;;; Lisplab, level3-linalg-interface.lisp
;;; Matrix generic functions.

;;; Copyright (C) 2009 Joern Inge Vestgaarden
;;;
;;; This program is free software; you can redistribute it and/or modify
;;; it under the terms of the GNU General Public License as published by
;;; the Free Software Foundation; either version 2 of the License, or
;;; (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
;;; GNU General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License along
;;; with this program; if not, write to the Free Software Foundation, Inc.,
;;; 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

(in-package :lisplab)

(defgeneric mtp (matrix)
  (:documentation "Matrix transpose."))

(defgeneric mtp! (matrix)
  (:documentation "Matrix transpose. Destructive."))

(defgeneric mct (matrix)
  (:documentation "Matrix conjugate transpose."))

(defgeneric mct! (matrix)
  (:documentation "Matrix conjugate transpose. Destructive."))

(defgeneric mtr (matrix)
  (:documentation "Matrix trace (sum of diagonal elements)."))

(defgeneric mdet (matrix)
  (:documentation "Matrix determinant.")
  (:method :before (m)
	   (assert (= (rows m) (cols m)))))

(defgeneric minv! (a)
  (:documentation "Matrix inverse. Destructive."))

(defgeneric minv (a)
  (:documentation "Matrix inverse.")
  (:method :before (m)
	   (assert (= (rows m) (cols m)))))

(defgeneric m* (a b)
  (:documentation "Matrix multiplication.")
  (:method :before (a b)
	   (assert (= (cols a) (rows b)))))

(defgeneric m*! (a b)
  (:documentation "Matrix product. Destructive."))

(defgeneric m/ (a b)
  (:documentation "Short for (m* a (minv b))."))

(defgeneric m/! (a b)
  (:documentation "Short for (m*! a (minv b)). Destructive."))

(defgeneric LU-factor! (matrix pivotes)
  (:documentation "LU-factorization with pivoting. Destructive. 
Ouputs a combined LU matrix where the diagonals belong to U and a
permutation vector."))

(defgeneric LU-factor (matrix)
  (:documentation "LU-factorization with pivoting. Outputs (L U P) where 
L is low diagonal with unity at diagnoals, U is upper diagnoal and 
P is an permutation matrix, so that A = P L U."))

(defgeneric LU-solve! (LU x)
  (:documentation "Solves the linear equation system LUx=b, where LU is an output 
from LU-factor!."))

(defgeneric lin-solve (A b)
  (:documentation  "Solves the linear system of equations Ax=b."))

(defgeneric eigenvectors (a)
  (:documentation "Returns (P d) where P is matrix of right eigenvector and d is a vector of eigenvalues."))

(defgeneric eigenvalues (a)
  (:documentation "Returns the vector of eigenvalues."))