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scipy.optimize.

# rosen

scipy.optimize.rosen(x)

  The Rosenbrock function.

  The function computed is:

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

  Parameters:
    x array_like

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

  Returns:
    f float

      The value of the Rosenbrock function.

  See also

  `rosen_der`, `rosen_hess`, `rosen_hess_prod`

  Notes

  `rosen` 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

      >>> 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()