numpy.trapz¶

numpy.trapz(y,x=None,dx=1.0,axis=-1)[source]¶

Integrate along the given axis using the composite trapezoidal rule.

Integratey (x) along given axis.

Parameters:	y:array_like Input array to integrate. x:array_like, optional The sample points corresponding to they values. Ifx is None,the sample points are assumed to be evenly spaceddx apart. Thedefault is None. dx:scalar, optional The spacing between sample points whenx 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[2] illustrates trapezoidal rule – y-axis locations of pointswill be taken fromy array, by default x-axis distances betweenpoints will be 1.0, alternatively they can be provided withx arrayor withdx scalar. Return value will be equal to combined area underthe red lines.

References

[1]	Wikipedia page:http://en.wikipedia.org/wiki/Trapezoidal_rule

[2]	(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)>>>aarray([[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.])