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equivalent_posynomials.py
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equivalent_posynomials.py
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from builtins import range
from builtins import object
import numpy as np
from gpkit import Variable, Monomial
from gpkit.nomials import NomialMap
from gpkit.small_classes import HashVector
from robust.robust_gp_tools import RobustGPTools
class EquivalentPosynomials(object):
"""
replaces a posynomial by an equivalent set of posynomials
"""
main_p = None
p_uncertain_vars = []
p_indirect_uncertain_vars = []
m = None
simple_model = None
dependent_uncertainties = None
no_data_constraints = []
data_constraints = []
def __init__(self, p, m, simple_model, dependent_uncertainties):
"""
:param p: the posynomial to be simplified
:param m: the index of the posynomial
:param simple_model: if a simple model is preferred
:param dependent_uncertainties: if the uncertainty set is dependent or not
"""
self.simple_model = simple_model
self.m = m
self.dependent_uncertainties = dependent_uncertainties
direct_p_uncertain_vars = [var for var in p.varkeys if RobustGPTools.is_directly_uncertain(var)]
self.p_indirect_uncertain_vars = [var for var in p.varkeys if RobustGPTools.is_indirectly_uncertain(var)]
new_direct_uncertain_vars = []
for var in self.p_indirect_uncertain_vars:
new_direct_uncertain_vars += list(RobustGPTools.\
replace_indirect_uncertain_variable_by_equivalent(var.key.rel, 1).keys())
new_direct_uncertain_vars = [var for var in new_direct_uncertain_vars
if RobustGPTools.is_directly_uncertain(var)]
self.p_uncertain_vars = list(set(direct_p_uncertain_vars) | set(new_direct_uncertain_vars))
self.no_data_constraints = []
self.data_constraints = []
if len(p.exps[0]) == 0:
self.main_p = p
return
number_of_p_uncertain_vars = len(self.p_uncertain_vars)
if number_of_p_uncertain_vars == 0:
self.no_data_constraints += [p <= 1]
self.main_p = p
return
uncertain_vars_exps = []
uncertain_vars_exps_mons = []
# Determines the exponents and the location of exponents
# of uncertain variables
for i in range(len(p.exps)):
m_uncertain_vars_exps = {}
only_uncertain_vars_monomial_exps = RobustGPTools.\
only_uncertain_vars_monomial(p.exps[i])
for var in list(only_uncertain_vars_monomial_exps.keys()):
if RobustGPTools.is_directly_uncertain(var):
m_uncertain_vars_exps[var] = only_uncertain_vars_monomial_exps[var]
if m_uncertain_vars_exps in uncertain_vars_exps: # if a given exponent on a variable exists
index = uncertain_vars_exps.index(m_uncertain_vars_exps)
uncertain_vars_exps_mons[index].append(i)
else:
uncertain_vars_exps.append(m_uncertain_vars_exps) # exponents
uncertain_vars_exps_mons.append([i]) # locations
all_data_mons = []
monomials = p.chop()
for i, mon_list in enumerate(uncertain_vars_exps_mons):
if len(mon_list) > 1 and uncertain_vars_exps[i]:
# Really clunky way of creating monomials from exponents...
# Should streamline/speed up in the future.
new_no_data_posynomial = 0
hmap = NomialMap({HashVector(uncertain_vars_exps[i]): 1.0})
unitarr = [k.units**v for k, v in list(uncertain_vars_exps[i].items()) if k.units]
try:
hmap.units = np.prod(unitarr)
except:
hmap.units = unitarr[0].units
uncertain_monomial = Monomial(hmap)
for j in mon_list:
new_no_data_posynomial += monomials[j]/uncertain_monomial
com_variable = Variable('com_%s^%s' % (m, i))
# Add to no_data_constraints the constraints with zero uncertain variables
self.no_data_constraints += [new_no_data_posynomial <= com_variable]
all_data_mons.append(uncertain_monomial*com_variable)
else:
temp = sum([monomials[mon_ind] for mon_ind in mon_list])
all_data_mons.append(temp)
# Redefine main_p and chop
self.main_p = sum(all_data_mons)
if len(self.main_p.exps) == 1:
self.data_constraints += [self.main_p <= 1]
return
# if all(len(i) == 1 for i in uncertain_vars_exps_mons) and all():
# self.dependent_uncertainties = False
if not simple_model:
coupled_monomial_partitions = self.correlated_monomials()
else:
coupled_monomial_partitions = []
# Check if all the monomials are related:
if len(coupled_monomial_partitions) != 0 and len(coupled_monomial_partitions[0]) == len(self.main_p.exps):
self.data_constraints += [self.main_p <= 1]
return
ts = []
elements = list(range(len(self.main_p.exps)))
singleton_monomials = [element for element in elements if
not EquivalentPosynomials.check_if_in_list_of_lists(element,
coupled_monomial_partitions)]
main_monomials = self.main_p.chop()
super_script = 0
for i in singleton_monomials:
if RobustGPTools.\
check_if_no_data(self.p_uncertain_vars + self.p_indirect_uncertain_vars, self.main_p.exps[i]):
ts.append(main_monomials[i])
else:
t = Variable('t_%s^%s' % (m, super_script))
super_script += 1
ts.append(t)
self.data_constraints += [main_monomials[i] <= t]
for i in range(len(coupled_monomial_partitions)):
if coupled_monomial_partitions[i]:
posynomial = 0
t = Variable('t_%s^%s' % (m, super_script))
super_script += 1
ts.append(t)
for j in coupled_monomial_partitions[i]:
posynomial += main_monomials[j]
self.data_constraints += [posynomial <= t]
self.no_data_constraints += [sum(ts) <= 1]
return
@staticmethod
def merge_intersected_lists(coupled_partition):
"""
merges a list of lists so that the resulting list of lists is a partition
:param coupled_partition: the list of lists to be merged
:return: the partition
"""
l = len(coupled_partition)
if l <= 1:
return coupled_partition
half = int(np.floor(l / 2.0))
first_half_partitions = EquivalentPosynomials.merge_intersected_lists(coupled_partition[0:half])
second_half_partitions = EquivalentPosynomials.merge_intersected_lists(coupled_partition[half:l])
len_first, len_second = len(first_half_partitions), len(second_half_partitions)
relations, path = {}, {}
first_to_delete, second_to_delete = set(), set()
i = 0
while i < len_first:
j = 0
while j < len_second:
if list(set(first_half_partitions[i]) & set(second_half_partitions[j])):
second_to_delete.add(j)
temp_one = i
while temp_one in path:
temp_one = path[temp_one] # i]
first_half_partitions[temp_one] = \
list(set(first_half_partitions[temp_one]) | set(second_half_partitions[j]))
if j in relations:
temp_two = relations[j]
while temp_two in path:
temp_two = path[temp_two] # i]
if temp_two != temp_one:
first_to_delete.add(temp_one)
path[temp_one] = temp_two
first_half_partitions[temp_two] = \
list(set(first_half_partitions[temp_two]) | set(first_half_partitions[temp_one]))
else:
relations[j] = temp_one
j += 1
i += 1
first_to_delete = list(first_to_delete)
first_to_delete.reverse()
second_to_delete = list(second_to_delete)
second_to_delete.reverse()
for k in first_to_delete:
del first_half_partitions[k]
for k in second_to_delete:
del second_half_partitions[k]
return first_half_partitions + second_half_partitions
@staticmethod
def same_sign(a):
"""
Checks if the elements of a have the same sign
:param a: the list to be checked
:return: True or False
"""
j = 0
while j < len(a):
if a[j] == 0:
j += 1
else:
break
if j == len(a):
return True
for i in range(len(a) - 1):
if a[j] * a[i + 1] < 0:
return False
return True
def correlated_monomials(self):
"""
Creates partitions of correlated monomials
:return: the list of coupled partitions
"""
number_of_monomials = len(self.main_p.exps)
coupled_partition = []
if self.dependent_uncertainties:
for j in range(number_of_monomials):
only_uncertain_vars_monomial_exps = RobustGPTools.\
only_uncertain_vars_monomial(self.main_p.exps[j])
for var in self.p_uncertain_vars:
if var.key in only_uncertain_vars_monomial_exps:
coupled_partition.append(j)
break
return [coupled_partition]
else:
for var in self.p_uncertain_vars:
partition = []
check_sign = []
for j in range(number_of_monomials):
only_uncertain_vars_monomial_exps = RobustGPTools.\
only_uncertain_vars_monomial(self.main_p.exps[j])
if var in only_uncertain_vars_monomial_exps:
partition.append(j)
check_sign.append(only_uncertain_vars_monomial_exps.get(var.key))
if not EquivalentPosynomials.same_sign(check_sign):
coupled_partition.append(partition)
coupled_partition = EquivalentPosynomials.merge_intersected_lists(coupled_partition)
return coupled_partition
@staticmethod
def check_if_in_list_of_lists(element, list_of_lists):
for i in range(len(list_of_lists)):
if element in list_of_lists[i]:
return True
return False
if __name__ == '__main__':
pass