# Source code for cvxpy.atoms.harmonic_mean

"""

you may not use this file except in compliance with the License.
You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
"""

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)