SRC/DEPRECATED/stzrqf.f(3)                            Library Functions Manual

NAME
       SRC/DEPRECATED/stzrqf.f

SYNOPSIS
   Functions/Subroutines
       subroutine stzrqf (m, n, a, lda, tau, info)
           STZRQF

Function/Subroutine Documentation
   subroutine stzrqf (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, integer info)
       STZRQF

       Purpose:


           !>
           !> This routine is deprecated and has been replaced by routine STZRZF.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.
           !>

       Parameters
           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
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Further Details:


           !>
           !>  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 ).
           !>

       Definition at line 137 of file stzrqf.f.

Author
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LAPACK                          Version 3.12.0      SRC/DEPRECATED/stzrqf.f(3)