/// <inheritdoc/>
public FieldMatrix <T> power(int p)
{
if (p < 0)
{
throw new NotPositiveException <Int32>(p);
}
if (!isSquare())
{
throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());
}
if (p == 0)
{
return(MatrixUtils.createFieldIdentityMatrix(this.getField(), this.getRowDimension()));
}
if (p == 1)
{
return(this.copy());
}
int power = p - 1;
/*
* Only log_2(p) operations is used by doing as follows:
* 5^214 = 5^128 * 5^64 * 5^16 * 5^4 * 5^2
*
* In general, the same approach is used for A^p.
*/
char[] binaryRepresentation = Convert.ToString(power, 2).ToCharArray();
List <Int32> nonZeroPositions = new List <Int32>();
for (int i = 0; i < binaryRepresentation.Length; ++i)
{
if (binaryRepresentation[i] == '1')
{
int pos = binaryRepresentation.Length - i - 1;
nonZeroPositions.Add(pos);
}
}
List <FieldMatrix <T> > results = new List <FieldMatrix <T> >(binaryRepresentation.Length);
results[0] = this.copy();
for (int i = 1; i < binaryRepresentation.Length; ++i)
{
FieldMatrix <T> s = results[i - 1];
FieldMatrix <T> r = s.multiply(s);
results[i] = r;
}
FieldMatrix <T> result = this.copy();
foreach (int i in nonZeroPositions)
{
result = result.multiply(results[i]);
}
return(result);
}
