option nolet
print "-------------------------------------------------------------------------"
print " general code :reduced row echelon form matrix=A0 :rref(A0),version 1.0  "
print " peter.vlasschaert@gmail.com,19/10/2019                                  "
print "-------------------------------------------------------------------------"
! ref : code : maple : 'Prof Dr Denis Constales ( UGent)',website. '*.png'
! file name = TRUEBASICRREFDATAVERSION1final
print
!************************************
! matrix input : read -data statement
!************************************
dim A0(1,1),A(1,1)       ! init matrix
print "***********************************************"
print " example = 1 , example = 2 ,input 'matrix' = 3 "
print "***********************************************"
print
input prompt " input integer : from '1 to 3' => ":s
print
print
!*******************
! first example = 1
!*******************
if s=1 then 
m0 = 2    ! number of rows
n0 = 4    ! number of columns
mat redim A0(m0,n0),A(m0,n0)
for i = 1 to  m0
   for j = 1 to n0
  read  A0(i,j)
   next j
next i
end if
!*******************
! second example = 2
!*******************
if s=2 then 
m0 = 3    ! number of rows
n0 = 4    ! number of columns
mat redim A0(m0,n0),A(m0,n0)
for i = 1 to  m0
   for j = 1 to n0
  read  A0(i,j)
   next j
next i
end if
!**********************
! thrid 'input matrix'
!**********************
if s=3 then
print "--------------"
print "data 1,2,3,8  "
print "data 4,8,12,16"
print "--------------"
print
input prompt " number of rows    (m) = ":m0
input prompt " number of columns (n) = ":n0
print
mat redim A0(m0,n0),A(m0,n0)
for i = 1 to m0
  for j = 1 to n0
print "A0(";i;",";j;") = ";
input A0(i,j)
 next j
next  i
end if 
print
print "******************************"
print " input matrix 'A0':rref(A0)=> "
print "******************************"
print
mat print A0
print
print "******************************"
print " ouput matrix 'A':rref(A0)=>  "
print "******************************"
print
!*********************************
! algo : rref(A0), 'sub' & 'call'
!*********************************

!********************************************************************
! rem mat A = A0 =>          ! copy : maple,maxima code     
! number rows    : size(A0,1) => 'load(linearalgebra)=> matrix_size '
! number columns : size(A0,2) => 'load(linearalgebra)=> matrix_size '
!********************************************************************
call rref(A0(,),A(,))
mat print A
!*******************
! input : rref(data)
!*******************
data 1,2,3,8
data 4,8,12,16
!********************
! output : rref(data)
!********************
! example
!********************
!matrix(
!		[1,	2,	3,	0],
!		[0,	0,	0,	1]
!	)
data 2,5,9,7
end

sub rref(A0(,),A(,))
!*****************************************
! input  = A0 => matrix
! output = A  => matrix
!*****************************************
! second argument rref : maxima : return(A)
!                      : maple  : A
!*****************************************
mat A = A0     ! copy matrix 'A0'
m = size(A,1)  ! matrix_size
n = size(A,2)  ! matrix_size
i0 = 1
j0 = 1
do while i0 <= m and j0 <= n
i1 = 0
    for i = i0 to  m 
      if  A(i, j0) <> 0 then i1 = i
    next i
    if i1 = 0 then
      j0 = j0 + 1    
    else 
      if i1 <> i0 then
       for j = j0 to n
          t = A(i0, j)
          A(i0, j) = A(i1,j)
          A (i1, j) = t
        next j 
      end if
        p = a(i0,j0)
        for j = j0 to n 
a(i0, j)=10*(a(i0, j)/p)/10! notation correction
        next j
        for i = 1  to m 
          if i <> i0 then 
            p = A(i, j0)
            for j = j0 to n
                   A(i, j)= A(i, j) - p*A(i0, j)
            next j
           end if
         next i
        i0 = i0 + 1       
        j0 = j0 + 1
     end if
loop
end sub