/// <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 static void Normal(Vector mean, PositiveDefiniteMatrix variance, Vector result, IPolyrand random = null)
{
LowerTriangularMatrix L = new LowerTriangularMatrix(variance.Rows, variance.Rows);
bool isPosDef = L.SetToCholesky(variance);
if (!isPosDef)
{
throw new ArgumentException("PROB.Random.Normal(Vector,Matrix,Vector): variance must be positive definite", nameof(variance));
}
NormalChol(mean, L, result, random);
}
public static void NormalP(Vector mean, PositiveDefiniteMatrix precision, Vector result, IPolyrand random = null)
{
LowerTriangularMatrix L = new LowerTriangularMatrix(precision.Rows, precision.Rows);
bool isPosDef = L.SetToCholesky(precision);
if (!isPosDef)
{
throw new ArgumentException("PROB.Random.NormalP(Vector,Matrix,Vector): precision must be positive definite", nameof(precision));
}
UpperTriangularMatrix U = UpperTriangularMatrix.TransposeInPlace(L);
NormalPChol(mean, U, result, random);
}
/// <summary>
/// Sets this positive-definite matrix to inverse of a given positive-definite matrix
/// where a lower triangular workspace is passed.
/// </summary>
/// <param name="A">A symmetric positive-definite matrix, same size as <c>this</c>. Can be the same object as <c>this</c>.</param>
/// <param name="L">A workspace, same size as <paramref name="A"/>.</param>
/// <returns><c>this</c></returns>
/// <exception cref="PositiveDefiniteMatrixException">If <paramref name="A"/> is not positive definite.</exception>
public PositiveDefiniteMatrix SetToInverse(PositiveDefiniteMatrix A, LowerTriangularMatrix L)
{
CheckCompatible(L, nameof(L));
// Algorithm:
// A = L*L'
// inv(A) = inv(L')*inv(L)
bool isPD = L.SetToCholesky(A);
if (!isPD)
{
throw new PositiveDefiniteMatrixException();
}
L.SetToInverse(L);
SetToOuterTranspose(L);
return(this);
}
public double LogDeterminant(LowerTriangularMatrix L, bool ignoreInfinity = false)
{
L.SetToCholesky(this);
return(2 * L.LogDeterminant(ignoreInfinity));
}