MB01RX - SLICOT Library Routine Documentation

## MB01RX

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

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

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.

Specification

          SUBROUTINE MB01RX( 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,*)

Arguments

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'.

Input/Output Parameters

      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'.

Error Indicator

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

Method

      The matrix expression is evaluated taking the triangular
      structure into account. BLAS 2 operations are used. A block
      algorithm can be easily constructed; it can use BLAS 3 GEMM
      operations for most computations, and calls of this BLAS 2
      algorithm for computing the triangles.

Further Comments

      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'.

Example

Program Text

      None

Program Data

      None

Program Results

      None

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