/// <summary>
/// Creates a jagged magic square matrix.
/// </summary>
///
public static double[][] Magic(int size)
{
return(Matrix.Magic(size).ToJagged());
}
/// <summary>
/// Creates a magic square matrix.
/// </summary>
public static double[,] Magic(int size)
{
if (size < 3)
{
throw new ArgumentOutOfRangeException("size", size,
"The square size must be greater or equal to 3.");
}
double[,] matrix = new double[size, size];
// First algorithm: Odd order
if ((size % 2) == 1)
{
int a = (size + 1) / 2;
int b = (size + 1);
for (int j = 0; j < size; j++)
{
for (int i = 0; i < size; i++)
{
matrix[i, j] = size * ((i + j + a) % size) + ((i + 2 * j + b) % size) + 1;
}
}
}
// Second algorithm: Even order (double)
else if ((size % 4) == 0)
{
for (int j = 0; j < size; j++)
{
for (int i = 0; i < size; i++)
{
if (((i + 1) / 2) % 2 == ((j + 1) / 2) % 2)
{
matrix[i, j] = size * size - size * i - j;
}
else
{
matrix[i, j] = size * i + j + 1;
}
}
}
}
// Third algorithm: Even order (single)
else
{
int n = size / 2;
int p = (size - 2) / 4;
double t;
double[,] block = Matrix.Magic(n);
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
double e = block[i, j];
matrix[i, j] = e;
matrix[i, j + n] = e + 2 * n * n;
matrix[i + n, j] = e + 3 * n * n;
matrix[i + n, j + n] = e + n * n;
}
}
for (int i = 0; i < n; i++)
{
// Swap M[i,j] and M[i+n,j]
for (int j = 0; j < p; j++)
{
t = matrix[i, j];
matrix[i, j] = matrix[i + n, j];
matrix[i + n, j] = t;
}
for (int j = size - p + 1; j < size; j++)
{
t = matrix[i, j];
matrix[i, j] = matrix[i + n, j];
matrix[i + n, j] = t;
}
}
// Continue swaping in the boundary
t = matrix[p, 0];
matrix[p, 0] = matrix[p + n, 0];
matrix[p + n, 0] = t;
t = matrix[p, p];
matrix[p, p] = matrix[p + n, p];
matrix[p + n, p] = t;
}
return(matrix); // return the magic square.
}
/// <summary>
/// Creates a jagged magic square matrix.
/// </summary>
///
public static double[][] Magic(int size)
{
return(Matrix.Magic(size).ToArray());
}
