SRIMatrix.hpp File Reference

---

Detailed Description

Template routines for efficient manipulation of square root matricies, used for least squares estimation and the SRI form of the Kalman filter.

Definition in file SRIMatrix.hpp.

#include "Vector.hpp"
#include "Matrix.hpp"
#include "StringUtils.hpp"

Include dependency graph for SRIMatrix.hpp:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Namespaces
namespace	gpstk
Functions
template<class T>
void	SrifMU (Matrix< T > &R, Vector< T > &Z, Matrix< T > &A, unsigned int M=0) throw (MatrixException)
	Square root information measurement update, with new data in the form of a single matrix concatenation of H and D: A = H || D.
template<class T>
void	SrifMU (Matrix< T > &R, Vector< T > &Z, const Matrix< T > &H, Vector< T > &D, unsigned int M=0) throw (MatrixException)
	Square root information filter (Srif) measurement update (MU).
template<class T>
Matrix< T >	lowerCholesky (const Matrix< T > &A) throw (MatrixException)
	Compute lower triangular square root of a symmetric positive definite matrix (Cholesky decomposition) Crout algorithm.
template<class T>
Matrix< T >	upperCholesky (const Matrix< T > &A) throw (MatrixException)
	Compute upper triangular square root of a symmetric positive definite matrix (Cholesky decomposition) Crout algorithm; that is A = transpose(U)*U.
template<class T>
Matrix< T >	inverseCholesky (const Matrix< T > &A) throw (MatrixException)
	Compute inverse of a symmetric positive definite matrix using Cholesky decomposition.
template<class T>
Matrix< T >	inverseUT (const Matrix< T > &UT, T *ptrSmall=NULL, T *ptrBig=NULL) throw (MatrixException)
	Compute inverse of upper triangular matrix, returning smallest and largest eigenvalues.
template<class T>
Matrix< T >	UTtimesTranspose (const Matrix< T > &UT) throw (MatrixException)
	Compute the product of an upper triangular matrix and its transpose.

---

Function Documentation

Matrix<T> inverseCholesky (  const Matrix< T > &  A  )  throw (MatrixException)

Compute inverse of a symmetric positive definite matrix using Cholesky decomposition. Parameters: A  Matrix to be inverted; symmetric and positive definite, unchanged Returns: Matrix inverse of input matrix Exceptions: MatrixException  if input Matrix is not square SingularMatrixException  if input Matrix is singular Definition at line 306 of file SRIMatrix.hpp. References GPSTK_RETHROW, gpstk::inverseUT(), gpstk::lowerCholesky(), gpstk::transpose(), and gpstk::UTtimesTranspose().

Matrix<T> inverseUT (  const Matrix< T > &  UT, T *  ptrSmall = NULL, T *  ptrBig = NULL )  throw (MatrixException)

Compute inverse of upper triangular matrix, returning smallest and largest eigenvalues. Parameters: UT  upper triangular matrix to be inverted ptrS  pointer to <t> small, on output *ptrS contains smallest eigenvalue. ptrB  pointer to <t> small, on output *ptrB contains largest eigenvalue. Returns: inverse of input matrix. Exceptions: MatrixException  if input is not square (assumed upper triangular also). SingularMatrixException  if input is singular. Definition at line 336 of file SRIMatrix.hpp. References GPSTK_THROW, Matrix::rows(), and gpstk::sum(). Referenced by SRI::getStateAndCovariance(), and gpstk::inverseCholesky().

Matrix<T> lowerCholesky (  const Matrix< T > &  A  )  throw (MatrixException)

Compute lower triangular square root of a symmetric positive definite matrix (Cholesky decomposition) Crout algorithm. Parameters: A  Matrix to be decomposed; symmetric and positive definite, unchanged Returns: Matrix lower triangular square root of input matrix Exceptions: MatrixException  if input Matrix is not square MatrixException  if input Matrix is not positive definite Definition at line 250 of file SRIMatrix.hpp. References GPSTK_THROW, and Matrix::rows(). Referenced by gpstk::inverseCholesky(), and gpstk::upperCholesky().

void SrifMU (  Matrix< T > &  R, Vector< T > &  Z, const Matrix< T > &  H, Vector< T > &  D, unsigned int  M = 0 )  throw (MatrixException)

Square root information filter (Srif) measurement update (MU). Use the Householder transformation to combine the information stored in the square root information (SRI) covariance matrix R and state Z with new information in the given partials matrix and data vector to produce an updated SRI {R,Z}. Measurement noise associated with the new information (H and D) is assumed to be white with unit covariance. If necessary, the data may be 'whitened' by multiplying H and D by the inverse of the lower triangular square root of the covariance matrix; that is, compute L = Cholesky(Measurement covariance) and let H = L*H, D = L*D. Parameters: R  Upper triangluar apriori SRI covariance matrix of dimension N Z  A priori SRI state vector of length N H  Partials matrix of dimension MxN, unchanged on output. D  Data vector of length M; on output contains the residuals of fit. M  If H and D have dimension M' > M, then call with M = data length; otherwise M = 0 (the default) and is ignored. Exceptions: MatrixException  if the input has inconsistent dimensions. Definition at line 208 of file SRIMatrix.hpp. References ConstMatrixBase< T, Matrix< T > >::colCopy(), Matrix::cols(), and GPSTK_RETHROW. Referenced by SRI::addAPrioriInformation(), SRI::measurementUpdate(), SRI::permute(), and SRI::transform().

void SrifMU (  Matrix< T > &  R, Vector< T > &  Z, Matrix< T > &  A, unsigned int  M = 0 )  throw (MatrixException)

Square root information measurement update, with new data in the form of a single matrix concatenation of H and D: A = H || D. See doc for the overloaded SrifMU(). Definition at line 125 of file SRIMatrix.hpp. References gpstk::beta(), GPSTK_THROW, and gpstk::sum(). Referenced by SRIleastSquares::dataUpdate(), and SRIFilter::measurementUpdate().

Matrix<T> upperCholesky (  const Matrix< T > &  A  )  throw (MatrixException)

Compute upper triangular square root of a symmetric positive definite matrix (Cholesky decomposition) Crout algorithm; that is A = transpose(U)*U. Note that this result will be equal to transpose(lowerCholesky(A)) == transpose(Ch.L from class Cholesky), NOT Ch.U; class Cholesky computes L,U where A = L*LT = U*UT [while A=UT*U here]. Parameters: A  Matrix to be decomposed; symmetric and positive definite, unchanged Returns: Matrix upper triangular square root of input matrix Exceptions: MatrixException  if input Matrix is not square MatrixException  if input Matrix is not positive definite Definition at line 294 of file SRIMatrix.hpp. References gpstk::lowerCholesky(), and gpstk::transpose().

Matrix<T> UTtimesTranspose (  const Matrix< T > &  UT  )  throw (MatrixException)

Compute the product of an upper triangular matrix and its transpose. Parameters: UT  upper triangular matrix Returns: product UT * transpose(UT) Exceptions: MatrixException  if input is not square (assumed upper triangular also). Definition at line 399 of file SRIMatrix.hpp. References GPSTK_THROW, Matrix::rows(), and gpstk::sum(). Referenced by SRI::getStateAndCovariance(), and gpstk::inverseCholesky().

---