cumulative_trapezoid¶

paddle. cumulative_trapezoid ( y, x=None, dx=None, axis=- 1, name=None ) [source]

Integrate along the given axis using the composite trapezoidal rule. Use the cumsum method

Parameters

• y (Tensor) – Input tensor to integrate. It’s data type should be float16, float32, float64.

• x (Tensor, optional) – The sample points corresponding to the y values, the same type as y. It is known that the size of y is [d_1, d_2, … , d_n] and \(axis=k\), then the size of x can only be [d_k] or [d_1, d_2, … , d_n ]. If x is None, the sample points are assumed to be evenly spaced dx apart. The default is None.

• dx (float, optional) – The spacing between sample points when x is None. If neither x nor dx is provided then the default is \(dx = 1\).

• axis (int, optional) – The axis along which to integrate. The default is -1.

• name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, Definite integral of y is N-D tensor as approximated along a single axis by the trapezoidal rule. The result is an N-D tensor.

Examples

>>> import paddle

>>> y = paddle.to_tensor([4, 5, 6], dtype='float32')

>>> paddle.cumulative_trapezoid(y)
Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
[4.50000000, 10.       ])

>>> paddle.cumulative_trapezoid(y, dx=2.)
>>> # Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
>>> #        [9. , 20.])

>>> y = paddle.to_tensor([4, 5, 6], dtype='float32')
>>> x = paddle.to_tensor([1, 2, 3], dtype='float32')

>>> paddle.cumulative_trapezoid(y, x)
Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True,
[4.50000000, 10.       ])

>>> y = paddle.to_tensor([1, 2, 3], dtype='float64')
>>> x = paddle.to_tensor([8, 6, 4], dtype='float64')

>>> paddle.cumulative_trapezoid(y, x)
Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=True,
[-3., -8.])

>>> y = paddle.arange(6).reshape((2, 3)).astype('float32')

>>> paddle.cumulative_trapezoid(y, axis=0)
Tensor(shape=[1, 3], dtype=float32, place=Place(cpu), stop_gradient=True,
[[1.50000000, 2.50000000, 3.50000000]])
>>> paddle.cumulative_trapezoid(y, axis=1)
Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True,
[[0.50000000, 2.        ],
 [3.50000000, 8.        ]])