pytorch中的广播机制

超、凢脫俗 2023-06-27 03:23 13阅读 0赞

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pytorch中的广播机制和numpy中的广播机制一样, 因为都是数组的广播机制

#### 两个维度不同的Tensor可以相乘, 示例 ####

a = torch.arange(0,6).reshape((6,))
    ''' tensor([0, 1, 2, 3, 4, 5]) shape: torch.Size([6]) ndim: 1 '''
    
    b = torch.arange(0,12).reshape((2,6))
    ''' tensor([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11]]) shape: torch.Size([2, 6]) ndim: 2 '''
    # a和b的ndim不同, 但是可以element-wise相乘, 因为用到了广播机制
    res = torch.mul(a,b)
    ''' tensor([[ 0, 1, 4, 9, 16, 25], [ 0, 7, 16, 27, 40, 55]]) shape: torch.Size([2, 6]) ndim: 2 '''

#### 如何理解数组的广播机制 ####

##### 以数组A和数组B的相加为例, 其余数学运算同理 #####

**核心:如果相加的两个数组的shape不同, 就会触发广播机制, 1)程序会自动执行操作使得A.shape==B.shape, 2)对应位置进行相加**  
**运算结果的shape是:A.shape和B.shape对应位置的最大值**,比如:A.shape=(1,9,4),B.shape=(15,1,4),那么A+B的shape是(15,9,4)

##### 有两种情况能够进行广播 #####

1.  A.ndim > B.ndim, 并且A.shape最后几个元素包含B.shape, 比如下面三种情况, 注意不要混淆ndim和shape这两个基本概念
    
     *  A.shape=(2,3,4,5), B.shape=(3,4,5)
     *  A.shape=(2,3,4,5), B.shape=(4,5)
     *  A.shape=(2,3,4,5), B.shape=(5)
2.  A.ndim == B.ndim, 并且**A.shape和B.shape对应位置的元素要么相同要么其中一个是1**, 比如
    
     *  A.shape=(1,9,4), B.shape=(15,1,4)
     *  A.shape=(1,9,4), B.shape=(15,1,1)

下面分别进行举例

#### A.ndim 大于 B.ndim ####

# a.shape=(2,2,3,4)
    a = np.arange(1,49).reshape((2,2,3,4))
    # b.shape=(3,4)
    b = np.arange(1,13).reshape((3,4))
    # numpy会将b.shape调整至(2,2,3,4), 这一步相当于numpy自动实现np.tile(b,[2,2,1,1])
    res = a + b
    print('===================================')
    print(a)
    print(a.shape)
    print('===================================')
    print(b)
    print(b.shape)
    print('===================================')
    print(res)
    print(res.shape)
    print('===================================')
    print(a+b == a + np.tile(b,[2,2,1,1]) )

#### A.ndim 等于 B.ndim ####

#示例1
    # a.shape=(4,3)
    a = np.arange(12).reshape(4,3)
    # b.shape=(4,1)
    b = np.arange(4).reshape(4,1)
    # numpy会将b.shape调整至(4,3), 这一步相当于numpy自动实现np.tile(b,[1,3])
    res = a + b
    print('===================================')
    print(a)
    print(a.shape)
    print('===================================')
    print(b)
    print(b.shape)
    print('===================================')
    print(res)
    print(res.shape)
    print('===================================')
    print((a+b == a + np.tile(b,[1,3])) )  # 打印结果都是True
    
    #示例2
    # a.shape=(1,9,4)
    a = np.arange(1,37).reshape((1,9,4))
    # b.shape=(15,1,4)
    b = np.arange(1,61).reshape((15,1,4))
    res = a + b
    print('===================================')
    # print(a)
    print(a.shape)
    print('===================================')
    # print(b)
    print(b.shape)
    print('===================================')
    # print(res)
    print(res.shape)
    print('===================================')
    q = np.tile(a,[15,1,1]) + np.tile(b,[1,9,1])
    print(q == res)	# 打印结果都是True

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