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3.4.2 Integrating functions, given fixed samples
SciPy Reference Guide, Release 0.8.dev
trapz(y[, x, dx, axis]) Integrate along the given axis using the composite trapezoidal rule.
cumtrapz(y[, x, dx, Cumulatively integrate y(x) using samples along the given axis and the composite
axis])
trapezoidal rule.
simps(y[, x, dx, axis,
even])
Integrate y(x) using samples along the given axis and the composite
romb(y[, dx, axis,
show])
Romberg integration using samples of a function
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.
See Also:
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
Returns
out : float
sum, cumsum
Notes
Specify the axis.
Definite integral as approximated by trapezoidal rule.
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], [R3]
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]])
3.4. Integration and ODEs (scipy.integrate) 183