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C Library Functions  - magic_square (3)

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NAME

magic_square(3f) - [M_math] create an N x N magic square array, N>2

CONTENTS

Synopsis
Description
Options
Author
Example

SYNOPSIS

subroutine magic_square(array)

   class(*) :: array

DESCRIPTION

This procedure returns a magic squares array, an n by n matrix in which each integer 1, 2, ..., n*n appears exactly once; and all columns, rows, and diagonals sum to the same number.

OPTIONS

array	An array to fill with the magic square values. The smallest dimension should be >= 3. Since a square is required only the values array(1:n,1:n) will be filled, where n=min(rows,columns). The array may be INTEGER, REAL, or DOUBLEPRECISION. Note that the routine allocates an integer array of the size determined by the input routine during execution.

AUTHOR

John S. Urban

Based on an algorithm for magic squares from

    Mathematical Recreations and Essays, 12th ed.,
    by W. W. Rouse Ball and H. S. M. Coxeter

EXAMPLE

Sample program

   program demo_magic_square
   use M_math, only : magic_square
   implicit none
   integer           :: arr(15,15)
   integer           :: i, j, k
      do k=1,15
         write(*,*)’K=’,k
         call magic_square(arr(:k,:k))
         do i=1,k
            write(*,’(i2,":",*(i5):)’)i,(int(arr(i,j)),j=1,k),sum(arr(k,:k))
         enddo
      enddo
   end program demo_magic_square

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Nemo Release 3.1

magic_square (3)

February 23, 2025

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