Pytorch深度学习addmm()和addmm_()函数用法解析

目录

• 一、函数解释
• 二、代码范例
• 三、代码运行结果

一、函数解释

在torch/_C/_VariableFunctions.py的有该定义，意义就是实现一下公式：

换句话说，就是需要传入5个参数，mat里的每个元素乘以beta，mat1和mat2进行矩阵乘法（左行乘右列）后再乘以alpha，最后将这2个结果加在一起。但是这样说可能没啥概念，接下来博主为大家写上一段代码，大家就明白了~

    def addmm(self, beta=1, mat, alpha=1, mat1, mat2, out=None): # real signature unknown; restored from __doc__
        """
        addmm(beta=1, mat, alpha=1, mat1, mat2, out=None) -> Tensor
        Performs a matrix multiplication of the matrices :attr:`mat1` and :attr:`mat2`.
        The matrix :attr:`mat` is added to the final result.
        If :attr:`mat1` is a :math:`(n \times m)` tensor, :attr:`mat2` is a
        :math:`(m \times p)` tensor, then :attr:`mat` must be
        :ref:`broadcastable <broadcasting-semantics>` with a :math:`(n \times p)` tensor
        and :attr:`out` will be a :math:`(n \times p)` tensor.
        :attr:`alpha` and :attr:`beta` are scaling factors on matrix-vector product between
        :attr:`mat1` and :attr`mat2` and the added matrix :attr:`mat` respectively.
        .. math::
            out = \beta\ mat + \alpha\ (mat1_i \mathbin{@} mat2_i)
        For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and
        :attr:`alpha` must be real numbers, otherwise they should be integers.
        Args:
            beta (Number, optional): multiplier for :attr:`mat` (:math:`\beta`)
            mat (Tensor): matrix to be added
            alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
            mat1 (Tensor): the first matrix to be multiplied
            mat2 (Tensor): the second matrix to be multiplied
            out (Tensor, optional): the output tensor
        Example::
            >>> M = torch.randn(2, 3)
            >>> mat1 = torch.randn(2, 3)
            >>> mat2 = torch.randn(3, 3)
            >>> torch.addmm(M, mat1, mat2)
            tensor([[-4.8716,  1.4671, -1.3746],
                    [ 0.7573, -3.9555, -2.8681]])
        """
        pass

二、代码范例

1.先摆出代码，大家可以先复制粘贴运行一下，在之后博主会一一讲解

"""
@author:nickhuang1996
"""
import torch
rectangle_height = 3
rectangle_width = 3
inputs = torch.randn(rectangle_height, rectangle_width)
for i in range(rectangle_height):
    for j in range(rectangle_width):
        inputs[i] = i * torch.ones(rectangle_width)
'''
inputs and its transpose
-->inputs   =   tensor([[0., 0., 0.],
                        [1., 1., 1.],
                        [2., 2., 2.]])
-->inputs_t =   tensor([[0., 1., 2.],
                        [0., 1., 2.],
                        [0., 1., 2.]])
'''
print("inputs:\n", inputs)
inputs_t = inputs.t()
print("inputs_t:\n", inputs_t)
'''
inputs_t @ inputs_t    [[0., 1., 2.],       [[0., 1., 2.],          [[0., 3., 6.]
                    =   [0., 1., 2.],   @    [0., 1., 2.],     =     [0., 3., 6.]
                        [0., 1., 2.]]        [0., 1., 2.]]           [0., 3., 6.]]
'''
'''a, b, c and d = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
a = torch.addmm(input=inputs, mat1=inputs_t, mat2=inputs_t)
b = inputs.addmm(mat1=inputs_t, mat2=inputs_t)
c = torch.addmm(input=inputs, beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
d = inputs.addmm(beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
'''e and f = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
e = torch.addmm(inputs, inputs_t, inputs_t)
f = inputs.addmm(inputs_t, inputs_t)
'''1 * inputs + 1 * (inputs_t @ inputs_t)'''
g = inputs.addmm(1, inputs_t, inputs_t)
'''2 * inputs + 1 * (inputs_t @ inputs_t)'''
g2 = inputs.addmm(2, inputs_t, inputs_t)
'''h = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
h = inputs.addmm(1, 1, inputs_t, inputs_t)
'''h12 = 1 * inputs + 2 * (inputs_t @ inputs_t)'''
h12 = inputs.addmm(1, 2, inputs_t, inputs_t)
'''h21 = 2 * inputs + 1 * (inputs_t @ inputs_t)'''
h21 = inputs.addmm(2, 1, inputs_t, inputs_t)
print("a:\n", a)
print("b:\n", b)
print("c:\n", c)
print("d:\n", d)
print("e:\n", e)
print("f:\n", f)
print("g:\n", g)
print("g2:\n", g2)
print("h:\n", h)
print("h12:\n", h12)
print("h21:\n", h21)
print("inputs:\n", inputs)
'''inputs = 1 * inputs - 2 * (inputs @ inputs_t)'''
'''
inputs @ inputs_t       [[0., 0., 0.],       [[0., 1., 2.],          [[0., 0., 0.]
                    =    [1., 1., 1.],   @    [0., 1., 2.],     =     [0., 3., 6.]
                         [2., 2., 2.]]        [0., 1., 2.]]           [0., 6., 12.]]
'''
inputs.addmm_(1, -2, inputs, inputs_t)  # In-place
print("inputs:\n", inputs)

2.其中

inputs是一个3×3的矩阵，为

tensor([[0., 0., 0.],
        [1., 1., 1.],
        [2., 2., 2.]])

inputs_t也是一个3×3的矩阵，是inputs的转置矩阵，为

tensor([[0., 1., 2.],
        [0., 1., 2.],
        [0., 1., 2.]])

* inputs_t @ inputs_t为

'''
inputs_t @ inputs_t    [[0., 1., 2.],       [[0., 1., 2.],          [[0., 3., 6.]
                    =   [0., 1., 2.],   @    [0., 1., 2.],     =     [0., 3., 6.]
                        [0., 1., 2.]]        [0., 1., 2.]]           [0., 3., 6.]]
'''

3.代码中a，b，c和d展示的是完全形式，即标明了位置参数和传入参数。可以看到input这个位置参数可以写在函数的前面，即

torch.addmm(input, mat1, mat2) = inputs.addmm(mat1, mat2)

完成的公式为：

1 × inputs + 1 ×（inputs_t @ inputs_t）

'''a, b, c and d = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
a = torch.addmm(input=inputs, mat1=inputs_t, mat2=inputs_t)
b = inputs.addmm(mat1=inputs_t, mat2=inputs_t)
c = torch.addmm(input=inputs, beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
d = inputs.addmm(beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)

a:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
b:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
c:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
d:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])

4.下面的例子更好了说明了input参数的位置可变性，并且beta和alpha都缺省了：

完成的公式为：

1 × inputs + 1 ×（inputs_t @ inputs_t）

'''e and f = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
e = torch.addmm(inputs, inputs_t, inputs_t)
f = inputs.addmm(inputs_t, inputs_t)

e:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
f:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])

5.加一个参数，实际上是添加了beta这个参数

完成的公式为：

g   = 1 × inputs + 1 ×（inputs_t @ inputs_t）

g2 = 2 × inputs + 1 ×（inputs_t @ inputs_t）

'''1 * inputs + 1 * (inputs_t @ inputs_t)'''
g = inputs.addmm(1, inputs_t, inputs_t)
'''2 * inputs + 1 * (inputs_t @ inputs_t)'''
g2 = inputs.addmm(2, inputs_t, inputs_t)

g:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
g2:
tensor([[ 0.,  3.,  6.],
        [ 2.,  5.,  8.],
        [ 4.,  7., 10.]])

6.再加一个参数，实际上是添加了alpha这个参数

完成的公式为：

h   = 1 × inputs + 1 ×（inputs_t @ inputs_t）

h12 = 1 × inputs + 2 ×（inputs_t @ inputs_t）

h21 = 2 × inputs + 1 ×（inputs_t @ inputs_t）

'''h = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
h = inputs.addmm(1, 1, inputs_t, inputs_t)
'''h12 = 1 * inputs + 2 * (inputs_t @ inputs_t)'''
h12 = inputs.addmm(1, 2, inputs_t, inputs_t)
'''h21 = 2 * inputs + 1 * (inputs_t @ inputs_t)'''
h21 = inputs.addmm(2, 1, inputs_t, inputs_t)

h:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
h12:
tensor([[ 0.,  6., 12.],
        [ 1.,  7., 13.],
        [ 2.,  8., 14.]])
h21:
tensor([[ 0.,  3.,  6.],
        [ 2.,  5.,  8.],
        [ 4.,  7., 10.]])

7.当然，以上的步骤inputs没有变化，还是为

inputs:
tensor([[0., 0., 0.],
        [1., 1., 1.],
        [2., 2., 2.]])

8.addmm_()的操作和addmm()函数功能相同，区别就是addmm_()有inplace的操作，也就是在原对象基础上进行修改，即把改变之后的变量再赋给原来的变量。例如：

inputs的值变成了改变之后的值，不用再去写 某个变量=addmm_() 了，因为inputs就是改变之后的变量！

*inputs@ inputs_t为

'''
inputs @ inputs_t       [[0., 0., 0.],       [[0., 1., 2.],          [[0., 0., 0.]
                    =    [1., 1., 1.],   @    [0., 1., 2.],     =     [0., 3., 6.]
                         [2., 2., 2.]]        [0., 1., 2.]]           [0., 6., 12.]]
'''

完成的公式为：

inputs   = 1 × inputs - 2 ×（inputs @ inputs_t）

'''inputs = 1 * inputs - 2 * (inputs @ inputs_t)'''
inputs.addmm_(1, -2, inputs, inputs_t)  # In-place

inputs:
tensor([[  0.,   0.,   0.],
        [  1.,  -5., -11.],
        [  2., -10., -22.]])

三、代码运行结果

inputs:
tensor([[0., 0., 0.],
        [1., 1., 1.],
        [2., 2., 2.]])
inputs_t:
tensor([[0., 1., 2.],
        [0., 1., 2.],
        [0., 1., 2.]])
a:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
b:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
c:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
d:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
e:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
f:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
g:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
g2:
tensor([[ 0.,  3.,  6.],
        [ 2.,  5.,  8.],
        [ 4.,  7., 10.]])
h:
tensor([[0., 3., 6.],
        [1., 4., 7.],
        [2., 5., 8.]])
h12:
tensor([[ 0.,  6., 12.],
        [ 1.,  7., 13.],
        [ 2.,  8., 14.]])
h21:
tensor([[ 0.,  3.,  6.],
        [ 2.,  5.,  8.],
        [ 4.,  7., 10.]])
inputs:
tensor([[0., 0., 0.],
        [1., 1., 1.],
        [2., 2., 2.]])
inputs:
tensor([[  0.,   0.,   0.],
        [  1.,  -5., -11.],
        [  2., -10., -22.]])

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