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<HTML>
<HEAD><TITLE>MB04QB - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB04QB">MB04QB</A></H2>
<H3>
Applying a product of symplectic reflectors and Givens rotations to two general real matrices
</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 overwrite general real m-by-n matrices C and D, or their
transposes, with
[ op(C) ]
Q * [ ] if TRANQ = 'N', or
[ op(D) ]
T [ op(C) ]
Q * [ ] if TRANQ = 'T',
[ op(D) ]
where Q is defined as the product of symplectic reflectors and
Givens rotations,
Q = diag( H(1),H(1) ) G(1) diag( F(1),F(1) )
diag( H(2),H(2) ) G(2) diag( F(2),F(2) )
....
diag( H(k),H(k) ) G(k) diag( F(k),F(k) ).
Blocked version.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB04QB( TRANC, TRAND, TRANQ, STOREV, STOREW, M, N, K,
$ V, LDV, W, LDW, C, LDC, D, LDD, CS, TAU, DWORK,
$ LDWORK, INFO )
C .. Scalar Arguments ..
CHARACTER STOREV, STOREW, TRANC, TRAND, TRANQ
INTEGER INFO, K, LDC, LDD, LDV, LDW, LDWORK, M, N
C .. Array Arguments ..
DOUBLE PRECISION C(LDC,*), CS(*), D(LDD,*), DWORK(*), TAU(*),
$ V(LDV,*), W(LDW,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
TRANC CHARACTER*1
Specifies the form of op( C ) as follows:
= 'N': op( C ) = C;
= 'T': op( C ) = C';
= 'C': op( C ) = C'.
TRAND CHARACTER*1
Specifies the form of op( D ) as follows:
= 'N': op( D ) = D;
= 'T': op( D ) = D';
= 'C': op( D ) = D'.
TRANQ CHARACTER*1
= 'N': apply Q;
= 'T': apply Q'.
STOREV CHARACTER*1
Specifies how the vectors which define the concatenated
Householder reflectors contained in V are stored:
= 'C': columnwise;
= 'R': rowwise.
STOREW CHARACTER*1
Specifies how the vectors which define the concatenated
Householder reflectors contained in W are stored:
= 'C': columnwise;
= 'R': rowwise.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
M (input) INTEGER
The number of rows of the matrices op(C) and op(D).
M >= 0.
N (input) INTEGER
The number of columns of the matrices op(C) and op(D).
N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q. M >= K >= 0.
V (input) DOUBLE PRECISION array, dimension
(LDV,K) if STOREV = 'C',
(LDV,M) if STOREV = 'R'
On entry with STOREV = 'C', the leading M-by-K part of
this array must contain in its columns the vectors which
define the elementary reflectors F(i).
On entry with STOREV = 'R', the leading K-by-M part of
this array must contain in its rows the vectors which
define the elementary reflectors F(i).
LDV INTEGER
The leading dimension of the array V.
LDV >= MAX(1,M), if STOREV = 'C';
LDV >= MAX(1,K), if STOREV = 'R'.
W (input) DOUBLE PRECISION array, dimension
(LDW,K) if STOREW = 'C',
(LDW,M) if STOREW = 'R'
On entry with STOREW = 'C', the leading M-by-K part of
this array must contain in its columns the vectors which
define the elementary reflectors H(i).
On entry with STOREW = 'R', the leading K-by-M part of
this array must contain in its rows the vectors which
define the elementary reflectors H(i).
LDW INTEGER
The leading dimension of the array W.
LDW >= MAX(1,M), if STOREW = 'C';
LDW >= MAX(1,K), if STOREW = 'R'.
C (input/output) DOUBLE PRECISION array, dimension
(LDC,N) if TRANC = 'N',
(LDC,M) if TRANC = 'T' or TRANC = 'C'
On entry with TRANC = 'N', the leading M-by-N part of
this array must contain the matrix C.
On entry with TRANC = 'C' or TRANC = 'T', the leading
N-by-M part of this array must contain the transpose of
the matrix C.
On exit with TRANC = 'N', the leading M-by-N part of
this array contains the updated matrix C.
On exit with TRANC = 'C' or TRANC = 'T', the leading
N-by-M part of this array contains the transpose of the
updated matrix C.
LDC INTEGER
The leading dimension of the array C.
LDC >= MAX(1,M), if TRANC = 'N';
LDC >= MAX(1,N), if TRANC = 'T' or TRANC = 'C'.
D (input/output) DOUBLE PRECISION array, dimension
(LDD,N) if TRAND = 'N',
(LDD,M) if TRAND = 'T' or TRAND = 'C'
On entry with TRAND = 'N', the leading M-by-N part of
this array must contain the matrix D.
On entry with TRAND = 'C' or TRAND = 'T', the leading
N-by-M part of this array must contain the transpose of
the matrix D.
On exit with TRAND = 'N', the leading M-by-N part of
this array contains the updated matrix D.
On exit with TRAND = 'C' or TRAND = 'T', the leading
N-by-M part of this array contains the transpose of the
updated matrix D.
LDD INTEGER
The leading dimension of the array D.
LDD >= MAX(1,M), if TRAND = 'N';
LDD >= MAX(1,N), if TRAND = 'T' or TRAND = 'C'.
CS (input) DOUBLE PRECISION array, dimension (2*K)
On entry, the first 2*K elements of this array must
contain the cosines and sines of the symplectic Givens
rotations G(i).
TAU (input) DOUBLE PRECISION array, dimension (K)
On entry, the first K elements of this array must
contain the scalar factors of the elementary reflectors
F(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 = -20, DWORK(1) returns the minimum
value of LDWORK.
LDWORK INTEGER
The length of the array DWORK. LDWORK >= MAX(1,N).
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] 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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