TensorFlow2-数学运算(9)

左手的ㄟ右手 2022-11-29 03:04 167阅读 0赞

### 文章目录 ###

*  数学运算
 *   *  运算符
     *  Operation type 操作类型
     *  \+-\*/%
     *  tf.math.log tf.e
     *  log2, log10?
     *  pow, sqrt
     *  @ matm
     *   *  同数据形状
         *  不同数据形状
         *  With broadcasting
     *  Recap 扼要重述
     *  Y = X @ W + b
     *  out = relu(X @ W + b)

# 数学运算 #

## 运算符 ##

*  ±\*/
 *  \*\*, pow, square
 *  sqrt
 *  //, %
 *  exp, log
 *  @, matmul
 *  linear layer

## Operation type 操作类型 ##

*  element-wise 元素方面
    
     *  ±\*/
 *  matrix-wise 矩阵式
    
     *  @, matmul
 *  dim-wise 维度操作
    
     *  reduce\_mean/max/min/sum

import tensorflow as tf
    import numpy as np

## ±\*/% ##

b=tf.fill([2,2],value=2.)
    a=tf.ones([2,2])

a+b,a-b,a*b,a/b

(<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[3., 3.],
            [3., 3.]], dtype=float32)>,
     <tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[-1., -1.],
            [-1., -1.]], dtype=float32)>,
     <tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[2., 2.],
            [2., 2.]], dtype=float32)>,
     <tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[0.5, 0.5],
            [0.5, 0.5]], dtype=float32)>)

b//a, b%a

(<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[2., 2.],
            [2., 2.]], dtype=float32)>,
     <tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[0., 0.],
            [0., 0.]], dtype=float32)>)

## tf.math.log tf.e ##

a=tf.ones([2,2])

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[1., 1.],
           [1., 1.]], dtype=float32)>

log ⁡ e 1 = 0 \\log\_\{e\}1 = 0 loge1=0

log ⁡ e e 0 = 0 \\log\_\{e\}e^0 = 0 logee0=0

e 0 = 1 e^0=1 e0=1

y = log ⁡ e x y = \\log\_e x y=logex

# 计算a元素的自然对数。
    tf.math.log(a)

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[0., 0.],
           [0., 0.]], dtype=float32)>

y = e x y = e^x y=ex

# 计算a元素的指数
    tf.exp(a)

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[2.7182817, 2.7182817],
           [2.7182817, 2.7182817]], dtype=float32)>

## log2, log10? ##

log ⁡ a b / log ⁡ a c = log ⁡ c b \\log\_\{a\}b / \\log\_\{a\}c = \\log\_\{c\}b logab/logac=logcb

tf.math.log(8.)/tf.math.log(2.)

<tf.Tensor: shape=(), dtype=float32, numpy=3.0>

tf.math.log(100.)/tf.math.log(10.)

<tf.Tensor: shape=(), dtype=float32, numpy=2.0>

## pow, sqrt ##

b=tf.fill([2,2],value=2.)

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[2., 2.],
           [2., 2.]], dtype=float32)>

# 平方
    tf.pow(b,3)

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[8., 8.],
           [8., 8.]], dtype=float32)>

b**3

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[8., 8.],
           [8., 8.]], dtype=float32)>

# 开方
    tf.sqrt(b)

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[1.4142135, 1.4142135],
           [1.4142135, 1.4142135]], dtype=float32)>

## @ matm ##

### 同数据形状 ###

a=tf.ones([2,2])
    b=tf.fill([2,2],value=2.)

a,b

(<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[1., 1.],
            [1., 1.]], dtype=float32)>,
     <tf.Tensor: shape=(2, 2), dtype=float32, numpy=
     array([[2., 2.],
            [2., 2.]], dtype=float32)>)

a@b

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[4., 4.],
           [4., 4.]], dtype=float32)>

tf.matmul(a,b)

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
    array([[4., 4.],
           [4., 4.]], dtype=float32)>

### 不同数据形状 ###

a=tf.ones([4,2,3])
    b=tf.fill([4,3,5],value=2.)

# [4,2,3]*[4,3,5] -> [2,3]*[3,5] -> [2,5]
    # [4,2,5]
    a@b

<tf.Tensor: shape=(4, 2, 5), dtype=float32, numpy=
    array([[[6., 6., 6., 6., 6.],
            [6., 6., 6., 6., 6.]],
    
           [[6., 6., 6., 6., 6.],
            [6., 6., 6., 6., 6.]],
    
           [[6., 6., 6., 6., 6.],
            [6., 6., 6., 6., 6.]],
    
           [[6., 6., 6., 6., 6.],
            [6., 6., 6., 6., 6.]]], dtype=float32)>

tf.matmul(a,b)

### With broadcasting ###

a=tf.ones([4,2,3])
    b=tf.fill([3,5],value=2.)

a.shape, b.shape

(TensorShape([4, 2, 3]), TensorShape([3, 5]))

# [3,5] -> [1,3,5] -> [4,3,5]
    bb=tf.broadcast_to(b,[4,3,5])

# [4,2,3]*[4,3,5]
    a@bb

## Recap 扼要重述 ##

*  矩阵相乘最重要的方法是一般矩阵乘积。它只有在第一个矩阵的列数（column）和第二个矩阵的行数（row）相同时才有意义。一般单指矩阵乘积时，指的便是一般矩阵乘积。一个m×n的矩阵就是m×n个数排成m行n列的一个数阵。
 *  y = w \* x + b
 *  Y = X @ W + b
 *  $  
    \\begin\{bmatrix\}  
    x\_\{0\}^\{0\}, x\_\{0\}^\{1\} \\  
    x\_\{1\}^\{0\}, x\_\{1\}^\{1\}  
    \\end\{bmatrix\}  
    \\begin\{bmatrix\}  
    w\_\{0\}^\{0\}, w\_\{0\}^\{1\}, w\_\{0\}^\{2\} \\  
    w\_\{1\}^\{0\}, w\_\{1\}^\{1\}, w\_\{1\}^\{2\}  
    \\end\{bmatrix\} +  
    \[b\_\{0\},b\_\{1\},b\_\{2\}\]  
    \\rightarrow  
    \\begin\{bmatrix\}  
    y\_\{0\}^\{0\}, y\_\{0\}^\{1\}, y\_\{0\}^\{2\} \\  
    y\_\{1\}^\{0\}, y\_\{1\}^\{1\}, y\_\{1\}^\{2\}  
    \\end\{bmatrix\}  
    $
    
     *   y 0 0 = x 0 0 ∗ w 0 0 + x 0 1 ∗ w 1 0 + b 0 y\_\{0\}^\{0\}=x\_\{0\}^\{0\}\*w\_\{0\}^\{0\} + x\_\{0\}^\{1\}\*w\_\{1\}^\{0\} + b\_\{0\} y00=x00∗w00\+x01∗w10\+b0
     *   y 0 1 = x 0 0 ∗ w 0 1 + x 0 1 ∗ w 1 1 + b 0 y\_\{0\}^\{1\}=x\_\{0\}^\{0\}\*w\_\{0\}^\{1\} + x\_\{0\}^\{1\}\*w\_\{1\}^\{1\} + b\_\{0\} y01=x00∗w01\+x01∗w11\+b0
     *   y 0 2 = x 0 0 ∗ w 0 2 + x 0 1 ∗ w 1 2 + b 0 y\_\{0\}^\{2\}=x\_\{0\}^\{0\}\*w\_\{0\}^\{2\} + x\_\{0\}^\{1\}\*w\_\{1\}^\{2\} + b\_\{0\} y02=x00∗w02\+x01∗w12\+b0
 *  \[b,2\] -> \[b,3\]
    
     *  X:\[2,2\] W:\[3,2\]
     *  \[3,2\].T -> \[2,3\]
     *  \[2,2\]@\[2,3\]
     *  \[2,3\]

## Y = X @ W + b ##

x=tf.ones([4,2])

w=tf.ones([2,1])

b=tf.constant(0.1)

# [4,2]@[2,1] + [1]
    # [4,1] + [1] -> [4,1] + [1,1] -> [4,1] + [4,1]
    # [4,1]
    x@w+b

<tf.Tensor: shape=(4, 1), dtype=float32, numpy=
    array([[2.1],
           [2.1],
           [2.1],
           [2.1]], dtype=float32)>

## out = relu(X @ W + b) ##

x=tf.ones([4,2])

w=tf.ones([2,1])

b=tf.constant(0.1)

out = x@w+b
    out

<tf.Tensor: shape=(4, 1), dtype=float32, numpy=
    array([[2.1],
           [2.1],
           [2.1],
           [2.1]], dtype=float32)>