MB01ZD

Computing H := alpha op( T ) H, or H := alpha H op( T ), with H Hessenberg-like, T triangular

Purpose

  To compute the matrix product

     H := alpha*op( T )*H,   or   H := alpha*H*op( T ),

  where alpha is a scalar, H is an m-by-n upper or lower
  Hessenberg-like matrix (with l nonzero subdiagonals or
  superdiagonals, respectively), T is a unit, or non-unit,
  upper or lower triangular matrix, and op( T ) is one of

     op( T ) = T   or   op( T ) = T'.

      SUBROUTINE MB01ZD( SIDE, UPLO, TRANST, DIAG, M, N, L, ALPHA, T,
     $                   LDT, H, LDH, INFO )
C     .. Scalar Arguments ..
      CHARACTER          DIAG, SIDE, TRANST, UPLO
      INTEGER            INFO, L, LDH, LDT, M, N
      DOUBLE PRECISION   ALPHA
C     .. Array Arguments ..
      DOUBLE PRECISION   H( LDH, * ), T( LDT, * )

Mode Parameters

  SIDE    CHARACTER*1
          Specifies whether the triangular matrix T appears on the
          left or right in the matrix product, as follows:
          = 'L':  the product alpha*op( T )*H is computed;
          = 'R':  the product alpha*H*op( T ) is computed.

  UPLO    CHARACTER*1
          Specifies the form of the matrices T and H, as follows:
          = 'U':  the matrix T is upper triangular and the matrix H
                  is upper Hessenberg-like;
          = 'L':  the matrix T is lower triangular and the matrix H
                  is lower Hessenberg-like.

  TRANST  CHARACTER*1
          Specifies the form of op( T ) to be used, as follows:
          = 'N':  op( T ) = T;
          = 'T':  op( T ) = T';
          = 'C':  op( T ) = T'.

  DIAG    CHARACTER*1.
          Specifies whether or not T is unit triangular, as follows:
          = 'U':  the matrix T is assumed to be unit triangular;
          = 'N':  the matrix T is not assumed to be unit triangular.

  M       (input) INTEGER
          The number of rows of H.  M >= 0.

  N       (input) INTEGER
          The number of columns of H.  N >= 0.

  L       (input) INTEGER
          If UPLO = 'U', matrix H has L nonzero subdiagonals.
          If UPLO = 'L', matrix H has L nonzero superdiagonals.
          MAX(0,M-1) >= L >= 0, if UPLO = 'U';
          MAX(0,N-1) >= L >= 0, if UPLO = 'L'.

  ALPHA   (input) DOUBLE PRECISION
          The scalar alpha. When alpha is zero then T is not
          referenced and H need not be set before entry.

  T       (input) DOUBLE PRECISION array, dimension (LDT,k), where
          k is m when SIDE = 'L' and is n when SIDE = 'R'.
          If UPLO = 'U', the leading k-by-k upper triangular part
          of this array must contain the upper triangular matrix T
          and the strictly lower triangular part is not referenced.
          If UPLO = 'L', the leading k-by-k lower triangular part
          of this array must contain the lower triangular matrix T
          and the strictly upper triangular part is not referenced.
          Note that when DIAG = 'U', the diagonal elements of T are
          not referenced either, but are assumed to be unity.

  LDT     INTEGER
          The leading dimension of array T.
          LDT >= MAX(1,M), if SIDE = 'L';
          LDT >= MAX(1,N), if SIDE = 'R'.

  H       (input/output) DOUBLE PRECISION array, dimension (LDH,N)
          On entry, if UPLO = 'U', the leading M-by-N upper
          Hessenberg part of this array must contain the upper
          Hessenberg-like matrix H.
          On entry, if UPLO = 'L', the leading M-by-N lower
          Hessenberg part of this array must contain the lower
          Hessenberg-like matrix H.
          On exit, the leading M-by-N part of this array contains
          the matrix product alpha*op( T )*H, if SIDE = 'L',
          or alpha*H*op( T ), if SIDE = 'R'. If TRANST = 'N', this
          product has the same pattern as the given matrix H;
          the elements below the L-th subdiagonal (if UPLO = 'U'),
          or above the L-th superdiagonal (if UPLO = 'L'), are not
          referenced in this case. If TRANST = 'T', the elements
          below the (N+L)-th row (if UPLO = 'U', SIDE = 'R', and
          M > N+L), or at the right of the (M+L)-th column
          (if UPLO = 'L', SIDE = 'L', and N > M+L), are not set to
          zero nor referenced.

  LDH     INTEGER
          The leading dimension of array H.  LDH >= max(1,M).

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  The calculations are efficiently performed taking the problem
  structure into account.

  The matrix H may have the following patterns, when m = 7, n = 6,
  and l = 2 are used for illustration:

            UPLO = 'U'                    UPLO = 'L'

         [ x x x x x x ]               [ x x x 0 0 0 ]
         [ x x x x x x ]               [ x x x x 0 0 ]
         [ x x x x x x ]               [ x x x x x 0 ]
     H = [ 0 x x x x x ],          H = [ x x x x x x ].
         [ 0 0 x x x x ]               [ x x x x x x ]
         [ 0 0 0 x x x ]               [ x x x x x x ]
         [ 0 0 0 0 x x ]               [ x x x x x x ]

  The products T*H or H*T have the same pattern as H, but the
  products T'*H or H*T' may be full matrices.

  If m = n, the matrix H is upper or lower triangular, for l = 0,
  and upper or lower Hessenberg, for l = 1.

  This routine is a specialization of the BLAS 3 routine DTRMM.
  BLAS 1 calls are used when appropriate, instead of in-line code,
  in order to increase the efficiency. If the matrix H is full, or
  its zero triangle has small order, an optimized DTRMM code could
  be faster than MB01ZD.

Program Text

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