/// <summary>
/// Returns the inverse of this lower triangular matrix
/// </summary>
/// <returns></returns>
public new LowerTriangularMatrix Inverse()
{
LowerTriangularMatrix L = new LowerTriangularMatrix(rows, cols);
L.SetToInverse(this);
return(L);
}
/// <summary>
/// Creates a full clone of this instance (including the data)
/// </summary>
/// <returns></returns>
public override object Clone()
{
LowerTriangularMatrix result = new LowerTriangularMatrix(rows, cols);
result.SetTo(this);
return(result);
}
/// <summary>
/// Return the transpose of this upper triangular matrix
/// </summary>
/// <returns></returns>
public new LowerTriangularMatrix Transpose()
{
LowerTriangularMatrix L = new LowerTriangularMatrix(cols, rows);
L.SetToTranspose(this);
return(L);
}
/// <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)
{
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);
}
public static void Wishart(double a, LowerTriangularMatrix result)
{
Assert.IsTrue(result.Rows == result.Cols);
for (int i = 0; i < result.Rows; ++i)
{
for (int j = 0; j < i; ++j)
{
result[i, j] = Normal() * MMath.SqrtHalf;
result[j, i] = 0;
}
result[i, i] = System.Math.Sqrt(Gamma(a - i * 0.5));
}
}
/// <summary>
/// Sets b to inv(A)*b.
/// </summary>
/// <param name="b"></param>
/// <param name="A"></param>
public static void PredivideBy(DenseVector b, LowerTriangularMatrix A)
{
Assert.IsTrue(A.Rows == A.Cols);
Assert.IsTrue(A.Rows == b.Count);
// Lapack is column-major, so we tell it that A is upper triangular and transposed
char side = 'L', uplo = 'U', trans = 'T', diag = 'N';
double alpha = 1;
ptrdiff_t m = b.Count, n = 1;
fixed (double* sA = A.SourceArray, sB = b.SourceArray) {
double* pA = sA, pB = sB;
dtrsm(&side, &uplo, &trans, &diag, &m, &n, &alpha, pA, &m, pB, &m);
}
}
public static void NormalP(Vector mean, PositiveDefiniteMatrix precision, Vector result)
{
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);
}
/// <summary>
/// Sets B to A'\B.
/// </summary>
/// <param name="B"></param>
/// <param name="A"></param>
public static void PredivideByTranspose(Matrix B, LowerTriangularMatrix A)
{
Assert.IsTrue(A.Rows == A.Cols);
Assert.IsTrue(A.Rows == B.Rows);
Assert.IsTrue(!object.ReferenceEquals(B, A));
// Lapack is column-major, so we tell it that A is upper triangular and switch sides:
// inv(A)*B = (B'*inv(A'))'
char side = 'R', uplo = 'U', trans = 'T', diag = 'N';
double alpha = 1;
ptrdiff_t m = B.Cols, n = B.Rows;
fixed (double* sA = A.SourceArray, sB = B.SourceArray) {
double* pA = sA, pB = sB;
dtrsm(&side, &uplo, &trans, &diag, &m, &n, &alpha, pA, &n, pB, &m);
}
}
public static void NormalChol(Vector mean, LowerTriangularMatrix varChol, Vector result)
{
if (ReferenceEquals(mean, result))
{
throw new ArgumentException("mean and result are the same object");
}
Vector temp = Vector.Zero(result.Count);
for (int i = 0; i < result.Count; i++)
{
temp[i] = Normal();
}
result.SetToProduct(varChol, temp);
result.SetToSum(mean, result);
// result = mean + varChol*N(0,1)
}
/// <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 UpperTriangularMatrix GetsTranspose(LowerTriangularMatrix L)
{
if (rows != L.Cols || cols != L.Rows)
{
throw new ArgumentException("Output matrix is not compatible with the transpose", "that");
}
L.CheckLowerTriangular();
// lower triangle of this is assumed to be zero
for (int i = 0; i < rows; ++i)
{
for (int j = i; j < cols; ++j)
{
this[i, j] = L[j, i];
}
}
CheckUpperTriangular();
return(this);
}
/// <remarks>U is no longer a valid upper triangular matrix.</remarks>
public static LowerTriangularMatrix TransposeInPlace(UpperTriangularMatrix U)
{
U.CheckUpperTriangular();
LowerTriangularMatrix L = new LowerTriangularMatrix(U.Cols, U.Rows,
U.SourceArray, U.Start);
Assert.IsTrue(L.Rows == L.Cols);
for (int i = 0; i < L.Rows; ++i)
{
for (int j = 0; j < i; ++j)
{
L[i, j] = L[j, i];
L[j, i] = 0;
}
}
L.CheckLowerTriangular();
return(L);
}
/// <summary>
/// Transposes a given lower triangular matrix in place.
/// </summary>
/// <param name="L">Matrix to transpose. Contents are corrupted on exit.</param>
/// <returns>An upper triangular wrapper of L's source array.</returns>
/// <remarks>L is no longer a valid lower triangular matrix.</remarks>
public static UpperTriangularMatrix TransposeInPlace(LowerTriangularMatrix L)
{
L.CheckLowerTriangular();
UpperTriangularMatrix U = new UpperTriangularMatrix(L.Cols, L.Rows,
L.SourceArray);
Assert.IsTrue(U.Rows == U.Cols);
for (int i = 0; i < U.Rows; ++i)
{
for (int j = i + 1; j < U.Cols; ++j)
{
U[i, j] = U[j, i];
U[j, i] = 0;
}
}
U.CheckUpperTriangular();
return(U);
}
/// <summary>
/// Modifies <c>this</c> to be the inverse of A.
/// </summary>
/// <param name="A">Can be the same object as <c>this</c></param>
public void SetToInverse(LowerTriangularMatrix A)
{
#if LAPACK
if (object.ReferenceEquals(this, A))
{
A = (LowerTriangularMatrix)A.Clone();
}
this.SetToIdentity();
Lapack.PredivideBy(this, A);
#else
// Reference: Golub and van Loan (1996)
Assert.IsTrue(A.Rows == A.Cols);
Assert.IsTrue(A.Rows == this.Rows);
for (int k = 0; k < rows; k++)
{
if (A[k, k] == 0)
{
throw new MatrixSingularException(A);
}
}
for (int j = 0; j < cols; j++)
{
int index1 = j;
// k < j case
for (int k = 0; k < j; k++)
{
//B[k, j] = 0.0;
data[index1] = 0.0;
index1 += cols;
}
// k == j case
int index2 = j + j * cols;
double v = 1.0 / A.data[index2];
data[index1] = v;
for (int i = j + 1; i < rows; i++)
{
// B[i, j] = -v * A[i, j];
index1 += cols;
index2 += cols;
data[index1] = -v * A.data[index2];
}
// k > j case
for (int k = j + 1; k < rows; k++)
{
index1 = j + k * cols;
index2 = k + k * cols;
if (data[index1] != 0)
{
//double u = B[k,j]/A[k,k];
//B[k, j] = u;
// TM: this style of indexing may look ugly but it runs much faster
double u = data[index1] / A.data[index2];
data[index1] = u;
for (int i = k + 1; i < rows; i++)
{
// B[i, j] -= u * A[i, k];
index1 += cols;
index2 += cols;
data[index1] -= u * A.data[index2];
}
}
}
}
#endif
}
public bool SetToCholesky(Matrix A)
{
A.CheckSymmetry("A");
#if LAPACK
SetTo(A);
bool isPosDef = Lapack.CholeskyInPlace(this);
#else
CheckCompatible(A, "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);
}
/// <summary>
/// Returns the natural logarithm of the determinant of this positive-definite matrix.
/// </summary>
/// <param name="ignoreInfinity">If true, +infinity on the diagonal is treated as 1.</param>
/// <returns>The log-determinant of <c>this</c>.</returns>
public double LogDeterminant(bool ignoreInfinity = false)
{
LowerTriangularMatrix L = new LowerTriangularMatrix(rows, cols);
return(LogDeterminant(L, ignoreInfinity));
}
public double LogDeterminant(LowerTriangularMatrix L, bool ignoreInfinity = false)
{
L.SetToCholesky(this);
return(2 * L.LogDeterminant(ignoreInfinity));
}