MB01RB

Computation of a triangle of matrix expression alpha R + beta A B or alpha R + beta B A

Purpose

  To compute either the upper or lower triangular part of one of the
  matrix formulas
     _
     R = alpha*R + beta*op( A )*B,                               (1)
     _
     R = alpha*R + beta*B*op( A ),                               (2)
                                          _
  where alpha and beta are scalars, R and R are m-by-m matrices,
  op( A ) and B are m-by-n and n-by-m matrices for (1), or n-by-m
  and m-by-n matrices for (2), respectively, and op( A ) is one of

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

  The result is overwritten on R.

      SUBROUTINE MB01RB( SIDE, UPLO, TRANS, M, N, ALPHA, BETA, R, LDR,
     $                   A, LDA, B, LDB, INFO )
C     .. Scalar Arguments ..
      CHARACTER         SIDE, TRANS, UPLO
      INTEGER           INFO, LDA, LDB, LDR, M, N
      DOUBLE PRECISION  ALPHA, BETA
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA,*), B(LDB,*), R(LDR,*)

Mode Parameters

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

  UPLO    CHARACTER*1                               _
          Specifies which triangles of the matrices R and R are
          computed and given, respectively, as follows:
          = 'U':  the upper triangular part;
          = 'L':  the lower triangular part.

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

  M       (input) INTEGER           _
          The order of the matrices R and R, the number of rows of
          the matrix op( A ) and the number of columns of the
          matrix B, for SIDE = 'L', or the number of rows of the
          matrix B and the number of columns of the matrix op( A ),
          for SIDE = 'R'.  M >= 0.

  N       (input) INTEGER
          The number of rows of the matrix B and the number of
          columns of the matrix op( A ), for SIDE = 'L', or the
          number of rows of the matrix op( A ) and the number of
          columns of the matrix B, for SIDE = 'R'.  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 A and B are not
          referenced.

  R       (input/output) DOUBLE PRECISION array, dimension (LDR,M)
          On entry with UPLO = 'U', the leading M-by-M upper
          triangular part of this array must contain the upper
          triangular part of the matrix R; the strictly lower
          triangular part of the array is not referenced.
          On entry with UPLO = 'L', the leading M-by-M lower
          triangular part of this array must contain the lower
          triangular part of the matrix R; the strictly upper
          triangular part of the array is not referenced.
          On exit, the leading M-by-M 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,M).

  A       (input) DOUBLE PRECISION array, dimension (LDA,k), where
          k = N  when  SIDE = 'L', and TRANS =  'N', or
                       SIDE = 'R', and TRANS <> 'T';
          k = M  when  SIDE = 'R', and TRANS = 'N', or
                       SIDE = 'L', and TRANS <> 'T'.
          On entry, if SIDE = 'L', and TRANS =  'N', or
                       SIDE = 'R', and TRANS <> 'T',
          the leading M-by-N part of this array must contain the
          matrix A.
          On entry, if SIDE = 'R', and TRANS =  'N', or
                       SIDE = 'L', and TRANS <> 'T',
          the leading N-by-M part of this array must contain the
          matrix A.

  LDA     INTEGER
          The leading dimension of array A.  LDA >= MAX(1,l), where
          l = M  when  SIDE = 'L', and TRANS =  'N', or
                       SIDE = 'R', and TRANS <> 'T';
          l = N  when  SIDE = 'R', and TRANS =  'N', or
                       SIDE = 'L', and TRANS <> 'T'.

  B       (input) DOUBLE PRECISION array, dimension (LDB,p), where
          p = M  when  SIDE = 'L';
          p = N  when  SIDE = 'R'.
          On entry, the leading N-by-M part, if SIDE = 'L', or
          M-by-N part, if SIDE = 'R', of this array must contain the
          matrix B.

  LDB     INTEGER
          The leading dimension of array B.
          LDB >= MAX(1,N), if SIDE = 'L';
          LDB >= MAX(1,M), if SIDE = 'R'.

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

  The matrix expression is evaluated taking the triangular
  structure into account. A block algorithm is used.

  The main application of this routine is when the result should
  be a symmetric matrix, e.g., when B = X*op( A )', for (1), or
  B = op( A )'*X, for (2), where B is already available and X = X'.
  The required triangle only is computed and overwritten, contrary
  to a general matrix multiplication operation.

  This is a BLAS 3 version of the SLICOT Library routine MB01RX.

Program Text

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