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dlarft examples
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Man Page Details
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NAME
       DLARFT  -  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 DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

           CHARACTER      DIRECT, STOREV

           INTEGER        K, LDT, LDV, N

           DOUBLE         PRECISION T( LDT, * ), TAU( * ), V( LDV, * )

 Purpose
 =======

  DLARFT 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'

  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 * 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):
          = 'C': columnwise
          = '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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i).

  T       (output) DOUBLE PRECISION 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 )

