scipy.integrate.cumtrapz

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

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
>>> 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()