numpy.trapz¶
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numpy.
trapz
(y, x=None, dx=1.0, axis=-1)[source]¶ Integrate along the given axis using the composite trapezoidal rule.
Integrate y (x) along given axis.
Parameters: y : array_like
Input array 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.
Returns: trapz : float
Definite integral as approximated by trapezoidal rule.
Notes
Image [R296] 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
[R295] Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule [R296] (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.])