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## ctprfb()

subroutine ctprfb | ( | character | side,
|  | character | trans,
|  | character | direct,
|  | character | storev,
|  | integer | m,
|  | integer | n,
|  | integer | k,
|  | integer | l,
|  | complex, dimension( ldv, * ) | v,
|  | integer | ldv,
|  | complex, dimension( ldt, * ) | t,
|  | integer | ldt,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex, dimension( ldwork, * ) | work,
|  | integer | ldwork )

CTPRFB applies a complex "triangular-pentagonal" block reflector to a complex matrix, which is composed of two blocks.

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

Purpose:

      !>
      !> CTPRFB applies a complex  block reflector H or its
      !> conjugate transpose H**H to a complex matrix C, which is composed of two
      !> blocks A and B, either from the left or right.
      !>
      !>

Parameters

  [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': Columns
      !>          = 'R': Rows
      !>

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix B.
      !>          M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix B.
      !>          N >= 0.
      !>

  [in]

  K

      !>          K is INTEGER
      !>          The order of the matrix T, i.e. the number of elementary
      !>          reflectors whose product defines the block reflector.
      !>          K >= 0.
      !>

  [in]

  L

      !>          L is INTEGER
      !>          The order of the trapezoidal part of V.
      !>          K >= L >= 0.  See Further Details.
      !>

  [in]

  V

      !>          V is COMPLEX array, dimension
      !>                                (LDV,K) if STOREV = 'C'
      !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
      !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
      !>          The pentagonal matrix V, which contains the elementary reflectors
      !>          H(1), H(2), ..., H(K).  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 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]

  A

      !>          A is COMPLEX array, dimension
      !>          (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'
      !>          On entry, the K-by-N or M-by-K matrix A.
      !>          On exit, A is overwritten by the corresponding block of
      !>          H*C or H**H*C or C*H or C*H**H.  See Further Details.
      !>

  [in]

  LDA

      !>          LDA is INTEGER
      !>          The leading dimension of the array A.
      !>          If SIDE = 'L', LDA >= max(1,K);
      !>          If SIDE = 'R', LDA >= max(1,M).
      !>

  [in,out]

  B

      !>          B is COMPLEX array, dimension (LDB,N)
      !>          On entry, the M-by-N matrix B.
      !>          On exit, B is overwritten by the corresponding block of
      !>          H*C or H**H*C or C*H or C*H**H.  See Further Details.
      !>

  [in]

  LDB

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

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension
      !>          (LDWORK,N) if SIDE = 'L',
      !>          (LDWORK,K) if SIDE = 'R'.
      !>

  [in]

  LDWORK

      !>          LDWORK is INTEGER
      !>          The leading dimension of the array WORK.
      !>          If SIDE = 'L', LDWORK >= K;
      !>          if SIDE = 'R', LDWORK >= M.
      !>

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

Further Details:

      !>
      !>  The matrix C is a composite matrix formed from blocks A and B.
      !>  The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
      !>  and if SIDE = 'L', A is of size K-by-N.
      !>
      !>  If SIDE = 'R' and DIRECT = 'F', C = [A B].
      !>
      !>  If SIDE = 'L' and DIRECT = 'F', C = [A]
      !>                                      [B].
      !>
      !>  If SIDE = 'R' and DIRECT = 'B', C = [B A].
      !>
      !>  If SIDE = 'L' and DIRECT = 'B', C = [B]
      !>                                      [A].
      !>
      !>  The pentagonal matrix V is composed of a rectangular block V1 and a
      !>  trapezoidal block V2.  The size of the trapezoidal block is determined by
      !>  the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
      !>  if L=0, there is no trapezoidal block, thus V = V1 is rectangular.
      !>
      !>  If DIRECT = 'F' and STOREV = 'C':  V = [V1]
      !>                                         [V2]
      !>     - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)
      !>
      !>  If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]
      !>
      !>     - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)
      !>
      !>  If DIRECT = 'B' and STOREV = 'C':  V = [V2]
      !>                                         [V1]
      !>     - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)
      !>
      !>  If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]
      !>
      !>     - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)
      !>
      !>  If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.
      !>
      !>  If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.
      !>
      !>  If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.
      !>
      !>  If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.
      !>