torch.cumulative_trapezoid

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

沿 dim 累积计算 梯形法则。默认情况下，元素之间的间隔假定为 1，但 dx 可用于指定不同的恒定间隔，x 可用于沿 dim 指定任意间隔。

更多详情，请参阅 torch.trapezoid()。 torch.trapezoid() 和此函数之间的区别在于，torch.trapezoid() 为每次积分返回一个值，而此函数为积分内的每个间隔返回一个累积值。这类似于 .sum 返回一个值而 .cumsum 返回一个累积和。

参数

• y (Tensor) – 计算梯形法则时使用的值。

• x (Tensor) – 如果指定，则如上定义值之间的间隔。

关键字参数

• dx (float) – 值之间的恒定间隔。如果未指定 x 或 dx，则默认为 1。有效地将结果乘以其值。

• dim (int) – 计算梯形法则的维度。默认为最后一个（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.]])