Poly (lp.Lp.Poly)

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. 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 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

The monomial of constant zero.

val one : t

The monomial of constant one.

val sort : t -> t

Sort terms in the polynomial.

val compare : t -> t -> int

Compare the polynomial.

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

Get string expression of the polynomial.

val partition : t -> t * t

Partition terms into pair of (quad or linear, const) terms.

val classify : t -> classified

Classify terms into three categories: quad, linear, and const (classified).

val decompose : t -> decomposed

Decompose the polynomial into decomposed.

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 polynomial (negate all terms in the polynomial).

val (~--) : t -> t

Negate the polynomial (negate all terms in the 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

Infix equivalent of expand.

val dot : t -> t -> t

Regard two polynomials as vectors and take dot product.

raises Failure
if the lengths of two polynomials are different.

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

Infix equivalent of dot.

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

Infix equivalent of div.

val with_bound : string -> float -> float -> t -> t

with_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_binary 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.

raises 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.

raises Failure
if non-linear terms exist.

val length : t -> int

Get number of terms (length) of a polynomial.

val take_linear_coeffs : t -> float list

Make list of coefficients in linear terms in a polynomial.