#include <tnt_linalg.h>
Public Member Functions | |
QR (const Matrix< Real > &A) | |
int | isFullRank () const |
Matrix< Real > | getHouseholder (void) const |
Matrix< Real > | getR () const |
Matrix< Real > | getQ () const |
Vector< Real > | solve (const Vector< Real > &b) const |
Matrix< Real > | solve (const Matrix< Real > &B) const |
Private Attributes | |
Matrix< Real > | QR_ |
int | m |
int | n |
Vector< Real > | Rdiag |
The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns 0 (false).
The Q and R factors can be retrived via the getQ() and getR() methods. Furthermore, a solve() method is provided to find the least squares solution of Ax=b using the QR factors.
(Adapted from JAMA, a Java Matrix Library, developed by jointly by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).
Definition at line 1565 of file tnt_linalg.h.
TNT::Linear_Algebra::QR< Real >::QR | ( | const Matrix< Real > & | A | ) | [inline] |
Create a QR factorization object for A.
A | rectangular (m>=n) matrix. |
Definition at line 1593 of file tnt_linalg.h.
Matrix<Real> TNT::Linear_Algebra::QR< Real >::getHouseholder | ( | void | ) | const [inline] |
Retreive the Householder vectors from QR factorization
Definition at line 1660 of file tnt_linalg.h.
Matrix<Real> TNT::Linear_Algebra::QR< Real >::getQ | ( | ) | const [inline] |
Definition at line 1712 of file tnt_linalg.h.
Matrix<Real> TNT::Linear_Algebra::QR< Real >::getR | ( | ) | const [inline] |
Return the upper triangular factor, R, of the QR factorization
Definition at line 1687 of file tnt_linalg.h.
int TNT::Linear_Algebra::QR< Real >::isFullRank | ( | ) | const [inline] |
Flag to denote the matrix is of full rank.
Definition at line 1641 of file tnt_linalg.h.
Matrix<Real> TNT::Linear_Algebra::QR< Real >::solve | ( | const Matrix< Real > & | B | ) | const [inline] |
Least squares solution of A*X = B
B | m x k Array (must conform). |
Definition at line 1797 of file tnt_linalg.h.
Vector<Real> TNT::Linear_Algebra::QR< Real >::solve | ( | const Vector< Real > & | b | ) | const [inline] |
Least squares solution of A*x = b
b | right hand side (m-length vector). |
Definition at line 1746 of file tnt_linalg.h.
int TNT::Linear_Algebra::QR< Real >::m [private] |
Definition at line 1578 of file tnt_linalg.h.
int TNT::Linear_Algebra::QR< Real >::n [private] |
Definition at line 1578 of file tnt_linalg.h.
Matrix<Real> TNT::Linear_Algebra::QR< Real >::QR_ [private] |
Definition at line 1572 of file tnt_linalg.h.
Vector<Real> TNT::Linear_Algebra::QR< Real >::Rdiag [private] |
Definition at line 1583 of file tnt_linalg.h.