lp 0.2.0 · OCaml Package

Module for polynomial expression type

type t

Type for the polynomial with order up to two (quadratic).

type classified = {

const : t;
linear : t;
quad : t;

}

Type for the polynomial classified by orders

type decomposed = {

const : float;
lcs : float list;
lvs : Var.t list;
qcs : float list;
qv0s : Var.t list;
qv1s : Var.t list;

}

Type for the decomposed expression of the polynomial

val c : float -> t

Make monomial of a constant value

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

Make monomial of a variable

val of_var : Var.t -> t

Make monomial from a Var.t

val of_term : Term.t -> t

Make monomial from a Term.t

val binary : string -> t

Make monomial of a binary variable

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

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

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

Make an array of monomials of a binary variable

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

Make 2D array of monomials of a binary variable

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

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

val concat : t array -> t

Concatenate an array of polynomials into single polynomial

val concat_list : t list -> t

Concatenate a list of polynomials into single polynomial

val of_float_array : float array -> t

Convert a float array into a polynomial

val of_term_list : Term.t list -> t

Convert a list of terms into a polynomial

val to_float : t -> float

Convert a Constant monomial to float. * Raises Failure if it's not constant monomial

val zero : t

Constant zero

val one : t

Constant one

val sort : t -> t

Sort terms in the polynomial

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

Get string expression of the polynomial

val partition : t -> t * t

Partition terms into pair ( quad or linear, const )

val classify : t -> classified

Classify terms into three categories quad, linear, const

val decompose : t -> decomposed

Decompose the polynomial into const, lcs, lvs, qcs, qv0s, qv1s

val collision : t -> bool

Check if any variable collision exist in the polynomial

val simplify : ?eps:float -> t -> t

Simplify the polynomial. The polynomial is sorted and terms with same variables are accumulated. After that, near-zero terms are dropped. eps specifies the threshold of near-zero, defaulting to 10. *. epsilon_float.

val degree : t -> int

Get the degree of polynomial

val take_vars : t -> Var.t list

List up all the variables in the polynomial

val uniq_vars : t -> Var.t list

List up all the unique variables in the polynomial

val linear_coeff : t -> Var.t -> float

take linear coefficient of a variable in a polynomial

val quad_coeff : t -> Var.t -> Var.t -> float

take quad coefficient of the variables in a polynomial

val neg : t -> t

Negate the whole polynomial

val (~--) : t -> t

Negate the whole polynomial

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

Add (concatenate) two polynomials

val (--) : t -> t -> t

Subtract two polynomials (concatenate left with negated right )

val expand : t -> t -> t

Multiply two polynomials. specifically, performs polynomial expansion.

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

Multiply two polynomials. specifically, performs polynomial expansion.

val dot : t -> t -> t

Regard two polynomials as vectors and take dot product.

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

Regard two polynomials as vectors and take dot product.

val equiv : ?eps:float -> t -> t -> bool

Check if two polynomials are equivalent

val divt : t -> Term.t -> t

Divide polynomial by a term.

val div : t -> t -> t

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

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

equivalent to div

val trans_bound : string -> float -> float -> t -> t

trans_bound name lb ub transforms the bounds of the variable name with lb and ub

val to_integer : string -> t -> t

to_integer name transforms the variable name into general integer variable

val to_binary : string -> t -> t

to_integer name transforms the variable name into binary variable

val double_quad : t -> t

double the coefficients in all quadratic terms in the polynomial

val half_quad : t -> t

half the coefficients in all quadratic terms in the polynomial

val map : (Term.t -> 'a) -> t -> 'a list

apply a function to all terms in the polynomial and build a list

val map_linear : (float -> Var.t -> 'a) -> t -> 'a list

apply a function only to linear terms in the polynomial and build a list. * Raise Failure if non-linear terms exist.

val mapi : (int -> Term.t -> 'a) -> t -> 'a list

apply a function to all terms in the polynomial and build a list

val iter : (Term.t -> unit) -> t -> unit

apply a function to all terms in the polynomial

val iteri : (int -> Term.t -> unit) -> t -> unit

apply a function to all terms in the polynomial

val iter_linear : (float -> Var.t -> unit) -> t -> unit

apply a function only to linear terms in the polynomial. * non-linear terms are just ignored.

val iter_linear_exn : (float -> Var.t -> unit) -> t -> unit

apply a function only to linear terms in the polynomial. * Raise Failure if non-linear terms exist.

val length : t -> int

val take_linear_coeffs : t -> float list

package lp