1""" 2Copyright, the CVXPY authors 3 4Licensed under the Apache License, Version 2.0 (the "License"); 5you may not use this file except in compliance with the License. 6You may obtain a copy of the License at 7 8 http://www.apache.org/licenses/LICENSE-2.0 9 10Unless required by applicable law or agreed to in writing, software 11distributed under the License is distributed on an "AS IS" BASIS, 12WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13See the License for the specific language governing permissions and 14limitations under the License. 15""" 16from cvxpy.atoms.elementwise.inv_pos import inv_pos 17from cvxpy.atoms.elementwise.power import power 18from cvxpy.atoms.geo_mean import geo_mean 19 20 21def inv_prod(value): 22 """The reciprocal of a product of the entries of a vector ``x``. 23 24 Parameters 25 ---------- 26 x : Expression or numeric 27 The expression whose reciprocal product is to be computed. Must have 28 positive entries. 29 30 Returns 31 ------- 32 Expression 33 .. math:: 34 \\left(\\prod_{i=1}^n x_i\\right)^{-1}, 35 36 where :math:`n` is the length of :math:`x`. 37 """ 38 return power(inv_pos(geo_mean(value)), sum(value.shape)) 39