## MB01OC

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

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

Purpose

      To perform one of the special symmetric rank 2k operations

         R := alpha*R + beta*H*X + beta*X*H',
      or
         R := alpha*R + beta*H'*X + beta*X*H,

      where alpha and beta are scalars, R and X are N-by-N symmetric
      matrices, and H is an N-by-N upper Hessenberg matrix.

Specification

          SUBROUTINE MB01OC( UPLO, TRANS, N, ALPHA, BETA, R, LDR, H, LDH, X,
         $                   LDX, INFO )
    C     .. Scalar Arguments ..
          CHARACTER         TRANS, UPLO
          INTEGER           INFO, LDH, LDR, LDX, N
          DOUBLE PRECISION  ALPHA, BETA
    C     .. Array Arguments ..
          DOUBLE PRECISION  H(LDH,*), R(LDR,*), X(LDX,*)

Arguments

Mode Parameters

      UPLO    CHARACTER*1
              Specifies which triangles of the symmetric matrices R
              and X are 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':         R := alpha*R + beta*H*X  + beta*X*H';
              = 'T' or 'C':  R := alpha*R + beta*H'*X + beta*X*H.

Input/Output Parameters

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

      ALPHA   (input) DOUBLE PRECISION
              The scalar alpha. When alpha is zero then R need not be
              set before entry, except when R is identified with X in
              the call.

      BETA    (input) DOUBLE PRECISION
              The scalar beta. When beta is zero then H and X 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 the 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 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).

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 inline code and BLAS1 routines.

Numerical Aspects

      The algorithm requires approximately N**3/2 operations.

Further Comments

      This routine acts as a specialization of BLAS Library routine
      DSYR2K.

Example

Program Text

      None

Program Data

      None

Program Results

      None

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