def magic_matrix ( n ):

#*****************************************************************************80
#
## magic_matrix() returns a magic matrix of odd order n as a numpy array.
#
#  Discussion:
#
#    Every row and column of the matrix has the same sum.
#
#    The algorithm proceeds as follows:
#
#    a) Start in the middle of the top row, and let k = 1
#    b) Insert k into the grid.
#    c) If k = n^2, you are done.
#    d) Increment k.
#    e) Move diagonally up and to the right, but wrap to the first
#       column, or to the last row, if you leave the grid.
#    f) If that cell is already occupied, drop down one space from
#       your current position.
#    g) Return to step (b).  
# 
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    22 January 2023
#
#  Author:
#
#    Original Python version by Christian Hill.
#    This version by John Burkardt.
#
#  Reference:
#
#    Christian Hill,
#    Learning Scientific Programming with Python,
#    Cambridge University Press,
#    Second Edition, 2020,
#    ISBN: 978-1108745918
#
#  Input:
#
#    integer n: the number of rows and columns in the matrix,
#    which must be odd.
#
#  Output:
#
#    integer A(n,n): the magic matrix.
#
  import numpy as np

  if ( ( n % 2 ) != 1 ):
    print ( '' )
    print ( 'magic_matrix(): Fatal error!' )
    print ( '  Input value n must be an odd integer.' )
    raise Exception ( 'magic_matrix(): Fatal error!' )

  A = np.zeros ( [ n, n ], dtype = int )

  k = 1
  i = 0
  j = n // 2

  while ( k <= n**2 ):

    A[i,j] = k
    k = k + 1

    new_i = ( i - 1 ) % n
    new_j = ( j + 1 ) % n

    if ( A[new_i,new_j] ):
      i = i + 1
    else:
      i = new_i
      j = new_j

  return A