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<HTML>
<HEAD><TITLE>TF01PD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="TF01PD">TF01PD</A></H2>
<H3>
Block Toeplitz expansion of a multivariable parameter sequence
</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 construct the block Toeplitz expansion T of a multivariable
parameter sequence M(1),...,M(NR+NC-1), where each parameter M(k)
is an NH1-by-NH2 block matrix and k = 1,2,...,(NR+NC-1).
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE TF01PD( NH1, NH2, NR, NC, H, LDH, T, LDT, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDH, LDT, NC, NH1, NH2, NR
C .. Array Arguments ..
DOUBLE PRECISION H(LDH,*), T(LDT,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
NH1 (input) INTEGER
The number of rows in each parameter M(k). NH1 >= 0.
NH2 (input) INTEGER
The number of columns in each parameter M(k). NH2 >= 0.
NR (input) INTEGER
The number of parameters required in each column of the
block Toeplitz expansion matrix T. NR >= 0.
NC (input) INTEGER
The number of parameters required in each row of the
block Toeplitz expansion matrix T. NC >= 0.
H (input) DOUBLE PRECISION array, dimension
(LDH,(NR+NC-1)*NH2)
The leading NH1-by-(NR+NC-1)*NH2 part of this array must
contain the multivariable sequence M(k), where k = 1,2,
...,(NR+NC-1). Specifically, each parameter M(k) is an
NH1-by-NH2 matrix whose (i,j)-th element must be stored in
H(i,(k-1)*NH2+j) for i = 1,2,...,NH1 and j = 1,2,...,NH2.
LDH INTEGER
The leading dimension of array H. LDH >= MAX(1,NH1).
T (output) DOUBLE PRECISION array, dimension (LDT,NH2*NC)
The leading NH1*NR-by-NH2*NC part of this array contains
the block Toeplitz expansion of the multivariable sequence
M(k).
LDT INTEGER
The leading dimension of array T. LDT >= MAX(1,NH1*NR).
</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 NH1-by-NH2 dimensional parameters M(k) of a multivariable
sequence are arranged into a matrix T in Toeplitz form such that
| M(NC) M(NC-1) M(NC-2) . . . M(1) |
| |
| M(NC+1) M(NC) M(NC-1) . . . M(2) |
T = | . . . . |.
| . . . . |
| . . . . |
| |
| M(NR+NC-1) M(NR+NC-2) M(NR+NC-3) . . . M(NR) |
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Johvidov, J.S.
Hankel and Toeplitz Matrices and Forms: Algebraic Theory,
(translated by G.P.A. Thijsse, I. Gohberg, ed.).
Birkhaeuser, Boston, 1982.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The time taken is approximately proportional to
NH1 x NH2 x NR x NC.
</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>
* TF01PD EXAMPLE PROGRAM TEXT
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER NH1MAX, NH2MAX, NRMAX, NCMAX
PARAMETER ( NH1MAX = 20, NH2MAX = 20, NRMAX = 20,
$ NCMAX = 20 )
INTEGER LDH, LDT
PARAMETER ( LDH = NH1MAX, LDT = NH1MAX*NRMAX )
* .. Local Scalars ..
INTEGER I, INFO, J, NC, NCT, NH1, NH2, NR, NRT
* .. Local Arrays ..
DOUBLE PRECISION H(LDH,(NRMAX+NCMAX-1)*NH2MAX),
$ T(LDT,NH2MAX*NCMAX)
* .. External Subroutines ..
EXTERNAL TF01PD
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) NH1, NH2, NR, NC
IF ( NH1.LE.0 .OR. NH1.GE.NH1MAX ) THEN
WRITE ( NOUT, FMT = 99995 ) NH1
ELSE IF ( NH2.LE.0 .OR. NH2.GT.NH2MAX ) THEN
WRITE ( NOUT, FMT = 99994 ) NH2
ELSE IF ( NR.LE.0 .OR. NR.GT.NRMAX ) THEN
WRITE ( NOUT, FMT = 99993 ) NR
ELSE IF ( NC.LE.0 .OR. NC.GT.NCMAX ) THEN
WRITE ( NOUT, FMT = 99992 ) NC
ELSE
READ ( NIN, FMT = * )
$ ( ( H(I,J), I = 1,NH1 ), J = 1,( NR+NC-1 )*NH2 )
* Construct the NRT by NCT block Toeplitz expansion of M(k).
CALL TF01PD( NH1, NH2, NR, NC, H, LDH, T, LDT, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
NRT = NH1*NR
NCT = NH2*NC
WRITE ( NOUT, FMT = 99997 ) NRT, NCT
DO 20 I = 1, NRT
WRITE ( NOUT, FMT = 99996 ) ( T(I,J), J = 1,NCT )
20 CONTINUE
END IF
END IF
STOP
*
99999 FORMAT (' TF01PD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from TF01PD = ',I2)
99997 FORMAT (' The ',I2,' by ',I2,' matrix T is ')
99996 FORMAT (20(1X,F8.4))
99995 FORMAT (/' NH1 is out of range.',/' NH1 = ',I5)
99994 FORMAT (/' NH2 is out of range.',/' NH2 = ',I5)
99993 FORMAT (/' NR is out of range.',/' NR = ',I5)
99992 FORMAT (/' NC is out of range.',/' NC = ',I5)
END
</PRE>
<B>Program Data</B>
<PRE>
TF01PD EXAMPLE PROGRAM DATA
2 2 3 3
1.0647 -0.4282 -0.4922 -1.2072
-0.3043 0.6883 -0.0926 0.7167
-0.1844 -0.8507 0.4441 -0.0478
0.7195 0.0500 -0.3955 0.5674
1.3387 -0.2801 0.1073 -0.5315
</PRE>
<B>Program Results</B>
<PRE>
TF01PD EXAMPLE PROGRAM RESULTS
The 6 by 6 matrix T is
-0.1844 0.4441 -0.3043 -0.0926 1.0647 -0.4922
-0.8507 -0.0478 0.6883 0.7167 -0.4282 -1.2072
0.7195 -0.3955 -0.1844 0.4441 -0.3043 -0.0926
0.0500 0.5674 -0.8507 -0.0478 0.6883 0.7167
1.3387 0.1073 0.7195 -0.3955 -0.1844 0.4441
-0.2801 -0.5315 0.0500 0.5674 -0.8507 -0.0478
</PRE>
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