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<HTML>
<HEAD><TITLE>MB02CV - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB02CV">MB02CV</A></H2>
<H3>
Applying the MB02CU transformations on other columns / rows of the generator
</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 transformations created by the SLICOT Library routine
MB02CU on other columns / rows of the generator, contained in the
arrays F1, F2 and G.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB02CV( TYPEG, STRUCG, K, N, P, Q, NB, RNK, A1, LDA1,
$ A2, LDA2, B, LDB, F1, LDF1, F2, LDF2, G, LDG,
$ CS, DWORK, LDWORK, INFO )
C .. Scalar Arguments ..
CHARACTER STRUCG, TYPEG
INTEGER INFO, K, LDA1, LDA2, LDB, LDF1, LDF2, LDG,
$ LDWORK, N, NB, P, Q, RNK
C .. Array Arguments ..
DOUBLE PRECISION A1(LDA1,*), A2(LDA2,*), B(LDB,*), CS(*),
$ DWORK(*), F1(LDF1,*), F2(LDF2,*), G(LDG,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
TYPEG CHARACTER*1
Specifies the type of the generator, as follows:
= 'D': generator is column oriented and rank
deficient;
= 'C': generator is column oriented and not rank
deficient;
= 'R': generator is row oriented and not rank
deficient.
Note that this parameter must be equivalent with the
used TYPEG in the call of MB02CU.
STRUCG CHARACTER*1
Information about the structure of the generators,
as follows:
= 'T': the trailing block of the positive generator
is upper / lower triangular, and the trailing
block of the negative generator is zero;
= 'N': no special structure to mention.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
K (input) INTEGER
The number of rows in A1 to be processed. K >= 0.
N (input) INTEGER
If TYPEG = 'D' or TYPEG = 'C', the number of rows in F1;
if TYPEG = 'R', the number of columns in F1. N >= 0.
P (input) INTEGER
The number of columns of the positive generator. P >= K.
Q (input) INTEGER
The number of columns in B.
If TYPEG = 'D', Q >= K;
If TYPEG = 'C' or 'R', Q >= 0.
NB (input) INTEGER
On entry, if TYPEG = 'C' or TYPEG = 'R', NB specifies
the block size to be used in the blocked parts of the
algorithm. NB must be equivalent with the used block size
in the routine MB02CU.
RNK (input) INTEGER
If TYPEG = 'D', the number of linearly independent columns
in the generator as returned by MB02CU. 0 <= RNK <= K.
If TYPEG = 'C' or 'R', the value of this parameter is
irrelevant.
A1 (input) DOUBLE PRECISION array, dimension
(LDA1, K)
On entry, if TYPEG = 'D', the leading K-by-K part of this
array must contain the matrix A1 as returned by MB02CU.
If TYPEG = 'C' or 'R', this array is not referenced.
LDA1 INTEGER
The leading dimension of the array A1.
If TYPEG = 'D', LDA1 >= MAX(1,K);
if TYPEG = 'C' or TYPEG = 'R', LDA1 >= 1.
A2 (input) DOUBLE PRECISION array,
if TYPEG = 'D' or TYPEG = 'C', dimension (LDA2, P-K);
if TYPEG = 'R', dimension (LDA2, K).
On entry, if TYPEG = 'D' or TYPEG = 'C', the leading
K-by-(P-K) part of this array must contain the matrix
A2 as returned by MB02CU.
On entry, if TYPEG = 'R', the leading (P-K)-by-K part of
this array must contain the matrix A2 as returned by
MB02CU.
LDA2 INTEGER
The leading dimension of the array A2.
If P = K, LDA2 >= 1;
If P > K and (TYPEG = 'D' or TYPEG = 'C'),
LDA2 >= MAX(1,K);
if P > K and TYPEG = 'R', LDA2 >= P-K.
B (input) DOUBLE PRECISION array,
if TYPEG = 'D' or TYPEG = 'C', dimension (LDB, Q);
if TYPEG = 'R', dimension (LDB, K).
On entry, if TYPEG = 'D' or TYPEG = 'C', the leading
K-by-Q part of this array must contain the matrix B as
returned by MB02CU.
On entry, if TYPEG = 'R', the leading Q-by-K part of this
array must contain the matrix B as returned by MB02CU.
LDB INTEGER
The leading dimension of the array B.
If Q = 0, LDB >= 1;
If Q > 0 and (TYPEG = 'D' or TYPEG = 'C'),
LDB >= MAX(1,K);
if Q > 0 and TYPEG = 'R', LDB >= Q.
F1 (input/output) DOUBLE PRECISION array,
if TYPEG = 'D' or TYPEG = 'C', dimension (LDF1, K);
if TYPEG = 'R', dimension (LDF1, N).
On entry, if TYPEG = 'D' or TYPEG = 'C', the leading
N-by-K part of this array must contain the first part
of the positive generator to be processed.
On entry, if TYPEG = 'R', the leading K-by-N part of this
array must contain the first part of the positive
generator to be processed.
On exit, if TYPEG = 'D' or TYPEG = 'C', the leading
N-by-K part of this array contains the first part of the
transformed positive generator.
On exit, if TYPEG = 'R', the leading K-by-N part of this
array contains the first part of the transformed positive
generator.
LDF1 INTEGER
The leading dimension of the array F1.
If TYPEG = 'D' or TYPEG = 'C', LDF1 >= MAX(1,N);
if TYPEG = 'R', LDF1 >= MAX(1,K).
F2 (input/output) DOUBLE PRECISION array,
if TYPEG = 'D' or TYPEG = 'C', dimension (LDF2, P-K);
if TYPEG = 'R', dimension (LDF2, N).
On entry, if TYPEG = 'D' or TYPEG = 'C', the leading
N-by-(P-K) part of this array must contain the second part
of the positive generator to be processed.
On entry, if TYPEG = 'R', the leading (P-K)-by-N part of
this array must contain the second part of the positive
generator to be processed.
On exit, if TYPEG = 'D' or TYPEG = 'C', the leading
N-by-(P-K) part of this array contains the second part of
the transformed positive generator.
On exit, if TYPEG = 'R', the leading (P-K)-by-N part of
this array contains the second part of the transformed
positive generator.
LDF2 INTEGER
The leading dimension of the array F2.
If P = K, LDF2 >= 1;
If P > K and (TYPEG = 'D' or TYPEG = 'C'),
LDF2 >= MAX(1,N);
if P > K and TYPEG = 'R', LDF2 >= P-K.
G (input/output) DOUBLE PRECISION array,
if TYPEG = 'D' or TYPEG = 'C', dimension (LDG, Q);
if TYPEG = 'R', dimension (LDG, N).
On entry, if TYPEG = 'D' or TYPEG = 'C', the leading
N-by-Q part of this array must contain the negative part
of the generator to be processed.
On entry, if TYPEG = 'R', the leading Q-by-N part of this
array must contain the negative part of the generator to
be processed.
On exit, if TYPEG = 'D' or TYPEG = 'C', the leading
N-by-Q part of this array contains the transformed
negative generator.
On exit, if TYPEG = 'R', the leading Q-by-N part of this
array contains the transformed negative generator.
LDG INTEGER
The leading dimension of the array G.
If Q = 0, LDG >= 1;
If Q > 0 and (TYPEG = 'D' or TYPEG = 'C'),
LDG >= MAX(1,N);
if Q > 0 and TYPEG = 'R', LDG >= Q.
CS (input) DOUBLE PRECISION array, dimension (x)
If TYPEG = 'D' and P = K, x = 3*K;
If TYPEG = 'D' and P > K, x = 5*K;
If (TYPEG = 'C' or TYPEG = 'R') and P = K, x = 4*K;
If (TYPEG = 'C' or TYPEG = 'R') and P > K, x = 6*K.
On entry, the first x elements of this array must contain
Givens and modified hyperbolic rotation parameters, and
scalar factors of the Householder transformations as
returned by MB02CU.
</PRE>
<B>Workspace</B>
<PRE>
DWORK DOUBLE PRECISION array, dimension (LDWORK)
On exit, if INFO = -23, DWORK(1) returns the minimum
value of LDWORK.
LDWORK INTEGER
The length of the array DWORK.
TYPEG = 'D': LDWORK >= MAX(1,N);
(TYPEG = 'C' or TYPEG = 'R') and NB <= 0:
LDWORK >= MAX(1,N);
(TYPEG = 'C' or TYPEG = 'R') and NB >= 1:
LDWORK >= MAX(1,( N + K )*NB).
</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="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The algorithm requires 0(N*K*( P + Q )) floating point operations.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The Householder transformations and modified hyperbolic rotations
computed by SLICOT Library routine MB02CU are applied to the
corresponding parts of the matrices F1, F2 and G.
</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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