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## ztpmlqt()

subroutine ztpmlqt | ( | character | side,
|  | character | trans,
|  | integer | m,
|  | integer | n,
|  | integer | k,
|  | integer | l,
|  | integer | mb,
|  | complex*16, dimension( ldv, * ) | v,
|  | integer | ldv,
|  | complex*16, dimension( ldt, * ) | t,
|  | integer | ldt,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex*16, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex*16, dimension( * ) | work,
|  | integer | info )

ZTPMLQT

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

Purpose:

      !>
      !> ZTPMLQT applies a complex unitary matrix Q obtained from a
      !>  complex block reflector H to a general
      !> complex matrix C, which consists of two blocks A and B.
      !>

Parameters

  [in]

  SIDE

      !>          SIDE is CHARACTER*1
      !>          = 'L': apply Q or Q**H from the Left;
      !>          = 'R': apply Q or Q**H from the Right.
      !>

  [in]

  TRANS

      !>          TRANS is CHARACTER*1
      !>          = 'N':  No transpose, apply Q;
      !>          = 'C':  Conjugate transpose, apply Q**H.
      !>

  [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 number of elementary reflectors whose product defines
      !>          the matrix Q.
      !>

  [in]

  L

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

  [in]

  MB

      !>          MB is INTEGER
      !>          The block size used for the storage of T.  K >= MB >= 1.
      !>          This must be the same value of MB used to generate T
      !>          in ZTPLQT.
      !>

  [in]

  V

      !>          V is COMPLEX*16 array, dimension (LDV,K)
      !>          The i-th row must contain the vector which defines the
      !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
      !>          ZTPLQT in B.  See Further Details.
      !>

  [in]

  LDV

      !>          LDV is INTEGER
      !>          The leading dimension of the array V. LDV >= K.
      !>

  [in]

  T

      !>          T is COMPLEX*16 array, dimension (LDT,K)
      !>          The upper triangular factors of the block reflectors
      !>          as returned by ZTPLQT, stored as a MB-by-K matrix.
      !>

  [in]

  LDT

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

  [in,out]

  A

      !>          A is COMPLEX*16 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
      !>          Q*C or Q**H*C or C*Q or C*Q**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*16 array, dimension (LDB,N)
      !>          On entry, the M-by-N matrix B.
      !>          On exit, B is overwritten by the corresponding block of
      !>          Q*C or Q**H*C or C*Q or C*Q**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*16 array. The dimension of WORK is
      !>           N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value
      !>

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

Further Details:

      !>
      !>  The columns of the pentagonal matrix V contain the elementary reflectors
      !>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
      !>  trapezoidal block V2:
      !>
      !>        V = [V1] [V2].
      !>
      !>
      !>  The size of the trapezoidal block V2 is determined by the parameter L,
      !>  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
      !>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;
      !>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
      !>
      !>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
      !>                      [B]
      !>
      !>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
      !>
      !>  The complex unitary matrix Q is formed from V and T.
      !>
      !>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
      !>
      !>  If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
      !>
      !>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
      !>
      !>  If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
      !>