scipy.integrate.

romb#

scipy.integrate.romb(y, dx=1.0, axis=-1, show=False)[source]#

Romberg integration using samples of a function.

Parameters:
yarray_like

A vector of 2**k + 1 equally-spaced samples of a function.

dxfloat, optional

The sample spacing. Default is 1.

axisint, optional

The axis along which to integrate. Default is -1 (last axis).

showbool, optional

When y is a single 1-D array, then if this argument is True print the table showing Richardson extrapolation from the samples. Default is False.

Returns:
rombndarray

The integrated result for axis.

See also

quad

adaptive quadrature using QUADPACK

fixed_quad

fixed-order Gaussian quadrature

dblquad

double integrals

tplquad

triple integrals

simpson

integrators for sampled data

cumulative_trapezoid

cumulative integration for sampled data

Notes

romb has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library

CPU

GPU

NumPy

n/a

CuPy

n/a

PyTorch

JAX

Dask

n/a

See Support for the array API standard for more information.

Examples

>>> from scipy import integrate
>>> import numpy as np
>>> x = np.arange(10, 14.25, 0.25)
>>> y = np.arange(3, 12)
>>> integrate.romb(y)
56.0
>>> y = np.sin(np.power(x, 2.5))
>>> integrate.romb(y)
-0.742561336672229
>>> integrate.romb(y, show=True)
Richardson Extrapolation Table for Romberg Integration
======================================================
-0.81576
 4.63862  6.45674
-1.10581 -3.02062 -3.65245
-2.57379 -3.06311 -3.06595 -3.05664
-1.34093 -0.92997 -0.78776 -0.75160 -0.74256
======================================================
-0.742561336672229  # may vary