mvpa2.misc.errorfx.trapz¶
-
mvpa2.misc.errorfx.
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
The sample points corresponding to the
y
values. Ifx
is None, the sample points are assumed to be evenly spaceddx
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.
See also
sum
,cumsum
Notes
Image [R20] 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 withx
array or withdx
scalar. Return value will be equal to combined area under the red lines.References
[R19] Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule [R20] (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.])