# Source code for cvxpy.atoms.harmonic_mean

"""
Copyright 2013 Steven Diamond
This file is part of CVXPY.
CVXPY is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
CVXPY is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with CVXPY. If not, see <http://www.gnu.org/licenses/>.
"""
from cvxpy.atoms.pnorm import pnorm
from cvxpy.expressions.expression import Expression
[docs]def harmonic_mean(x):
"""The harmonic mean of ``x``.
Parameters
----------
x : Expression or numeric
The expression whose harmonic mean is to be computed. Must have
positive entries.
Returns
-------
Expression
.. math::
\\frac{n}{\\left(\\sum_{i=1}^{n} x_i^{-1} \\right)},
where :math:`n` is the length of :math:`x`.
"""
x = Expression.cast_to_const(x)
# TODO(akshayka): Behavior of the below is incorrect when x has negative
# entries. Either fail fast or provide a correct expression with
# unknown curvature.
return x.size*pnorm(x, -1)