stzrqf3

!>
!> This routine is deprecated and has been replaced by routine STZRZF.
!>
!> STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
!> to upper triangular form by means of orthogonal transformations.
!>
!> The upper trapezoidal matrix A is factored as
!>
!>    A = ( R  0 ) * Z,
!>
!> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
!> triangular matrix.
!> 

M

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= M.
!> 

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the leading M-by-N upper trapezoidal part of the
!>          array A must contain the matrix to be factorized.
!>          On exit, the leading M-by-M upper triangular part of A
!>          contains the upper triangular matrix R, and elements M+1 to
!>          N of the first M rows of A, with the array TAU, represent the
!>          orthogonal matrix Z as a product of M elementary reflectors.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!> 

TAU

!>          TAU is REAL array, dimension (M)
!>          The scalar factors of the elementary reflectors.
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 

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!>
!>  The factorization is obtained by Householder's method.  The kth
!>  transformation matrix, Z( k ), which is used to introduce zeros into
!>  the ( m - k + 1 )th row of A, is given in the form
!>
!>     Z( k ) = ( I     0   ),
!>              ( 0  T( k ) )
!>
!>  where
!>
!>     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
!>                                                   (   0    )
!>                                                   ( z( k ) )
!>
!>  tau is a scalar and z( k ) is an ( n - m ) element vector.
!>  tau and z( k ) are chosen to annihilate the elements of the kth row
!>  of X.
!>
!>  The scalar tau is returned in the kth element of TAU and the vector
!>  u( k ) in the kth row of A, such that the elements of z( k ) are
!>  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
!>  the upper triangular part of A.
!>
!>  Z is given by
!>
!>     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
!>