Lp (lp.Lp)

module Var : sig ... end

Module for LP variable. Typically, users don't need to use this module directly. See higher-level module for polynomials (Poly) instead.

module Term : sig ... end

Module for a term in the polynomial. Typically, users don't need to use this module directly. See higher-level module for polynomials (Poly) instead.

module Poly : sig ... end

Module for polynomial expression.

module Cnstr : sig ... end

Module for the constraint.

module Objective : sig ... end

Module for the objective.

module Problem : sig ... end

Module for the optimization problem (model).

module Pclass = Problem.Pclass

Module for the optimization problem class.

module PMap : Stdlib.Map.S with type key = Poly.t

Map with Poly.t key. It can be used to pack optimization result.

val c : float -> Poly.t

Make monomial of a constant value.

val var : ?integer:bool -> ?lb:float -> ?ub:float -> string -> Poly.t

Make monomial of a variable. You can optionally set its bounds (lb and ub) and whether it is an integer. By default, it becomes continuous and non-negative (integer = false, lb = Float.zero, and ub = Float.infinity).

val binary : string -> Poly.t

Make monomial of a binary variable.

val range : 
  ?integer:bool ->
  ?lb:float ->
  ?ub:float ->
  ?start:int ->
  int ->
  string ->
  Poly.t array

Make an array of monomials of a variable with uniform bounds.

val range2 : 
  ?integer:bool ->
  ?lb:float ->
  ?ub:float ->
  ?start0:int ->
  ?start1:int ->
  int ->
  int ->
  string ->
  Poly.t array array

Make 2D array of monomials of a variable with uniform bounds.

val range3 : 
  ?integer:bool ->
  ?lb:float ->
  ?ub:float ->
  ?start0:int ->
  ?start1:int ->
  ?start2:int ->
  int ->
  int ->
  int ->
  string ->
  Poly.t array array array

Make 3D array of monomials of a variable with uniform bounds.

val rangeb : ?start:int -> int -> string -> Poly.t array

Make an array of monomials of a binary variable.

val range2b : 
  ?start0:int ->
  ?start1:int ->
  int ->
  int ->
  string ->
  Poly.t array array

Make 2D array of monomials of a binary variable.

val range3b : 
  ?start0:int ->
  ?start1:int ->
  ?start2:int ->
  int ->
  int ->
  int ->
  string ->
  Poly.t array array array

Make 3D array of monomials of a binary variable.

val rangev : 
  ?integer:bool ->
  ?lb:float array ->
  ?ub:float array ->
  ?start:int ->
  int ->
  string ->
  Poly.t array

Make an array of monomials of a variable with different bounds.

val range2v : 
  ?integer:bool ->
  ?lb:float array array ->
  ?ub:float array array ->
  ?start0:int ->
  ?start1:int ->
  int ->
  int ->
  string ->
  Poly.t array array

Make 2D array of monomials of a variable with different bounds.

val range3v : 
  ?integer:bool ->
  ?lb:float array array array ->
  ?ub:float array array array ->
  ?start0:int ->
  ?start1:int ->
  ?start2:int ->
  int ->
  int ->
  int ->
  string ->
  Poly.t array array array

Make 3D array of monomials of a variable with different bounds.

val concat : Poly.t array -> Poly.t

Concatenate an array of polynomials into single polynomial.

val of_float_array : float array -> Poly.t

Convert a float array into a polynomial.

val zero : Poly.t

The monomial of constant zero.

val one : Poly.t

The monomial of constant one.

val (~--) : Poly.t -> Poly.t

Negate the polynomial (negate all terms in the polynomial).

val (++) : Poly.t -> Poly.t -> Poly.t

Add (concatenate) two polynomials.

val (--) : Poly.t -> Poly.t -> Poly.t

Subtract two polynomials (concatenate left with negated right).

val expand : Poly.t -> Poly.t -> Poly.t

Multiply two polynomials. Specifically, performs polynomial expansion.

val (*~) : Poly.t -> Poly.t -> Poly.t

Infix equivalent of expand.

val dot : Poly.t -> Poly.t -> Poly.t

Regard two polynomials as vectors and take dot product.

raises Failure
if the lengths of two polynomials are different.

val (*@) : Poly.t -> Poly.t -> Poly.t

Infix equivalent of dot.

val div : Poly.t -> Poly.t -> Poly.t

Divide polynomial by a univariate polynomial. Be careful as this function raises exception in some cases.

raises Failure
if failed to divide (with zero remainder) or denominator is multivariate polynomial.

raises Division_by_zero
if denominator is zero.

val (/~) : Poly.t -> Poly.t -> Poly.t

Infix equivalent of div.

val eq : ?eps:float -> ?name:string -> Poly.t -> Poly.t -> Cnstr.t

Build an equality constraint. Optional name can be given. Polynomials are simplified (Poly.simplify) on build. eps specifies the threshold of near-zero, defaulting to 10. *. epsilon_float.

val (=~) : Poly.t -> Poly.t -> Cnstr.t

Build an unnamed equality constraint. Polynomials are simplified on build.

val lt : ?eps:float -> ?name:string -> Poly.t -> Poly.t -> Cnstr.t

Build an inequality constraint. Optional name can be given. Polynomials are simplified (Poly.simplify) on build. eps specifies the threshold of near-zero, defaulting to 10. *. epsilon_float.

val (<~) : Poly.t -> Poly.t -> Cnstr.t

Build an unnamed inequality constraint. Polynomials are simplified on build.

val gt : ?eps:float -> ?name:string -> Poly.t -> Poly.t -> Cnstr.t

Build an inequality constraint. Optional name can be given. Polynomials are simplified (Poly.simplify) on build. eps specifies the threshold of near-zero, defaulting to 10. *. epsilon_float.

val (>~) : Poly.t -> Poly.t -> Cnstr.t

Build an unnamed inequality constraint. Polynomials are simplified on build.

val maximize : ?eps:float -> Poly.t -> Objective.t

Build an objective to maximize a polynomial. The polynomial is simplified (Poly.simplify) on build. eps specifies the threshold of near-zero, defaulting to 10. *. epsilon_float.

val minimize : ?eps:float -> Poly.t -> Objective.t

Build an objective to minimize a polynomial. The polynomial is simplified (Poly.simplify) on build. eps specifies the threshold of near-zero, defaulting to 10. *. epsilon_float.

val make : ?name:string -> Objective.t -> Cnstr.t list -> Problem.t

Make problem from an Objective.t and a constraint (Cnstr.t) list. String name can be given optionally.

val validate : Problem.t -> bool

Validate the problem. true (false) means the problem is valid (invalid).

val classify : Problem.t -> Pclass.t

Classify the problem into Pclass.t.

val vname_list : Problem.t -> string list

Make (unique and sorted) list of the variables in a problem.

val to_string : ?short:bool -> Problem.t -> string

Express the problem in LP file format string.

val of_string : string -> Problem.t

Parse an LP file format string to build the problem.

val write : ?short:bool -> string -> Problem.t -> unit

write fname problem writes out problem to an LP file fname.

val read : string -> Problem.t

Parse an LP file to build the problem.

val compute_term : float PMap.t -> Term.t -> float

Compute the value of a term.

raises Not_found
the one of the variable in the term is not in the pmap.

val compute_poly : float PMap.t -> Poly.t -> float

Compute the value of a polynom.

raises Not_found
the one of the variable in the term is not in the pmap.