/// <summary>
/// Gets the Cholesky decomposition of the matrix (L*L' = A), replacing its contents.
/// </summary>
/// <param name="isPosDef">True if <c>this</c> is positive definite, otherwise false.</param>
/// <returns>The Cholesky decomposition L. If <c>this</c> is positive semidefinite,
/// then L will satisfy L*L' = A.
/// Otherwise, L will only approximately satisfy L*L' = A.</returns>
/// <remarks>
/// <c>this</c> must be symmetric, but need not be positive definite.
/// </remarks>
public LowerTriangularMatrix CholeskyInPlace(out bool isPosDef)
{
LowerTriangularMatrix L = new LowerTriangularMatrix(rows, cols, data);
#if LAPACK
isPosDef = Lapack.CholeskyInPlace(this);
#else
isPosDef = L.SetToCholesky(this);
#endif
return(L);
}
public bool SetToCholesky(Matrix A)
{
A.CheckSymmetry(nameof(A));
#if LAPACK
SetTo(A);
bool isPosDef = Lapack.CholeskyInPlace(this);
#else
CheckCompatible(A, nameof(A));
bool isPosDef = true;
LowerTriangularMatrix L = this;
// compute the Cholesky factor
// Reference: Golub and van Loan (1996)
for (int i = 0; i < A.Cols; i++)
{
// upper triangle
for (int j = 0; j < i; j++)
{
L[j, i] = 0;
}
// lower triangle
for (int j = i; j < A.Rows; j++)
{
double sum = A[i, j];
int index1 = i * cols;
int index2 = j * cols;
for (int k = 0; k < i; k++)
{
//sum -= L[i, k] * L[j, k];
sum -= data[index1++] * data[index2++];
}
if (i == j)
{
// diagonal entry
if (sum <= 0)
{
isPosDef = false;
L[i, i] = 0;
}
else
{
L[i, i] = System.Math.Sqrt(sum);
}
}
else
{
// off-diagonal entry
if (L[i, i] > 0)
{
L[j, i] = sum / L[i, i];
}
else
{
L[j, i] = 0;
}
}
}
}
CheckLowerTriangular();
#endif
return(isPosDef);
}
