Integrate along the given axis using the composite trapezoidal rule.
Integrate y (x) along given axis.
Parameters : | y : array_like
x : array_like, optional
dx : scalar, optional
axis : int, optional
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Returns : | out : float
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See also
sum, cumsum
Notes
Image [R3] illustrates trapezoidal rule – y-axis locations of points will be taken from y array, by default x-axis distances between points will be 1.0, alternatively they can be provided with x array or with dx scalar. Return value will be equal to combined area under the red lines.
References
[R2] | Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule |
[R3] | (1, 2) Illustration image: http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png |
Examples
>>> np.trapz([1,2,3])
4.0
>>> np.trapz([1,2,3], x=[4,6,8])
8.0
>>> np.trapz([1,2,3], dx=2)
8.0
>>> a = np.arange(6).reshape(2, 3)
>>> a
array([[0, 1, 2],
[3, 4, 5]])
>>> np.trapz(a, axis=0)
array([ 1.5, 2.5, 3.5])
>>> np.trapz(a, axis=1)
array([ 2., 8.])