# 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
#
# 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