core/mthQR_8h_source.html

 #ifndef MTH_QR_H

 #define MTH_QR_H


 #include "mthMatrix.h"


 namespace mth {


 template <class T, unsigned M, unsigned N>

 unsigned decomposeQR(

     Matrix<T,M,N> const& a,

     Matrix<T,M,M>& q,

     Matrix<T,M,N>& r);


 template <class T, unsigned M, unsigned N>

 void backsubUT(

     Matrix<T,M,N> const& r,

     Vector<T,M> const& b,

     Vector<T,N>& x);


 template <class T, unsigned M, unsigned N>

 void solveFromQR(Matrix<T,M,M> const& q,

     Matrix<T,M,N> const& r,

     Vector<T,M> const& b, Vector<T,N>& x);


 template <class T, unsigned M, unsigned N>

 bool solveQR(Matrix<T,M,N> const& a,

     Vector<T,M> const& b, Vector<T,N>& x);


 template <class T, unsigned M>

 void reduceToHessenberg(Matrix<T,M,M> const& a, Matrix<T,M,M>& q,

     Matrix<T,M,M>& h);


 template <class T, unsigned M>

 bool eigenQR(Matrix<T,M,M> const& a,

     Matrix<T,M,M>& l,

     Matrix<T,M,M>& q,

     unsigned max_iters);


 }


 #endif

mth::Matrix
compile-time (static) matrix
Definition: mthMatrix.h:24

mth::Vector
compile-time (static) vector of size N
Definition: mthVector.h:30

mthMatrix.h
Small compile-time and run-time linear algebra matrices.

mth
All MTH functions are contained in this namespace.

mth::decomposeQR
unsigned decomposeQR(Matrix< T, M, N > const &a, Matrix< T, M, M > &q, Matrix< T, M, N > &r)
finds the QR decomposition of A

mth::eigenQR
bool eigenQR(Matrix< T, M, M > const &a, Matrix< T, M, M > &l, Matrix< T, M, M > &q, unsigned max_iters)
computes the eigendecomposition of A

mth::solveFromQR
void solveFromQR(Matrix< T, M, M > const &q, Matrix< T, M, N > const &r, Vector< T, M > const &b, Vector< T, N > &x)
solves Ax = b given A's QR factorization

mth::backsubUT
void backsubUT(Matrix< T, M, N > const &r, Vector< T, M > const &b, Vector< T, N > &x)
solves Rx = b for upper triangular R

mth::solveQR
bool solveQR(Matrix< T, M, N > const &a, Vector< T, M > const &b, Vector< T, N > &x)
solves Ax = b using A's QR factorization