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

Array API Standard Support

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

>>> integrate.romb([[1, 2, 3], [4, 5, 6]], show=True)
*** Printing table only supported for integrals of a single data set.
array([ 4., 10.])