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<HEAD><TITLE>MB01OT - SLICOT Library Routine Documentation</TITLE>
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<H2><A Name="MB01OT">MB01OT</A></H2>
<H3>
Computation of matrix expression alpha R + beta ( op(E) op(T)' + op(T) op(E)' ) with R symmetric and E, T upper triangular
</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 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.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
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,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
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.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
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).
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
A particularization of the algorithm used in the BLAS 3 routine
DSYR2K is used.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The algorithm requires approximately N**3/3 operations.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
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<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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