The congress.datalog.arithmetic_solvers
Module¶

class
congress.datalog.arithmetic_solvers.
LpLang
¶ Bases:
object
Represent (mostly) linear programs generated from Datalog.

exception
LpConversionFailure
(message=None, **kwargs)¶

MIN_THRESHOLD
= 1e05¶

arith_to_lt_zero
(expr)¶ Returns Arith expression equivalent to expr but of the form A < 0.
:param expr is an Expression Returns an expression equivalent to expr but of the form A < 0.

create_intermediate
(exp)¶ Given expression, create var = expr and return (var, var=expr).

flatten
(exp, indicator=True)¶ Remove toplevel embedded and/ors by creating new equalities.
:param exp is an Expression of the form var = (arith11 ^ … ^ arith1n)  …  (arithk1 ^ … ^ arithkn) where arithij is either a variable or an arithmetic expression where the degenerate cases are permitted as well.
:param indicator controls whether the method Returns a single variable (with supporting expressions) or it Returns an expression that has operator with (flat) arguments
Returns a collection of expressions each of one of the following forms: var1 = var2 * … * varn var1 = var2 + … + varn var1 = arith
Returns (newexpression, supportingexpressions)

freshVar
(**meta)¶

indicator_to_pure_lp
(exp, bounds)¶ Translate exp into LP constraints without indicator variable.
:param exp is an Expression of the form var = arith :param bounds is a dictionary from variable to its upper bound
Returns [EXP] if it is of the wrong form. Otherwise, translates into the form y = x < 0, and then returns two constraints where upper(x) is the upper bound of the expression x:
x <= y * upper(x) x < (1  y) * upper(x)Taken from section 7.4 of http://www.aimms.com/aimms/download/manuals/ aimms3om_integerprogrammingtricks.pdf

classmethod
isAnd
(thing)¶

classmethod
isArith
(thing)¶

classmethod
isBoolArith
(thing)¶

classmethod
isConstant
(thing)¶

classmethod
isEqual
(thing)¶

classmethod
isNotEqual
(thing)¶

classmethod
isOr
(thing)¶

classmethod
isVariable
(thing)¶

classmethod
makeAnd
(*args, **meta)¶

classmethod
makeArith
(*args, **meta)¶

classmethod
makeBoolVariable
(*args, **meta)¶

classmethod
makeEqual
(arg1, arg2, **meta)¶

classmethod
makeExpr
(obj)¶

classmethod
makeIntVariable
(*args, **meta)¶

classmethod
makeNotEqual
(arg1, arg2, **meta)¶

classmethod
makeOr
(*args, **meta)¶

classmethod
makeVariable
(*args, **meta)¶

operator_to_constructor
(operator)¶ Given the operator, return the corresponding constructor.

pure_lp
(exp, bounds)¶ Rewrite EXP to a pure LP problem.
:param exp is an Expression of the form var = (arith11 ^ … ^ arith1n)  …  (arithk1 ^ … ^ arithkn) where the degenerate cases are permitted as well.
Returns a collection of expressions each of the form: a1*x1 + … + an*xn [<=, ==, >=] b.

pure_lp_term
(exp, bounds)¶ Rewrite term exp to a pure LP term.
:param exp is an Expression of the form (arith11 ^ … ^ arith1n)  …  (arithk1 ^ … ^ arithkn) where the degenerate cases are permitted as well.
Returns (newexp, support) where newexp is a term, and support is a expressions of the following form. a1*x1 + … + an*xn [<=, ==, >=] b.

remove_and_or
(exp)¶ Translate and/or operators into times/plus arithmetic.
:param exp is an Expression that takes one of the following forms. var [!]= term1 ^ … ^ termn var [!]= term1  …  termn var [!]= term1 where termi is an indicator variable.
Returns an expression equivalent to exp but without any ands/ors.

remove_and_or_term
(exp)¶

upper_bound
(expr, bounds)¶ Returns number giving an upper bound on the given expr.
:param expr is an Expression :param bounds is a dictionary from tuple versions of variables to the size of their upper bound.

classmethod
variables
(exp)¶

exception

class
congress.datalog.arithmetic_solvers.
PulpLpLang
¶ Bases:
congress.datalog.arithmetic_solvers.LpLang
Algorithms for translating LpLang into PuLP library problems.

MIN_THRESHOLD
= 1e05¶

problem
(optimization, constraints, bounds)¶ Return PuLP problem for given optimization and constraints.
 :param optimization is an LpLang.Expression that is either a sum
 or product to minimize.
 :param constraints is a collection of LpLang.Expression that
 each evaluate to true/false (typically equalities)
 :param bounds is a dictionary mapping LpLang.Expression variable
 tuples to their upper bounds.
Returns a pulp.LpProblem.

pulpify
(expr, variables, values)¶ Return PuLP version of expr.
:param expr is an Expression of one of the following forms. arith arith = arith arith <= arith arith >= arith :param vars is a dictionary from Expression variables to PuLP variables
Returns a PuLP representation of expr.
