MB01UW

Computation of matrix expressions alpha H A or alpha A H, over A, H Hessenberg matrix

Purpose

  To compute one of the matrix products

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

  where alpha is a scalar, A is an m-by-n matrix, H is an upper
  Hessenberg matrix, and op( H ) is one of

     op( H ) = H   or   op( H ) = H',  the transpose of H.

      SUBROUTINE MB01UW( SIDE, TRANS, M, N, ALPHA, H, LDH, A, LDA,
     $                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         SIDE, TRANS
      INTEGER           INFO, LDA, LDH, LDWORK, M, N
      DOUBLE PRECISION  ALPHA
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA,*), DWORK(*), H(LDH,*)

Mode Parameters

  SIDE    CHARACTER*1
          Specifies whether the Hessenberg matrix H appears on the
          left or right in the matrix product as follows:
          = 'L':  A := alpha*op( H ) * A;
          = 'R':  A := alpha*A * op( H ).

  TRANS   CHARACTER*1
          Specifies the form of op( H ) to be used in the matrix
          multiplication as follows:
          = 'N':  op( H ) = H;
          = 'T':  op( H ) = H';
          = 'C':  op( H ) = H'.

  M       (input) INTEGER
          The number of rows of the matrix A.  M >= 0.

  N       (input) INTEGER
          The number of columns of the matrix A.  N >= 0.

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

  H       (input) DOUBLE PRECISION array, dimension (LDH,k)
          where k is M when SIDE = 'L' and is N when SIDE = 'R'.
          On entry with SIDE = 'L', the leading M-by-M upper
          Hessenberg part of this array must contain the upper
          Hessenberg matrix H.
          On entry with SIDE = 'R', the leading N-by-N upper
          Hessenberg part of this array must contain the upper
          Hessenberg matrix H.
          The elements below the subdiagonal are not referenced,
          except possibly for those in the first column, which
          could be overwritten, but are restored on exit.

  LDH     INTEGER
          The leading dimension of the array H.  LDH >= max(1,k),
          where k is M when SIDE = 'L' and is N when SIDE = 'R'.

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the leading M-by-N part of this array must
          contain the matrix A.
          On exit, the leading M-by-N part of this array contains
          the computed product.

  LDA     INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = 0, alpha <> 0, and LDWORK >= M*N > 0,
          DWORK contains a copy of the matrix A, having the leading
          dimension M.
          This array is not referenced when alpha = 0.

  LDWORK  The length of the array DWORK.
          LDWORK >= 0,   if  alpha =  0 or MIN(M,N) = 0;
          LDWORK >= M-1, if  SIDE  = 'L';
          LDWORK >= N-1, if  SIDE  = 'R'.
          For maximal efficiency LDWORK should be at least M*N.

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

  The required matrix product is computed in two steps. In the first
  step, the upper triangle of H is used; in the second step, the
  contribution of the subdiagonal is added. If the workspace can
  accomodate a copy of A, a fast BLAS 3 DTRMM operation is used in
  the first step.

  None

Program Text

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