TensorFlow 张量Basicsoperation

1. 张量 concepts

张量 (Tensor) is TensorFlowin最basic datastructure, class似于NumPyin array, 但具 has 更强 big functions, such asGPU加速, 自动微分etc.. 张量可以看作 is many 维array, 根据维度不同, 可以分 for 以 under 几种class型:

• 标量 (0阶张量) : 单个数值, such as 5 or 3.14
• 向量 (1阶张量) : 一维array, such as [1, 2, 3]
• 矩阵 (2阶张量) : 二维array, such as [[1, 2], [3, 4]]
• high 阶张量: 三维及以 on array, such as三维张量可以表示彩色graph像 ( high 度×宽度×通道)

2. creation张量

TensorFlowproviding了 many 种creation张量 method, 以 under is 常用 几种:

2.1 using常量creation张量

using tf.constant() function可以creation常量张量:

import tensorflow as tf

# creation标量
a = tf.constant(5)
print("标量:", a)
print("形状:", a.shape)
print("dataclass型:", a.dtype)

# creation向量
b = tf.constant([1, 2, 3])
print("\n向量:", b)
print("形状:", b.shape)

# creation矩阵
c = tf.constant([[1, 2], [3, 4]])
print("\n矩阵:", c)
print("形状:", c.shape)

# creation三维张量
d = tf.constant([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
print("\n三维张量:", d)
print("形状:", d.shape)

2.2 using特殊值creation张量

TensorFlowproviding了creation特殊值张量 function:

# creation全零张量
zeros = tf.zeros([2, 3])
print("全零张量:", zeros)

# creation全一张量
ones = tf.ones([3, 2])
print("\n全一张量:", ones)

# creation填充张量
filled = tf.fill([2, 2], 5)
print("\n填充张量:", filled)

# creation随机张量
# 均匀分布随机张量
uniform = tf.random.uniform([2, 3], minval=0, maxval=1)
print("\n均匀分布随机张量:", uniform)

# 正态分布随机张量
normal = tf.random.normal([2, 3], mean=0, stddev=1)
print("\n正态分布随机张量:", normal)

2.3 from NumPyarraycreation张量

可以using tf.convert_to_tensor() function将NumPyarray转换 for TensorFlow张量:

import numpy as np

# creationNumPyarray
np_array = np.array([[1, 2], [3, 4]])

# 转换 for TensorFlow张量
tf_tensor = tf.convert_to_tensor(np_array)
print("NumPyarray:", np_array)
print("TensorFlow张量:", tf_tensor)
print("class型转换:", type(np_array), "->", type(tf_tensor))

3. 张量 property

每个张量都 has 以 under important property:

• 形状 (shape) : 张量 维度 and 每个维度 big small
• dataclass型 (dtype) : 张量in元素 dataclass型, such as tf.float32, tf.int32 etc.
• 设备 (device) : 张量where 设备, such as CPU or GPU

tensor = tf.constant([[1, 2, 3], [4, 5, 6]], dtype=tf.float32)

print("张量:", tensor)
print("形状:", tensor.shape)
print("dataclass型:", tensor.dtype)
print("设备:", tensor.device)

4. 张量 basicoperation

TensorFlowproviding了丰富 张量operation, including数学运算, 形状变换, index and 切片etc..

4.1 数学运算

TensorFlowsupport所 has basic 数学运算:

a = tf.constant([1, 2, 3])
b = tf.constant([4, 5, 6])

# 加法
add = tf.add(a, b)
#  or 直接using + 运算符
add_op = a + b
print("加法:", add, add_op)

# 减法
sub = tf.subtract(a, b)
#  or 直接using - 运算符
sub_op = a - b
print("\n减法:", sub, sub_op)

# 乘法 (元素级) 
mul = tf.multiply(a, b)
#  or 直接using * 运算符
mul_op = a * b
print("\n乘法 (元素级) :", mul, mul_op)

# 除法
div = tf.divide(a, b)
#  or 直接using / 运算符
div_op = a / b
print("\n除法:", div, div_op)

# 矩阵乘法
matrix_a = tf.constant([[1, 2], [3, 4]])
matrix_b = tf.constant([[5, 6], [7, 8]])
matmul = tf.matmul(matrix_a, matrix_b)
#  or using @ 运算符
matmul_op = matrix_a @ matrix_b
print("\n矩阵乘法:", matmul, matmul_op)

4.2 形状变换

形状变换 is 张量operationin常用 operation, including重塑, 转置, scale维度etc.:

tensor = tf.constant([[1, 2, 3], [4, 5, 6]])
print("原张量:", tensor)
print("原形状:", tensor.shape)

# 重塑张量
reshaped = tf.reshape(tensor, [3, 2])
print("\n重塑 after :", reshaped)
print("形状:", reshaped.shape)

# 转置张量
transposed = tf.transpose(tensor)
print("\n转置 after :", transposed)
print("形状:", transposed.shape)

# scale维度
expanded = tf.expand_dims(tensor, axis=0)
print("\nscale维度 after :", expanded)
print("形状:", expanded.shape)

# 压缩维度
compressed = tf.squeeze(expanded, axis=0)
print("\n压缩维度 after :", compressed)
print("形状:", compressed.shape)

4.3 index and 切片

张量 index and 切片 and NumPyarrayclass似:

tensor = tf.constant([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print("原张量:", tensor)

# 获取单个元素
element = tensor[0, 1]
print("\n获取单个元素 [0, 1]:", element)

# 切片operation
# 获取第一行
row = tensor[0, :]
print("\n获取第一行:", row)

# 获取第一列
col = tensor[:, 0]
print("\n获取第一列:", col)

# 获取子张量
sub_tensor = tensor[0:2, 1:3]
print("\n获取子张量 [0:2, 1:3]:", sub_tensor)

# using步 long 
step = tensor[::2, ::2]
print("\nusing步 long  [::2, ::2]:", step)

4.4 aggregateoperation

TensorFlowproviding了各种aggregateoperation:

tensor = tf.constant([[1, 2, 3], [4, 5, 6]])
print("原张量:", tensor)

# 求 and 
sum_all = tf.reduce_sum(tensor)
print("\n求 and  (所 has 元素) :", sum_all)

# 按行求 and 
sum_rows = tf.reduce_sum(tensor, axis=0)
print("按行求 and :", sum_rows)

# 按列求 and 
sum_cols = tf.reduce_sum(tensor, axis=1)
print("按列求 and :", sum_cols)

# 求平均值
mean_all = tf.reduce_mean(tensor)
print("\n平均值 (所 has 元素) :", mean_all)

# 求最 big 值
max_all = tf.reduce_max(tensor)
print("\n最 big 值 (所 has 元素) :", max_all)

# 求最 small 值
min_all = tf.reduce_min(tensor)
print("\n最 small 值 (所 has 元素) :", min_all)

# 求标准差
std = tf.math.reduce_std(tf.cast(tensor, tf.float32))
print("\n标准差:", std)

5. 张量 dataclass型转换

TensorFlowsupport不同dataclass型之间 转换:

tensor = tf.constant([1, 2, 3], dtype=tf.int32)
print("原张量:", tensor)
print("原dataclass型:", tensor.dtype)

# 转换 for float32
tensor_float = tf.cast(tensor, tf.float32)
print("\n转换 for float32:", tensor_float)
print("dataclass型:", tensor_float.dtype)

# 转换 for bool
tensor_bool = tf.cast(tensor, tf.bool)
print("\n转换 for bool:", tensor_bool)
print("dataclass型:", tensor_bool.dtype)

6. variable and 常量

in TensorFlowin, has 两种主要 张量class型:

• 常量 (Constant) : 值不可变 张量, using tf.constant() creation
• variable (Variable) : 值可变 张量, using tf.Variable() creation, 常用于modelparameter

# creation常量
const = tf.constant([1, 2, 3])
print("常量:", const)

# creationvariable
var = tf.Variable([1, 2, 3])
print("\nvariable:", var)

# modifyvariable值
var.assign([4, 5, 6])
print("\nmodifyvariable after :", var)

# 增加variable值
var.assign_add([1, 1, 1])
print("\n增加variable after :", var)

# reducingvariable值
var.assign_sub([2, 2, 2])
print("\nreducingvariable after :", var)

7. 张量 and NumPy互operation

TensorFlow张量 and NumPyarray可以方便地for互operation:

# TensorFlow张量转NumPyarray
tf_tensor = tf.constant([[1, 2], [3, 4]])
np_array = tf_tensor.numpy()
print("TensorFlow张量:", tf_tensor)
print("转换 for NumPyarray:", np_array)
print("class型:", type(np_array))

# NumPyarray转TensorFlow张量
np_array = np.array([[5, 6], [7, 8]])
tf_tensor = tf.convert_to_tensor(np_array)
print("\nNumPyarray:", np_array)
print("转换 for TensorFlow张量:", tf_tensor)
print("class型:", type(tf_tensor))

8. 自动微分mechanism

TensorFlow 自动微分mechanism is 其corefeatures之一, 用于计算张量operation 梯度:

# creationvariable
tx = tf.Variable(3.0)

tf.GradientTape() as tape:
    y = tx ** 2

# 计算梯度
grad = tape.gradient(y, tx)
print("y = tx ** 2, tx = 3.0")
print("dy/dtx =", grad)

9. 练习