/
relax.py
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/
relax.py
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"""Models for assessing primal feasibility"""
from .set import ConstraintSet
from ..nomials import Variable, VectorVariable, parse_subs, NomialArray
from ..keydict import KeyDict
from .. import NamedVariables, SignomialsEnabled
from ..small_scripts import appendsolwarning, mag
class ConstraintsRelaxedEqually(ConstraintSet):
"""Relax constraints the same amount, as in Eqn. 10 of [Boyd2007].
Arguments
---------
constraints : iterable
Constraints which will be relaxed (made easier).
Attributes
----------
relaxvar : Variable
The variable controlling the relaxation. A solved value of 1 means no
relaxation. Higher values indicate the amount by which all constraints
have been made easier: e.g., a value of 1.5 means all constraints were
50 percent easier in the final solution than in the original problem.
[Boyd2007] : "A tutorial on geometric programming", Optim Eng 8:67-122
"""
def __init__(self, original_constraints):
if not isinstance(original_constraints, ConstraintSet):
original_constraints = ConstraintSet(original_constraints)
self.original_constraints = original_constraints
original_substitutions = original_constraints.substitutions
with NamedVariables("Relax"):
self.relaxvar = Variable("C")
with SignomialsEnabled():
relaxed_constraints = [c.relaxed(self.relaxvar)
for c in original_constraints.flat()]
ConstraintSet.__init__(self, {
"minimum relaxation": self.relaxvar >= 1,
"relaxed constraints": relaxed_constraints}, original_substitutions)
def process_result(self, result):
"Warns if any constraints were relaxed"
ConstraintSet.process_result(self, result)
self.check_relaxed(result)
def check_relaxed(self, result):
"Adds relaxation warnings to the result"
for val, msg in get_relaxed([result["freevariables"][self.relaxvar]],
["All constraints relaxed by %i%%"]):
appendsolwarning(msg % (0.9+(val-1)*100), self, result,
"Relaxed Constraints")
class ConstraintsRelaxed(ConstraintSet):
"""Relax constraints, as in Eqn. 11 of [Boyd2007].
Arguments
---------
constraints : iterable
Constraints which will be relaxed (made easier).
Attributes
----------
relaxvars : Variable
The variables controlling the relaxation. A solved value of 1 means no
relaxation was necessary or optimal for a particular constraint.
Higher values indicate the amount by which that constraint has been
made easier: e.g., a value of 1.5 means it was made 50 percent easier
in the final solution than in the original problem.
[Boyd2007] : "A tutorial on geometric programming", Optim Eng 8:67-122
"""
def __init__(self, original_constraints):
if not isinstance(original_constraints, ConstraintSet):
original_constraints = ConstraintSet(original_constraints)
self.original_constraints = original_constraints
original_substitutions = original_constraints.substitutions
with NamedVariables("Relax"):
self.relaxvars = VectorVariable(len(original_constraints), "C")
with SignomialsEnabled():
relaxed_constraints = [
c.relaxed(self.relaxvars[i])
for i, c in enumerate(original_constraints.flat())]
ConstraintSet.__init__(self, {
"minimum relaxation": self.relaxvars >= 1,
"relaxed constraints": relaxed_constraints}, original_substitutions)
def process_result(self, result):
"Warns if any constraints were relaxed"
ConstraintSet.process_result(self, result)
self.check_relaxed(result)
def check_relaxed(self, result):
"Adds relaxation warnings to the result"
relaxed = get_relaxed(result["freevariables"][self.relaxvars],
range(len(self["relaxed constraints"])))
for relaxval, i in relaxed:
relax_percent = "%i%%" % (0.5+(relaxval-1)*100)
oldconstraint = self.original_constraints[i]
newconstraint = self["relaxed constraints"][i][0]
subs = {self.relaxvars[i]: relaxval}
relaxdleft = newconstraint.left.sub(subs)
relaxdright = newconstraint.right.sub(subs)
oldleftstr = str(oldconstraint.left)
relaxedleftstr = str(relaxdleft)
padding = len(relaxedleftstr) - len(oldleftstr)
if padding > 0:
oldleftstr = " " * padding + oldleftstr
elif padding < 0:
relaxedleftstr = " " * padding + relaxedleftstr
msg = (" %3i: %5s relaxed, from %s %s %s\n"
" to %s %s %s"
% (i, relax_percent, oldleftstr,
oldconstraint.oper, oldconstraint.right,
relaxedleftstr, newconstraint.oper, relaxdright))
appendsolwarning(msg, oldconstraint, result, "Relaxed Constraints")
class ConstantsRelaxed(ConstraintSet):
"""Relax constants in a constraintset.
Arguments
---------
constraints : iterable
Constraints which will be relaxed (made easier).
include_only : set (optional)
variable names must be in this set to be relaxed
exclude : set (optional)
variable names in this set will never be relaxed
Attributes
----------
relaxvars : Variable
The variables controlling the relaxation. A solved value of 1 means no
relaxation was necessary or optimal for a particular constant.
Higher values indicate the amount by which that constant has been
made easier: e.g., a value of 1.5 means it was made 50 percent easier
in the final solution than in the original problem. Of course, this
can also be determined by looking at the constant's new value directly.
"""
# pylint:disable=too-many-locals
def __init__(self, constraints, *, include_only=None, exclude=None):
exclude = frozenset(exclude) if exclude else frozenset()
include_only = frozenset(include_only) if include_only else frozenset()
with NamedVariables("Relax") as (self.lineage, _):
pass # gives this model the correct lineage.
if not isinstance(constraints, ConstraintSet):
constraints = ConstraintSet(constraints)
substitutions = KeyDict(constraints.substitutions)
constants, _, linked = parse_subs(constraints.varkeys, substitutions)
if linked:
kdc = KeyDict(constants)
constrained_varkeys = constraints.constrained_varkeys()
constants.update({k: f(kdc) for k, f in linked.items()
if k in constrained_varkeys})
self._derelax_map = {}
relaxvars, self.freedvars, relaxation_constraints = [], [], {}
for const, val in sorted(constants.items(), key=lambda i: i[0].eqstr):
if val == 0:
substitutions[const] = 0
continue
if include_only and const.name not in include_only:
continue
if const.name in exclude:
continue
# set up the lineage
const.descr.pop("gradients", None) # nothing wants an old gradient
newconstd = const.descr.copy()
newconstd.pop("veckey", None) # only const wants an old veckey
# everything but const wants a new lineage, to distinguish them
newconstd["lineage"] = (newconstd.pop("lineage", ())
+ (self.lineage[-1],))
# make the relaxation variable, free to get as large as it needs
relaxedd = newconstd.copy()
relaxedd["unitrepr"] = "-" # and unitless, importantly
relaxvar = Variable(**relaxedd)
relaxvars.append(relaxvar)
# the newly freed const can acquire a new value
del substitutions[const]
freed = Variable(**const.descr)
self.freedvars.append(freed)
# becuase the make the newconst will take its old value
newconstd["lineage"] += (("OriginalValues", 0),)
newconst = Variable(**newconstd)
substitutions[newconst] = val
self._derelax_map[newconst.key] = const
# add constraints so the newly freed's wiggle room
# is proportional to the value relaxvar, and it can't antirelax
relaxation_constraints[str(const)] = [relaxvar >= 1,
newconst/relaxvar <= freed,
freed <= newconst*relaxvar]
ConstraintSet.__init__(self, {
"original constraints": constraints,
"relaxation constraints": relaxation_constraints})
self.relaxvars = NomialArray(relaxvars) # so they can be .prod()'d
self.substitutions = substitutions
self.constants = constants
def process_result(self, result):
"Transfers constant sensitivities back to the original constants"
ConstraintSet.process_result(self, result)
constant_senss = result["sensitivities"]["variables"]
for new_constant, former_constant in self._derelax_map.items():
constant_senss[former_constant] = constant_senss[new_constant]
del constant_senss[new_constant]
self.check_relaxed(result)
def check_relaxed(self, result):
"Adds relaxation warnings to the result"
relaxed = get_relaxed([result["freevariables"][r]
for r in self.relaxvars], self.freedvars)
for (_, freed) in relaxed:
msg = (" %s: relaxed from %-.4g to %-.4g"
% (freed,
mag(self.constants[freed.key]),
mag(result["freevariables"][freed])))
appendsolwarning(msg, freed, result, "Relaxed Constants")
def get_relaxed(relaxvals, mapped_list):
"Returns 'relaxed' vals (those above an arbitrary threshold of 1.01)."
sortrelaxed = sorted(zip(relaxvals, mapped_list), key=lambda x: -x[0])
mostrelaxed = max(sortrelaxed[0][0], 1.01)
for i, (val, _) in enumerate(sortrelaxed):
if val <= 1.01 and (val-1) <= (mostrelaxed-1)/10:
return sortrelaxed[:i]
return sortrelaxed