cumulative_trapezoid(y, x=None, dx=1.0, axis=-1, initial=None)

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 : float, 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, insert this value at the beginning of the returned result. Typically this value should be 0. Default is None, which means no value at x[0] is returned and :None:None:`res` has one element less than y along the axis of integration.

Returns

res : ndarray

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

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

See Also

dblquad

double integrals

fixed_quad

fixed-order Gaussian quadrature

numpy.cumprod

numpy.cumsum

ode

ODE integrators

odeint

ODE integrators

quad

adaptive quadrature using QUADPACK

quadrature

adaptive Gaussian quadrature

romb

integrators for sampled data

romberg

adaptive Romberg quadrature

tplquad

triple integrals

Examples

>>> from scipy import integrate
... import matplotlib.pyplot as plt

>>> x = np.linspace(-2, 2, num=20)
... y = x
... y_int = integrate.cumulative_trapezoid(y, x, initial=0)
... plt.plot(x, y_int, 'ro', x, y[0] + 0.5 * x**2, 'b-')
... plt.show()

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.integrate._quadrature.simpson scipy.integrate._quadrature.quadrature scipy.integrate._quadrature.romb scipy.integrate._quadrature.fixed_quad scipy.integrate._quadrature.cumulative_trapezoid scipy.integrate._quadrature.cumtrapz scipy.integrate._quadrature.romberg

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