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;; Copyright 2005 by Barton Willis
;; This is free software; you can redistribute it and/or
;; modify it under the terms of the GNU General Public License,
;; http://www.gnu.org/copyleft/gpl.html.
;; This software has NO WARRANTY, not even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
($put '$linalgutilities 2 '$version)
(defun inform (level pck msg &rest arg)
(if (member level (member ($get '$infolevel pck) `($debug $verbose $silent)))
(apply 'mtell `(,msg ,@arg))))
(defun $require_nonempty_matrix (m pos fun)
(if (not (and ($matrixp m) (> ($length m) 0) (> ($length ($first m)) 0)))
(merror "The ~:M argument of the function ~:M must be a nonempty matrix" pos fun)))
;; Why both some and every? Because we want blockmatrixp(matrix()) --> false.
(defun $blockmatrixp (m)
(and ($matrixp m) ($some '$matrixp m) ($every '$matrixp m)))
(defun $require_matrix (m pos fun)
(if (not ($matrixp m))
(merror "The ~:M argument of the function ~:M must be a matrix" pos fun)))
(defun $require_unblockedmatrix (m pos fun)
(if (or (not ($matrixp m)) ($blockmatrixp m))
(merror "The ~:M argument of the function ~:M must be an unblocked matrix" pos fun)))
(defun $require_square_matrix (m pos fun)
(if (not (and ($matrixp m) (= ($length m) ($length ($first m)))))
(merror "The ~:M argument of the function ~:M must be a square matrix" pos fun)))
(defun array-elem (m i j)
(nth j (nth i m)))
(defun $require_symmetric_matrix (m pos fun)
(if (not ($matrixp m)) (merror "The ~:M argument to ~:M must be a matrix" pos fun))
(let ((n ($matrix_size m)))
(if (not (= ($first n) ($second n)))
(merror "The ~:M argument to ~:M must be a square matrix" pos fun))
(if (not ($zeromatrixp (sub m ($transpose m))))
(merror "The ~:M argument to ~:M must be a symmetric matrix" pos fun)))
'$done)
(defun $require_real_symmetric_matrix (m pos fun)
(if (not ($matrixp m)) (merror "The ~:M argument to ~:M must be a matrix" pos fun))
(let ((n ($matrix_size m)))
(if (not (= ($first n) ($second n)))
(merror "The ~:M argument to ~:M must be a square matrix" pos fun))
(if (and ($zeromatrixp (sub m ($transpose m))) ($zeromatrixp (sub m (take '($conjugate) m)))) '$done
(merror "The ~:M argument to ~:M must be a real symmetric matrix" pos fun))))
(defun $require_selfadjoint_matrix (m fun pos)
(if (not ($matrixp m)) (merror "The ~:M argument to ~:M must be a matrix" pos fun))
(let ((n ($matrix_size m)))
(if (not (= ($first n) ($second n)))
(merror "The ~:M argument to ~:M must be a square matrix" pos fun))
(if (not ($zeromatrixp (sub m ($ctranspose m))))
(merror "The ~:M argument to ~:M must be a selfadjoint (hermitian) matrix" pos fun)))
'$done)
;; matrix() is a 0 x 0 matrix, and matrix([]) is a 1 x 0 matrix.
;; There is no representation for a 0 x 1 matrix. Currently,
;; transpose(matrix([])) => matrix(). And that's a bug.
(defun $matrix_size(m)
($require_matrix m "$first" "$matrix_size")
`((mlist) ,($length ($args m)) ,(if ($emptyp ($args m)) 0 ($length ($first ($args m))))))
(defun $require_list (lst pos fun)
(if (not ($listp lst))
(merror "The ~:M argument of the function ~:M must be a list" pos fun)))
(defun $require_posinteger(i pos fun)
(if (not (and (integerp i) (> i 0)))
(merror "The ~:M argument of the function ~:M must be a positive integer" pos fun)))
(defun matrix-map (f mat)
(setq mat (mapcar 'cdr (cdr mat)))
(setq mat (mapcar #'(lambda (s) (mapcar f s)) mat))
(setq mat (mapcar #'(lambda (s) (cons `(mlist simp) s)) mat))
`(($matrix simp) ,@mat))
;; Map the lisp function fn over the matrix m. This function is block matrix friendly.
(defun full-matrix-map (fn m)
(if (or ($listp m) ($matrixp m))
(cons (car m) (mapcar #'(lambda (s) (full-matrix-map fn s)) (cdr m)))
(funcall fn m)))
(defun $zerofor (mat &optional (fld-name '$generalring))
(let* ((fld ($require_ring fld-name "$second" "$zerofor"))
(add-id (funcall (mring-mring-to-maxima fld) (funcall (mring-add-id fld)))))
(zerofor mat add-id)))
(defun zerofor (mat zero)
(if (or ($matrixp mat) ($listp mat))
(cons (car mat) (mapcar #'(lambda (s) (zerofor s zero)) (cdr mat)))
zero))
;; Return an identity matrix that has the same shape as the matrix
;; mat. The first argument 'mat' should be a square Maxima matrix or a
;; non-matrix. When 'mat' is a matrix, each entry of 'mat' can be a
;; square matrix -- thus 'mat' can be a blocked Maxima matrix. The
;; matrix can be blocked to any (finite) depth.
(defun $identfor (mat &optional (fld-name '$generalring))
(let* ((fld ($require_ring fld-name "$second" "$zerofor"))
(add-id (funcall (mring-mring-to-maxima fld) (funcall (mring-add-id fld))))
(mult-id (funcall (mring-mring-to-maxima fld) (funcall (mring-mult-id fld)))))
(if ($matrixp mat) (identfor mat add-id mult-id) mult-id)))
(defun identfor (mat zero one)
(let ((i) (acc) (j) (new-mat))
(setq mat (rest mat))
(setq i 0)
(dolist (row mat)
(setq row (rest row))
(setq acc nil)
(setq j 0)
(dolist (aij row)
(push (cond (($matrixp aij)
(if (= i j) (identfor aij zero one) (zerofor aij zero)))
((= i j) one)
(t zero)) acc)
(incf j))
(incf i)
(push '(mlist) acc)
(push acc new-mat))
(push '($matrix) new-mat)))
(defun $ctranspose (m)
(mfuncall '$transpose (full-matrix-map #'(lambda (s) (simplifya `(($conjugate) ,s) nil)) m)))
(defun $zeromatrixp (m)
(if (or ($matrixp m) ($listp m)) (every '$zeromatrixp (cdr m))
(eq '$zero (csign ($rectform m)))))
(defun array-to-row-list (mat &optional (fn 'identity))
(let ((acc) (r (array-dimensions mat)) (row) (c))
(setq c (second r))
(setq r (first r))
(dotimes (i r)
(setq row nil)
(dotimes (j c)
(push (funcall fn (aref mat i j)) row))
(setq row (reverse row))
(push row acc))
(reverse acc)))
(defun array-to-maxima-matrix (mat &optional (fn 'identity))
(cons '($matrix) (mapcar #'(lambda (s) (cons '(mlist) s)) (array-to-row-list mat fn))))
(defun array-to-maxima-list (ar &optional (fn 'identity))
(cons '(mlist) (mapcar fn (coerce ar 'list))))
(defun maxima-to-array (mat &optional (fn 'identity) typ)
(let ((r ($matrix_size mat)) (c))
(setq c ($second r))
(setq r ($first r))
(setq mat (mapcar #'cdr (cdr mat)))
(setq mat (mapcar #'(lambda (s) (mapcar #'(lambda (w) (funcall fn w)) s)) mat))
(if typ (make-array (list r c) :element-type typ :initial-contents mat)
(make-array (list r c) :initial-contents mat))))
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