Purpose
To generate benchmark examples for time-invariant,
continuous-time dynamical systems
.
E x(t) = A x(t) + B u(t)
y(t) = C x(t) + D u(t)
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
CTDSX (Version 1.0) described in [1].
Specification
SUBROUTINE BD01AD( 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,*)
Arguments
Mode Parameters
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.
Input/Output Parameters
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 Examples 2.1 and 2.2, DPAR(1) defines the parameter
'epsilon'.
For Example 2.4, DPAR(1), ..., DPAR(7) define 'b', 'mu',
'r', 'r_c', 'k_l', 'sigma', 'a', respectively.
For Example 2.7, DPAR(1) and DPAR(2) define 'mu' and 'nu',
respectively.
For Example 4.1, DPAR(1), ..., DPAR(7) define 'a', 'b',
'c', 'beta_1', 'beta_2', 'gamma_1', 'gamma_2',
respectively.
For Example 4.2, DPAR(1), ..., DPAR(3) define 'mu',
'delta', 'kappa', 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 Examples 2.3, 2.5, and 2.6, IPAR(1) defines the
parameter 's'.
For Example 3.1, IPAR(1) defines 'q'.
For Examples 3.2 and 3.3, IPAR(1) defines 'n'.
For Example 3.4, IPAR(1) defines 'l'.
For Example 4.1, IPAR(1) defines 'n'.
For Example 4.2, IPAR(1) defines 'l'.
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.
Workspace
DWORK DOUBLE PRECISION array, dimension (LDWORK)
LDWORK INTEGER
The length of the array DWORK.
For Example 3.4, LDWORK >= 4*IPAR(1) is required.
For the other examples, no workspace is needed, i.e.,
LDWORK >= 1.
Error Indicator
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.
References
[1] Kressner, D., Mehrmann, V. and Penzl, T.
CTDSX - a Collection of Benchmark Examples for State-Space
Realizations of Continuous-Time Dynamical Systems.
SLICOT Working Note 1998-9. 1998.
Numerical Aspects
NoneFurther Comments
NoneExample
Program Text
C BD01AD EXAMPLE PROGRAM TEXT
C Copyright (c) 2002-2017 NICONET e.V.
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 = 4*NMAX)
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 BD01AD
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 BD01AD(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 (' BD01AD EXAMPLE PROGRAM RESULTS', /1X)
99998 FORMAT (' INFO on exit from BD01AD = ', 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
Program Data
BD01AD EXAMPLE PROGRAM DATA D 1 1Program Results
BD01AD EXAMPLE PROGRAM RESULTS Laub 1979, Ex.1 Order of matrix A: N = 2 Number of columns in matrix B: M = 1 Number of rows in matrix C: P = 2 E is the identity matrix. A = 0.0000 1.0000 0.0000 0.0000 B = 0.0000 1.0000 C = 1.0000 0.0000 0.0000 1.0000 D is of zeros.