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<HTML>
<HEAD><TITLE>MB04WR - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB04WR">MB04WR</A></H2>
<H3>
Generating orthogonal symplectic matrices defined as products of symplectic reflectors and Givens rotations
</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 generate orthogonal symplectic matrices U or V, defined as
products of symplectic reflectors and Givens rotations
U = diag( HU(1),HU(1) ) GU(1) diag( FU(1),FU(1) )
diag( HU(2),HU(2) ) GU(2) diag( FU(2),FU(2) )
....
diag( HU(n),HU(n) ) GU(n) diag( FU(n),FU(n) ),
V = diag( HV(1),HV(1) ) GV(1) diag( FV(1),FV(1) )
diag( HV(2),HV(2) ) GV(2) diag( FV(2),FV(2) )
....
diag( HV(n-1),HV(n-1) ) GV(n-1) diag( FV(n-1),FV(n-1) ),
as returned by the SLICOT Library routines MB04TS or MB04TB. The
matrices U and V are returned in terms of their first N/2 rows:
[ U1 U2 ] [ V1 V2 ]
U = [ ], V = [ ].
[ -U2 U1 ] [ -V2 V1 ]
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB04WR( JOB, TRANS, N, ILO, Q1, LDQ1, Q2, LDQ2, CS,
$ TAU, DWORK, LDWORK, INFO )
C .. Scalar Arguments ..
CHARACTER JOB, TRANS
INTEGER ILO, INFO, LDQ1, LDQ2, LDWORK, N
C .. Array Arguments ..
DOUBLE PRECISION CS(*), DWORK(*), Q1(LDQ1,*), Q2(LDQ2,*), TAU(*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
JOB CHARACTER*1
Specifies whether the matrix U or the matrix V is
required:
= 'U': generate U;
= 'V': generate V.
TRANS CHARACTER*1
If JOB = 'U' then TRANS must have the same value as
the argument TRANA in the previous call of MB04TS or
MB04TB.
If JOB = 'V' then TRANS must have the same value as
the argument TRANB in the previous call of MB04TS or
MB04TB.
N (input) INTEGER
The order of the matrices Q1 and Q2. N >= 0.
ILO (input) INTEGER
ILO must have the same value as in the previous call of
MB04TS or MB04TB. U and V are equal to the unit matrix
except in the submatrices
U([ilo:n n+ilo:2*n], [ilo:n n+ilo:2*n]) and
V([ilo+1:n n+ilo+1:2*n], [ilo+1:n n+ilo+1:2*n]),
respectively.
1 <= ILO <= N, if N > 0; ILO = 1, if N = 0.
Q1 (input/output) DOUBLE PRECISION array, dimension (LDQ1,N)
On entry, if JOB = 'U' and TRANS = 'N' then the
leading N-by-N part of this array must contain in its i-th
column the vector which defines the elementary reflector
FU(i).
If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the
leading N-by-N part of this array must contain in its i-th
row the vector which defines the elementary reflector
FU(i).
If JOB = 'V' and TRANS = 'N' then the leading N-by-N
part of this array must contain in its i-th row the vector
which defines the elementary reflector FV(i).
If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the
leading N-by-N part of this array must contain in its i-th
column the vector which defines the elementary reflector
FV(i).
On exit, if JOB = 'U' and TRANS = 'N' then the leading
N-by-N part of this array contains the matrix U1.
If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the
leading N-by-N part of this array contains the matrix
U1**T.
If JOB = 'V' and TRANS = 'N' then the leading N-by-N
part of this array contains the matrix V1**T.
If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the
leading N-by-N part of this array contains the matrix V1.
LDQ1 INTEGER
The leading dimension of the array Q1. LDQ1 >= MAX(1,N).
Q2 (input/output) DOUBLE PRECISION array, dimension (LDQ2,N)
On entry, if JOB = 'U' then the leading N-by-N part of
this array must contain in its i-th column the vector
which defines the elementary reflector HU(i).
If JOB = 'V' then the leading N-by-N part of this array
must contain in its i-th row the vector which defines the
elementary reflector HV(i).
On exit, if JOB = 'U' then the leading N-by-N part of
this array contains the matrix U2.
If JOB = 'V' then the leading N-by-N part of this array
contains the matrix V2**T.
LDQ2 INTEGER
The leading dimension of the array Q2. LDQ2 >= MAX(1,N).
CS (input) DOUBLE PRECISION array, dimension (2N)
On entry, if JOB = 'U' then the first 2N elements of
this array must contain the cosines and sines of the
symplectic Givens rotations GU(i).
If JOB = 'V' then the first 2N-2 elements of this array
must contain the cosines and sines of the symplectic
Givens rotations GV(i).
TAU (input) DOUBLE PRECISION array, dimension (N)
On entry, if JOB = 'U' then the first N elements of
this array must contain the scalar factors of the
elementary reflectors FU(i).
If JOB = 'V' then the first N-1 elements of this array
must contain the scalar factors of the elementary
reflectors FV(i).
</PRE>
<B>Workspace</B>
<PRE>
DWORK DOUBLE PRECISION array, dimension (LDWORK)
On exit, if INFO = 0, DWORK(1) returns the optimal
value of LDWORK.
On exit, if INFO = -12, DWORK(1) returns the minimum
value of LDWORK.
LDWORK INTEGER
The length of the array DWORK.
LDWORK >= MAX(1,2*(N-ILO+1)).
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of the
DWORK array, returns this value as the first entry of
the DWORK array, and no error message related to LDWORK
is issued by XERBLA.
</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="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Benner, P., Mehrmann, V., and Xu, H.
A numerically stable, structure preserving method for
computing the eigenvalues of real Hamiltonian or symplectic
pencils. Numer. Math., Vol 78 (3), pp. 329-358, 1998.
[2] Kressner, D.
Block algorithms for orthogonal symplectic factorizations.
BIT, 43 (4), pp. 775-790, 2003.
</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>
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