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~
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def addmm(self, beta=1, mat, alpha=1, mat1, mat2, out=None): # real signature unknown; restored from __doc__
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"""
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addmm(beta=1, mat, alpha=1, mat1, mat2, out=None) -> Tensor
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Performs a matrix multiplication of the matrices :attr:`mat1` and :attr:`mat2`.
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The matrix :attr:`mat` is added to the final result.
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If :attr:`mat1` is a :math:`(n \times m)` tensor, :attr:`mat2` is a
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:math:`(m \times p)` tensor, then :attr:`mat` must be
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:ref:`broadcastable <broadcasting-semantics>` with a :math:`(n \times p)` tensor
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and :attr:`out` will be a :math:`(n \times p)` tensor.
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:attr:`alpha` and :attr:`beta` are scaling factors on matrix-vector product between
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:attr:`mat1` and :attr`mat2` and the added matrix :attr:`mat` respectively.
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.. math::
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out = \beta\ mat + \alpha\ (mat1_i \mathbin{@} mat2_i)
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For inputs of type `FloatTensor` or `DoubleTensor`, arguments :attr:`beta` and
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:attr:`alpha` must be real numbers, otherwise they should be integers.
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Args:
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beta (Number, optional): multiplier for :attr:`mat` (:math:`\beta`)
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mat (Tensor): matrix to be added
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alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
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mat1 (Tensor): the first matrix to be multiplied
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mat2 (Tensor): the second matrix to be multiplied
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out (Tensor, optional): the output tensor
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Example::
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>>> M = torch.randn(2, 3)
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>>> mat1 = torch.randn(2, 3)
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>>> mat2 = torch.randn(3, 3)
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>>> torch.addmm(M, mat1, mat2)
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tensor([[-4.8716, 1.4671, -1.3746],
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[ 0.7573, -3.9555, -2.8681]])
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"""
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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
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"""
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@author:nickhuang1996
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"""
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import torch
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rectangle_height = 3
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rectangle_width = 3
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inputs = torch.randn(rectangle_height, rectangle_width)
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for i in range(rectangle_height):
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for j in range(rectangle_width):
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inputs[i] = i * torch.ones(rectangle_width)
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'''
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inputs and its transpose
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-->inputs = tensor([[0., 0., 0.],
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[1., 1., 1.],
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[2., 2., 2.]])
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-->inputs_t = tensor([[0., 1., 2.],
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[0., 1., 2.],
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[0., 1., 2.]])
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'''
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print("inputs:\n", inputs)
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inputs_t = inputs.t()
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print("inputs_t:\n", inputs_t)
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'''
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inputs_t @ inputs_t [[0., 1., 2.], [[0., 1., 2.], [[0., 3., 6.]
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= [0., 1., 2.], @ [0., 1., 2.], = [0., 3., 6.]
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[0., 1., 2.]] [0., 1., 2.]] [0., 3., 6.]]
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'''
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'''a, b, c and d = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
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a = torch.addmm(input=inputs, mat1=inputs_t, mat2=inputs_t)
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b = inputs.addmm(mat1=inputs_t, mat2=inputs_t)
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c = torch.addmm(input=inputs, beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
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d = inputs.addmm(beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
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'''e and f = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
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e = torch.addmm(inputs, inputs_t, inputs_t)
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f = inputs.addmm(inputs_t, inputs_t)
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'''1 * inputs + 1 * (inputs_t @ inputs_t)'''
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g = inputs.addmm(1, inputs_t, inputs_t)
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'''2 * inputs + 1 * (inputs_t @ inputs_t)'''
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g2 = inputs.addmm(2, inputs_t, inputs_t)
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'''h = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
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h = inputs.addmm(1, 1, inputs_t, inputs_t)
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'''h12 = 1 * inputs + 2 * (inputs_t @ inputs_t)'''
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h12 = inputs.addmm(1, 2, inputs_t, inputs_t)
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'''h21 = 2 * inputs + 1 * (inputs_t @ inputs_t)'''
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h21 = inputs.addmm(2, 1, inputs_t, inputs_t)
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print("a:\n", a)
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print("b:\n", b)
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print("c:\n", c)
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print("d:\n", d)
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print("e:\n", e)
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print("f:\n", f)
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print("g:\n", g)
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print("g2:\n", g2)
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print("h:\n", h)
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print("h12:\n", h12)
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print("h21:\n", h21)
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print("inputs:\n", inputs)
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'''inputs = 1 * inputs - 2 * (inputs @ inputs_t)'''
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'''
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inputs @ inputs_t [[0., 0., 0.], [[0., 1., 2.], [[0., 0., 0.]
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= [1., 1., 1.], @ [0., 1., 2.], = [0., 3., 6.]
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[2., 2., 2.]] [0., 1., 2.]] [0., 6., 12.]]
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'''
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inputs.addmm_(1, -2, inputs, inputs_t) # In-place
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print("inputs:\n", inputs)
2.其中
inputs是一个3×3的矩阵，为
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tensor([[0., 0., 0.],
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[1., 1., 1.],
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[2., 2., 2.]])
inputs_t也是一个3×3的矩阵，是inputs的转置矩阵，为
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tensor([[0., 1., 2.],
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[0., 1., 2.],
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[0., 1., 2.]])
* inputs_t @ inputs_t为
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'''
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inputs_t @ inputs_t [[0., 1., 2.], [[0., 1., 2.], [[0., 3., 6.]
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= [0., 1., 2.], @ [0., 1., 2.], = [0., 3., 6.]
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[0., 1., 2.]] [0., 1., 2.]] [0., 3., 6.]]
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'''
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）
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'''a, b, c and d = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
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a = torch.addmm(input=inputs, mat1=inputs_t, mat2=inputs_t)
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b = inputs.addmm(mat1=inputs_t, mat2=inputs_t)
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c = torch.addmm(input=inputs, beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
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d = inputs.addmm(beta=1, mat1=inputs_t, mat2=inputs_t, alpha=1)
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a:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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b:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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c:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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d:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[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）
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'''e and f = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
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e = torch.addmm(inputs, inputs_t, inputs_t)
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f = inputs.addmm(inputs_t, inputs_t)
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e:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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f:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[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）
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'''1 * inputs + 1 * (inputs_t @ inputs_t)'''
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g = inputs.addmm(1, inputs_t, inputs_t)
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'''2 * inputs + 1 * (inputs_t @ inputs_t)'''
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g2 = inputs.addmm(2, inputs_t, inputs_t)
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g:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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g2:
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tensor([[ 0., 3., 6.],
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[ 2., 5., 8.],
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[ 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）
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'''h = 1 * inputs + 1 * (inputs_t @ inputs_t)'''
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h = inputs.addmm(1, 1, inputs_t, inputs_t)
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'''h12 = 1 * inputs + 2 * (inputs_t @ inputs_t)'''
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h12 = inputs.addmm(1, 2, inputs_t, inputs_t)
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'''h21 = 2 * inputs + 1 * (inputs_t @ inputs_t)'''
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h21 = inputs.addmm(2, 1, inputs_t, inputs_t)
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h:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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h12:
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tensor([[ 0., 6., 12.],
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[ 1., 7., 13.],
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[ 2., 8., 14.]])
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h21:
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tensor([[ 0., 3., 6.],
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[ 2., 5., 8.],
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[ 4., 7., 10.]])
7.当然，以上的步骤inputs没有变化，还是为
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inputs:
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tensor([[0., 0., 0.],
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[1., 1., 1.],
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[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
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'''
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inputs @ inputs_t [[0., 0., 0.], [[0., 1., 2.], [[0., 0., 0.]
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= [1., 1., 1.], @ [0., 1., 2.], = [0., 3., 6.]
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[2., 2., 2.]] [0., 1., 2.]] [0., 6., 12.]]
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'''
完成的公式为：
inputs = 1 × inputs - 2 ×（inputs @ inputs_t）
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'''inputs = 1 * inputs - 2 * (inputs @ inputs_t)'''
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inputs.addmm_(1, -2, inputs, inputs_t) # In-place
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inputs:
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tensor([[ 0., 0., 0.],
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[ 1., -5., -11.],
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[ 2., -10., -22.]])
三、代码运行结果
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inputs:
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tensor([[0., 0., 0.],
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[1., 1., 1.],
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[2., 2., 2.]])
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inputs_t:
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tensor([[0., 1., 2.],
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[0., 1., 2.],
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[0., 1., 2.]])
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a:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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b:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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c:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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d:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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e:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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f:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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g:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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g2:
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tensor([[ 0., 3., 6.],
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[ 2., 5., 8.],
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[ 4., 7., 10.]])
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h:
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tensor([[0., 3., 6.],
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[1., 4., 7.],
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[2., 5., 8.]])
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h12:
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tensor([[ 0., 6., 12.],
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[ 1., 7., 13.],
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[ 2., 8., 14.]])
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h21:
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tensor([[ 0., 3., 6.],
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[ 2., 5., 8.],
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[ 4., 7., 10.]])
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inputs:
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tensor([[0., 0., 0.],
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[1., 1., 1.],
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[2., 2., 2.]])
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inputs:
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tensor([[ 0., 0., 0.],
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[ 1., -5., -11.],
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[ 2., -10., -22.]])
文章来源: nickhuang1996.blog.csdn.net，作者：悲恋花丶无心之人，版权归原作者所有，如需转载，请联系作者。
原文链接：nickhuang1996.blog.csdn.net/article/details/90638449