Module Linear_algebra

module Linear_algebra: sig .. end

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 .. end

Vectors

module Mat: sig .. end

Matrices

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.

mul A B computes the matrix product A * B. If transa (default: false) is true, then we compute A' * B where A' denotes the transpose of A.

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.