## MB01OO

### Computation of P or P' with P = op(H) X op(E)' with X symmetric, H upper Hessenberg, and E upper triangular

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

      To compute either P or P', with P defined by the matrix formula

         P = op( H )*X*op( E )',

      where H is an upper Hessenberg matrix, X is a symmetric matrix,
      E is an upper triangular matrix, and op( M ) is one of

         op( M ) = M   or   op( M ) = M'.

Specification

          SUBROUTINE MB01OO( UPLO, TRANS, N, H, LDH, X, LDX, E, LDE, P, LDP,
         $                   INFO )
    C     .. Scalar Arguments ..
          INTEGER           INFO, LDE, LDH, LDP, LDX, N
          CHARACTER         TRANS, UPLO
    C     .. Array Arguments ..
          DOUBLE PRECISION  E(LDE,*), H(LDH,*), P(LDP,*), X(LDX,*)

Arguments

Mode Parameters

      UPLO    CHARACTER*1
              Specifies which triangle of the symmetric matrix X is
              given as follows:
              = 'U':  the upper triangular part is given;
              = 'L':  the lower triangular part is given.

      TRANS   CHARACTER*1
              Specifies the operation to be performed as follows:
              = 'N':         compute P  = H*X*E';
              = 'T' or 'C':  compute P' = E'*X*H.

Input/Output Parameters

      N       (input) INTEGER
              The order of the matrices H, X, E, and P.  N >= 0.

      H       (input) DOUBLE PRECISION array, dimension (LDH,N)
              On entry, the leading N-by-N upper Hessenberg part of this
              array must contain the upper Hessenberg matrix H.
              The remaining part of this array is not referenced.

      LDH     INTEGER
              The leading dimension of the array H.  LDH >= MAX(1,N).

      X       (input) DOUBLE PRECISION array, dimension (LDX,N)
              On entry, if UPLO = 'U', the leading N-by-N upper
              triangular part of this array must contain the upper
              triangular part of the symmetric matrix X and the strictly
              lower triangular part of the array is not referenced.
              On entry, if UPLO = 'L', the leading N-by-N lower
              triangular part of this array must contain the lower
              triangular part of the symmetric matrix X and the strictly
              upper triangular part of the array is not referenced.

      LDX     INTEGER
              The leading dimension of the array X.  LDX >= MAX(1,N).

      E       (input) DOUBLE PRECISION array, dimension (LDE,N)
              On entry, the leading N-by-N upper triangular part of this
              array must contain the upper triangular matrix E.
              The remaining part of this array is not referenced.

      LDE     INTEGER
              The leading dimension of array E.  LDE >= MAX(1,N).

      P       (output) DOUBLE PRECISION array, dimension (LDP,N)
              On exit, the leading N-by-N part of this array contains
              the computed matrix P  = H*X*E', if TRANS = 'N', or
              the computed matrix P' = E'*X*H, if TRANS = 'T'.

      LDP     INTEGER
              The leading dimension of the array P.  LDP >= MAX(1,N).

Error Indicator

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

Method

      The matrix expression is efficiently evaluated taking the
      structure into account, and using BLAS and SLICOT routines.
      Let W = H*X, or W = X*H, computed using SLICOT Library routine
      MB01OS. The result is then obtained calling BLAS 3 routine DTRMM.

Numerical Aspects

      The algorithm requires approximately N**3 operations.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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