scipy.integrate.trapz

scipy.integrate.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.

Parameters:

y : array_like

Input array to integrate.

x : array_like, optional

If x is None, then spacing between all y elements is dx.

dx : scalar, optional

If x is None, spacing given by dx is assumed. Default is 1.

axis : int, optional

Specify the axis.

Returns:

trapz : float

Definite integral as approximated by trapezoidal rule.

See also

sum, cumsum

Notes

Image [R42] 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

[R41]

Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule

[R42]

(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.])