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

NAME

       LAPACK-3  - forms the triangular factor T of a complex block reflector H of order n, which
       is defined as a product of k elementary reflectors

SYNOPSIS

       SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

           CHARACTER      DIRECT, STOREV

           INTEGER        K, LDT, LDV, N

           COMPLEX*16     T( LDT, * ), TAU( * ), V( LDV, * )

PURPOSE

       ZLARFT forms the triangular factor T of a complex block reflector H of order n,  which  is
       defined as a product of k elementary reflectors.
        If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
        If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
        If STOREV = 'C', the vector which defines the elementary reflector
        H(i) is stored in the i-th column of the array V, and
           H  =  I - V * T * V**H
        If STOREV = 'R', the vector which defines the elementary reflector
        H(i) is stored in the i-th row of the array V, and
           H  =  I - V**H * T * V

ARGUMENTS

        DIRECT  (input) CHARACTER*1
                Specifies the order in which the elementary reflectors are
                multiplied to form the block reflector:
                = 'F': H = H(1) H(2) . . . H(k) (Forward)
                = 'B': H = H(k) . . . H(2) H(1) (Backward)

        STOREV  (input) CHARACTER*1
                Specifies how the vectors which define the elementary
                reflectors are stored (see also Further Details):
                = 'R': rowwise

        N       (input) INTEGER
                The order of the block reflector H. N >= 0.

        K       (input) INTEGER
                The order of the triangular factor T (= the number of
                elementary reflectors). K >= 1.

        V       (input/output) COMPLEX*16 array, dimension
                (LDV,K) if STOREV = 'C'
                (LDV,N) if STOREV = 'R'
                The matrix V. See further details.

        LDV     (input) INTEGER
                The leading dimension of the array V.
                If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.

        TAU     (input) COMPLEX*16 array, dimension (K)
                TAU(i) must contain the scalar factor of the elementary
                reflector H(i).

        T       (output) COMPLEX*16 array, dimension (LDT,K)
                The k by k triangular factor T of the block reflector.
                If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
                lower triangular. The rest of the array is not used.

        LDT     (input) INTEGER
                The leading dimension of the array T. LDT >= K.

FURTHER DETAILS

        The shape of the matrix V and the storage of the vectors which define
        the H(i) is best illustrated by the following example with n = 5 and
        k = 3. The elements equal to 1 are not stored; the corresponding
        array elements are modified but restored on exit. The rest of the
        array is not used.
        DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
                     V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                         ( v1  1    )                     (     1 v2 v2 v2 )
                         ( v1 v2  1 )                     (        1 v3 v3 )
                         ( v1 v2 v3 )
                         ( v1 v2 v3 )
        DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
                     V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                         ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                         (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                         (     1 v3 )
                         (        1 )

 LAPACK auxiliary routine (version 3.3.1)   April 2011                            ZLARFT(3lapack)