/// <summary>
/// Explicitly creates the upper triangular matrix U that resulted from the Cholesky factorization: A = transpose(U) * U,
/// where A and U are n-by-n.
/// This method is safe to use as the factorization data are copied (if necessary). However, it is inefficient if the
/// generated matrix is only used once.
/// </summary>
public TriangularUpper GetFactorU()
{
// The factorization A = transpose(u) * D * u, u = unit upper triangular is stored. Thus U = sqrt(D) * u.
// Since D is diagonal, we need to scale each column j of u by sqrt(D[j,j]).
var upper = TriangularUpper.CreateZero(Order);
for (int j = 0; j < Order; ++j)
{
int colheight = diagOffsets[j + 1] - diagOffsets[j] - 1;
for (int t = 0; t < colheight + 1; ++t)
{
int i = j - t;
upper[i, j] = values[diagOffsets[j] + t];
}
}
return(upper);
}
/// <summary>
/// Copies the upper triangular matrix U and diagonal matrix D that resulted from the Cholesky factorization:
/// A = transpose(U) * D * U to a new <see cref="TriangularUpper"/> matrix.
/// </summary>
public (Vector diagonal, TriangularUpper upper) GetFactorsDU() //TODO: not sure if this is ever needed.
{
double[] diag = new double[Order];
var upper = TriangularUpper.CreateZero(Order);
for (int j = 0; j < Order; ++j)
{
int diagOffset = diagOffsets[j];
int colTop = j - diagOffsets[j + 1] + diagOffset + 1;
diag[j] = values[diagOffset];
upper[j, j] = 1.0;
for (int i = j - 1; i >= colTop; --i)
{
int offset = diagOffset + j - i;
upper[i, j] = values[offset];
}
}
return(Vector.CreateFromArray(diag, false), upper);
}