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

NAME

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

SYNOPSIS

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

           CHARACTER      DIRECT, STOREV

           INTEGER        K, LDT, LDV, N

           REAL           T( LDT, * ), TAU( * ), V( LDV, * )

PURPOSE

       SLARZT forms the triangular factor T of a real 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**T
        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**T * T * V
        Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

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, not supported yet)
                = '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) REAL 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) REAL array, dimension (K)
                TAU(i) must contain the scalar factor of the elementary
                reflector H(i).

        T       (output) REAL 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

        Based on contributions by
          A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
        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_____
               (   v1   v2   v3  )                         /                     (  v1  v2  v3  )
       ( v1 v1 v1 v1 v1 . . . . 1 )
           V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
               ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
               ( v1 v2 v3 )
                  .  .  .
                  .  .  .
                  1  .  .
                     1  .
                        1
        DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
                                                              ______V_____
                  1                                            /                          .     1
       ( 1 . . . . v1 v1 v1 v1 v1 )
                  .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
                  .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
                  .  .  .
               ( v1 v2 v3 )
               ( v1 v2 v3 )
           V = ( v1 v2 v3 )
               ( v1 v2 v3 )
               ( v1 v2 v3 )

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