;;; A simple demonstration of how to use lisplab

(in-package :ll-user)

;;; 19 ways to create a matrix
(defparameter *test-matrices* 
  (list 
   ;; Blank matrices
   
   (mnew 'matrix-dge 0 3 5)
     ; same as
   (dnew 0 3 5)
     ; same as
   (mnew '(:d :ge :any) 0 3 5)
   (mnew 'matrix-zge 0 3 5)
     ; same as
   (znew 0 3 5)
     ; same as
   (mnew '(:z :ge :any) 0 3 5)

   (drow 2 4 2)
   (dcol 2 3 1)
   (zrow 2 %i 1)
   (zcol 2 %i 1)

   ;; Read macro
   #md((1 2) (-1 4))
   #mz((1 2) (-1 4))
   #mm((1 2) (-1 4))

   ;; Setting of individual elements
   (dmat '((0 4 -2) 
	   (1 3 -5) 
	   (-2 4 0)))
   (zmat '((0 #c(0 2) -2) 
	   (1 3 -5) 
	   (-2 #c(0 1) 0)))

   ;; Setting of structure
   (funmat '(4 4) (lambda (i j) 
		    (if (= i j) 1 0))) 
   (fmat 'matrix-dge '(3 4) (lambda (i j) 
			      (if (< i j) 1 0.5)))

   ;; From another matrix
   (copy #md((1 4) (-2 3)))
  
   (mcreate #md((1 4) (-2 3)))
   (convert '((3 2 4) (1 4 2)) 'matrix-dge)
   (convert (funmat '(3 3) (lambda (i j) (random 1.0))) 'matrix-dge)
   (mmap '(:z :ge :any) #'random (mnew '(:d :ge :any) 1 3 3))
   (.+ 3 #md((2 3) (-2 9)))

   ))

(mapcar (lambda (x) (mref x 0 0)) *test-matrices*)

(mapcar (lambda (x) (vref x 2)) *test-matrices*)

;; Arithmetics 

(let ((a #md((0 4 -2) 
	     (1 3 -5) 
	     (-2 4 0)))
      (b #mz((0 (.* 2 %i) -2) 
	     (1 3 -5) 
	     (-2 %i 0))))  
  (.+ (.* 3 a) b))

;; Infix arithmetics 

(let ((a #md((0 4 -2) 
	     (1 3 -5) 
	     (-2 4 0)))
      (b #mz((0 #c(0 2) -2) 
	     (1 3 -5) 
	     (-2 %i 0))))  
  (w/infix 3 .* a .+ b))


;; Matrix inversion

(minv #md((0 4 -2) (1 3 -5) (-2 4 0)))