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<HTML>
<HEAD><TITLE>MB01WD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB01WD">MB01WD</A></H2>
<H3>
Residuals of Lyapunov or Stein equations for Cholesky factored solutions
</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 the matrix formula
_
R = alpha*( op( A )'*op( T )'*op( T ) + op( T )'*op( T )*op( A ) )
+ beta*R, (1)
if DICO = 'C', or
_
R = alpha*( op( A )'*op( T )'*op( T )*op( A ) - op( T )'*op( T ))
+ beta*R, (2)
_
if DICO = 'D', where alpha and beta are scalars, R, and R are
symmetric matrices, T is a triangular matrix, A is a general or
Hessenberg matrix, and op( M ) is one of
op( M ) = M or op( M ) = M'.
The result is overwritten on R.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB01WD( DICO, UPLO, TRANS, HESS, N, ALPHA, BETA, R,
$ LDR, A, LDA, T, LDT, INFO )
C .. Scalar Arguments ..
CHARACTER DICO, HESS, TRANS, UPLO
INTEGER INFO, LDA, LDR, LDT, N
DOUBLE PRECISION ALPHA, BETA
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), R(LDR,*), T(LDT,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
DICO CHARACTER*1
Specifies the formula to be evaluated, as follows:
= 'C': formula (1), "continuous-time" case;
= 'D': formula (2), "discrete-time" case.
UPLO CHARACTER*1
Specifies which triangles of the symmetric matrix R and
triangular matrix T are given, as follows:
= 'U': the upper triangular parts of R and T are given;
= 'L': the lower triangular parts of R and T are given;
TRANS CHARACTER*1
Specifies the form of op( M ) to be used, as follows:
= 'N': op( M ) = M;
= 'T': op( M ) = M';
= 'C': op( M ) = M'.
HESS CHARACTER*1
Specifies the form of the matrix A, as follows:
= 'F': matrix A is full;
= 'H': matrix A is Hessenberg (or Schur), either upper
(if UPLO = 'U'), or lower (if UPLO = 'L').
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrices R, A, and T. N >= 0.
ALPHA (input) DOUBLE PRECISION
The scalar alpha. When alpha is zero then the arrays A
and T are not referenced.
BETA (input) DOUBLE PRECISION
The scalar beta. When beta is zero then the array R need
not be set before entry.
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.
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).
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the matrix A. If HESS = 'H' the elements below the
first subdiagonal, if UPLO = 'U', or above the first
superdiagonal, if UPLO = 'L', need not be set to zero,
and are not referenced if DICO = 'D'.
On exit, the leading N-by-N part of this array contains
the following matrix product
alpha*T'*T*A, if TRANS = 'N', or
alpha*A*T*T', otherwise,
if DICO = 'C', or
T*A, if TRANS = 'N', or
A*T, otherwise,
if DICO = 'D' (and in this case, these products have a
Hessenberg form, if HESS = 'H').
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,N).
T (input) DOUBLE PRECISION array, dimension (LDT,N)
If UPLO = 'U', the leading N-by-N upper triangular part of
this array must contain the upper triangular matrix T and
the strictly lower triangular part need not be set to zero
(and it is not referenced).
If UPLO = 'L', the leading N-by-N lower triangular part of
this array must contain the lower triangular matrix T and
the strictly upper triangular part need not be set to zero
(and it is not referenced).
LDT INTEGER
The leading dimension of array T. LDT >= MAX(1,N).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -k, the k-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The matrix expression (1) or (2) is efficiently evaluated taking
the structure into account. BLAS 3 operations (DTRMM, DSYRK and
their specializations) are used throughout.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
If A is a full matrix, the algorithm requires approximately
3
N operations, if DICO = 'C';
3
7/6 x N operations, if DICO = 'D'.
</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>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
<HR>
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