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<HTML>
<HEAD><TITLE>MB04XY - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB04XY">MB04XY</A></H2>
<H3>
Applying the Householder transformations for bidiagonalization (stored in factored form) to specified one or two matrices, from the left
</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 apply the Householder transformations Pj stored in factored
form into the columns of the array X, to the desired columns of
the matrix U by premultiplication, and/or the Householder
transformations Qj stored in factored form into the rows of the
array X, to the desired columns of the matrix V by
premultiplication. The Householder transformations Pj and Qj
are stored as produced by LAPACK Library routine DGEBRD.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB04XY( JOBU, JOBV, M, N, X, LDX, TAUP, TAUQ, U,
$ LDU, V, LDV, INUL, INFO )
C .. Scalar Arguments ..
CHARACTER JOBU, JOBV
INTEGER INFO, LDU, LDV, LDX, M, N
C .. Array Arguments ..
LOGICAL INUL(*)
DOUBLE PRECISION TAUP(*), TAUQ(*), U(LDU,*), V(LDV,*),
$ X(LDX,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
JOBU CHARACTER*1
Specifies whether to transform the columns in U as
follows:
= 'N': Do not transform the columns in U;
= 'A': Transform the columns in U (U has M columns);
= 'S': Transform the columns in U (U has min(M,N)
columns).
JOBV CHARACTER*1
Specifies whether to transform the columns in V as
follows:
= 'N': Do not transform the columns in V;
= 'A': Transform the columns in V (V has N columns);
= 'S': Transform the columns in V (V has min(M,N)
columns).
</PRE>
<B>Input/Output Parameters</B>
<PRE>
M (input) INTEGER
The number of rows of the matrix X. M >= 0.
N (input) INTEGER
The number of columns of the matrix X. N >= 0.
X (input) DOUBLE PRECISION array, dimension (LDX,N)
The leading M-by-N part contains in the columns of its
lower triangle the Householder transformations Pj, and
in the rows of its upper triangle the Householder
transformations Qj in factored form.
X is modified by the routine but restored on exit.
LDX INTEGER
The leading dimension of the array X. LDX >= MAX(1,M).
TAUP (input) DOUBLE PRECISION array, dimension (MIN(M,N))
The scalar factors of the Householder transformations Pj.
TAUQ (input) DOUBLE PRECISION array, dimension (MIN(M,N))
The scalar factors of the Householder transformations Qj.
U (input/output) DOUBLE PRECISION array, dimension (LDU,*)
On entry, U contains the M-by-M (if JOBU = 'A') or
M-by-min(M,N) (if JOBU = 'S') matrix U.
On exit, the Householder transformations Pj have been
applied to each column i of U corresponding to a parameter
INUL(i) = .TRUE.
NOTE that U is not referenced if JOBU = 'N'.
LDU INTEGER
The leading dimension of the array U.
LDU >= MAX(1,M), if JOBU = 'A' or JOBU = 'S';
LDU >= 1, if JOBU = 'N'.
V (input/output) DOUBLE PRECISION array, dimension (LDV,*)
On entry, V contains the N-by-N (if JOBV = 'A') or
N-by-min(M,N) (if JOBV = 'S') matrix V.
On exit, the Householder transformations Qj have been
applied to each column i of V corresponding to a parameter
INUL(i) = .TRUE.
NOTE that V is not referenced if JOBV = 'N'.
LDV INTEGER
The leading dimension of the array V.
LDV >= MAX(1,M), if JOBV = 'A' or JOBV = 'S';
LDV >= 1, if JOBV = 'N'.
INUL (input) LOGICAL array, dimension (MAX(M,N))
INUL(i) = .TRUE. if the i-th column of U and/or V is to be
transformed, and INUL(i) = .FALSE., otherwise.
(1 <= i <= MAX(M,N)).
</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 Householder transformations Pj or Qj are applied to the
columns of U or V indexed by I for which INUL(I) = .TRUE..
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The algorithm is backward stable.
</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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