# [SciPy-User] scipy.interpolate.rbf: how is "smooth" defined?

Gael Varoquaux gael.varoquaux@normalesup....
Mon Aug 30 11:22:29 CDT 2010

```On Mon, Aug 30, 2010 at 12:18:58PM -0400, josef.pktd@gmail.com wrote:
> Please do, I can also use it for other things. (I never read the small
> print in Ledoit-Wolf.)

There you go (BSD licensed). This will land in scikit learn at some point
because we are going to need it in different places, but I haven't found
the time to polish it.

Gael

def ledoit_wolf(x, return_factor=False):
""" Estimates the shrunk Ledoit-Wolf covariance matrix.

Parameters
----------
x: 2D ndarray, shape (n, p)
The data matrix, with p features and n samples.
return_factor: boolean, optional
If return_factor is True, the regularisation_factor is
returned.

Returns
-------
regularised_cov: 2D ndarray
Regularized covariance
regularisation_factor: float
Regularisation factor

Notes
-----
The regularised covariance is::

(1 - regularisation_factor)*cov
+ regularisation_factor*np.identity(n_features)
"""
n_samples, n_features = x.shape
if n_features == 1:
if return_factor:
return np.atleast_2d(x.std()), 0
return np.atleast_2d(x.std())
cov = np.dot(x.T, x)/n_samples
i = np.identity(n_features)
mu = np.trace(cov)/n_features
delta = ((cov - mu*i)**2).sum()/n_features
x2 = x**2
beta_ = 1./(n_features*n_samples) * np.sum(
np.dot(x2.T, x2)/n_samples - cov**2
)

beta = min(beta_, delta)
alpha = delta - beta
if not return_factor:
return beta/delta * mu * i + alpha/delta * cov
else:
return beta/delta * mu * i + alpha/delta * cov, beta/delta

```