design-2d-covariance-matrix.py

def covar_2d(e, s):
  """Returns a 2D covariance matrix with main diagonal in direction e and second diagonal perpendicular to e with proportional length s.

  Params:
  -------
  e: array-like
    Direction of the main diagonal.
  s: float
    Proportional scale of the second diagonal.

  Returns:
  --------
  cov : ndarray
    A psd matrix with the properties defined above.

  Example:
  --------

    >>> covar_2d([1,5], .3)
    matrix([[ 0.32692308,  0.13461538],
            [ 0.13461538,  0.97307692]])

    >>> X = np.random.multivariate_normal([0,0], covar_2d([1,5], .3), 10000)
    >>> pylab.scatter(X[:,0], X[:,1])
  """
  Q = np.matrix([e[:2], [e[1], -e[0]]])
  return Q * np.matrix([[1, 0], [0, s]]) * np.linalg.inv(Q)