module Linear_algebra

: sig

A module internal to Core_bench. Please look at [root:Bench].

Some basic linear algebra code, so that basic operations can be done without introducing a dependency on Lacaml/LAPACK. Currently only has the minimum needed to do ordinary least squares.

Matrices are represented via float array array, in row-major order.

module Vec : sig

Vectors

type t = float array

val copy : t -> t

Copy a vector

val create0 : int -> t

create0 len sreate a vector of 0s of length len.

val sumsq : t -> float

The sum of squares of entries in a vector

val norm : t -> float

The Euclidean length of a vector

val t_of_sexp : Sexplib.Sexp.t -> t

val sexp_of_t : t -> Sexplib.Sexp.t

end

module Mat : sig

Matrices

type t = float array array

val copy : t -> t

Copy a matrix

val create0 : rows:int -> cols:int -> t

Create a matrix of 0s

val create_per_row : rows:int -> cols:int -> f:(int -> float) -> t

val get_column : t -> int -> Vec.t

Extract a column. Data is copied. Indices start at 0.

val t_of_sexp : Sexplib.Sexp.t -> t

val sexp_of_t : t -> Sexplib.Sexp.t

end

val qr : ?in_place:bool -> Mat.t -> Mat.t * Mat.t

qr A returns the QR-decomposition of A as a pair (Q,R). A must have at least as many rows as columns and have full rank.

If in_place (default: false) is true, then A is overwritten with Q.

val triu_solve : Mat.t -> Vec.t -> Vec.t Core.Std.Or_error.t

triu_solve R b solves R x = b where R is an m x m upper-triangular matrix and b is an m x 1 column vector.

val mul_mv : ?transa:bool -> Mat.t -> Vec.t -> Vec.t

mul_mv A x computes the product A * x (where M is a matrix and x is a column vector).

val ols : ?in_place:bool -> Mat.t -> Vec.t -> Vec.t Core.Std.Or_error.t

ols A b computes the ordinary least-squares solution to A x = b. A must have at least as many rows as columns and have full rank.

This can be used to compute solutions to non-singular square systems, but is somewhat sub-optimal for that purpose. The algorithm is to factor A = Q * R and solve R x = Q' b where Q' denotes the transpose of Q.

If in_place (default: false) is true, then A will be destroyed.

end