SciPy

scipy.integrate.cumtrapzΒΆ

scipy.integrate.cumtrapz(y, x=None, dx=1.0, axis=-1, initial=None)[source]ΒΆ

Cumulatively integrate y(x) using the composite trapezoidal rule.

Parameters:

y : array_like

Values to integrate.

x : array_like, optional

The coordinate to integrate along. If None (default), use spacing dx between consecutive elements in y.

dx : int, optional

Spacing between elements of y. Only used if x is None.

axis : int, optional

Specifies the axis to cumulate. Default is -1 (last axis).

initial : scalar, optional

If given, uses this value as the first value in the returned result. Typically this value should be 0. Default is None, which means no value at x[0] is returned and res has one element less than y along the axis of integration.

Returns:

res : ndarray

The result of cumulative integration of y along axis. If initial is None, the shape is such that the axis of integration has one less value than y. If initial is given, the shape is equal to that of y.

See also

numpy.cumsum, numpy.cumprod

quad
adaptive quadrature using QUADPACK
romberg
adaptive Romberg quadrature
quadrature
adaptive Gaussian quadrature
fixed_quad
fixed-order Gaussian quadrature
dblquad
double integrals
tplquad
triple integrals
romb
integrators for sampled data
ode
ODE integrators
odeint
ODE integrators

Examples

>>> from scipy import integrate
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-2, 2, num=20)
>>> y = x
>>> y_int = integrate.cumtrapz(y, x, initial=0)
>>> plt.plot(x, y_int, 'ro', x, y[0] + 0.5 * x**2, 'b-')
>>> plt.show()

(Source code)

../_images/scipy-integrate-cumtrapz-1.png