## MB01OE

### Computation of matrix expression alpha R + beta ( op(H) op(E)' + op(E) op(H)' ) with R symmetric, H upper Hessenberg, and E upper triangular

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

Purpose

      To compute one of the symmetric rank 2k operations

         R := alpha*R + beta*H*E' + beta*E*H',

      or

         R := alpha*R + beta*H'*E + beta*E'*H,

      where alpha and beta are scalars, R, E, and H are N-by-N matrices,
      with H upper Hessenberg and E upper triangular.

Specification

          SUBROUTINE MB01OE( UPLO, TRANS, N, ALPHA, BETA, R, LDR, H, LDH, E,
         $                   LDE )
    C     .. Scalar Arguments ..
          DOUBLE PRECISION  ALPHA, BETA
          INTEGER           LDE, LDH, LDR, N
          CHARACTER         TRANS, UPLO
    C     .. Array Arguments ..
          DOUBLE PRECISION  E(LDE,*), H(LDH,*), R(LDR,*)

Arguments

Mode Parameters

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

      TRANS   CHARACTER*1
              Specifies the form of H to be used in the matrix
              multiplication as follows:
              = 'N':  R := alpha*R + beta*H*E' + beta*E*H';
              = 'T':  R := alpha*R + beta*H'*E + beta*E'*H;
              = 'C':  R := alpha*R + beta*H'*E + beta*E'*H.

Input/Output Parameters

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

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

      BETA    (input) DOUBLE PRECISION
              The scalar beta. When beta is zero then E and H are not
              referenced.

      R       (input/output) DOUBLE PRECISION array, dimension (LDR,N)
              On entry with UPLO = 'U', the leading N-by-N upper
              triangular part of this array must contain the upper
              triangular part of the symmetric matrix R.
              On entry with UPLO = 'L', the leading N-by-N lower
              triangular part of this array must contain the lower
              triangular part of the symmetric matrix R.
              In both cases, the other strictly triangular part is not
              referenced.
              On exit, the leading N-by-N upper triangular part (if
              UPLO = 'U'), or lower triangular part (if UPLO = 'L'), of
              this array contains the corresponding triangular part of
              the computed matrix R.

      LDR     INTEGER
              The leading dimension of array R.  LDR >= MAX(1,N).

      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 array H.  LDH >= 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).

Method

      E particularization of the algorithm used in the BLAS 3 routine
      DSYR2K is used.

Numerical Aspects

      The algorithm requires approximately N**3/3 operations.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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