/// <summary>
/// Get the inverse of the decomposed matrix.
/// </summary>
/// <returns>the inverse matrix.</returns>
public RealMatrix getInverse()
{
return(solve(MatrixUtils.createRealIdentityMatrix(lTData.Length)));
}
/// <inheritdoc/>
public RealMatrix power(int p)
{
if (p < 0)
{
throw new NotPositiveException <Int32>(new LocalizedFormats("NOT_POSITIVE_EXPONENT"), p);
}
if (!isSquare())
{
throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());
}
if (p == 0)
{
return(MatrixUtils.createRealIdentityMatrix(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>();
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] = this.copy();
for (int i = 1; i <= maxI; ++i)
{
results[i] = results[i - 1].multiply(results[i - 1]);
}
RealMatrix result = this.copy();
foreach (Int32 i in nonZeroPositions)
{
result = result.multiply(results[i]);
}
return(result);
}
