scipy.optimize.

rosen#

scipy.optimize.rosen(x)[source]#

The Rosenbrock function.

The function computed is:

sum(100.0*(x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0)

Parameters:

xarray_like: 1-D array of points at which the Rosenbrock function is to be computed.

Returns:

ffloat: The value of the Rosenbrock function.

See also

rosen_der, rosen_hess, rosen_hess_prod

Notes

Array API Standard Support

rosen has support for Python Array API Standard compatible backends in addition to NumPy. 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

>>> import numpy as np
>>> from scipy.optimize import rosen
>>> X = 0.1 * np.arange(10)
>>> rosen(X)
76.56

For higher-dimensional input rosen broadcasts. In the following example, we use this to plot a 2D landscape. Note that rosen_hess does not broadcast in this manner.

>>> import matplotlib.pyplot as plt
>>> from mpl_toolkits.mplot3d import Axes3D
>>> x = np.linspace(-1, 1, 50)
>>> X, Y = np.meshgrid(x, x)
>>> ax = plt.subplot(111, projection='3d')
>>> ax.plot_surface(X, Y, rosen([X, Y]))
>>> plt.show()

../../_images/scipy-optimize-rosen-1.png