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<HTML>
<HEAD><TITLE>BD02AD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="BD02AD">BD02AD</A></H2>
<H3>
Benchmark examples for time-invariant discrete-time dynamical systems
</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 benchmark examples for time-invariant,
discrete-time dynamical systems
E x_k+1 = A x_k + B u_k
y_k = C x_k + D u_k
E, A are real N-by-N matrices, B is N-by-M, C is P-by-N, and
D is P-by-M. In many examples, E is the identity matrix and D is
the zero matrix.
This routine is an implementation of the benchmark library
DTDSX (Version 1.0) described in [1].
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE BD02AD( DEF, NR, DPAR, IPAR, VEC, N, M, P, E, LDE, A,
1 LDA, B, LDB, C, LDC, D, LDD, NOTE, DWORK,
2 LDWORK, INFO )
C .. Scalar Arguments ..
CHARACTER DEF
CHARACTER*70 NOTE
INTEGER INFO, LDA, LDB, LDC, LDD, LDE, LDWORK, M, N, P
C .. Array Arguments ..
LOGICAL VEC(8)
INTEGER IPAR(*), NR(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*), DPAR(*),
1 DWORK(*), E(LDE,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
DEF CHARACTER*1
Specifies the kind of values used as parameters when
generating parameter-dependent and scalable examples
(i.e., examples with NR(1) = 2, 3, or 4):
= 'D': Default values defined in [1] are used;
= 'N': Values set in DPAR and IPAR are used.
This parameter is not referenced if NR(1) = 1.
Note that the scaling parameter of examples with
NR(1) = 3 or 4 is considered as a regular parameter in
this context.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
NR (input) INTEGER array, dimension (2)
Specifies the index of the desired example according
to [1].
NR(1) defines the group:
1 : parameter-free problems of fixed size
2 : parameter-dependent problems of fixed size
3 : parameter-free problems of scalable size
4 : parameter-dependent problems of scalable size
NR(2) defines the number of the benchmark example
within a certain group according to [1].
DPAR (input/output) DOUBLE PRECISION array, dimension (7)
On entry, if DEF = 'N' and the desired example depends on
real parameters, then the array DPAR must contain the
values for these parameters.
For an explanation of the parameters see [1].
For Example 2.1, DPAR(1), ..., DPAR(3) define the
parameters 'tau', 'delta', 'K', respectively.
On exit, if DEF = 'D' and the desired example depends on
real parameters, then the array DPAR is overwritten by the
default values given in [1].
IPAR (input/output) INTEGER array, dimension (1)
On entry, if DEF = 'N' and the desired example depends on
integer parameters, then the array IPAR must contain the
values for these parameters.
For an explanation of the parameters see [1].
For Example 3.1, IPAR(1) defines the parameter 'n'.
On exit, if DEF = 'D' and the desired example depends on
integer parameters, then the array IPAR is overwritten by
the default values given in [1].
VEC (output) LOGICAL array, dimension (8)
Flag vector which displays the availabilty of the output
data:
VEC(1), ..., VEC(3) refer to N, M, and P, respectively,
and are always .TRUE..
VEC(4) is .TRUE. iff E is NOT the identity matrix.
VEC(5), ..., VEC(7) refer to A, B, and C, respectively,
and are always .TRUE..
VEC(8) is .TRUE. iff D is NOT the zero matrix.
N (output) INTEGER
The actual state dimension, i.e., the order of the
matrices E and A.
M (output) INTEGER
The number of columns in the matrices B and D.
P (output) INTEGER
The number of rows in the matrices C and D.
E (output) DOUBLE PRECISION array, dimension (LDE,N)
The leading N-by-N part of this array contains the
matrix E.
NOTE that this array is overwritten (by the identity
matrix), if VEC(4) = .FALSE..
LDE INTEGER
The leading dimension of array E. LDE >= N.
A (output) DOUBLE PRECISION array, dimension (LDA,N)
The leading N-by-N part of this array contains the
matrix A.
LDA INTEGER
The leading dimension of array A. LDA >= N.
B (output) DOUBLE PRECISION array, dimension (LDB,M)
The leading N-by-M part of this array contains the
matrix B.
LDB INTEGER
The leading dimension of array B. LDB >= N.
C (output) DOUBLE PRECISION array, dimension (LDC,N)
The leading P-by-N part of this array contains the
matrix C.
LDC INTEGER
The leading dimension of array C. LDC >= P.
D (output) DOUBLE PRECISION array, dimension (LDD,M)
The leading P-by-M part of this array contains the
matrix D.
NOTE that this array is overwritten (by the zero
matrix), if VEC(8) = .FALSE..
LDD INTEGER
The leading dimension of array D. LDD >= P.
NOTE (output) CHARACTER*70
String containing short information about the chosen
example.
</PRE>
<B>Workspace</B>
<PRE>
DWORK DOUBLE PRECISION array, dimension (LDWORK)
NOTE that DWORK is not used in the current version
of BD02AD.
LDWORK INTEGER
LDWORK >= 1.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value; in particular, INFO = -3 or -4 indicates
that at least one of the parameters in DPAR or
IPAR, respectively, has an illegal value;
= 1: data file can not be opened or has wrong format.
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Kressner, D., Mehrmann, V. and Penzl, T.
DTDSX - a Collection of Benchmark Examples for State-Space
Realizations of Discrete-Time Dynamical Systems.
SLICOT Working Note 1998-10. 1998.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
None
</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>
C BD02AD EXAMPLE PROGRAM TEXT
C
C .. Parameters ..
INTEGER NIN, NOUT
PARAMETER (NIN = 5, NOUT = 6)
INTEGER NMAX, MMAX, PMAX
PARAMETER (NMAX = 421, MMAX = 211, PMAX = 211)
INTEGER LDA, LDB, LDC, LDD, LDE, LDWORK
PARAMETER (LDA = NMAX, LDB = NMAX, LDC = PMAX, LDD = PMAX,
1 LDE = NMAX, LDWORK = 1)
C .. Local Scalars ..
CHARACTER DEF
INTEGER I, INFO, J, LDPAR, LIPAR, M, N, P
CHARACTER*70 NOTE
C .. Local Arrays ..
DOUBLE PRECISION A(LDA,NMAX), B(LDB,MMAX), C(LDC,NMAX),
1 D(LDD,MMAX), DPAR(7), DWORK(LDWORK), E(LDE,NMAX)
INTEGER NR(2), IPAR(7)
LOGICAL VEC(8)
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL BD02AD
C .. Executable Statements ..
WRITE (NOUT, FMT = 99999)
C Skip the heading in the data file and read the data.
READ (NIN, FMT = '()')
READ (NIN, FMT = *) DEF
READ (NIN, FMT = *) (NR(I), I = 1, 2)
IF (LSAME(DEF,'N')) THEN
READ (NIN, FMT = *) LDPAR
IF (LDPAR .GT. 0) READ (NIN, FMT = *) (DPAR(I), I = 1, LDPAR)
READ (NIN, FMT = *) LIPAR
IF (LIPAR .GT. 0) READ (NIN, FMT = *) (IPAR(I), I = 1, LIPAR)
END IF
C Generate benchmark example
CALL BD02AD(DEF, NR, DPAR, IPAR, VEC, N, M, P, E, LDE, A, LDA,
1 B, LDB, C, LDC, D, LDD, NOTE, DWORK, LDWORK, INFO)
C
IF (INFO .NE. 0) THEN
WRITE (NOUT, FMT = 99998) INFO
ELSE
WRITE (NOUT, FMT = *) NOTE
WRITE (NOUT, FMT = 99997) N
WRITE (NOUT, FMT = 99996) M
WRITE (NOUT, FMT = 99995) P
IF (VEC(4)) THEN
WRITE (NOUT, FMT = 99994)
DO 10 I = 1, N
WRITE (NOUT, FMT = 99987) (E(I,J), J = 1, N)
10 CONTINUE
ELSE
WRITE (NOUT, FMT = 99993)
END IF
WRITE (NOUT,FMT = 99992)
DO 20 I = 1, N
WRITE (NOUT, FMT = 99987) (A(I,J), J = 1, N)
20 CONTINUE
WRITE (NOUT,FMT = 99991)
DO 30 I = 1, N
WRITE (NOUT, FMT = 99987) (B(I,J), J = 1, M)
30 CONTINUE
WRITE (NOUT,FMT = 99990)
DO 40 I = 1, P
WRITE (NOUT, FMT = 99987) (C(I,J), J = 1, N)
40 CONTINUE
IF (VEC(8)) THEN
WRITE (NOUT,FMT = 99989)
DO 50 I = 1, P
WRITE (NOUT, FMT = 99987) (D(I,J), J = 1, M)
50 CONTINUE
ELSE
WRITE (NOUT, FMT = 99988)
END IF
END IF
C
99999 FORMAT (' BD02AD EXAMPLE PROGRAM RESULTS', /1X)
99998 FORMAT (' INFO on exit from BD02AD = ', I3)
99997 FORMAT (/' Order of matrix A: N = ', I3)
99996 FORMAT (' Number of columns in matrix B: M = ', I3)
99995 FORMAT (' Number of rows in matrix C: P = ', I3)
99994 FORMAT (/' E = ')
99993 FORMAT (/' E is the identity matrix.')
99992 FORMAT (' A = ')
99991 FORMAT (' B = ')
99990 FORMAT (' C = ')
99989 FORMAT (' D = ')
99988 FORMAT (' D is of zeros.')
99987 FORMAT (20(1X,F8.4))
C
END
</PRE>
<B>Program Data</B>
<PRE>
BD02AD EXAMPLE PROGRAM DATA
D
1 1
</PRE>
<B>Program Results</B>
<PRE>
BD02AD EXAMPLE PROGRAM RESULTS
Laub 1979, Ex. 2: uncontrollable-unobservable data
Order of matrix A: N = 2
Number of columns in matrix B: M = 1
Number of rows in matrix C: P = 1
E is the identity matrix.
A =
4.0000 3.0000
-4.5000 -3.5000
B =
1.0000
-1.0000
C =
3.0000 2.0000
D is of zeros.
</PRE>
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