Source code for idaes.core.util.math

# -*- coding: UTF-8 -*-
##############################################################################
# Institute for the Design of Advanced Energy Systems Process Systems
# Engineering Framework (IDAES PSE Framework) Copyright (c) 2018-2019, by the
# software owners: The Regents of the University of California, through
# Lawrence Berkeley National Laboratory,  National Technology & Engineering
# Solutions of Sandia, LLC, Carnegie Mellon University, West Virginia
# University Research Corporation, et al. All rights reserved.
#
# Please see the files COPYRIGHT.txt and LICENSE.txt for full copyright and
# license information, respectively. Both files are also available online
# at the URL "https://github.com/IDAES/idaes-pse".
##############################################################################
"""
This module contains utility functions for mathematical operators of use in
equation oriented models.
"""

from pyomo.environ import Param

__author__ = "Andrew Lee"


[docs]def smooth_abs(a, eps=1e-4): """General function for creating an expression for a smooth minimum or maximum. .. math:: |a| = sqrt(a^2 + eps^2) Args: a : term to get absolute value from (Pyomo component, float or int) eps : smoothing parameter (Param, float or int) (default=1e-4) Returns: An expression for the smoothed absolute value operation. """ # Check type of eps if not (isinstance(eps, (float, int, Param))): raise TypeError("smooth_abs eps argument must be a float, int or " "Pyomo Param") # Create expression try: expr = (a**2 + eps**2)**0.5 except TypeError: raise TypeError("Unsupported argument type for smooth_abs. Must be " "a Pyomo Var, Param or Expression, or a float or int.") return expr
[docs]def smooth_minmax(a, b, eps=1e-4, sense='max'): """General function for creating an expression for a smooth minimum or maximum. Uses the smooth_abs operator. .. math:: minmax(a, b) = 0.5*(a+b +- |a-b|) Args: a : first term in mix or max function (Pyomo component, float or int) b : second term in min or max function (Pyomo component, float or int) eps : smoothing parameter (Param, float or int) (default=1e-4) sense : 'mim' or 'max' (default = 'max') Returns: An expression for the smoothed minimum or maximum operation. """ # Check type of eps if not (isinstance(eps, (float, int, Param))): raise TypeError("Smooth {} eps argument must be a float, int or " "Pyomo Param".format(sense)) # Set sense of expression if sense == 'max': mm = 1 elif sense == 'min': mm = -1 else: raise ValueError("Unrecognised sense argument to smooth_minmax. " "Must be 'min' or 'max'.") # Create expression try: expr = 0.5*(a+b+mm*smooth_abs(a-b, eps)) except TypeError: raise TypeError("Unsupported argument type for smooth_{}. Must be " "a Pyomo Var, Param or Expression, or a float or int." .format(sense)) return expr
[docs]def smooth_max(a, b, eps=1e-4): """Smooth maximum operator, using smooth_abs operator. .. math:: max(a, b) = 0.5*(a+b + |a-b|) Args: a : first term in max function b : second term in max function eps : smoothing parameter (Param or float, default = 1e-4) Returns: An expression for the smoothed maximum operation. """ expr = smooth_minmax(a, b, eps, sense='max') return expr
[docs]def smooth_min(a, b, eps=1e-4): """Smooth minimum operator, using smooth_abs operator. .. math:: max(a, b) = 0.5*(a+b - |a-b|) Args: a : first term in min function b : second term in min function eps : smoothing parameter (Param or float, default = 1e-4) Returns: An expression for the smoothed minimum operation. """ expr = smooth_minmax(a, b, eps, sense='min') return expr