/// <summary>
/// Constructs a new Cholesky Decomposition.
/// </summary>
///
/// <param name="value">
/// The symmetric matrix, given in upper triangular form, to be decomposed.</param>
/// <param name="robust">
/// True to perform a square-root free LDLt decomposition, false otherwise.</param>
/// <param name="inPlace">
/// True to perform the decomposition in place, storing the factorization in the
/// lower triangular part of the given matrix.</param>
/// <param name="valueType">
/// How to interpret the matrix given to be decomposed. Using this parameter, a lower or
/// upper-triangular matrix can be interpreted as a symmetric matrix by assuming both lower
/// and upper parts contain the same elements. Use this parameter in conjunction with inPlace
/// to save memory by storing the original matrix and its decomposition at the same memory
/// location (lower part will contain the decomposition's L matrix, upper part will contains
/// the original matrix).</param>
///
public CholeskyDecompositionF(Single[,] value, bool robust = false,
bool inPlace = false, MatrixType valueType = MatrixType.UpperTriangular)
{
if (value.Rows() != value.Columns())
{
throw new DimensionMismatchException("value", "Matrix is not square.");
}
if (!inPlace)
{
value = value.Copy();
}
this.n = value.Rows();
this.L = value.ToUpperTriangular(valueType, result: value);
this.robust = robust;
if (robust)
{
LDLt(); // Compute square-root free decomposition
}
else
{
LLt(); // Compute standard Cholesky decomposition
}
}
/// <summary>Least squares solution of <c>X * A = B</c></summary>
/// <param name="value">Right-hand-side matrix with as many columns as <c>A</c> and any number of rows.</param>
/// <returns>A matrix that minimized the two norm of <c>X * Q * R - B</c>.</returns>
/// <exception cref="T:System.ArgumentException">Matrix column dimensions must be the same.</exception>
/// <exception cref="T:System.InvalidOperationException">Matrix is rank deficient.</exception>
public Single[,] SolveTranspose(Single[,] value)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (value.Columns() != qr.Rows())
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!this.FullRank)
{
throw new InvalidOperationException("Matrix is rank deficient.");
}
// Copy right hand side
int count = value.Rows();
var X = value.Transpose();
// Compute Y = transpose(Q)*B
for (int k = 0; k < p; k++)
{
for (int j = 0; j < count; j++)
{
Single s = 0;
for (int i = k; i < n; i++)
{
s += qr[i, k] * X[i, j];
}
s = -s / qr[k, k];
for (int i = k; i < n; i++)
{
X[i, j] += s * qr[i, k];
}
}
}
// Solve R*X = Y;
for (int k = m - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * qr[i, k];
}
}
}
return(Matrix.Create(count, p, X, transpose: true));
}
/// <summary>
/// Creates a new Cholesky decomposition directly from
/// an already computed left triangular matrix <c>L</c>.
/// </summary>
/// <param name="leftTriangular">The left triangular matrix from a Cholesky decomposition.</param>
///
public static CholeskyDecompositionF FromLeftTriangularMatrix(Single[,] leftTriangular)
{
var chol = new CholeskyDecompositionF();
chol.n = leftTriangular.Rows();
chol.L = leftTriangular;
chol.positiveDefinite = true;
chol.robust = false;
chol.D = Vector.Ones <Single>(chol.n);
return(chol);
}
/// <summary>Constructs a QR decomposition.</summary>
/// <param name="value">The matrix A to be decomposed.</param>
/// <param name="transpose">True if the decomposition should be performed on
/// the transpose of A rather than A itself, false otherwise. Default is false.</param>
/// <param name="inPlace">True if the decomposition should be done in place,
/// overriding the given matrix <paramref name="value"/>. Default is false.</param>
/// <param name="economy">True to perform the economy decomposition, where only
///.the information needed to solve linear systems is computed. If set to false,
/// the full QR decomposition will be computed.</param>
public QrDecompositionF(Single[,] value, bool transpose = false,
bool economy = true, bool inPlace = false)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if ((!transpose && value.Rows() < value.Columns()) ||
(transpose && value.Columns() < value.Rows()))
{
throw new ArgumentException("Matrix has more columns than rows.", "value");
}
// https://www.inf.ethz.ch/personal/gander/papers/qrneu.pdf
if (transpose)
{
this.p = value.Rows();
if (economy)
{
// Compute the faster, economy-sized QR decomposition
this.qr = value.Transpose(inPlace: inPlace);
}
else
{
// Create room to store the full decomposition
this.qr = Matrix.Create(value.Columns(), value.Columns(), value, transpose: true);
}
}
else
{
this.p = value.Columns();
if (economy)
{
// Compute the faster, economy-sized QR decomposition
this.qr = inPlace ? value : value.Copy();
}
else
{
// Create room to store the full decomposition
this.qr = Matrix.Create(value.Rows(), value.Rows(), value, transpose: false);
}
}
this.economy = economy;
this.n = qr.Rows();
this.m = qr.Columns();
this.Rdiag = new Single[m];
for (int k = 0; k < m; k++)
{
// Compute 2-norm of k-th column without under/overflow.
Single nrm = 0;
for (int i = k; i < n; i++)
{
nrm = Tools.Hypotenuse(nrm, qr[i, k]);
}
if (nrm != 0)
{
// Form k-th Householder vector.
if (qr[k, k] < 0)
{
nrm = -nrm;
}
for (int i = k; i < n; i++)
{
qr[i, k] /= nrm;
}
qr[k, k] += 1;
// Apply transformation to remaining columns.
for (int j = k + 1; j < m; j++)
{
Single s = 0;
for (int i = k; i < n; i++)
{
s += qr[i, k] * qr[i, j];
}
s = -s / qr[k, k];
for (int i = k; i < n; i++)
{
qr[i, j] += s * qr[i, k];
}
}
}
this.Rdiag[k] = -nrm;
}
}
/// <summary>
/// Solves a set of equation systems of type <c>A * X = B</c>.
/// </summary>
///
/// <param name="value">Right hand side matrix with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>Matrix <c>X</c> so that <c>L * L' * X = B</c>.</returns>
/// <exception cref="T:System.ArgumentException">Matrix dimensions do not match.</exception>
/// <exception cref="T:System.NonSymmetricMatrixException">Matrix is not symmetric.</exception>
/// <exception cref="T:System.NonPositiveDefiniteMatrixException">Matrix is not positive-definite.</exception>
/// <param name="inPlace">True to compute the solving in place, false otherwise.</param>
///
public Single[,] Solve(Single[,] value, bool inPlace)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.Rows() != n)
{
throw new ArgumentException("Argument matrix should have the same number of rows as the decomposed matrix.", "value");
}
if (!robust && !positiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Decomposed matrix is not positive definite.");
}
if (undefined)
{
throw new InvalidOperationException("The decomposition is undefined (zero in diagonal).");
}
if (destroyed)
{
throw new InvalidOperationException("The decomposition has been destroyed.");
}
// int count = value.Columns();
var B = inPlace ? value : value.MemberwiseClone();
int m = B.Columns();
// Solve L*Y = B;
for (int k = 0; k < n; k++)
{
for (int j = 0; j < m; j++)
{
for (int i = 0; i < k; i++)
{
B[k, j] -= B[i, j] * L[k, i];
}
B[k, j] /= L[k, k];
}
}
if (robust)
{
for (int k = 0; k < D.Length; k++)
{
for (int j = 0; j < m; j++)
{
B[k, j] /= D[k];
}
}
}
// Solve L'*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < m; j++)
{
for (int i = k + 1; i < n; i++)
{
B[k, j] -= B[i, j] * L[i, k];
}
B[k, j] /= L[k, k];
}
}
return(B);
}