matqr

Function: matqr
Section: linear_algebra
C-Name: matqr
Prototype: GD0,L,p
Help: matqr(M,{flag=0}): returns [Q,R], the QR-decomposition of the square
 invertible matrix M. If flag=1, Q is given as a sequence of Householder
 transforms (faster and stabler).
Doc: returns $[Q,R]$, the \idx{QR-decomposition} of the square invertible
 matrix $M$ with real entries: $Q$ is orthogonal and $R$ upper triangular. If
 $\fl=1$, the orthogonal matrix is returned as a sequence of Householder
 transforms: applying such a sequence is stabler and faster than
 multiplication by the corresponding $Q$ matrix.\sidx{Householder transform}
 More precisely, if
 \bprog
   [Q,R] = matqr(M);
   [q,r] = matqr(M, 1);
 @eprog\noindent then $r = R$ and \kbd{mathouseholder}$(q, M)$ is
 (close to) $R$; furthermore
 \bprog
   mathouseholder(q, matid(#M)) == Q~
 @eprog\noindent the inverse of $Q$. This function raises an error if the
 precision is too low or $x$ is singular.