NAME

       dtzrqf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtzrqf (M, N, A, LDA, TAU, INFO)
           DTZRQF

Function/Subroutine Documentation

   subroutine dtzrqf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
       double precision, dimension( * )TAU, integerINFO)
       DTZRQF

       Purpose:

            This routine is deprecated and has been replaced by routine DTZRZF.

            DTZRQF 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.

       Date:
           November 2011

       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 139 of file dtzrqf.f.

Author

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