torch.cumulative_trapezoid

torch.cumulative_trapezoid(y, x=None, *, dx=None, dim=-1) → Tensor

沿dim维度累积计算梯形规则。默认情况下，元素之间的间距为1，但可以通过dx指定不同的常量间距，或者通过x指定沿dim的任意间距。

更多详细信息，请阅读torch.trapezoid()。与这个函数不同的是，torch.trapezoid()为每个积分返回一个值，而此函数则在每个间隔内返回累积值。这类似于.sum 返回单个值和.cumsum 返回累积和的方式。

参数

y (Tensor) – 计算梯形法则时使用的值。
x (Tensor) – 如果指定了 x，则定义了值之间的间隔。

关键字参数

dx (float) – 值之间的常量间隔。如果未指定 x 或 dx，则默认为 1。实际上会将其值乘到结果上。
dim (int) – 计算梯形规则的维度，默认为最后一维（最内层维度）。

示例:

>>> # Cumulatively computes the trapezoidal rule in 1D, spacing is implicitly 1.
>>> y = torch.tensor([1, 5, 10])
>>> torch.cumulative_trapezoid(y)
tensor([3., 10.5])

>>> # Computes the same trapezoidal rule directly up to each element to verify
>>> (1 + 5) / 2
3.0
>>> (1 + 10 + 10) / 2
10.5

>>> # Cumulatively computes the trapezoidal rule in 1D with constant spacing of 2
>>> # NOTE: the result is the same as before, but multiplied by 2
>>> torch.cumulative_trapezoid(y, dx=2)
tensor([6., 21.])

>>> # Cumulatively computes the trapezoidal rule in 1D with arbitrary spacing
>>> x = torch.tensor([1, 3, 6])
>>> torch.cumulative_trapezoid(y, x)
tensor([6., 28.5])

>>> # Computes the same trapezoidal rule directly up to each element to verify
>>> ((3 - 1) * (1 + 5)) / 2
6.0
>>> ((3 - 1) * (1 + 5) + (6 - 3) * (5 + 10)) / 2
28.5

>>> # Cumulatively 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.cumulative_trapezoid(y)
tensor([[ 0.5,  2.],
        [ 3.5,  8.],
        [ 6.5, 14.]])

>>> # Cumulatively computes the trapezoidal rule for each column of the matrix
>>> torch.cumulative_trapezoid(y, dim=0)
tensor([[ 1.5,  2.5,  3.5],
        [ 6.0,  8.0, 10.0]])

>>> # Cumulatively 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.cumulative_trapezoid(y, x)
tensor([[2., 5.],
        [2., 5.],
        [2., 5.]])

>>> # Cumulatively 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.cumulative_trapezoid(y, x)
tensor([[1., 2.],
        [2., 4.],
        [3., 6.]])