## MB01RB

### 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 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,*)

```
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. 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.

```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```