MB01OT

Computation of matrix expression alpha R + beta ( op(E) op(T)' + op(T) op(E)' ) with R symmetric and E, T upper triangular

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

Purpose

  To compute one of the symmetric rank 2k operations

     R := alpha*R + beta*E*T' + beta*T*E',

  or

     R := alpha*R + beta*E'*T + beta*T'*E,

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

Specification
      SUBROUTINE MB01OT( UPLO, TRANS, N, ALPHA, BETA, R, LDR, E, LDE, T,
     $                   LDT )
C     .. Scalar Arguments ..
      DOUBLE PRECISION  ALPHA, BETA
      INTEGER           LDE, LDR, LDT, N
      CHARACTER         TRANS, UPLO
C     .. Array Arguments ..
      DOUBLE PRECISION  E(LDE,*), R(LDR,*), T(LDT,*)

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 E to be used in the matrix
          multiplication as follows:
          = 'N':  R := alpha*R + beta*E*T' + beta*T*E';
          = 'T':  R := alpha*R + beta*E'*T + beta*T'*E;
          = 'C':  R := alpha*R + beta*E'*T + beta*T'*E.

Input/Output Parameters
  N       (input) INTEGER
          The order of the matrices R, T, and E.  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 T and E 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).

  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).

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

  LDT     INTEGER
          The leading dimension of array T.  LDT >= MAX(1,N).

Method
  A 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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