[人工智能]Pytorch学习笔记2——Pytoch基础

4.基本数据类型

4.1 All is about Tensor

4.2 How to denote string

• One-hot：[0, 1, 0, 0,…]
• Embedding：Word2vec，glove

4.3 Data type

4.4 Type check

a = torch.randn(2, 3)
print(a)    # tensor([[ 0.3765,  0.6532, -0.8246],
            #         [ 1.3567, -0.3963,  0.1719]])
print(a.type())     # torch.FloatTensor
print(type(a))      # <class 'torch.Tensor'>
print(isinstance(a, torch.FloatTensor)) # True

# 数据位置对数据类型的影响
print(isinstance(a, torch.cuda.FloatTensor))    # False
a = a.cuda()
print(isinstance(a, torch.cuda.FloatTensor))    # True

4.5 Dimension / rank

• Dimension 0 ：Loss
• Dimension 1 ：Bias和Linear Input
• Dimension 2 ：Linear Input batch
• Dimension 3 ：RNN Input Batch
• Dimension 4 ：CNN[b, c, h, w]

4.6 Mixed

a = torch.rand(2, 3, 4, 5)
print(a.size())     # torch.Size([2, 3, 4, 5])
print(a.shape)      # torch.Size([2, 3, 4, 5])
print(len(a.shape)) # 4
print(a.dim())      # 维度：4
print(a.numel())    # 具体的数据大小：120

5.创建Tensor

5.1 Import from numpy

a = np.ones(2)
print(a)            # [1. 1.]
print(torch.from_numpy(a))  # tensor([1., 1.], dtype=torch.float64)

5.2 Import from List

a = torch.tensor([2, 3.2])
print(a)    # tensor([2.0000, 3.2000])

torch.Tensor()接受数据的类型
torch.tensor()接收现成的数据

5.3 uninitialized

初始化的数据可能会非常大或者非常小，不建议使用

• torch.empty()
• torch.FloatTensor(d1, d2, d3)
• torch.IntTensor(d1, d2, d3)

5.4 set default type

print(torch.tensor([1.2, 3]).type())    # torch.FloatTensor
torch.set_default_tensor_type(torch.DoubleTensor)
print(torch.tensor([1.2, 3]).type())    # torch.DoubleTensor

5.5 rand / rand_like, randint, randn

推荐使用这个随机初始化

a = torch.rand(2, 1)
print(a)    # tensor([[0.1746],
            #         [0.6831]])
print(torch.rand_like(a))   # tensor([[0.5452],
                            #        [0.4782]])
print(torch.randint(1, 5, [2, 1]))  # tensor([[3],
# 限定了最小值和最大值，左闭右开        #        [4]])

torch.randn() 输出随机数服从正态分布(0, 1)
torch.normal(mean=torch.full([10], 0), std=torch.arrange(1, 0, -0.1)) 自定义正态分布均值和标准差

5.6 full

print(torch.full([], 7))    # 标量：tensor(7)
print(torch.full([1], 7))   # 张量：tensor([7])

5.7 arrange / range

print(torch.arange(0, 10, 2))   # tensor([0, 2, 4, 6, 8])
print(torch.range(0, 10, 2))    # 不建议使用，tensor([ 0.,  2.,  4.,  6.,  8., 10.])

5.8 linspace / logspace

print(torch.linspace(0, 10, steps=3))    # 等差均分为steps份：tensor([ 0.,  5., 10.])
print(torch.logspace(0, -1, steps=5))    # 对数均分为steps份：tensor([1.0000, 0.5623, 0.3162, 0.1778, 0.1000])

5.9 Ones / zeros / eye

print(torch.ones(1, 2))     # 全1矩阵：tensor([[1., 1.]])
print(torch.zeros(1, 2))    # 全0矩阵：tensor([[0., 0.]])
print(torch.eye(2))         # 单位矩阵：tensor([[1., 0.],
                            #                  [0., 1.]])

5.10 randperm

a = torch.rand(4, 3)
print(a)
idx = torch.randperm(3)     # 随机生成索引
print(idx)
print(a[[1, 0, 2]])
"""
tensor([[0.1708, 0.2821, 0.8163],
        [0.8898, 0.6628, 0.2350],
        [0.3743, 0.4281, 0.5309],
        [0.4996, 0.7259, 0.5485]])
tensor([1, 0, 2])
tensor([[0.8898, 0.6628, 0.2350],
        [0.1708, 0.2821, 0.8163],
        [0.3743, 0.4281, 0.5309]])
"""

6.索引与切片

索引和切片的方式同python list[start:end:steps]

• Indexing
• select first / last N
• select by steps
• select by specific index

6.1 …

连续全部取值

a = torch.rand(4, 3, 28, 28)
print(a[0, 1].shape)    # torch.Size([28, 28])
print(a[0, 0, 2, 4])    # tensor(0.9485)
print(a.index_select(2, torch.arange(8)).shape)         # torch.Size([4, 3, 8, 28])
print(a[:,:1,...].shape)       #torch.Size([4, 1, 28, 28])

6.2 select by mask

x = torch.randn(3, 4)
print(x)
mask = x.ge(0.5)	# 元素大于0.5的
print(mask)
print(torch.masked_select(x, mask))
"""
tensor([[-1.8692,  0.9687, -0.4978,  0.7836],
        [-2.5662,  0.0487,  0.3978, -0.3676],
        [-1.5896, -0.1129, -1.9687,  0.5585]])
tensor([[False,  True, False,  True],
        [False, False, False, False],
        [False, False, False,  True]])
tensor([0.9687, 0.7836, 0.5585])
"""

6.3 select by flatten index

reshape为一维后取索引

src = torch.tensor([[4, 3, 5],
					[6, 7, 8]])
print(torch.take(src, torch.tensor([0, 2, 5])))       # tensor([4, 5, 8])

7.维度变换

7.1 View / reshape

view的size前后必须一致，view的size要有实际意义，避免产生数据污染

a = torch.rand(4, 1, 28, 28)
print(a.view(4, 28*28).shape)   # torch.Size([4, 784])
print(a.unsqueeze(4).shape)     # torch.Size([4, 1, 28, 28, 1])

7.2 Sequeeze / unsqueeze

unsqueeze插入一个维度，不会改变数据本身
squeeze若给定的挤压维度为1则被挤压掉，若不为1则保持原来数据维度不变

b = torch.tensor([1, 2])
print(b.unsqueeze(-1))  # tensor([[1],
                        #         [2]])
print(b.unsqueeze(0))   # tensor([[1, 2]])

c = torch.rand(1, 31, 1, 1)
print(c.shape)                  # torch.Size([1, 31, 1, 1])
print(c.squeeze().shape)        # torch.Size([31])
print(c.squeeze(0).shape)       # torch.Size([31, 1, 1])
print(c.squeeze(1).shape)       # torch.Size([1, 31, 1, 1])

7.3 Expand / repeat

• Expand(broadcasting)
• repeat(memory copied)

a = torch.rand(1,32,1,1)
print(a.shape)                          # torch.Size([1, 32, 1, 1])
print(a.expand(4,32,14,14).shape)       # torch.Size([4, 32, 14, 14])
print(a.repeat(4,32,1,1).shape)         # torch.Size([4, 1024, 1, 1])

7.4 Transpose / t / permute

t()只能转置二维矩阵，否则报错

a = torch.rand(2,3)
print(a.t().shape)      # torch.Size([3, 2])

b = torch.rand(4,3,28,28)
print(b.transpose(1,3).transpose(1,2).shape)    # torch.Size([4, 28, 28, 3])
print(b.permute(0,2,3,1).shape)                 # torch.Size([4, 28, 28, 3])

8. Broadcasting

• Expand
• without copying data

key idea

• insert 1 dim ahead
• Expand dims with size 1 to same size
  
  Why broadcasting
• for actual demanding
• memory consumption

Is it broadcating-able?

• Match from Last dim
  if current dim=1, expand to same
  if either has no dim, insert one dim and expand to same
  otherwise, NOT broadcasting-able

9.拼接与拆分

9.1 Cat

只能在维度不同的dim上进行cat

a = torch.rand(4, 32, 8)
b = torch.rand(5, 32, 8)
print(torch.cat([a, b], dim=0).shape)	# torch.Size([9, 32, 8])

9.2 Stack

会创建新的维度，两个维度必须一致

a = torch.rand(32, 8)
b = torch.rand(32, 8)
print(torch.stack([a, b], dim=0).shape)	# torch.Size([2, 32, 8])

9.3 split: by len

a = torch.rand(4, 32, 8)
aa, bb = a.split(2, dim=0)
print(aa.shape, bb.shape)	# torch.Size([2, 32, 8]) torch.Size([2, 32, 8])
cc, dd = a.split([3, 1], dim=0)
print(cc.shape, dd.shape)	# torch.Size([3, 32, 8]) torch.Size([1, 32, 8])

9.4 Chunk: by num

a = torch.rand(4, 32, 8)
aa, bb = a.chunk(2, dim=0)
print(aa.shape, bb.shape)	#torch.Size([2, 32, 8]) torch.Size([2, 32, 8])

10.基本运算

• Add / minus / multiply / divide
  torch.add() torch.sub() torch.mul() torch.div()
• Matmul矩阵乘法
  torh.mm() only for 2d
  torch.matmul()
@
• Pow
  tensor.pow(n) = tensor**(n)
• Sqrt / rsqrt
  sqrt()开平方
  rsqrt()开平方的倒数
• Exp log
  torch.exp()
torch.log()
• Approximation
  tensor.floor() tensor.ceil() tensor.round()
tensor.trunc()整数部分 tensor.frac()小数部分
• clamp
  gradient clipping

import torch
import numpy as np

grad = torch.rand(2, 3) * 15
print(grad)
print(grad.min())
print(grad.median())
print(grad.max())
print(grad.clamp(10))
print(grad.clamp(0, 10))
"""
tensor([[11.9217,  3.4733,  1.3133],
        [ 7.1854, 13.8410, 13.8098]])
tensor(1.3133)
tensor(7.1854)
tensor(13.8410)
tensor([[11.9217, 10.0000, 10.0000],
        [10.0000, 13.8410, 13.8098]])
tensor([[10.0000,  3.4733,  1.3133],
        [ 7.1854, 10.0000, 10.0000]])
"""

11.数据统计

• norm-p 范数（简单的理解）、范数的用途、什么是范数1

import torch
import numpy as np

a = torch.full([8], 1.0)
print(a)
b = a.view(2, 4)
print(b)
c = a.view(2, 2, 2)
print(c)

print(a.norm(1), b.norm(1), c.norm(1))
print(a.norm(2), b.norm(2), c.norm(2))

print(b.norm(1, dim=1))
print(b.norm(2, dim=1))

print(c.norm(1, dim=0))
print(c.norm(2, dim=0))
"""
tensor([1., 1., 1., 1., 1., 1., 1., 1.])
tensor([[1., 1., 1., 1.],
        [1., 1., 1., 1.]])
tensor([[[1., 1.],
         [1., 1.]],

        [[1., 1.],
         [1., 1.]]])
tensor(8.) tensor(8.) tensor(8.)
tensor(2.8284) tensor(2.8284) tensor(2.8284)
tensor([4., 4.])
tensor([2., 2.])
tensor([[2., 2.],
        [2., 2.]])
tensor([[1.4142, 1.4142],
        [1.4142, 1.4142]])
"""

• tensor.mean()均值
• tensor.prod()累乘
• tensor.sum() 累加
• tensor.argmin(), tensor.argmax() 最大、小值索引
• dim=n, keepdim=True 设置维度，保持维度不变
• kthvalue, topk
  tensor.topk(n, dim=, largest=False) 某一维度上最小的前n个
  tensor.kthvalue(n, dim=) 某一维度上最小的第n个
• compare

a = torch.rand(2, 3)
print(a)
print(torch.gt(a, 0.5))		# 大于0.5
print(torch.eq(a, a))
print(torch.equal(a, a))
"""
tensor([[0.5229, 0.7868, 0.0872],
        [0.3480, 0.4691, 0.2402]])
tensor([[ True,  True, False],
        [False, False, False]])
tensor([[True, True, True],
        [True, True, True]])
True
"""

12.高级OP

12.1 Where

torch.where(condition, x, y)

• Return a tensor of elements selected from either x or y, depending on condition.
• where相较于python的if else优点是可以部署在GPU上，实现高度并行

12.2 Gather

torch.gather(input, dim, index, out=None)

• Gathers values along an axis specified by dim.
• retrieve global label
  argmax(pred) to get relative labeling
  On some condtion, our label is dinstinct from relative labeling

import torch
import numpy as np

prob = torch.randn(4, 10)
idx = prob.topk(dim=1, k=3)
print(idx)
"""
torch.return_types.topk(
values=tensor([[1.3319, 0.8338, 0.4407],
        [2.0854, 0.9303, 0.2608],
        [1.7225, 1.0136, 0.5523],
        [1.3715, 1.3115, 1.0049]]),
indices=tensor([[2, 9, 3],
        [1, 3, 8],
        [3, 5, 0],
        [3, 7, 1]]))
"""

label = torch.arange(10) + 100
print(label)
"""
tensor([100, 101, 102, 103, 104, 105, 106, 107, 108, 109])
"""

print(torch.gather(label.expand(4, 10), dim=1, index=idx[1].long()))
"""
tensor([[102, 109, 103],
        [101, 103, 108],
        [103, 105, 100],
        [103, 107, 101]])
"""