congress.datalog.arithmetic_solvers.
LpLang
¶Bases: object
Represent (mostly) linear programs generated from Datalog.
LpConversionFailure
(message=None, **kwargs)¶MIN_THRESHOLD
= 1e-05¶arith_to_lt_zero
(expr)¶Returns Arith expression equivalent to expr but of the form A < 0.
expr – is an Expression
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.
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.
indicator – controls whether the method Returns a single variable (with supporting expressions) or it Returns an expression that has operator with (flat) arguments
a collection of expressions each of one of the following forms: var1 = var2 * … * varn var1 = var2 + … + varn var1 = arith
(new-expression, supporting-expressions)
freshVar
(**meta)¶indicator_to_pure_lp
(exp, bounds)¶Translate exp into LP constraints without indicator variable.
exp – is an Expression of the form var = arith
bounds – is a dictionary from variable to its upper bound
[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
isAnd
(thing)¶isArith
(thing)¶isBoolArith
(thing)¶isConstant
(thing)¶isEqual
(thing)¶isNotEqual
(thing)¶isOr
(thing)¶isVariable
(thing)¶makeAnd
(*args, **meta)¶makeArith
(*args, **meta)¶makeBoolVariable
(*args, **meta)¶makeEqual
(arg1, arg2, **meta)¶makeExpr
(obj)¶makeIntVariable
(*args, **meta)¶makeNotEqual
(arg1, arg2, **meta)¶makeOr
(*args, **meta)¶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.
exp – is an Expression of the form var = (arith11 ^ … ^ arith1n) | … | (arithk1 ^ … ^ arithkn) where the degenerate cases are permitted as well.
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.
exp – is an Expression of the form (arith11 ^ … ^ arith1n) | … | (arithk1 ^ … ^ arithkn) where the degenerate cases are permitted as well.
(new-exp, support) where new-exp 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.
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.
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.
expr – is an Expression
bounds – is a dictionary from tuple versions of variables to the size of their upper bound.
variables
(exp)¶congress.datalog.arithmetic_solvers.
PulpLpLang
¶Bases: congress.datalog.arithmetic_solvers.LpLang
Algorithms for translating LpLang into PuLP library problems.
MIN_THRESHOLD
= 1e-05¶problem
(optimization, constraints, bounds)¶Return PuLP problem for given optimization and constraints.
optimization is an LpLang.Expression that is either a sum or product to minimize.
constraints is a collection of LpLang.Expression that each evaluate to true/false (typically equalities)
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.
expr is an Expression of one of the following forms. arith arith = arith arith <= arith arith >= arith
vars is a dictionary from Expression variables to PuLP variables
Returns a PuLP representation of expr.
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