Source code for cvxpy.atoms.harmonic_mean

"""

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
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)