f01qcf

Purpose

Synopsis

[a,zeta,ifail] = f01qcf(a<,ifail>)

Description

 
 The m by n matrix A is factorized as
 
           (R)       
        A=Q(0)       when m>n,
 
        A=QR         when m=n,
 
 where Q is an m by m orthogonal matrix and R is an n by n upper 
 triangular matrix. The factorization is obtained by Householder's
 method. The kth transformation matrix, Q , which is used to 
                                         k                  
 introduce zeros into the kth column of A is given in the form
 
                                (I 0 )
                             Q =(0 T )
                              k (   k)
 
 where
 
                                    T
                            T =I-u u ,
                             k    k k
 
                              ((zeta) )
                              (      k)
                           u =( z     ),
                            k (  k    )
 
 (zeta)  is a scalar and z  is an (m-k) element vector. (zeta)  
       k                  k                                   k
 and z  are chosen to annihilate the elements below the triangular
      k                                                 
 part of A.
 
 The vector u  is returned in the kth element of the array ZETA 
             k                                                 
 and in the kth column of A, such that (zeta)  is in ZETA(k) and 
                                             k                  
 the elements of z  are in A(k+1,k),...,A(m,k). The elements of R 
                  k                                              
 are returned in the upper triangular part of A.
 
 Q is given by
 
                                        T
                         Q=(Q Q   ...Q ) .
                             n n-1    1  
 

Parameters

f01qcf

Required Input Arguments:

a (:,:)                               real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

a (:,:)                               real
zeta (:)                              real
ifail                                 integer