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<HTML>
<HEAD><TITLE>MB01RX - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB01RX">MB01RX</A></H2>
<H3>
Computation of a triangle of matrix expression alpha R + beta A B or alpha R + beta B A
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
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.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
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,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
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'.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
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'.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
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.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
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'.
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
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