[人工智能]2、预备知识

2.预备知识

2.1 数据操作

import tensorflow as tf

x = tf.range(12)
x

<tf.Tensor: shape=(12,), dtype=int32, numpy=array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])>

x.shape

TensorShape([12])

tf.size(x)

<tf.Tensor: shape=(), dtype=int32, numpy=12>

X = tf.reshape(x,(3,-1))
X

<tf.Tensor: shape=(3, 4), dtype=int32, numpy=
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])>

tf.zeros((2,3,4))

<tf.Tensor: shape=(2, 3, 4), dtype=float32, numpy=
array([[[0., 0., 0., 0.],
        [0., 0., 0., 0.],
        [0., 0., 0., 0.]],

       [[0., 0., 0., 0.],
        [0., 0., 0., 0.],
        [0., 0., 0., 0.]]], dtype=float32)>

tf.ones((2,3,4))

<tf.Tensor: shape=(2, 3, 4), dtype=float32, numpy=
array([[[1., 1., 1., 1.],
        [1., 1., 1., 1.],
        [1., 1., 1., 1.]],

       [[1., 1., 1., 1.],
        [1., 1., 1., 1.],
        [1., 1., 1., 1.]]], dtype=float32)>

x = tf.range(12)
x

<tf.Tensor: shape=(12,), dtype=int32, numpy=array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])>

tf.random.normal(shape=[3,4])

<tf.Tensor: shape=(3, 4), dtype=float32, numpy=
array([[ 0.20366655,  0.76086736,  0.11236531,  0.7315972 ],
       [-0.2376917 ,  2.199889  ,  0.08802697, -1.2448792 ],
       [-0.42119586,  1.4910423 , -0.88865596, -0.8695782 ]],
      dtype=float32)>

tf.constant([[1,2,4,3],[1,2,3,4],[4,3,2,1]])

<tf.Tensor: shape=(3, 4), dtype=int32, numpy=
array([[1, 2, 4, 3],
       [1, 2, 3, 4],
       [4, 3, 2, 1]])>

x = tf.constant([1.0, 2, 4,8])
y = tf.constant([2.0,2,2,2])
x + y,x-y,x*y,x/y,x**y

(<tf.Tensor: shape=(4,), dtype=float32, numpy=array([ 3.,  4.,  6., 10.], dtype=float32)>,
 <tf.Tensor: shape=(4,), dtype=float32, numpy=array([-1.,  0.,  2.,  6.], dtype=float32)>,
 <tf.Tensor: shape=(4,), dtype=float32, numpy=array([ 2.,  4.,  8., 16.], dtype=float32)>,
 <tf.Tensor: shape=(4,), dtype=float32, numpy=array([0.5, 1. , 2. , 4. ], dtype=float32)>,
 <tf.Tensor: shape=(4,), dtype=float32, numpy=array([ 1.,  4., 16., 64.], dtype=float32)>)

tf.exp(x)

<tf.Tensor: shape=(4,), dtype=float32, numpy=
array([2.7182817e+00, 7.3890562e+00, 5.4598152e+01, 2.9809580e+03],
      dtype=float32)>

X = tf.reshape(tf.range(12,dtype=tf.float32),(3,4))
Y = tf.constant([[2.0,1,4,3],[1,2,3,4],[4,3,2,1]])
tf.concat([X,Y],axis=0),tf.concat([X,Y],axis=1)

(<tf.Tensor: shape=(6, 4), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.],
        [ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.],
        [ 2.,  1.,  4.,  3.],
        [ 1.,  2.,  3.,  4.],
        [ 4.,  3.,  2.,  1.]], dtype=float32)>,
 <tf.Tensor: shape=(3, 8), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.,  2.,  1.,  4.,  3.],
        [ 4.,  5.,  6.,  7.,  1.,  2.,  3.,  4.],
        [ 8.,  9., 10., 11.,  4.,  3.,  2.,  1.]], dtype=float32)>)

tf.concat 张量连接

X ==Y

<tf.Tensor: shape=(3, 4), dtype=bool, numpy=
array([[False,  True, False,  True],
       [False, False, False, False],
       [False, False, False, False]])>

tf.reduce_sum(X)

<tf.Tensor: shape=(), dtype=float32, numpy=66.0>

a = tf.reshape(tf.range(3),(3,1))
b = tf.reshape(tf.range(2),(1,2))
a,b

(<tf.Tensor: shape=(3, 1), dtype=int32, numpy=
 array([[0],
        [1],
        [2]])>,
 <tf.Tensor: shape=(1, 2), dtype=int32, numpy=array([[0, 1]])>)

a+b

<tf.Tensor: shape=(3, 2), dtype=int32, numpy=
array([[0, 1],
       [1, 2],
       [2, 3]])>

矩阵a将复制列，矩阵b将复制行，然后再按元素相加。

X[-1],X[1:3]

(<tf.Tensor: shape=(4,), dtype=float32, numpy=array([ 8.,  9., 10., 11.], dtype=float32)>,
 <tf.Tensor: shape=(2, 4), dtype=float32, numpy=
 array([[ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.]], dtype=float32)>)

X_var = tf.Variable(X)
#X_var[1,2].assign(9)
X_var

<tf.Variable 'Variable:0' shape=(3, 4) dtype=float32, numpy=
array([[ 0.,  1.,  2.,  3.],
       [ 4.,  5.,  6.,  7.],
       [ 8.,  9., 10., 11.]], dtype=float32)>

X_var = tf.Variable(X)
X_var[0:2,:].assign(tf.ones(X_var[0:2,:].shape)*12)
X_var

<tf.Variable 'Variable:0' shape=(3, 4) dtype=float32, numpy=
array([[12., 12., 12., 12.],
       [12., 12., 12., 12.],
       [ 8.,  9., 10., 11.]], dtype=float32)>

before = id(Y)
Y=Y + X
id(Y) == before

False

Z = tf.Variable(tf.zeros_like(Y))
print('id(Z):',id(Z))
Z.assign(X+Y)
print('id(Z)',id(Z))

id(Z): 2370919107408
id(Z) 2370919107408

@tf.function
def computation(X,Y):
    Z = tf.zeros_like(Y)
    A = X+Y
    B = A + Y
    C = B + Y
    return C + Y

computation(X,Y)

<tf.Tensor: shape=(3, 4), dtype=float32, numpy=
array([[  8.,  17.,  42.,  51.],
       [ 56.,  73.,  90., 107.],
       [120., 129., 138., 147.]], dtype=float32)>

X,Y

(<tf.Tensor: shape=(3, 4), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.],
        [ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.]], dtype=float32)>,
 <tf.Tensor: shape=(3, 4), dtype=float32, numpy=
 array([[ 2.,  4., 10., 12.],
        [13., 17., 21., 25.],
        [28., 30., 32., 34.]], dtype=float32)>)

A = X.numpy()
B = tf.constant(A)
type(A),type(B)

(numpy.ndarray, tensorflow.python.framework.ops.EagerTensor)

a = tf.constant([3.5]).numpy()
a,a.item(),float(a),int(a)

(array([3.5], dtype=float32), 3.5, 3.5, 3)

2.2 数据预处理

在Python中常用的数据分析工具中，通常使用pandas软件包。主要学习使用pandas预处理原始数据并将原始数据转换成张量格式的步骤

import os

os.makedirs(os.path.join('..','data'),exist_ok=True)
data_file = os.path.join('..','data',';house_tiny.csv')
with open(data_file,'w') as f:
    f.write('NumRooms,Alley,Price\n')#列名   房间数量、巷子类型、房屋价格，NA表示未知
    f.write('NA,Pave,127500\n')#每行表示一个数据样本
    f.write('2,NA,106000\n')
    f.write('4,NA,178100\n')
    f.write('NA,NA,140000\n')

import pandas as pd#pandas用于数据分析，各种形式数据

data = pd.read_csv(data_file)#读取数据格式为_cvs的数据
print(data)

   NumRooms Alley   Price
0       NaN  Pave  127500
1       2.0   NaN  106000
2       4.0   NaN  178100
3       NaN   NaN  140000

NaN代表数据缺失，处理缺失数据一般用插值和删除。插值使用代替值代替缺失值，删除则是直接忽略缺失值

inputs,outputs = data.iloc[:,0:2],data.iloc[:,2]
inputs = inputs.fillna(inputs.mean())
print(inputs)

   NumRooms Alley
0       3.0  Pave
1       2.0   NaN
2       4.0   NaN
3       3.0   NaN

.iloc位置索引

inputs = pd.get_dummies(inputs)
print(inputs)

   NumRooms  Alley_Pave  Alley_nan
0       3.0           1          0
1       2.0           0          1
2       4.0           0          1
3       3.0           0          1

pd.get_dummies()#one-hot编码

import tensorflow as tf

X,y = tf.constant(inputs.values),tf.constant(outputs.values)
X,y

(<tf.Tensor: shape=(4, 3), dtype=float64, numpy=
 array([[3., 1., 0.],
        [2., 0., 1.],
        [4., 0., 1.],
        [3., 0., 1.]])>,
 <tf.Tensor: shape=(4,), dtype=int64, numpy=array([127500, 106000, 178100, 140000], dtype=int64)>)

这部分主要学习了pd.read_csv和pd.get_dummies()

2.3线性代数

标量由只有一个元素的张量表示。

import tensorflow as tf

x = tf.constant([3.0])
y = tf.constant([2.0])

x+y,x-y,x*y,x/y,x**y

(<tf.Tensor: shape=(1,), dtype=float32, numpy=array([5.], dtype=float32)>,
 <tf.Tensor: shape=(1,), dtype=float32, numpy=array([1.], dtype=float32)>,
 <tf.Tensor: shape=(1,), dtype=float32, numpy=array([6.], dtype=float32)>,
 <tf.Tensor: shape=(1,), dtype=float32, numpy=array([1.5], dtype=float32)>,
 <tf.Tensor: shape=(1,), dtype=float32, numpy=array([9.], dtype=float32)>)

向量由标量组成的列表。标量值成为向量的元素（element）或者分量（componnent）

x = tf.range(4)
x

<tf.Tensor: shape=(4,), dtype=int32, numpy=array([0, 1, 2, 3])>

列向量是向量的默认方向

x[3]

<tf.Tensor: shape=(), dtype=int32, numpy=3>

向量的长度称为向量的维度，可以用len（）函数访问向量长度

len(x)

4

当用张量表示一个向量（只有一个轴）时，我们也可以通过.shape属性访问向量的长度。形状（shape）是一个元组，列出了张量沿每个轴的长度（维数）。对于只有一个轴的张量，形状只有一个元素。

x.shape

TensorShape([4])

矩阵，表示有两个轴的张量。当有轴时，轴的数量就是张量的维数。

A = tf.reshape(tf.range(20),(5,4))
A

<tf.Tensor: shape=(5, 4), dtype=int32, numpy=
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15],
       [16, 17, 18, 19]])>

tf.transpose(A)#矩阵的转置，即交换矩阵的行和列

<tf.Tensor: shape=(4, 5), dtype=int32, numpy=
array([[ 0,  4,  8, 12, 16],
       [ 1,  5,  9, 13, 17],
       [ 2,  6, 10, 14, 18],
       [ 3,  7, 11, 15, 19]])>

B = tf.constant([[1,2,3],[2,0,4],[3,4,5]])
B

<tf.Tensor: shape=(3, 3), dtype=int32, numpy=
array([[1, 2, 3],
       [2, 0, 4],
       [3, 4, 5]])>

B == tf.transpose(B)

<tf.Tensor: shape=(3, 3), dtype=bool, numpy=
array([[ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True]])>

矩阵的默认方向是列向量，但是在表示数据集的矩阵中，将每个数据样本作为行向量更为常见

张量，任意数量轴的n维数组

X = tf.reshape(tf.range(24),(2,3,4))
X

<tf.Tensor: shape=(2, 3, 4), dtype=int32, numpy=
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],

       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])>

在图像处理中，图像以n维数组形式出现，三个轴通常对应高度宽度华人通道数。

A = tf.reshape(tf.range(20,dtype=tf.float32),(5,4))#dtype是为了确定数据类型
B = A
A, A+B

(<tf.Tensor: shape=(5, 4), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.],
        [ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.],
        [12., 13., 14., 15.],
        [16., 17., 18., 19.]], dtype=float32)>,
 <tf.Tensor: shape=(5, 4), dtype=float32, numpy=
 array([[ 0.,  2.,  4.,  6.],
        [ 8., 10., 12., 14.],
        [16., 18., 20., 22.],
        [24., 26., 28., 30.],
        [32., 34., 36., 38.]], dtype=float32)>)

A*B#矩阵中元素对应相乘，内积，也称哈达玛积。张量乘以或者加上一个标量并不会改变张量的形状，
#只是对应的元素运算

<tf.Tensor: shape=(5, 4), dtype=float32, numpy=
array([[  0.,   1.,   4.,   9.],
       [ 16.,  25.,  36.,  49.],
       [ 64.,  81., 100., 121.],
       [144., 169., 196., 225.],
       [256., 289., 324., 361.]], dtype=float32)>

a = 2
X = tf.reshape(tf.range(24),(2,3,4))
a+X,(a*X).shape

(<tf.Tensor: shape=(2, 3, 4), dtype=int32, numpy=
 array([[[ 2,  3,  4,  5],
         [ 6,  7,  8,  9],
         [10, 11, 12, 13]],
 
        [[14, 15, 16, 17],
         [18, 19, 20, 21],
         [22, 23, 24, 25]]])>,
 TensorShape([2, 3, 4]))

降维

x = tf.range(4,dtype=tf.float32)
x,tf.reduce_sum(x)#tf.reduce_sum()求和

(<tf.Tensor: shape=(4,), dtype=float32, numpy=array([0., 1., 2., 3.], dtype=float32)>,
 <tf.Tensor: shape=(), dtype=float32, numpy=6.0>)

A,A.shape,tf.reduce_sum(A)

(<tf.Tensor: shape=(5, 4), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.],
        [ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.],
        [12., 13., 14., 15.],
        [16., 17., 18., 19.]], dtype=float32)>,
 TensorShape([5, 4]),
 <tf.Tensor: shape=(), dtype=float32, numpy=190.0>)

A_sum_axis0 = tf.reduce_sum(A,axis=0)
A_sum_axis0,A_sum_axis0.shape

(<tf.Tensor: shape=(4,), dtype=float32, numpy=array([40., 45., 50., 55.], dtype=float32)>,
 TensorShape([4]))

A_sum_axis1 = tf.reduce_sum(A,axis=1)
A_sum_axis1,A_sum_axis1.shape

(<tf.Tensor: shape=(5,), dtype=float32, numpy=array([ 6., 22., 38., 54., 70.], dtype=float32)>,
 TensorShape([5]))

tf.reduce_sum(A)

<tf.Tensor: shape=(), dtype=float32, numpy=190.0>

tf.reduce_mean(A),tf.reduce_sum(A)/tf.size(A).numpy()

(<tf.Tensor: shape=(), dtype=float32, numpy=9.5>,
 <tf.Tensor: shape=(), dtype=float32, numpy=9.5>)

tf.reduce_mean(A,axis=0)

<tf.Tensor: shape=(4,), dtype=float32, numpy=array([ 8.,  9., 10., 11.], dtype=float32)>

无论是求和还是求均值，得到的都是列向量。并不是说对每列求和就会得到行向量

非降维求和

调用函数计算总和或均值时保持轴数不变

sum_A = tf.reduce_sum(A,axis=1,keepdims=True)#axis=1是按行相加，keepdims保持轴数不变
sum_A

<tf.Tensor: shape=(5, 1), dtype=float32, numpy=
array([[ 6.],
       [22.],
       [38.],
       [54.],
       [70.]], dtype=float32)>

A/sum_A

<tf.Tensor: shape=(5, 4), dtype=float32, numpy=
array([[0.        , 0.16666667, 0.33333334, 0.5       ],
       [0.18181819, 0.22727273, 0.27272728, 0.3181818 ],
       [0.21052632, 0.23684211, 0.2631579 , 0.28947368],
       [0.22222222, 0.24074075, 0.25925925, 0.2777778 ],
       [0.22857143, 0.24285714, 0.25714287, 0.27142859]], dtype=float32)>

A,tf.cumsum(A,axis=0)

(<tf.Tensor: shape=(5, 4), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.],
        [ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.],
        [12., 13., 14., 15.],
        [16., 17., 18., 19.]], dtype=float32)>,
 <tf.Tensor: shape=(5, 4), dtype=float32, numpy=
 array([[ 0.,  1.,  2.,  3.],
        [ 4.,  6.,  8., 10.],
        [12., 15., 18., 21.],
        [24., 28., 32., 36.],
        [40., 45., 50., 55.]], dtype=float32)>)

点积(Dot Product)

相同位置元素乘积的和

y = tf.ones(4,dtype=tf.float32)
x,y,tf.tensordot(x,y,axes=1)

(<tf.Tensor: shape=(4,), dtype=float32, numpy=array([0., 1., 2., 3.], dtype=float32)>,
 <tf.Tensor: shape=(4,), dtype=float32, numpy=array([1., 1., 1., 1.], dtype=float32)>,
 <tf.Tensor: shape=(), dtype=float32, numpy=6.0>)

tf.reduce_sum(x*y)

<tf.Tensor: shape=(), dtype=float32, numpy=6.0>

矩阵–向量积

线性代数里面学的最常见的矩阵乘法

A.shape,x.shape,tf.linalg.matvec(A,x)

(TensorShape([5, 4]),
 TensorShape([4]),
 <tf.Tensor: shape=(5,), dtype=float32, numpy=array([ 14.,  38.,  62.,  86., 110.], dtype=float32)>)

B = tf.ones((4,3),tf.float32)
tf.matmul(A,B)#矩阵相乘

<tf.Tensor: shape=(5, 3), dtype=float32, numpy=
array([[ 6.,  6.,  6.],
       [22., 22., 22.],
       [38., 38., 38.],
       [54., 54., 54.],
       [70., 70., 70.]], dtype=float32)>

范数

范数（norm）。非正式地说，一个向量的范数告诉我们一个向量有多大(无关维度，指分量的大小)。线代中，向量范数是将向量映射到标量的函数f。L2范数：欧几里得距离。

u = tf.constant([3.0,-4.0])
tf.norm(u)

<tf.Tensor: shape=(), dtype=float32, numpy=5.0>

L1范数，表示向量元素的绝对值之和。与L2范数相比，L1范数受异常值的影响较小。

tf.reduce_sum(tf.abs(u))

<tf.Tensor: shape=(), dtype=float32, numpy=7.0>

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tf.norm(tf.ones((4,9)))#所有元素平方和，然后开平方

<tf.Tensor: shape=(), dtype=float32, numpy=6.0>

a = tf.ones((4,9))
a

<tf.Tensor: shape=(4, 9), dtype=float32, numpy=
array([[1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1.]], dtype=float32)>

2.4微分

拟合模型的两个关键性问题：优化(optimization)和泛化(generalization).

%matplotlib inline
from matplotlib import pyplot as plt
import numpy as np
from IPython import display
from d2l import tensorflow as d2l


def f(x):
    return 3 * x ** 2 - 4 * x

def numerical_lim(f,x,h):
    return (f(x+h)-f(x))/h

h = 0.1
for i in range(5):
    print(f'h={h:.5f},numerical limit={numerical_lim(f,1,h):.5f}')
    h*=0.1

h=0.10000,numerical limit=2.30000
h=0.01000,numerical limit=2.03000
h=0.00100,numerical limit=2.00300
h=0.00010,numerical limit=2.00030
h=0.00001,numerical limit=2.00003

def use_svg_display():  #@save
    """使用svg格式在Jupyter中显示绘图。svg是矢量图"""
    display.set_matplotlib_formats('svg')

def set_figsize(figsize=(3.5, 2.5)):  #@save
    """设置matplotlib的图表大小。"""
    use_svg_display()
    d2l.plt.rcParams['figure.figsize'] = figsize

#@save
def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):
    """设置matplotlib的轴。"""
    axes.set_xlabel(xlabel)
    axes.set_ylabel(ylabel)
    axes.set_xscale(xscale)
    axes.set_yscale(yscale)
    axes.set_xlim(xlim)
    axes.set_ylim(ylim)
    if legend:
        axes.legend(legend)
    axes.grid()

#@save
def plot(X, Y=None, xlabel=None, ylabel=None, legend=None, xlim=None,
         ylim=None, xscale='linear', yscale='linear',
         fmts=('-', 'm--', 'g-.', 'r:'), figsize=(3.5, 2.5), axes=None):
    """绘制数据点。"""
    if legend is None:
        legend = []

    set_figsize(figsize)
    axes = axes if axes else d2l.plt.gca()

    # 如果 `X` 有一个轴，输出True
    def has_one_axis(X):
        return (hasattr(X, "ndim") and X.ndim == 1 or isinstance(X, list)
                and not hasattr(X[0], "__len__"))

    if has_one_axis(X):
        X = [X]
    if Y is None:
        X, Y = [[]] * len(X), X
    elif has_one_axis(Y):
        Y = [Y]
    if len(X) != len(Y):
        X = X * len(Y)
    axes.cla()
    for x, y, fmt in zip(X, Y, fmts):
        if len(x):
            axes.plot(x, y, fmt)
        else:
            axes.plot(y, fmt)
    set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend)

x = np.arange(0, 3, 0.1)
plot(x, [f(x), 2 * x - 3], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])#tangent line切线  legend应该就是角上的那个注释

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import numpy as np
from matplotlib import pyplot as plt

def fun1(x):
    return x**3-1/x

def numberical_lim(f,x):
    h=1e-4
    return (f(x+h)-f(x))/h

def tangent_line(f,x):
    """求切线，调用numberical"""
    d=numberical_lim(f,x)
    y=f(x)-d*x
    return lambda t:d*t+y

x=np.arange(0.0,20.0,0.1)
y=fun1(x)
plt.xlabel('x')
plt.ylabel('f(x)')
tf=tangent_line(fun1,1)
y2=tf(x)
plt.plot(x,y)
plt.plot(x,y2)
plt.show()

<ipython-input-27-83e068b80091>:2: RuntimeWarning: divide by zero encountered in true_divide
  return x**3-1/x

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2.5自动求导

import tensorflow as tf

x = tf.range(4,dtype=tf.float32)
x

<tf.Tensor: shape=(4,), dtype=float32, numpy=array([0., 1., 2., 3.], dtype=float32)>

在我们计算 y 关于 x 的梯度之前，我们需要一个地方来存储梯度

x = tf.Variable(x)

with tf.GradientTape() as t:
    y = 2 * tf.tensordot(x,x,axes=1)#计算y=2x?x
y

<tf.Tensor: shape=(), dtype=float32, numpy=28.0>

x_grad = t.gradient(y,x)
x_grad

<tf.Tensor: shape=(4,), dtype=float32, numpy=array([ 0.,  4.,  8., 12.], dtype=float32)>

x_grad == 4*x

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

with tf.GradientTape() as t:
    y = tf.reduce_sum(x)
y

<tf.Tensor: shape=(), dtype=float32, numpy=6.0>

t.gradient(y,x)

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

with tf.GradientTape() as t:
    y=x*x
t.gradient(y,x)#等价于y=tf.reduce_sum(x*x)
#可以认为这是一个一般求导的方法

<tf.Tensor: shape=(4,), dtype=float32, numpy=array([0., 2., 4., 6.], dtype=float32)>

#设置 persistent=True以多次运行t.gradient多次。（原本运行一次
#就会被删除以不占用空间）
with tf.GradientTape(persistent=True) as t:
    y = x*x
    u = tf.stop_gradient(y)#产生一个新变量u，与y具有相同的值，但
    #但丢弃计算图中如何计算y的任何信息。换句话说，梯度不会向后流
    #经u到x。因此，下面的反向传播函数计算z=u*x关于x的偏导数，同时
    #将u作为常数处理，而不是z=x*x*x关于x的偏导数。
    z = u*x
    
x_grad = t.gradient(z,x)
x_grad == u

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

t.gradient(y,x) == 2*x

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

t.gradient(u,x) == 2*x

False

def f(a):
    b = a*2
    while tf.norm(b)<1000:#tf.norm()求范数
        b=b*2
    if tf.reduce_sum(b)>0:
        c=b
    else:
        c=100*b
    return c

a = tf.Variable(tf.random.normal(shape=()))
with tf.GradientTape() as t:
    d = f(a)
d_grad = t.gradient(d, a)
d_grad

<tf.Tensor: shape=(), dtype=float32, numpy=409600.0>

d_grad ==d/a

<tf.Tensor: shape=(), dtype=bool, numpy=True>

2.6 概率

%matplotlib inline
import numpy as np
import tensorflow as tf 
import tensorflow_probability as tfp
from d2l import tensorflow as d2l

---------------------------------------------------------------------------

ImportError                               Traceback (most recent call last)

<ipython-input-28-d5324e917c9e> in <module>
      2 import numpy as np
      3 import tensorflow as tf
----> 4 import tensorflow_probability as tfp
      5 from d2l import tensorflow as d2l


~\anaconda3\lib\site-packages\tensorflow_probability\__init__.py in <module>
     18 # `python/__init__.py` as necessary.
     19 
---> 20 from tensorflow_probability import substrates
     21 # from tensorflow_probability.google import staging  # DisableOnExport
     22 # from tensorflow_probability.google import tfp_google  # DisableOnExport


~\anaconda3\lib\site-packages\tensorflow_probability\substrates\__init__.py in <module>
     19 from __future__ import print_function
     20 
---> 21 from tensorflow_probability.python.internal import all_util
     22 from tensorflow_probability.python.internal import lazy_loader  # pylint: disable=g-direct-tensorflow-import
     23 


~\anaconda3\lib\site-packages\tensorflow_probability\python\__init__.py in <module>
    140   # Non-lazy load of packages that register with tensorflow or keras.
    141   for pkg_name in _maybe_nonlazy_load:
--> 142     dir(globals()[pkg_name])  # Forces loading the package from its lazy loader.
    143 
    144 


~\anaconda3\lib\site-packages\tensorflow_probability\python\internal\lazy_loader.py in __dir__(self)
     59 
     60   def __dir__(self):
---> 61     module = self._load()
     62     return dir(module)
     63 


~\anaconda3\lib\site-packages\tensorflow_probability\python\internal\lazy_loader.py in _load(self)
     39     """Load the module and insert it into the parent's globals."""
     40     if callable(self._on_first_access):
---> 41       self._on_first_access()
     42       self._on_first_access = None
     43     # Import the target module and insert it into the parent's namespace


~\anaconda3\lib\site-packages\tensorflow_probability\python\__init__.py in _validate_tf_environment(package)
     61   if (distutils.version.LooseVersion(tf.__version__) <
     62       distutils.version.LooseVersion(required_tensorflow_version)):
---> 63     raise ImportError(
     64         'This version of TensorFlow Probability requires TensorFlow '
     65         'version >= {required}; Detected an installation of version {present}. '


ImportError: This version of TensorFlow Probability requires TensorFlow version >= 2.6; Detected an installation of version 2.3.0. Please upgrade TensorFlow to proceed.

fair_probs = tf.ones(6)/6
tfp.distribution.Multinomial(1,fair_probs).sample()

---------------------------------------------------------------------------

NameError                                 Traceback (most recent call last)

<ipython-input-29-b6ed5f3e2caa> in <module>
      1 fair_probs = tf.ones(6)/6
----> 2 tfp.distribution.Multinomial(1,fair_probs).sample()


NameError: name 'tfp' is not defined

tfp.distribution.Multinomial(10,fair_probs).sample()

---------------------------------------------------------------------------

NameError                                 Traceback (most recent call last)

<ipython-input-30-6fe67a5bcdde> in <module>
----> 1 tfp.distribution.Multinomial(10,fair_probs).sample()


NameError: name 'tfp' is not defined

count = tfp.distributions.Multinomial(1000,fair_probs).sample()
count / 1000

---------------------------------------------------------------------------

NameError                                 Traceback (most recent call last)

<ipython-input-33-433b26767ce2> in <module>
----> 1 count = tfp.distributions.Multinomial(1000,fair_probs).sample()
      2 count / 1000


NameError: name 'tfp' is not defined

2.7查阅文档

import tensorflow as tf
print(dir(tf.random))

['Algorithm', 'Generator', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__path__', '__spec__', '_sys', 'all_candidate_sampler', 'categorical', 'create_rng_state', 'experimental', 'fixed_unigram_candidate_sampler', 'gamma', 'get_global_generator', 'learned_unigram_candidate_sampler', 'log_uniform_candidate_sampler', 'normal', 'poisson', 'set_global_generator', 'set_seed', 'shuffle', 'stateless_binomial', 'stateless_categorical', 'stateless_gamma', 'stateless_normal', 'stateless_parameterized_truncated_normal', 'stateless_poisson', 'stateless_truncated_normal', 'stateless_uniform', 'truncated_normal', 'uniform', 'uniform_candidate_sampler']

help(tf.ones)

Help on function ones in module tensorflow.python.ops.array_ops:

ones(shape, dtype=tf.float32, name=None)
    Creates a tensor with all elements set to one (1).
    
    See also `tf.ones_like`, `tf.zeros`, `tf.fill`, `tf.eye`.
    
    This operation returns a tensor of type `dtype` with shape `shape` and
    all elements set to one.
    
    >>> tf.ones([3, 4], tf.int32)
    <tf.Tensor: shape=(3, 4), dtype=int32, numpy=
    array([[1, 1, 1, 1],
           [1, 1, 1, 1],
           [1, 1, 1, 1]], dtype=int32)>
    
    Args:
      shape: A `list` of integers, a `tuple` of integers, or
        a 1-D `Tensor` of type `int32`.
      dtype: Optional DType of an element in the resulting `Tensor`. Default is
        `tf.float32`.
      name: Optional string. A name for the operation.
    
    Returns:
      A `Tensor` with all elements set to one (1).

help(tf.random)

Help on package tensorflow._api.v2.random in tensorflow._api.v2:

NAME
    tensorflow._api.v2.random - Public API for tf.random namespace.

PACKAGE CONTENTS
    experimental (package)

FILE
    c:\users\23886\anaconda3\lib\site-packages\tensorflow\_api\v2\random\__init__.py

tf.ones([3,4,2])

<tf.Tensor: shape=(3, 4, 2), dtype=float32, numpy=
array([[[1., 1.],
        [1., 1.],
        [1., 1.],
        [1., 1.]],

       [[1., 1.],
        [1., 1.],
        [1., 1.],
        [1., 1.]],

       [[1., 1.],
        [1., 1.],
        [1., 1.],
        [1., 1.]]], dtype=float32)>

import random
print(random.randint(0,8))

2

print(random.random())
print(random.uniform(3,4))

0.32450031554967884
3.2835757453930174