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## dlarfb()

subroutine dlarfb | ( | character | side,
|  | character | trans,
|  | character | direct,
|  | character | storev,
|  | integer | m,
|  | integer | n,
|  | integer | k,
|  | double precision, dimension( ldv, * ) | v,
|  | integer | ldv,
|  | double precision, dimension( ldt, * ) | t,
|  | integer | ldt,
|  | double precision, dimension( ldc, * ) | c,
|  | integer | ldc,
|  | double precision, dimension( ldwork, * ) | work,
|  | integer | ldwork )

DLARFB applies a block reflector or its transpose to a general rectangular matrix.

Download DLARFB + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DLARFB applies a real block reflector H or its transpose H**T to a
      !> real m by n matrix C, from either the left or the right.
      !>

Parameters

  [in]

  SIDE

      !>          SIDE is CHARACTER*1
      !>          = 'L': apply H or H**T from the Left
      !>          = 'R': apply H or H**T from the Right
      !>

  [in]

  TRANS

      !>          TRANS is CHARACTER*1
      !>          = 'N': apply H (No transpose)
      !>          = 'T': apply H**T (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).
      !>          If SIDE = 'L', M >= K >= 0;
      !>          if SIDE = 'R', N >= K >= 0.
      !>

  [in]

  V

      !>          V is DOUBLE PRECISION array, dimension
      !>                                (LDV,K) if STOREV = 'C'
      !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
      !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
      !>          The matrix V. 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDC,N)
      !>          On entry, the m by n matrix C.
      !>          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
      !>

  [in]

  LDC

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

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION 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).
      !>

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

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 triangular part of V (including its diagonal) is not
      !>  referenced.
      !>
      !>  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 )
      !>