f01rcf

Purpose

Synopsis

[a,theta,ifail] = f01rcf(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 unitary matrix and R is an n by n upper 
 triangular matrix with real diagonal elements.
 
 The factorization is obtained by Householder's method. The kth 
 transformation matrix, Q , which is used to introduce zeros into 
                         k                                       
 the kth column of A is given in the form
 
                               (I 0 )
                            Q =(0 T ),
                             k (   k)
 
 where
 
                                        H
                        T =I-(gamma) u u ,
                         k          k k k
 
                              ((zeta) )
                              (      k)
                           u =(z      ),
                            k ( k     )
 
 (gamma)  is a scalar for which Re (gamma) =1.0, (zeta)  is a real
        k                                 k            k      
 scalar and z  is an (m-k) element vector. (gamma) , (zeta)  and 
             k                                    k        k    
 z  are chosen to annihilate the elements below the triangular 
  k                                                           
 part of A and to make the diagonal elements real.
 
 The scalar (gamma)  and the vector u  are returned in the kth 
                   k                 k                        
 element of the array THETA and in the kth column of A, such that 
 (theta) , given by
        k        
 
                  (theta) =((zeta) ,Im(gamma) ),
                         k        k          k
 
 is in THETA(k) and the elements of z  are in a     ,...,a   . The
                                     k         k+1,k      m,k  
 elements of R are returned in the upper triangular part of A.
 
 Q is given by
 
                                        H
                         Q=(Q Q   ...Q ) .
                             n n-1    1  
 

Parameters

f01rcf

Required Input Arguments:

a (:,:)                               complex

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

a (:,:)                               complex
theta (:)                             complex
ifail                                 integer