Provided by: liblapack-doc_3.3.1-1_all bug


       LAPACK-3 - routine i deprecated and has been replaced by routine CTZRZF



           INTEGER        INFO, LDA, M, N

           COMPLEX        A( LDA, * ), TAU( * )


       This routine is deprecated and has been replaced by routine CTZRZF.
        CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
        to upper triangular form by means of unitary transformations.
        The upper trapezoidal matrix A is factored as
           A = ( R  0 ) * Z,
        where Z is an N-by-N unitary matrix and R is an M-by-M upper
        triangular matrix.


        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.

        N       (input) INTEGER
                The number of columns of the matrix A.  N >= M.

        A       (input/output) COMPLEX 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
                unitary matrix Z as a product of M elementary reflectors.

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

        TAU     (output) COMPLEX array, dimension (M)
                The scalar factors of the elementary reflectors.

        INFO    (output) INTEGER
                = 0: successful exit
                < 0: if INFO = -i, the i-th argument had an illegal value


        The  factorization is obtained by Householder's method.  The kth
        transformation matrix, Z( k ), whose conjugate transpose 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 ) )
           T( k ) = I - tau*u( k )*u( k )**H,   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 ).

 LAPACK routine (version 3.3.1)             April 2011                            CTZRQF(3lapack)