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.

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.

`numpy.cumsum`, `numpy.cumprod`
`cumulative_simpson`

cumulative integration using Simpson’s 1/3 rule

`quad`

`fixed_quad`

`dblquad`

double integrals

`tplquad`

triple integrals

`romb`

integrators for sampled data

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()
```