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[Octave-cvsupdate] SF.net SVN: octave:[8488] trunk/octave-forge/main/control
|
From: <par...@us...> - 2011-09-03 18:50:42
|
Revision: 8488
http://octave.svn.sourceforge.net/octave/?rev=8488&view=rev
Author: paramaniac
Date: 2011-09-03 18:50:35 +0000 (Sat, 03 Sep 2011)
Log Message:
-----------
control: add bilinear transformation (c2d case)
Modified Paths:
--------------
trunk/octave-forge/main/control/devel/makefile_all.m
trunk/octave-forge/main/control/inst/@ss/__c2d__.m
trunk/octave-forge/main/control/inst/@tf/__c2d__.m
trunk/octave-forge/main/control/inst/ltimodels.m
trunk/octave-forge/main/control/src/Makefile
Added Paths:
-----------
trunk/octave-forge/main/control/devel/makefile_tustin.m
trunk/octave-forge/main/control/src/AB04MD.f
trunk/octave-forge/main/control/src/slab04md.cc
Modified: trunk/octave-forge/main/control/devel/makefile_all.m
===================================================================
--- trunk/octave-forge/main/control/devel/makefile_all.m 2011-09-03 16:37:43 UTC (rev 8487)
+++ trunk/octave-forge/main/control/devel/makefile_all.m 2011-09-03 18:50:35 UTC (rev 8488)
@@ -25,7 +25,7 @@
makefile_scale
makefile_ss2tf
makefile_staircase
+makefile_tustin
makefile_zero
-system ("rm *.o");
cd (homedir);
Added: trunk/octave-forge/main/control/devel/makefile_tustin.m
===================================================================
--- trunk/octave-forge/main/control/devel/makefile_tustin.m (rev 0)
+++ trunk/octave-forge/main/control/devel/makefile_tustin.m 2011-09-03 18:50:35 UTC (rev 8488)
@@ -0,0 +1,19 @@
+## ==============================================================================
+## Developer Makefile for OCT-files
+## ==============================================================================
+## USAGE: * fetch control from Octave-Forge by svn
+## * add control/inst, control/src and control/devel to your Octave path
+## * run makefile_*
+## ==============================================================================
+
+homedir = pwd ();
+develdir = fileparts (which ("makefile_tustin"));
+srcdir = [develdir, "/../src"];
+cd (srcdir);
+
+## bilinear transformation
+mkoctfile slab04md.cc \
+ AB04MD.f
+
+system ("rm *.o");
+cd (homedir);
Modified: trunk/octave-forge/main/control/inst/@ss/__c2d__.m
===================================================================
--- trunk/octave-forge/main/control/inst/@ss/__c2d__.m 2011-09-03 16:37:43 UTC (rev 8487)
+++ trunk/octave-forge/main/control/inst/@ss/__c2d__.m 2011-09-03 18:50:35 UTC (rev 8488)
@@ -44,6 +44,19 @@
sys.a = tmp (1:n, 1:n); # F
sys.b = tmp (1:n, n+(1:m)); # G
+ case {"tustin", "bilin"}
+ if (! isempty (sys.e))
+ if (rcond (sys.e) < eps)
+ error ("ss: c2d: tustin method requires proper system");
+ else
+ sys.a = sys.e \ sys.a;
+ sys.b = sys.e \ sys.b;
+ sys.e = []; # require ordinary state-space model
+ endif
+ endif
+
+ [sys.a, sys.b, sys.c, sys.d] = slab04md (sys.a, sys.b, sys.c, sys.d, 1, 2/tsam, false);
+
otherwise
error ("ss: c2d: %s is an invalid method", method);
Modified: trunk/octave-forge/main/control/inst/@tf/__c2d__.m
===================================================================
--- trunk/octave-forge/main/control/inst/@tf/__c2d__.m 2011-09-03 16:37:43 UTC (rev 8487)
+++ trunk/octave-forge/main/control/inst/@tf/__c2d__.m 2011-09-03 18:50:35 UTC (rev 8488)
@@ -26,13 +26,13 @@
[p, m] = size (sys);
- switch (method)
- case {"zoh", "std"}
+ ##switch (method)
+ ## case {"zoh", "std"}
error ("tf: c2d: not implemented yet");
- otherwise
- error ("tf: c2d: %s is an invalid method", method);
+ ## otherwise
+ ## error ("tf: c2d: %s is an invalid method", method);
- endswitch
+ ##endswitch
endfunction
\ No newline at end of file
Modified: trunk/octave-forge/main/control/inst/ltimodels.m
===================================================================
--- trunk/octave-forge/main/control/inst/ltimodels.m 2011-09-03 16:37:43 UTC (rev 8487)
+++ trunk/octave-forge/main/control/inst/ltimodels.m 2011-09-03 18:50:35 UTC (rev 8488)
@@ -1229,3 +1229,71 @@
%!
%!assert (NUM, NUMe, 1e-4);
%!assert (DEN, DENe, 1e-4);
+
+
+## bilinear transformation
+%!shared Mo, Me
+%! A = [ 1.0 0.5
+%! 0.5 1.0 ].';
+%!
+%! B = [ 0.0 -1.0
+%! 1.0 0.0 ].';
+%!
+%! C = [ -1.0 0.0
+%! 0.0 1.0 ].';
+%!
+%! D = [ 1.0 0.0
+%! 0.0 -1.0 ].';
+%!
+%! [Ao, Bo, Co, Do] = slab04md (A, B, C, D, 1.0, 1.0, false);
+%!
+%! Ae = [ -1.0000 -4.0000
+%! -4.0000 -1.0000 ];
+%!
+%! Be = [ 2.8284 0.0000
+%! 0.0000 -2.8284 ];
+%!
+%! Ce = [ 0.0000 2.8284
+%! -2.8284 0.0000 ];
+%!
+%! De = [ -1.0000 0.0000
+%! 0.0000 -3.0000 ];
+%!
+%! Mo = [Ao, Bo; Co, Do];
+%! Me = [Ae, Be; Ce, De];
+%!
+%!assert (Mo, Me, 1e-4);
+
+
+## bilinear transformation
+%!shared Mo, Me
+%! A = [ 1.0 0.5
+%! 0.5 1.0 ].';
+%!
+%! B = [ 0.0 -1.0
+%! 1.0 0.0 ].';
+%!
+%! C = [ -1.0 0.0
+%! 0.0 1.0 ].';
+%!
+%! D = [ 1.0 0.0
+%! 0.0 -1.0 ].';
+%!
+%! [Ao, Bo, Co, Do] = ssdata (c2d (ss (A, B, C, D), 2, "tustin"));
+%!
+%! Ae = [ -1.0000 -4.0000
+%! -4.0000 -1.0000 ];
+%!
+%! Be = [ 2.8284 0.0000
+%! 0.0000 -2.8284 ];
+%!
+%! Ce = [ 0.0000 2.8284
+%! -2.8284 0.0000 ];
+%!
+%! De = [ -1.0000 0.0000
+%! 0.0000 -3.0000 ];
+%!
+%! Mo = [Ao, Bo; Co, Do];
+%! Me = [Ae, Be; Ce, De];
+%!
+%!assert (Mo, Me, 1e-4);
Added: trunk/octave-forge/main/control/src/AB04MD.f
===================================================================
--- trunk/octave-forge/main/control/src/AB04MD.f (rev 0)
+++ trunk/octave-forge/main/control/src/AB04MD.f 2011-09-03 18:50:35 UTC (rev 8488)
@@ -0,0 +1,345 @@
+ SUBROUTINE AB04MD( TYPE, N, M, P, ALPHA, BETA, A, LDA, B, LDB, C,
+ $ LDC, D, LDD, IWORK, DWORK, LDWORK, INFO )
+C
+C SLICOT RELEASE 5.0.
+C
+C Copyright (c) 2002-2010 NICONET e.V.
+C
+C This program is free software: you can redistribute it and/or
+C modify it under the terms of the GNU General Public License as
+C published by the Free Software Foundation, either version 2 of
+C the License, or (at your option) any later version.
+C
+C This program is distributed in the hope that it will be useful,
+C but WITHOUT ANY WARRANTY; without even the implied warranty of
+C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+C GNU General Public License for more details.
+C
+C You should have received a copy of the GNU General Public License
+C along with this program. If not, see
+C <http://www.gnu.org/licenses/>.
+C
+C PURPOSE
+C
+C To perform a transformation on the parameters (A,B,C,D) of a
+C system, which is equivalent to a bilinear transformation of the
+C corresponding transfer function matrix.
+C
+C ARGUMENTS
+C
+C Mode Parameters
+C
+C TYPE CHARACTER*1
+C Indicates the type of the original system and the
+C transformation to be performed as follows:
+C = 'D': discrete-time -> continuous-time;
+C = 'C': continuous-time -> discrete-time.
+C
+C Input/Output Parameters
+C
+C N (input) INTEGER
+C The order of the state matrix A. N >= 0.
+C
+C M (input) INTEGER
+C The number of system inputs. M >= 0.
+C
+C P (input) INTEGER
+C The number of system outputs. P >= 0.
+C
+C ALPHA, (input) DOUBLE PRECISION
+C BETA Parameters specifying the bilinear transformation.
+C Recommended values for stable systems: ALPHA = 1,
+C BETA = 1. ALPHA <> 0, BETA <> 0.
+C
+C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
+C On entry, the leading N-by-N part of this array must
+C contain the state matrix A of the original system.
+C On exit, the leading N-by-N part of this array contains
+C _
+C the state matrix A of the transformed system.
+C
+C LDA INTEGER
+C The leading dimension of array A. LDA >= MAX(1,N).
+C
+C B (input/output) DOUBLE PRECISION array, dimension (LDB,M)
+C On entry, the leading N-by-M part of this array must
+C contain the input matrix B of the original system.
+C On exit, the leading N-by-M part of this array contains
+C _
+C the input matrix B of the transformed system.
+C
+C LDB INTEGER
+C The leading dimension of array B. LDB >= MAX(1,N).
+C
+C C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
+C On entry, the leading P-by-N part of this array must
+C contain the output matrix C of the original system.
+C On exit, the leading P-by-N part of this array contains
+C _
+C the output matrix C of the transformed system.
+C
+C LDC INTEGER
+C The leading dimension of array C. LDC >= MAX(1,P).
+C
+C D (input/output) DOUBLE PRECISION array, dimension (LDD,M)
+C On entry, the leading P-by-M part of this array must
+C contain the input/output matrix D for the original system.
+C On exit, the leading P-by-M part of this array contains
+C _
+C the input/output matrix D of the transformed system.
+C
+C LDD INTEGER
+C The leading dimension of array D. LDD >= MAX(1,P).
+C
+C Workspace
+C
+C IWORK INTEGER array, dimension (N)
+C
+C DWORK DOUBLE PRECISION array, dimension (LDWORK)
+C On exit, if INFO = 0, DWORK(1) returns the optimal value
+C of LDWORK.
+C
+C LDWORK INTEGER
+C The length of the array DWORK. LDWORK >= MAX(1,N).
+C For optimum performance LDWORK >= MAX(1,N*NB), where NB
+C is the optimal blocksize.
+C
+C Error Indicator
+C
+C INFO INTEGER
+C = 0: successful exit;
+C < 0: if INFO = -i, the i-th argument had an illegal
+C value;
+C = 1: if the matrix (ALPHA*I + A) is exactly singular;
+C = 2: if the matrix (BETA*I - A) is exactly singular.
+C
+C METHOD
+C
+C The parameters of the discrete-time system are transformed into
+C the parameters of the continuous-time system (TYPE = 'D'), or
+C vice-versa (TYPE = 'C') by the transformation:
+C
+C 1. Discrete -> continuous
+C _ -1
+C A = beta*(alpha*I + A) * (A - alpha*I)
+C _ -1
+C B = sqrt(2*alpha*beta) * (alpha*I + A) * B
+C _ -1
+C C = sqrt(2*alpha*beta) * C * (alpha*I + A)
+C _ -1
+C D = D - C * (alpha*I + A) * B
+C
+C which is equivalent to the bilinear transformation
+C
+C z - alpha
+C z -> s = beta --------- .
+C z + alpha
+C
+C of one transfer matrix onto the other.
+C
+C 2. Continuous -> discrete
+C _ -1
+C A = alpha*(beta*I - A) * (beta*I + A)
+C _ -1
+C B = sqrt(2*alpha*beta) * (beta*I - A) * B
+C _ -1
+C C = sqrt(2*alpha*beta) * C * (beta*I - A)
+C _ -1
+C D = D + C * (beta*I - A) * B
+C
+C which is equivalent to the bilinear transformation
+C
+C beta + s
+C s -> z = alpha -------- .
+C beta - s
+C
+C of one transfer matrix onto the other.
+C
+C REFERENCES
+C
+C [1] Al-Saggaf, U.M. and Franklin, G.F.
+C Model reduction via balanced realizations: a extension and
+C frequency weighting techniques.
+C IEEE Trans. Autom. Contr., AC-33, pp. 687-692, 1988.
+C
+C NUMERICAL ASPECTS
+C 3
+C The time taken is approximately proportional to N .
+C The accuracy depends mainly on the condition number of the matrix
+C to be inverted.
+C
+C CONTRIBUTORS
+C
+C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, and
+C A. Varga, German Aerospace Research Establishment,
+C Oberpfaffenhofen, Germany, Nov. 1996.
+C Supersedes Release 2.0 routine AB04AD by W. van der Linden, and
+C A.J. Geurts, Technische Hogeschool Eindhoven, Holland.
+C
+C REVISIONS
+C
+C -
+C
+C KEYWORDS
+C
+C Bilinear transformation, continuous-time system, discrete-time
+C system, state-space model.
+C
+C ******************************************************************
+C
+C .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE, TWO
+ PARAMETER ( ZERO=0.0D0, ONE=1.0D0, TWO=2.0D0 )
+C .. Scalar Arguments ..
+ CHARACTER TYPE
+ INTEGER INFO, LDA, LDB, LDC, LDD, LDWORK, M, N, P
+ DOUBLE PRECISION ALPHA, BETA
+C .. Array Arguments ..
+ INTEGER IWORK(*)
+ DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*), DWORK(*)
+C .. Local Scalars ..
+ LOGICAL LTYPE
+ INTEGER I, IP
+ DOUBLE PRECISION AB2, PALPHA, PBETA, SQRAB2
+C .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+C .. External Subroutines ..
+ EXTERNAL DGEMM, DGETRF, DGETRS, DGETRI, DLASCL, DSCAL,
+ $ DSWAP, XERBLA
+C .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, SIGN, SQRT
+C .. Executable Statements ..
+C
+ INFO = 0
+ LTYPE = LSAME( TYPE, 'D' )
+C
+C Test the input scalar arguments.
+C
+ IF( .NOT.LTYPE .AND. .NOT.LSAME( TYPE, 'C' ) ) THEN
+ INFO = -1
+ ELSE IF( N.LT.0 ) THEN
+ INFO = -2
+ ELSE IF( M.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( P.LT.0 ) THEN
+ INFO = -4
+ ELSE IF( ALPHA.EQ.ZERO ) THEN
+ INFO = -5
+ ELSE IF( BETA.EQ.ZERO ) THEN
+ INFO = -6
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -10
+ ELSE IF( LDC.LT.MAX( 1, P ) ) THEN
+ INFO = -12
+ ELSE IF( LDD.LT.MAX( 1, P ) ) THEN
+ INFO = -14
+ ELSE IF( LDWORK.LT.MAX( 1, N ) ) THEN
+ INFO = -17
+ END IF
+C
+ IF ( INFO.NE.0 ) THEN
+C
+C Error return.
+C
+ CALL XERBLA( 'AB04MD', -INFO )
+ RETURN
+ END IF
+C
+C Quick return if possible.
+C
+ IF ( MAX( N, M, P ).EQ.0 )
+ $ RETURN
+C
+C (Note: Comments in the code beginning "Workspace:" describe the
+C minimal amount of real workspace needed at that point in the
+C code, as well as the preferred amount for good performance.
+C NB refers to the optimal block size for the immediately
+C following subroutine, as returned by ILAENV.)
+C
+ IF (LTYPE) THEN
+C
+C Discrete-time to continuous-time with (ALPHA, BETA).
+C
+ PALPHA = ALPHA
+ PBETA = BETA
+ ELSE
+C
+C Continuous-time to discrete-time with (ALPHA, BETA) is
+C equivalent with discrete-time to continuous-time with
+C (-BETA, -ALPHA), if B and C change the sign.
+C
+ PALPHA = -BETA
+ PBETA = -ALPHA
+ END IF
+C
+ AB2 = PALPHA*PBETA*TWO
+ SQRAB2 = SIGN( SQRT( ABS( AB2 ) ), PALPHA )
+C -1
+C Compute (alpha*I + A) .
+C
+ DO 10 I = 1, N
+ A(I,I) = A(I,I) + PALPHA
+ 10 CONTINUE
+C
+ CALL DGETRF( N, N, A, LDA, IWORK, INFO )
+C
+ IF (INFO.NE.0) THEN
+C
+C Error return.
+C
+ IF (LTYPE) THEN
+ INFO = 1
+ ELSE
+ INFO = 2
+ END IF
+ RETURN
+ END IF
+C -1
+C Compute (alpha*I+A) *B.
+C
+ CALL DGETRS( 'No transpose', N, M, A, LDA, IWORK, B, LDB, INFO )
+C -1
+C Compute D - C*(alpha*I+A) *B.
+C
+ CALL DGEMM( 'No transpose', 'No transpose', P, M, N, -ONE, C,
+ $ LDC, B, LDB, ONE, D, LDD )
+C
+C Scale B by sqrt(2*alpha*beta).
+C
+ CALL DLASCL( 'General', 0, 0, ONE, SQRAB2, N, M, B, LDB, INFO )
+C -1
+C Compute sqrt(2*alpha*beta)*C*(alpha*I + A) .
+C
+ CALL DTRSM( 'Right', 'Upper', 'No transpose', 'Non-unit', P, N,
+ $ SQRAB2, A, LDA, C, LDC )
+C
+ CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', P, N, ONE,
+ $ A, LDA, C, LDC )
+C
+C Apply column interchanges to the solution matrix.
+C
+ DO 20 I = N-1, 1, -1
+ IP = IWORK(I)
+ IF ( IP.NE.I )
+ $ CALL DSWAP( P, C(1,I), 1, C(1,IP), 1 )
+ 20 CONTINUE
+C -1
+C Compute beta*(alpha*I + A) *(A - alpha*I) as
+C -1
+C beta*I - 2*alpha*beta*(alpha*I + A) .
+C
+C Workspace: need N; prefer N*NB.
+C
+ CALL DGETRI( N, A, LDA, IWORK, DWORK, LDWORK, INFO )
+C
+ DO 30 I = 1, N
+ CALL DSCAL(N, -AB2, A(1,I), 1)
+ A(I,I) = A(I,I) + PBETA
+ 30 CONTINUE
+C
+ RETURN
+C *** Last line of AB04MD ***
+ END
Property changes on: trunk/octave-forge/main/control/src/AB04MD.f
___________________________________________________________________
Added: svn:executable
+ *
Modified: trunk/octave-forge/main/control/src/Makefile
===================================================================
--- trunk/octave-forge/main/control/src/Makefile 2011-09-03 16:37:43 UTC (rev 8487)
+++ trunk/octave-forge/main/control/src/Makefile 2011-09-03 18:50:35 UTC (rev 8488)
@@ -4,6 +4,7 @@
sltb01pd.oct slsb03od.oct slsg03bd.oct slag08bd.oct sltg01jd.oct \
sltg01hd.oct sltg01id.oct slsg02ad.oct sltg04bx.oct sltb01id.oct \
sltg01ad.oct slsb10id.oct slsb10kd.oct slsb10zd.oct sltb04bd.oct \
+ slab04md.oct \
is_real_scalar.oct is_real_vector.oct is_real_matrix.oct \
is_real_square_matrix.oct
@@ -212,6 +213,11 @@
TB04BX.f MA02AD.f MB02RD.f MB01PD.f MB02SD.f \
MB01QD.f
+# bilinear transformation
+slab04md.oct: slab04md.cc
+ mkoctfile slab04md.cc \
+ AB04MD.f
+
# helpers
is_real_scalar.oct: is_real_scalar.cc
mkoctfile is_real_scalar.cc
Added: trunk/octave-forge/main/control/src/slab04md.cc
===================================================================
--- trunk/octave-forge/main/control/src/slab04md.cc (rev 0)
+++ trunk/octave-forge/main/control/src/slab04md.cc 2011-09-03 18:50:35 UTC (rev 8488)
@@ -0,0 +1,128 @@
+/*
+
+Copyright (C) 2011 Lukas F. Reichlin
+
+This file is part of LTI Syncope.
+
+LTI Syncope is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+LTI Syncope is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
+
+Discrete-time <--> continuous-time systems conversion
+by a bilinear transformation.
+Uses SLICOT AB04MD by courtesy of NICONET e.V.
+<http://www.slicot.org>
+
+Author: Lukas Reichlin <luk...@gm...>
+Created: September 2011
+Version: 0.1
+
+*/
+
+#include <octave/oct.h>
+#include <f77-fcn.h>
+#include "common.cc"
+
+extern "C"
+{
+ int F77_FUNC (ab04md, AB04MD)
+ (char& TYPE,
+ int& N, int& M, int& P,
+ double& ALPHA, double& BETA,
+ double* A, int& LDA,
+ double* B, int& LDB,
+ double* C, int& LDC,
+ double* D, int& LDD,
+ int* IWORK,
+ double* DWORK, int& LDWORK,
+ int& INFO);
+}
+
+DEFUN_DLD (slab04md, args, nargout,
+ "-*- texinfo -*-\n\
+Slicot AB04MD Release 5.0\n\
+No argument checking.\n\
+For internal use only.")
+{
+ int nargin = args.length ();
+ octave_value_list retval;
+
+ if (nargin != 7)
+ {
+ print_usage ();
+ }
+ else
+ {
+ // arguments in
+ char type;
+
+ Matrix a = args(0).matrix_value ();
+ Matrix b = args(1).matrix_value ();
+ Matrix c = args(2).matrix_value ();
+ Matrix d = args(3).matrix_value ();
+
+ double alpha = args(4).double_value ();
+ double beta = args(5).double_value ();
+ int discrete = args(6).int_value ();
+
+ if (discrete == 0)
+ type = 'C';
+ else
+ type = 'D';
+
+ int n = a.rows (); // n: number of states
+ int m = b.columns (); // m: number of inputs
+ int p = c.rows (); // p: number of outputs
+
+ int lda = max (1, n);
+ int ldb = max (1, n);
+ int ldc = max (1, p);
+ int ldd = max (1, p);
+
+ // workspace
+ int ldwork = max (1, n);
+
+ OCTAVE_LOCAL_BUFFER (int, iwork, n);
+ OCTAVE_LOCAL_BUFFER (double, dwork, ldwork);
+
+ // error indicator
+ int info;
+
+
+ // SLICOT routine AB04MD
+ F77_XFCN (ab04md, AB04MD,
+ (type,
+ n, m, p,
+ alpha, beta,
+ a.fortran_vec (), lda,
+ b.fortran_vec (), ldb,
+ c.fortran_vec (), ldc,
+ d.fortran_vec (), ldd,
+ iwork,
+ dwork, ldwork,
+ info));
+
+ if (f77_exception_encountered)
+ error ("slab04md: exception in SLICOT subroutine AB04MD");
+
+ if (info != 0)
+ error ("slab04md: AB04MD returned info = %d", info);
+
+ // return values
+ retval(0) = a;
+ retval(1) = b;
+ retval(2) = c;
+ retval(3) = d;
+ }
+
+ return retval;
+}
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