10,09_维度变换,view、reshape,unsqueeze,Squeeze,expand,repeat,矩阵转置,transpose维度交换,permute,Broadcasting

ゝ一纸荒年。 2022-10-25 14:03 161阅读 0赞

1.9.Tensor维度变换  
1.9.1.view、reshape  
1.9.2.unsqueeze  
1.9.3.Squeeze  
1.9.4.expand  
1.9.5.repeat  
1.9.6.矩阵转置  
1.9.7.transpose维度交换  
1.9.8.permute  
1.10.Broadcasting

## 1.9.Tensor维度变换 ##

### 1.9.1.view、reshape ###

1.两者功能一样：将数据依次展开后，再变形  
2.变形后的数据量与变形前数据量必须相等。即满足维度：ab…f = xy…z  
3.reshape是pytorch根据numpy中的reshape来的。  
4.-1表示，其他维度数据已给出情况下。

# -*- coding: UTF-8 -*-
    
    import torch
    a = torch.rand(2,3,2,3)
    print(a)
    """ 输出： tensor([[[[0.6265, 0.0326, 0.1273], [0.3120, 0.4449, 0.5718]], [[0.1046, 0.7776, 0.9645], [0.1902, 0.7404, 0.0302]], [[0.5433, 0.1578, 0.6770], [0.5591, 0.2102, 0.6344]]], [[[0.5778, 0.3997, 0.9127], [0.8123, 0.8689, 0.4470]], [[0.2341, 0.0349, 0.2872], [0.0609, 0.5397, 0.3100]], [[0.4623, 0.0076, 0.3278], [0.6248, 0.0155, 0.1211]]]]) """
    
    # 将数据依次展开后，再变形为对应维度。所以，数据的顺序是一样的。且总的数据维度是不变的。
    print(a.view(4, 9))
    """ 输出结果： tensor([[0.2667, 0.4700, 0.0454, 0.9939, 0.7008, 0.1362, 0.7544, 0.4472, 0.2111], [0.5638, 0.8971, 0.3139, 0.8841, 0.4913, 0.2058, 0.8583, 0.1505, 0.0892], [0.7533, 0.7021, 0.6080, 0.6848, 0.5243, 0.1918, 0.4089, 0.3315, 0.7276], [0.9459, 0.1081, 0.0461, 0.8141, 0.5869, 0.5843, 0.2659, 0.7687, 0.4242]]) """
    
    # reshape和view的效果一样
    print(a.reshape(4, 9))
    """ 输出结果： tensor([[0.7789, 0.1785, 0.6387, 0.7912, 0.1439, 0.2618, 0.6727, 0.4800, 0.0564], [0.3654, 0.0296, 0.6067, 0.3572, 0.0439, 0.6657, 0.4368, 0.2253, 0.2332], [0.3263, 0.7157, 0.4796, 0.1004, 0.6954, 0.6626, 0.0379, 0.4982, 0.9791], [0.5354, 0.4496, 0.7845, 0.4297, 0.7509, 0.0035, 0.1737, 0.8664, 0.2800]]) """
    
    # -1表示，除了其他维度以外的最大维度数据量
    # 此处为2*3*2*3=36, 36/4=9
    print(a.reshape(4, -1))
    """ 输出结果： tensor([[0.1846, 0.5650, 0.4715, 0.1910, 0.5250, 0.6251, 0.4083, 0.3805, 0.9292], [0.7696, 0.2830, 0.0341, 0.3543, 0.8685, 0.4288, 0.2090, 0.5807, 0.1181], [0.0733, 0.9524, 0.8143, 0.4773, 0.3792, 0.8397, 0.0287, 0.6018, 0.6265], [0.6263, 0.1427, 0.5324, 0.7368, 0.7149, 0.6638, 0.5361, 0.0298, 0.4793]]) """
    
    print("------------------------------------------")
    
    # 此处为2*3*2*3=36, 36/4=9
    print(a.reshape(4, -1))
    """ 输出结果： tensor([[0.3042, 0.5191, 0.7625, 0.9274, 0.1921, 0.0750, 0.1138, 0.5479, 0.3058], [0.2298, 0.8897, 0.2379, 0.9171, 0.3238, 0.9612, 0.1647, 0.8832, 0.4885], [0.0331, 0.8462, 0.4061, 0.5430, 0.9528, 0.8883, 0.0474, 0.5019, 0.2368], [0.7151, 0.5584, 0.2686, 0.6878, 0.0322, 0.3292, 0.9116, 0.4619, 0.3833]]) """
    
    print(">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>")
    # 36/(2 * 3) = 6
    # 所以此时-1表示6
    print(a.reshape(2, 3, -1))
    """ tensor([[[0.1343, 0.1076, 0.6838, 0.4183, 0.6465, 0.7390], [0.3154, 0.6980, 0.3021, 0.9203, 0.3105, 0.9567], [0.5732, 0.5508, 0.6185, 0.1907, 0.5157, 0.0187]], [[0.2193, 0.6670, 0.8597, 0.7905, 0.0997, 0.0762], [0.6765, 0.3075, 0.7198, 0.7030, 0.1858, 0.5082], [0.4665, 0.3556, 0.0429, 0.2645, 0.3454, 0.7767]]]) """
    
    print("======================================")
    
    # 给定的-1以外的其他维度数据的乘积，必须能整除总的数据量
    # 比如，此处的5不能整除36，所以会报错
    # print(a.reshape(5, -1))
    """ 输出结果： Traceback (most recent call last): File "D:\installed\Anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3326, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File "<ipython-input-2-7ad3dc423fa5>", line 1, in <module> runfile('E:/workspace/pytorch-learn/09_维度变换/09_维度变换.py', wdir='E:/workspace/pytorch-learn/09_维度变换') File "C:\Program Files\JetBrains\PyCharm 2019.2.4\helpers\pydev\_pydev_bundle\pydev_umd.py", line 197, in runfile pydev_imports.execfile(filename, global_vars, local_vars) # execute the script File "C:\Program Files\JetBrains\PyCharm 2019.2.4\helpers\pydev\_pydev_imps\_pydev_execfile.py", line 18, in execfile exec(compile(contents+"\n", file, 'exec'), glob, loc) File "E:/workspace/pytorch-learn/09_维度变换/09_维度变换.py", line 82, in <module> print(a.reshape(5, -1)) RuntimeError: shape '[5, -1]' is invalid for input of size 36 """
    
    print(a.view(4, 9).view(2, 3, 2, 3))
    """ tensor([[[[0.8306, 0.3289, 0.6837], [0.1553, 0.8128, 0.4839]], [[0.2005, 0.5720, 0.3754], [0.0711, 0.2138, 0.6295]], [[0.3155, 0.8848, 0.3345], [0.7782, 0.6487, 0.5341]]], [[[0.5153, 0.3421, 0.2283], [0.1855, 0.2059, 0.1031]], [[0.1763, 0.3316, 0.6055], [0.8860, 0.3544, 0.6888]], [[0.7657, 0.7608, 0.8756], [0.7559, 0.3434, 0.7446]]]]) """

### 1.9.2.unsqueeze ###

1.功能：指定维度，为其增加（插入）1个维度  
2.必须给定维度数据，不然会报错

# -*- coding: UTF-8 -*-
    
    import torch
    
    a = torch.randn(2, 3)
    print(a)
    """ 输出： tensor([[ 0.3445, 1.0431, 0.0649], [ 2.0011, -1.9437, 1.3459]]) """
    
    # 在0维处，增加1个维度
    print(a.unsqueeze(0))
    # 支持负数索引，等价于 a.unsqueeze(-3)
    """ 输出： tensor([[[ 0.1839, -0.2338, -0.7837], [ 0.5659, 0.1431, 0.6513]]]) """
    
    print(a.unsqueeze(1))
    # 等价于a.unsqueeze(-2)
    """ 输出： tensor([[[-0.9794, 1.5992, 1.6226]], [[-0.1168, -0.5305, 0.2656]]]) """
    
    print(a.unsqueeze(2))
    # 等价于a.unsqueeze(-1)
    """ 输出： tensor([[[-0.9512], [-0.0490], [ 0.3785]], [[-0.6573], [ 0.0302], [ 0.4737]]]) """
    
    # 分别在0和最后维度上面都增加了一个维度，相比上面的数据，外层多了一对[]括号
    a.unsqueeze(0).unsqueeze(-1)    
    """ tensor([[[-0.6981], [-0.8682], [-0.3138]], [[ 0.0167], [-0.1493], [ 0.1665]]]) """

### 1.9.3.Squeeze ###

Squeeze删除为1的维度

1.默认将所有为1的维度。  
2.传入指定维度，删除指定维度为1的维度。

# -*- coding: UTF-8 -*-
    
    import torch
    
    a = torch.rand(2, 1, 3, 1, 2, 1)
    print(a)
    """ tensor([[[[[[0.7556], [0.6847]]], [[[0.3153], [0.5923]]], [[[0.5427], [0.5048]]]]], [[[[[0.3298], [0.9076]]], [[[0.3010], [0.2370]]], [[[0.7194], [0.4149]]]]]]) """
    
    # 默认删除所有为1的维度，即(2, 1, 3, 1, 2, 1)删除后得到（2, 3, 2）
    print(a.squeeze())
    """ 输出： tensor([[[0.7331, 0.1108], [0.8523, 0.4815], [0.7817, 0.9866]], [[0.2483, 0.1248], [0.3179, 0.2502], [0.2722, 0.9329]]]) """
    
    print(a)
    """ tensor([[[[[[0.7331], [0.1108]]], [[[0.8523], [0.4815]]], [[[0.7817], [0.9866]]]]], [[[[[0.2483], [0.1248]]], [[[0.3179], [0.2502]]], [[[0.2722], [0.9329]]]]]]) """
    
    # 通过指定维度删除1，与上面效果相同
    print(a.squeeze(1).squeeze(2).squeeze(3))
    """ 输出： tensor([[[0.2862, 0.6455], [0.2383, 0.2630], [0.6638, 0.4293]], [[0.6390, 0.1212], [0.9523, 0.7255], [0.5178, 0.3208]]]) """

### 1.9.4.expand ###

扩大张量：torch.Tensor.expand(\*sizes) -->Tensor  
返回 tensor 的一个新视图，单个维度扩大为更大的尺寸。 tensor 也可以扩大为更高维，新增加的维度将附在前面。 扩大 tensor 不需要分配新内存，只是仅仅新建一个 tensor 的视图，其中通过将 stride 设为 0，一维将会扩展位更高维。任何一个一维的在不分配新内存情况下可扩展为任意的数值。

1.功能：扩展维度到指定维度。扩展的数据是复制当前维度的数据。  
2.只有只有维度大小为1的维度可以扩展  
3.-1表示保持原维度

# -*- coding: UTF-8 -*-
    
    import torch
    
    a = torch.rand(2,3,1)
    print(a)
    """ 输出结果： tensor([[[0.9564], [0.0760], [0.2326]], [[0.9647], [0.8662], [0.7067]]]) """
    
    # 扩展数据，只有维度为1的地方可以被扩展，(2, -1, 3)等价于(2, 3, 3)
    print(a.expand(2, -1, 3))
    """ 输出结果： tensor([[[0.9564, 0.9564, 0.9564], [0.0760, 0.0760, 0.0760], [0.2326, 0.2326, 0.2326]], [[0.9647, 0.9647, 0.9647], [0.8662, 0.8662, 0.8662], [0.7067, 0.7067, 0.7067]]]) """

### 1.9.5.repeat ###

torch.Tensor.repeat(\*sizes)  
沿着指定的维度重复tensor。不同于expand()，本函数复制的是tensor中的数据。

1.表示扩展数据到原维度的倍数。  
2.1表保持原维度。  
3.不建议使用此方法，因此复制数据会重新申请内存空间，比较占内存。

# -*- coding: UTF-8 -*-
    
    import torch
    
    a = torch.rand(2, 3, 1)
    
    print(a)
    """ tensor([[[0.8991], [0.5624], [0.0676]], [[0.9069], [0.2048], [0.0300]]]) """
    
    print(a.repeat(1, 1, 3))
    """ tensor([[[0.8991, 0.8991, 0.8991], [0.5624, 0.5624, 0.5624], [0.0676, 0.0676, 0.0676]], [[0.9069, 0.9069, 0.9069], [0.2048, 0.2048, 0.2048], [0.0300, 0.0300, 0.0300]]]) """

### 1.9.6.矩阵转置 ###

1.行列互换  
2…t()只支持2D的数据

a = torch.rand(5, 2)
    print(a)
    """ tensor([[0.2898, 0.7774], [0.3639, 0.1799], [0.7717, 0.8179], [0.9935, 0.7679], [0.6835, 0.4301]]) """
    
    print(a.t())
    """ tensor([[0.2898, 0.3639, 0.7717, 0.9935, 0.6835], [0.7774, 0.1799, 0.8179, 0.7679, 0.4301]]) """

### 1.9.7.transpose维度交换 ###

torch.transpose(input, dim0, dim1, out=None)–>Tensor  
返回输入矩阵input的转置。交换维度dim0和dim1。输出张量与输入张量共享内存，所以改变其中一个会导致另外一个也被修改。

1.相当于被选择的两个维度数据进行转置，即：行列互换  
2.也可以理解为，每一行数据顺时旋转90度为一列后，依次拼接在右边（最后面）

# -*- coding: UTF-8 -*-
    
    import torch
    
    a = torch.rand(2, 3, 4)
    print(a)
    """ tensor([[[0.7630, 0.1244, 0.0539, 0.9472], [0.6098, 0.4826, 0.5270, 0.7383], [0.7582, 0.1667, 0.1692, 0.1481]], [[0.1000, 0.7165, 0.1339, 0.3319], [0.4485, 0.0099, 0.5476, 0.5260], [0.5430, 0.3896, 0.9594, 0.6139]]]) """
    
    print(a.transpose(0, 2))
    """ tensor([[[0.7630, 0.1000], [0.6098, 0.4485], [0.7582, 0.5430]], [[0.1244, 0.7165], [0.4826, 0.0099], [0.1667, 0.3896]], [[0.0539, 0.1339], [0.5270, 0.5476], [0.1692, 0.9594]], [[0.9472, 0.3319], [0.7383, 0.5260], [0.1481, 0.6139]]]) """
    
    print(a.transpose(0, 2).contiguous().view(4, 6))
    """ tensor([[0.7630, 0.1000, 0.6098, 0.4485, 0.7582, 0.5430], [0.1244, 0.7165, 0.4826, 0.0099, 0.1667, 0.3896], [0.0539, 0.1339, 0.5270, 0.5476, 0.1692, 0.9594], [0.9472, 0.3319, 0.7383, 0.5260, 0.1481, 0.6139]]) """

### 1.9.8.permute ###

permute(dims)将tensor的维度换位。参数是一系列的整数，代表原来张量的维度。再比如图片img的size是（28,28,3）就可以利用img.permute(2,0,1)得到一个size为(3,28,28)的tensor.

与transpose不同的是：  
1.transpose一次只能进行两个维度之间的交换  
2.permute可以一次进行多个维度的交换。其实质就是实现多个transpose步骤。  
3.给定维度索引。

# -*- coding: UTF-8 -*-
    
    import torch
    
    a = torch.rand(2, 3)
    print(a)
    # print(a.size(0)) # a.size(0) 结果为2。 a.size(1) 结果为3
    """ 输出： tensor([[0.5538, 0.7207, 0.9182], [0.7058, 0.9794, 0.2337]]) """
    
    print(a.permute(1, 0))
    """ 输出： tensor([[0.5538, 0.7058], [0.7207, 0.9794], [0.9182, 0.2337]]) """
    
    # 通过2次transpose可以实现permute的效果
    print(a.transpose(0, 1))
    """ 输出： tensor([[0.5538, 0.7058], [0.7207, 0.9794], [0.9182, 0.2337]]) """

## 1.10.Broadcasting ##

1.定义：两个维度不同的数据相加，会自动将维度小的数据扩张到与大维度相同的维度。  
2.特点：自动扩展维度，并且不用复制数据，节省空间。  
3.前提：小维度的数据，要么不给定维度，要么给定1维，要么与原数据维度大小相同的维度，否则会报错。  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70]

# -*- coding: UTF-8 -*-
    
    import torch
    a = torch.rand(3, 4, 2)
    print(a)
    
    # b的第一维度为1，a的为3
    b = torch.rand(1, 4, 2)
    print(b)
    
    
    # 相加和，b被自动广播为3，然后再与a相加，得到结果
    print(a + b)

**输出结果：**

tensor([[[0.2051, 0.3002],
             [0.7875, 0.8702],
             [0.8102, 0.1946],
             [0.4178, 0.0421]],
            [[0.5986, 0.1744],
             [0.9141, 0.6217],
             [0.3636, 0.6171],
             [0.5568, 0.9626]],
            [[0.8271, 0.1875],
             [0.8445, 0.5693],
             [0.2277, 0.1845],
             [0.4858, 0.4569]]])
    tensor([[[0.5436, 0.3877],
             [0.8810, 0.7022],
             [0.9177, 0.0713],
             [0.8664, 0.9766]]])
    tensor([[[0.7487, 0.6879],
             [1.6685, 1.5723],
             [1.7280, 0.2660],
             [1.2842, 1.0187]],
    
            [[1.1422, 0.5621],
             [1.7951, 1.3239],
             [1.2814, 0.6885],
             [1.4232, 1.9393]],
    
            [[1.3707, 0.5752],
             [1.7255, 1.2715],
             [1.1454, 0.2558],
             [1.3523, 1.4336]]])

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70]: /images/20221024/0aa1a964bb4f408496eab4a073881ea3.png