torch.trapezoid¶
- torch.trapezoid(y, x=None, *, dx=None, dim=-1) Tensor ¶
沿着
dim
计算 梯形法则。默认情况下,假定元素之间的间距为 1,但可以使用dx
指定不同的恒定间距,并且可以使用x
指定沿着dim
的任意间距。假设
y
是一个一维张量,其元素为 , 则默认计算为当指定
dx
时,计算变为实际上就是将结果乘以
dx
。当指定x
时,假设x
也是一个一维张量,元素为 , 则计算变为当
x
和y
的大小相同时,计算如上所述,不需要广播。当它们的大小不同时,此函数的广播行为如下。对于x
和y
,函数计算沿维度dim
的连续元素之间的差。这实际上创建了两个张量,x_diff 和 y_diff,它们具有与原始张量相同的形状,除了它们沿维度dim
的长度减少了 1。之后,这两个张量一起广播以计算作为梯形法则的一部分的最终输出。有关详细信息,请参见下面的示例。注意
梯形法则是一种通过对左右黎曼和取平均值来逼近函数定积分的技术。随着划分分辨率的提高,近似值变得更加准确。
- 参数
- 关键字参数
示例
>>> # Computes the trapezoidal rule in 1D, spacing is implicitly 1 >>> y = torch.tensor([1, 5, 10]) >>> torch.trapezoid(y) tensor(10.5) >>> # Computes the same trapezoidal rule directly to verify >>> (1 + 10 + 10) / 2 10.5 >>> # Computes the trapezoidal rule in 1D with constant spacing of 2 >>> # NOTE: the result is the same as before, but multiplied by 2 >>> torch.trapezoid(y, dx=2) 21.0 >>> # Computes the trapezoidal rule in 1D with arbitrary spacing >>> x = torch.tensor([1, 3, 6]) >>> torch.trapezoid(y, x) 28.5 >>> # Computes the same trapezoidal rule directly to verify >>> ((3 - 1) * (1 + 5) + (6 - 3) * (5 + 10)) / 2 28.5 >>> # Computes the trapezoidal rule for each row of a 3x3 matrix >>> y = torch.arange(9).reshape(3, 3) tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> torch.trapezoid(y) tensor([ 2., 8., 14.]) >>> # Computes the trapezoidal rule for each column of the matrix >>> torch.trapezoid(y, dim=0) tensor([ 6., 8., 10.]) >>> # Computes the trapezoidal rule for each row of a 3x3 ones matrix >>> # with the same arbitrary spacing >>> y = torch.ones(3, 3) >>> x = torch.tensor([1, 3, 6]) >>> torch.trapezoid(y, x) array([5., 5., 5.]) >>> # Computes the trapezoidal rule for each row of a 3x3 ones matrix >>> # with different arbitrary spacing per row >>> y = torch.ones(3, 3) >>> x = torch.tensor([[1, 2, 3], [1, 3, 5], [1, 4, 7]]) >>> torch.trapezoid(y, x) array([2., 4., 6.])