#! /usr/bin/env python3 # def magic_matrix_test ( ): #*****************************************************************************80 # ## magic_matrix_test() tests magic_matrix(). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 22 December 2023 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'magic_matrix_test():' ) print ( ' Python version: ' + platform.python_version ( ) ) print ( ' Test magic_matrix()' ) magic_list_test ( ) magic_nparray_test ( ) # # Terminate. # print ( '' ) print ( 'magic_matrix_test():' ) print ( ' Normal end of execution.' ) def magic_list ( n ): #*****************************************************************************80 # ## magic_list() returns a magic matrix of odd order n as a list of lists. # # 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. # Modifications 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, as a list. # if ( ( n % 2 ) != 1 ): print ( '' ) print ( 'magic_list: Fatal error!' ) print ( ' Input value n must be an odd integer.' ) raise Exception ( 'magic_list(): Fatal error!' ) # # Awkwardly create an n x n list of lists. # row = [] for j in range ( 0, n ): row.append ( 0 ) A = [] for i in range ( 0, n ): A.append ( row.copy() ) # # Now fill it with integers 1 through n**2. # 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 def magic_list_test ( ): #*****************************************************************************80 # ## magic_list_test() tests magic_list(). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 22 December 2023 # # Author: # # John Burkardt # import pprint pp = pprint.PrettyPrinter ( indent = 2 ) print ( '' ) print ( 'magic_list_test():' ) print ( ' magic_list() creates a magic matrix as a list of lists.' ) for n in [ 3, 5 ]: A = magic_list ( n ) print ( '' ) print ( ' Magic matrix for n =', n ) pp.pprint ( A ) print ( ' Row sums:' ) for i in range ( 0, n ): rsum = 0 for j in range ( 0, n ): rsum = rsum + A[i][j] print ( ' ', rsum, end = '' ) print ( '' ) print ( ' Column sums:' ) for j in range ( 0, n ): csum = 0 for i in range ( 0, n ): csum = csum + A[i][j] print ( ' ', csum, end = '' ) print ( '' ) return def magic_nparray ( n ): #*****************************************************************************80 # ## magic_nparray() 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. # Modifications 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_nparray(): Fatal error!' ) print ( ' Input value n must be an odd integer.' ) raise Exception ( 'magic_nparray(): 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 def magic_nparray_test ( ): #*****************************************************************************80 # ## magic_nparray_test() tests magic_nparray(). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 December 2022 # # Author: # # John Burkardt # import numpy as np print ( '' ) print ( 'magic_nparray_test():' ) print ( ' magic_nparray() creates a magic matrix as a numpy array.' ) for n in [ 3, 5 ]: A = magic_nparray ( n ) print ( '' ) print ( ' Magic matrix for n =', n ) print ( A ) print ( ' Row sums:' ) rsum = np.sum ( A, axis = 1 ) print ( rsum ) print ( ' Column sums:' ) csum = np.sum ( A, axis = 0 ) print ( csum ) return def magic_matrix_old ( n ): #*****************************************************************************80 # ## magic_matrix_old() returns a magic matrix of odd order n. # # 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: # # 05 December 2022 # # Author: # # John Burkardt # # 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 = 1 j = ( n + 1 ) // 2 A[i-1,j-1] = k while ( k < n**2 ): k = k + 1 im1 = ( ( i - 2 ) % n ) + 1 jp1 = ( j % n ) + 1 if ( A[im1-1,jp1-1] != 0 ): im1 = i + 1 jp1 = j A[im1-1,jp1-1] = k i = im1 j = jp1 return A def timestamp ( ): #*****************************************************************************80 # ## timestamp() prints the date as a timestamp. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 21 August 2019 # # Author: # # John Burkardt # import time t = time.time ( ) print ( time.ctime ( t ) ) return if ( __name__ == '__main__' ): timestamp ( ) magic_matrix_test ( ) timestamp ( )