/// <summary>
/// Gets lower upper permutation with matrix C which calculate by formula:
/// <c>C=L+U-E</c>
/// </summary>
/// <typeparam name="T"></typeparam>
/// <returns></returns>
public static void GetLowerUpperPermutation <T>(this Matrix <T> matrix, out Matrix <T> matrixC, out Matrix <T> matrixP) where T : unmanaged
{
int n = matrix.Rows;
matrixC = matrix.Clone() as Matrix <T>;
if (matrixC is null)
{
throw new NullReferenceException();
}
// load to P identity matrix.
matrixP = BuildMatrix.CreateIdentityMatrix <T>(matrix.Rows, matrix.Columns);
var comparer = Comparer <T> .Default;
for (int i = 0; i < n; i++)
{
T pivotValue = default;
int pivot = -1;
for (int j = i; j < n; j++)
{
if (comparer.Compare(MathGeneric <T> .Abs(matrixC[j, i]), pivotValue) > 0)
{
pivotValue = MathGeneric <T> .Abs(matrixC[j, i]);
pivot = j;
}
}
if (pivot != 0)
{
matrixP.SwapRows(pivot, i);
matrixC.SwapRows(pivot, i);
for (int j = i + 1; j < n; j++)
{
matrixC[j, i] = MathGeneric <T> .Divide(matrixC[j, i], matrixC[i, i]);
for (int k = i + 1; k < n; k++)
{
matrixC[j, k] = MathUnsafe <T> .Sub(matrixC[j, k],
MathUnsafe <T> .Mul(matrixC[j, i], matrix[i, k]));
}
}
}
}
}
/// <summary>
/// Raises a matrix to a power.
/// </summary>
/// <param name="matrix">the matrix</param>
/// <param name="degree">the degree</param>
/// <typeparam name="T">unmanaged type</typeparam>
/// <returns>Pow</returns>
/// <exception cref="MatrixDotNetException"></exception>
public static Matrix <T> Pow <T>(this Matrix <T> matrix, uint degree)
where T : unmanaged
{
if (degree == 0)
{
return(BuildMatrix.CreateIdentityMatrix <T>(matrix.Rows, matrix.Columns));
}
if ((degree & 1) == 1)
{
return(matrix.Pow(degree - 1) * matrix);
}
var t = matrix.Pow(degree >> 1);
return(t * t);
}
