#! /usr/bin/env python3
#
def is_rref_test ( ):

#*****************************************************************************80
#
## is_rref_test() tests is_rref().
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    04 December 2024
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  print ( '' )
  print ( 'is_rref_test():' )
  print ( '  is_rref() reports whether a matrix is in reduced row echelon format.' )
#
#  Zero rows must come last.
#
  A0 = np.array ( [    \
    [ 1, 0, 0, 9, 4 ], \
    [ 0, 0, 1, 0, 8 ], \
    [ 0, 0, 0, 0, 0 ], \
    [ 0, 0, 0, 1, 0 ]  \
  ] )
#
#  First nonzero must be to right of first nonzero in previous row.
#
  A1 = np.array ( [    \
    [ 1, 0, 0, 9, 4 ], \
    [ 0, 0, 0, 1, 0 ], \
    [ 0, 0, 1, 0, 8 ], \
    [ 0, 0, 0, 0, 0 ] \
  ] )
#
#  First nonzero must be a 1.
#
  A2 = np.array ( [    \
    [ 1, 0, 0, 9, 4 ], \
    [ 0, 1, 0, 2, 8 ], \
    [ 0, 0, 3, 0, 0 ], \
    [ 0, 0, 0, 0, 0 ] \
  ] )
#
#  First nonzero must only nonzero in its column.
#
  A3 = np.array ( [    \
    [ 1, 0, 3, 9, 4 ], \
    [ 0, 1, 0, 2, 8 ], \
    [ 0, 0, 1, 0, 0 ], \
    [ 0, 0, 0, 0, 0 ] \
  ] )
#
#  RREF example.
#
  A4 = np.array ( [    \
    [ 1, 0, 3, 0, 4 ], \
    [ 0, 1, 2, 0, 8 ], \
    [ 0, 0, 0, 1, 0 ], \
    [ 0, 0, 0, 0, 0 ] \
  ] )

  for A, A_name in [ [ A0, 'A0' ], [ A1, 'A1' ], [ A2, 'A2' ], [ A3, 'A3' ], [ A4, 'A4' ] ]:
    print ( '' )
    print ( '  ' + A_name + ':' )
    print ( A )
    print ( '  is_rref(' + A_name + ') = ', is_rref ( A ) )

  return

def is_rref ( A ):

#*****************************************************************************80
#
## is_rref() determines if a matrix is in reduced row echelon format.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    14 December 2024
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    A[m,n]: a numpy array defining a matrix.
#
#  Output:
#
#    is_ref: True if A is in reduced row echelon form.
#
  m, n = A.shape

  c = -1

  for r in range ( 0, m ):
#
#  Increment the first legal column for next pivot.
#
    c = c + 1
#
#  Search for pivot p in this row.
#  If none, set p = n.
#
    p = n
    for j in range ( 0, n ):
      if ( A[r,j] != 0.0 ):
        p = j
        break
#
#  If p == n, go to next row.
#
    if ( p == n ):
      c = n - 1;
      continue
#
#  If p is too early, fail.
#
    if ( p < c ):
      print ( '  Nonzero A[', r, ',', p, '] occurs before column ', c, '.' )
      return False
#
#  Accept p as new c.
#
    c = p
#
#  If A(r,c) is not 1, fail
#
    if ( A[r,c] != 1.0 ):
      print ( '  A[', r, ',', c, '] is not 1.0.' )
      return False
#
#  If A(r,c) is not the only nonzero in column c, fail
#
    for i in range ( 0, m ):
      if ( i != r ):
        if ( A[i,c] != 0.0 ):
          print ( '  A[',i, ',', c, '] should be zero.' )
          return False

  return True

if ( __name__ == "__main__" ):
  is_rref_test ( )