/** {@inheritDoc} */
public RealMatrix power(int p)
{
if (p < 0)
{
throw new Exception("NotPositiveException");
}
if (!isSquare())
{
throw new Exception("NonSquareMatrixException");
}
if (p == 0)
{
return(MatrixUtils.CreateRealIdentityMatrix(getRowDimension()));
}
if (p == 1)
{
return(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 = Integer.ToBinaryString(power).ToCharArray();
List <Integer> nonZeroPositions = new List <Integer>();
int maxI = -1;
for (int i = 0; i < binaryRepresentation.Length; ++i)
{
if (binaryRepresentation[i] == '1')
{
int pos = binaryRepresentation.Length - i - 1;
nonZeroPositions.Add(pos);
// The positions are taken in turn, so maxI is only changed once
if (maxI == -1)
{
maxI = pos;
}
}
}
RealMatrix[] results = new RealMatrix[maxI + 1];
results[0] = copy();
for (int i = 1; i <= maxI; ++i)
{
results[i] = results[i - 1].multiply(results[i - 1]);
}
RealMatrix result = copy();
foreach (Integer i in nonZeroPositions)
{
result = result.multiply(results[i]);
}
return(result);
}
