Pytorch深度学习addmm()和addmm_()函数用法解析
作者:悲恋花丶无心之人
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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