32')
tf.to_int64(x, name='ToInt64')

tf.cast(x, dtype, name=None)  # Casts a tensor to a new type
# tensor `a` is [1.8, 2.2], dtype=tf.float
tf.cast(a, tf.int32) ==> [1, 2]  # dtype=tf.int32

# 其它
tf.bitcast
tf.saturate_cast
tf.to_bfloat16

2. Shapes and Shaping：取得张量形状和改变张量形状

# 改变 Tensor 的形状
tf.reshape(tensor, shape, name=None)
# Flatten：令 shape=[-1] 即可
# Reshape：shape 乘积不变即可，当某一维传入-1时，它会自动推得此维度的大小

# 转置
tf.transpose(a, perm=None, name='transpose')

# 返回 tensor 各个维度的大小
tf.shape(input, name=None)
# 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
sess.run(tf.shape(t)) ==> array([2, 2, 3], dtype=int32)   # 必须要 run 才能得出结果
# 亦可以使用 TF 变量对象 Var 的get_shape() 方法来实现Var.get_shape()

# 返回 tensor 中元素的总数
tf.size(input, name=None)

# 返回 Tensor 的维度(轴)的个数，类似于 Numpy 中的 ndim 属性
tf.rank(input, name=None)

# inserts a dimension of 1 into a tensor's shape
tf.expand_dims(
input,
axis=None,
name=None,
)
# 例1，'t' is a tensor of shape [2]
tf.shape(tf.expand_dims(t, 0))  # [1, 2]
tf.shape(tf.expand_dims(t, 1))  # [2, 1]
tf.shape(tf.expand_dims(t, -1))  # [2, 1]，支持负索引

# 例2，'t2' is a tensor of shape [2, 3, 5]
tf.shape(tf.expand_dims(t2, 0))  # [1, 2, 3, 5]， make it a batch of 1 image
tf.shape(tf.expand_dims(t2, 2))  # [2, 3, 1, 5]
tf.shape(tf.expand_dims(t2, 3))  # [2, 3, 5, 1]

# 若 axis 没指定，则移除 shape 中所有的 1，若指定某个轴，则只移除相应位置shape 中的 1
tf.squeeze(
input,
axis=None,
name=None,
)
# 例1，'t' is a tensor of shape [1, 2, 1, 3, 1, 1]
tf.shape(tf.squeeze(t))  # [2, 3]

# 例2， remove specific size 1 dimensions
tf.shape(tf.squeeze(t, axis=[2, 4]))  # [1, 2, 3, 1]

# 其它
tf.broadcast_dynamic_shape
tf.broadcast_static_shape
tf.shape_n
tf.meshgrid

3. Slicing and Joining：切片和连接

切片

切出 1 份

tf.slice(input_, begin, size, name=None)
# begin(zero-based)：切片的起点坐标，一般用 list 来表示
# size(one-based)：切出多大，size[i] is the number of elements of the 'i'th dimension of input that you want to slice
# If size[i] is -1, all remaining elements in dimension i are included in the slice

For example:
# 'input' is [[[1, 1, 1], [2, 2, 2]],
#             [[3, 3, 3], [4, 4, 4]],
#             [[5, 5, 5], [6, 6, 6]]]
tf.slice(input, [1, 0, 0], [1, 1, 3]) ==> [[[3, 3, 3]]]
tf.slice(input, [1, 0, 0], [1, 2, 3]) ==> [[[3, 3, 3],
[4, 4, 4]]]
tf.slice(input, [1, 0, 0], [2, 1, -1]) ==> [[[3, 3, 3]],
[[5, 5, 5]]]
# 亦可以使用 python 原始切片方式实现，eg: input[1, 0:2, 0:3]和第三个效果相同

分割

n 份

tf.split(value, num_or_size_splits, axis=0, num=None, name='split')
# num_or_size_splits
integer：splits value along dimension axis into integer smaller tensors
list：plits value along dimension axis into len(list) smaller tensors.等份每一份的大小是list[i]

For example:
# 'value' is a tensor with shape [5, 30]
# Split 'value' into 3 tensors with sizes [4, 15, 11] along dimension 1
split0, split1, split2 = tf.split(value, [4, 15, 11], 1)
tf.shape(split0) ==> [5, 4]
tf.shape(split1) ==> [5, 15]
tf.shape(split2) ==> [5, 11]
# Split 'value' into 3 tensors along dimension 1
split0, split1, split2 = tf.split(value, num_or_size_splits=3, axis=1)
tf.shape(split0) ==> [5, 10]

连接

tuple

list

tf.concat(values, axis, name='concat')  # 维度不变
For example:
t1 = [[1, 2, 3], [4, 5, 6]]
t2 = [[7, 8, 9], [10, 11, 12]]
tf.concat([t1, t2], 0) ==> [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
tf.concat([t1, t2], 1) ==> [[1, 2, 3, 7, 8, 9], [4, 5, 6, 10, 11, 12]]

# tensor t3 with shape [2, 3]
# tensor t4 with shape [2, 3]
tf.shape(tf.concat([t3, t4], 0)) ==> [4, 3]
tf.shape(tf.concat([t3, t4], 1)) ==> [2, 6]

tf.stack(values, axis, name='concat')  # 维度+1
# Stacks a list of rank-R tensors into one rank-(R+1) tensor
# Given a list of length N=2 of tensors of shape (3, 3);
if axis == 0 then the output tensor will have the shape (N, 3, 3).
if axis == 1 then the output tensor will have the shape (3, N, 3).
if axis == 1 then the output tensor will have the shape (3, 3, N).

a = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])

b = np.array([[ 2,  4,  6],
[ 8, 10, 12],
[14, 16, 18]])

# Note: 做 stack 之前把 a, b 的维度+1变为(1, 3, 3)
# 沿着 x 轴(垂直向下)连接 a, b 的第 0 维元素
sess.run(tf.stack([a,b], axis=0))
array([[[ 1,  2,  3],
[ 4,  5,  6],
[ 7,  8,  9]],

[[ 2,  4,  6],
[ 8, 10, 12],
[14, 16, 18]]])

# 沿着 y 轴(水平向右)连接 a, b 的第 1 维元素
sess.run(tf.stack([a,b], axis=1))
array([[[ 1,  2,  3],
[ 2,  4,  6]],

[[ 4,  5,  6],
[ 8, 10, 12]],

[[ 7,  8,  9],
[14, 16, 18]]])

# 沿着 z 轴(竖直向上)连接 a, b 的第 2 维元素
sess.run(tf.stack([a,b], axis=2))
array([[[ 1,  2],
[ 2,  4],
[ 3,  6]],

[[ 4,  8],
[ 5, 10],
[ 6, 12]],

[[ 7, 14],
[ 8, 16],
[ 9, 18]]])

补零

tf.pad(tensor, paddings, mode='CONSTANT', name=None)
paddings： is an integer tensor with shape [n, 2]，n是 tensor 的维度
For example:
# 't' is [[1, 2, 3], [4, 5, 6]].
# 'paddings' is [[1, 1,], [2, 2]].
# paddings[0, 0/1]: 沿着第 0 维(x轴)在 tensor 上方/下方补 1 圈零
# paddings[1, 0/1]: 沿着第 1 维(y轴)在 tensor 左方/右方补 2 圈零
tf.pad(t, paddings, "CONSTANT") ==> [[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 2, 3, 0, 0],
[0, 0, 4, 5, 6, 0, 0],
[0, 0, 0, 0, 0, 0, 0]]

one_hot 向量的生成

tf.one_hot(indices, depth, on_value=1, off_value=0, axis=-1, dtype=None, name=None)
# 将 indices 中的每个元素 j 扩展成一个深度为 depth 的向量，输出维度+1
# 此向量中索引位置 j 的取值为 1,其余位置的取值为 0
# If indices is a scalar the output shape will be a vector of length depth

# If indices is a vector of length features, the output shape will be:
features x depth if axis == -1
depth x features if axis == 0

# If indices is a matrix (batch) with shape [batch, features], the output shape will be:
batch x features x depth if axis == -1
batch x depth x features if axis == 1
depth x batch x features if axis == 0

# 使用onehot的直接原因是：现在多分类cnn网络的输出通常是softmax层，而它的输出是一个概率分布
# 从而要求输入的标签也以概率分布的形式出现，进而计算交叉熵之类

其它

tf.extract_image_patches
tf.strided_slice
tf.tile
tf.parallel_stack
tf.unstack
tf.reverse_sequence
tf.reverse
tf.reverse_v2
tf.space_to_batch_nd
tf.space_to_batch
tf.required_space_to_batch_paddings
tf.batch_to_space_nd
tf.batch_to_space
tf.space_to_depth
tf.depth_to_space
tf.gather
tf.gather_nd
tf.unique_with_counts
tf.scatter_nd
tf.dynamic_partition
tf.dynamic_stitch
tf.boolean_mask
tf.sequence_mask
tf.dequantize
tf.quantize_v2
tf.quantized_concat
tf.setdiff1d

七、Numpy VS TensorFLow

八、参考资料