torch.cumulative_trapezoid

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

累积计算沿 dim 的梯形法则。默认情况下，元素之间的间距假设为 1，但可以使用 dx 指定不同的常数间距，使用 x 可以指定沿 dim 的任意间距。

更多详情，请参阅 torch.trapezoid() 。与 torch.trapezoid() 函数的区别在于， torch.trapezoid() 为每次积分返回一个值，而此函数返回积分中每个间距的累积值。这与.sum 返回一个值和.cumsum 返回累积和的方式类似。

参数:

• y（张量）- 计算梯形法则时使用的值。

• x（张量）- 如果指定，则定义上述值之间的间距。

关键字参数:

• dx（浮点数）- 值之间的常数间距。如果没有指定 x 或 dx ，则默认为 1。实际上将结果乘以其值。

• dim（整数）- 计算梯形法则的维度。默认为最内层维度。

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.]])