scipy.integrate.cumulative_trapezoid#

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

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

Parameters:

yarray_like: Values to integrate.
xarray_like, optional: The coordinate to integrate along. If None (default), use spacing dx between consecutive elements in y.
dxfloat, optional: Spacing between elements of y. Only used if x is None.
axisint, optional: Specifies the axis to cumulate. Default is -1 (last axis).
initialscalar, optional: If given, insert this value at the beginning of the returned result. 0 or None are the only values accepted. Default is None, which means res has one element less than y along the axis of integration.

Deprecated since version 1.12.0: The option for non-zero inputs for initial will be deprecated in SciPy 1.15.0. After this time, a ValueError will be raised if initial is not None or 0.

Returns:

resndarray: 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
cumulative_simpson: cumulative integration using Simpson’s 1/3 rule
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 numpy as np
>>> 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()

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