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zlarfb examples
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Man Page Details
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 Online html documentation available at 
            http://www.netlib.org/lapack/explore-html/ 

 Definition:
 ===========

       SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
                          T, LDT, C, LDC, WORK, LDWORK )
 
       .. Scalar Arguments ..
       CHARACTER          DIRECT, SIDE, STOREV, TRANS
       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
       ..
       .. Array Arguments ..
       COMPLEX*16         C( LDC, * ), T( LDT, * ), V( LDV, * ),
      $                   WORK( LDWORK, * )
       ..
  

 Purpose:
 =============

 ZLARFB applies a complex block reflector H or its transpose H**H to a
 complex M-by-N matrix C, from either the left or the right.


 Arguments:
 ==========

  [in] SIDE

          SIDE is CHARACTER*1
          = 'L': apply H or H**H from the Left
          = 'R': apply H or H**H from the Right

  [in] TRANS

          TRANS is CHARACTER*1
          = 'N': apply H (No transpose)
          = 'C': apply H**H (Conjugate transpose)

  [in] DIRECT

          DIRECT is CHARACTER*1
          Indicates how H is formed from a product of elementary
          reflectors
          = 'F': H = H(1) H(2) . . . H(k) (Forward)
          = 'B': H = H(k) . . . H(2) H(1) (Backward)

  [in] STOREV

          STOREV is CHARACTER*1
          Indicates how the vectors which define the elementary
          reflectors are stored:
          = 'C': Columnwise
          = 'R': Rowwise

  [in] M

          M is INTEGER
          The number of rows of the matrix C.

  [in] N

          N is INTEGER
          The number of columns of the matrix C.

  [in] K

          K is INTEGER
          The order of the matrix T (= the number of elementary
          reflectors whose product defines the block reflector).

  [in] V

          V is COMPLEX*16 array, dimension
                                (LDV,K) if STOREV = 'C'
                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
          See Further Details.

  [in] LDV

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

  [in] T

          T is COMPLEX*16 array, dimension (LDT,K)
          The triangular K-by-K matrix T in the representation of the
          block reflector.

  [in] LDT

          LDT is INTEGER
          The leading dimension of the array T. LDT >= K.

  [in,out] C

          C is COMPLEX*16 array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.

  [in] LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).

  [out] WORK

          WORK is COMPLEX*16 array, dimension (LDWORK,K)

  [in] LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.
          If SIDE = 'L', LDWORK >= max(1,N);
          if SIDE = 'R', LDWORK >= max(1,M).

 Authors:
 ========

  Univ. of Tennessee 
  Univ. of California Berkeley 
  Univ. of Colorado Denver 
  NAG Ltd. 

 November 2011

 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 )

