- mars.tensor.trapz(y, x=None, dx=1.0, axis=- 1)¶
Integrate along the given axis using the composite trapezoidal rule.
Integrate y (x) along given axis.
y (array_like) – Input tensor to integrate.
x (array_like, optional) – The sample points corresponding to the y values. If x is None, the sample points are assumed to be evenly spaced dx apart. The default is None.
dx (scalar, optional) – The spacing between sample points when x is None. The default is 1.
axis (int, optional) – The axis along which to integrate.
trapz – Definite integral as approximated by trapezoidal rule.
- Return type
Image 2 illustrates trapezoidal rule – y-axis locations of points will be taken from y tensor, by default x-axis distances between points will be 1.0, alternatively they can be provided with x tensor or with dx scalar. Return value will be equal to combined area under the red lines.
Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule
Illustration image: https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png
>>> import mars.tensor as mt >>> mt.trapz([1,2,3]).execute() 4.0 >>> mt.trapz([1,2,3], x=[4,6,8]).execute() 8.0 >>> mt.trapz([1,2,3], dx=2).execute() 8.0 >>> a = mt.arange(6).reshape(2, 3) >>> a.execute() array([[0, 1, 2], [3, 4, 5]]) >>> mt.trapz(a, axis=0).execute() array([1.5, 2.5, 3.5]) >>> mt.trapz(a, axis=1).execute() array([2., 8.])