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<title>DAESolver - SLICOT Library Routine Documentation</title>
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<h2>
<a NAME="DAESolver"></a>DAESolver</h2>
<h3>
Solver for Algebraic Differential Equations (driver)</h3>
<b><a href="#Specification">[Specification]</a><a href="#Arguments">[Arguments]</a><a href="#Method">[Method]</a><a href="#References">[References]</a><a href="#Comments">[Comments]</a><a href="#Example">[Example]</a></b>
<p><b><font size=+1>Purpose</font></b>
<pre> Interface for using a common entry point, DSblock compatible for
defining Differential Algebraic Equations using several packages.</pre>
<pre> The equations follow the form (CASE A):
F(dx(t)/dt, x(t), u(t), p, t) = 0
y(t) = g(dx(t)/dx, x(t), u(t), p, t)
for the most general model which can only be solved by DASSL and
DASSPK.
A restricted case can be solved with RADAU5, LSODI, LSOIBT, if
the system is expressed as (CASE B):
F(x(t), u(t), p, t)*dx(t)/dt = A(x(t), u(t), p, t)
y(t) = g(dx(t)/dx, x(t), u(t), p, t)
And finally, the GELDA package is able to solve DAEs with the
expression (CASE C):
F(u(t), p, t)*dx(t)/dt = A(u(t), p, t)*x(t) + E(u(t), p, t)
The user must define the subroutines:
DAEDF: F(dx(t)/dt, x(t), u(t), p, t) for CASES: A, B and C
DAEDA: A(x(t), u(t), p, t) for CASES: B and C
DAEDE: E(u(t), p, t) for CASES: C
DAEOUT: g(dx(t)/dx, x(t), u(t), p, t)
and the Jacobians (JACFX, JACFU, JACFP) if used. The interface
adapts the structure to fit all the codes</pre>
<a NAME="Specification"></a><b><font size=+1>Specification</font></b>
<pre> SUBROUTINE DAESolver(ISOLVER,CDAEDF_,CDAEDA_,CDAEDE_,CDAEOUT_,
$ CJACFX_,CJACFU_,CJACFP_,CJACFXDOT_,
$ NX, NY, NU, NP, TINI, TOUT,
$ X, XDOTI, Y, U, P,
$ IPAR, RPAR, RTOL, ATOL,
$ IWORK, LIWORK, DWORK, LDWORK,
$ IWARN, INFO)
.. Scalar Arguments ..
DOUBLE PRECISION TINI, TOUT
INTEGER ISOLVER, IWARN, INFO,
$ NX, NY, NU, NP,
$ LDWORK, LIWORK
CHARACTER*9 CDAEDF_, CDAEDA_,CDAEDE_, CDAEOUT_,
$ CJACFX_, CJACFU_, CJACFP_, CJACFXDOT_,
$ CDAEDF, CDAEDA,CDAEDE, CDAEOUT,
$ CJACFX, CJACFU, CJACFP, CJACFXDOT
.. Array Arguments ..
DOUBLE PRECISION DWORK(LDWORK), RPAR(*), ATOL(*), RTOL(*)
$ X(NX), XDOTI(NX), Y(NY), U(NU), P(NP)
INTEGER IWORK(LIWORK), IPAR(*)</pre>
<a NAME="Arguments"></a><b><font size=+1>Arguments</font></b>
<p><b>Mode Parameters</b>
<pre> ISOLVER INTEGER
Indicates the nonlinear solver packages to be used
= 1: LSODI,
= 2: LSOIBT,
= 3: RADAU5,
= 4: DASSL,
= 5: DASPK,
= 6: DGELDA.</pre>
<b>Input/Output Parameters</b>
<br>
<pre><tt> DAEDF (input) EXTERNAL
Evaluates the F(dx(t)/dt, x(t), u(t), p, t).
DAEDA (input) EXTERNAL
Evaluates the A(x(t), u(t), p, t).
DAEDE (input) EXTERNAL
Evaluates the E(u(t), p, t).
DAEOUT (input) EXTERNAL
Evaluates the output signals function g.
JACFX (input) EXTERNAL
Evaluates the jacobian matrix with respect to X.
JACFU (input) EXTERNAL
Evaluates the jacobian matrix with respect to U.
JACFP (input) EXTERNAL
Evaluates the jacobian matrix with respect to P.
NX (input) INTEGER
Dimension of the state vector.
NY (input) INTEGER
Dimension of the output vector.
NU (input) INTEGER
Dimension of the input vector.
NP (input) INTEGER
Dimension of the parameter vector.
TINI (input) DOUBLE PRECISION
Initial value of time.
TOUT (input) DOUBLE PRECISION
Final value of time.
X (input/output) DOUBLE PRECISION array, dimension (NX)
On entry, array containing the initial state variables.
On exit, it has the last value of the state variables.
XDOTI (input) DOUBLE PRECISION array, dimension (NX)
Array containing dx(t)/dt at initial point.
Y (input/output) DOUBLE PRECISION array, dimension (NY)
On entry, array containing the initial values of Y.
On exit, it has the results of the system.
U (input) DOUBLE PRECISION array, dimension (NU)
Array containing the input initial values.
P (input) DOUBLE PRECISION array, dimension (NP)
Array containing the parameter variables.
IPAR (input/output) INTEGER array, dimension (201)
INPUT:
1..15 General
16..25 ODEPACK
26..35 RADAU5
36..50 DASSL/PK
51..60 GELDA
61..100 Reserved
OUTPUT:
101..110 General
111..125 ODEPACK
126..135 RADAU5
136..145 DASSL/PK
146..155 GELDA
156..200 Reserved
Any Mode:
201.. User Available
Common integer parameters for SOLVERS:
IPAR(1), Tolerance mode
0 : both rtol and atol are scalars
1 : rtol is a scalar and atol is a vector
2 : both rtol and atol are vectors
IPAR(2), Compute Output Values only at TOUT (and not
at the intermediate step). (1:Yes, 0:No)
IPAR(3), mfjac, Method flag for jacobian
0 : No jacobian used (non-stiff method).
1 : User supplied full jacobian (stiff).
2 : User supplied banded jacobian (stiff).
3 : User supplied sparse jacobian (stiff).
10 : internally generated full jacobian (stiff).
11 : internally generated banded jacobian (stiff).
12 : internally generated sparse jacobian (stiff).
IPAR(6), ml, lower half-bandwithds of the banded
jacobian, excluding tne main diagonal.
IPAR(7), mu, upper half-bandwithds of the banded
jacobian, excluding the main diagonal.
(Note: IPAR(6) and IPAR(7) are obligatories only if the
jacobian matrix is banded)
IPAR(101) = Number of steps taken for the problem.
IPAR(102) = Number of residual evaluations.
IPAR(103) = Number of jacobian evaluations.
Common parameters for RADAU5, ODEPACK and DGELDA:
IPAR(9), mfmass, Method flag for mass-matrix
0 : No mass-matrix used (non-stiff method).
1 : User supplied full mass-matrix (stiff).
2 : User supplied banded mass-matrix (stiff).
10 : Identity mass-matrix is used (stiff).
IPAR(10), mlmass, lower half-bandwithds of the banded
mass matrix, excluding the main diagonal.
IPAR(11), mumass, upper half-bandwithds of the banded
mass matrix, excluding the main diagonal.
IPAR(12), Maximum number of steps allowed during one
call to the solver.
Common parameters for ODEPACK, DASSL, DASPK and DGELDA:
IPAR(13), Maximum order to be allowed.
default values : 12 if meth = 1
5 if meth = 2
If exceds the default value, it will be reduced
to the default value.
In DASSL, DASPK and DGELDA : (1 .LE. MAXORD .LE. 5)
IPAR(111) = The method order last used(successfully).
IPAR(112) = The order to be attempted on the next step.
Common parameters for ODEPACK package:
IPAR(16), Status Flag
IPAR(17), Optional inputs, must be 0
IPAR(18), Maximum number of messages printed,
default value is 10.
IPAR(113) = Index of the component of largest in the
weighted local error vector ( e(i)/ewt(i) ).
IPAR(114) = Length of rwork actually required.
IPAR(115) = Length of iwork actually required.
- LSOIBIT
IPAR(24), mb, block size.
(mb .GE. 1) and mb*IPAR(28) = NX
IPAR(25), nb, number of blocks in the main diagonal.
(nb .ge. 4) and nb*IPAR(27) = NX
- RADAU5
IPAR(26) Transforms the Jacobian matrix to Hessenberg
form.(Only if IPAR(9)=1 and IPAR(3)=1 or 10)
IPAR(27) Maximum number of Newton iterations in
each step.
IPAR(28) Starting values for Newton's method
.EQ. 0 -> is taken the extrapolated collocation
solution
.NE. 0 -> zero values are used.
IPAR(29) Dimension of the index 1 variables( >0 ).
IPAR(30) Dimension of the index 2 variables.
IPAR(31) Dimension of the index 3 variables.
IPAR(32) Switch for step size strategy
0,1 Mod. Predictive controller(Gustafsson)
2 Classical step size control
IPAR(33) Value of M1 (default 0).
IPAR(34) Value of M2 (default(M2=M1).
IPAR(126), Number of accepted steps.
IPAR(127), Number of rejected steps.
IPAR(128), Number of LU-Decompositions of both
matrices
IPAR(129), Number of forward-backward substitutions,
of both systems.
Common parameters for DASSL, DASPK and DGELDA solvers:
IPAR(36), this parameter enables the code to
initialize itself. Must set to 0 to indicate the
start of every new problem.
0: Yes. (On each new problem)
1: No. (Allows 500 new steps)
IPAR(38), Solver try to compute the initial T, X
and XPRIME:
0: The initial T, X and XPRIME are
consistent.
1: Given X_d calculate X_a and X'_d
2: Given X' calculate X.
( X_d differential variables in X
X_a algebrac variables in X )
IPAR(136), Total number of error test failures so far.
Common parameters for DASSL and DASPK solvers:
IPAR(37), code solve the problem without invoking
any special non negativity constraints:
0: Yes
1: To have constraint checking only in the
initial condition calculation.
2: To enforze nonnegativity in X during the
integration.
3: To enforce both options 1 and 2.
IPAR(137), Total number of convergence test failures.
- DASPK
IPAR(39), DASPK use:
0: direct methods (dense or band)
1: Krylov method (iterative)
2: Krylov method + Jac (iterative)
IPAR(41), Proceed to the integration after the initial
condition calculation is done. Used when
IPAR(38) > 0: 0: Yes
1: No
IPAR(42), Errors are controled localy on all the
variables: 0:Yes
1: No
IPAR(8), Extra printing
0, no printing
1, for minimal printing
2, for full printing
IPAR(44), maximum number of iterations in the SPIGMR
algorithm. (.LE. NX)
IPAR(45), number of vectors on which orthogonalization
is done in the SPIGMR algorithm. (.LE. IPAR(44))
IPAR(46), maximum number of restarts of the SPIGMR
algorithm per nonlinear iteration. (.GE. 0)
IPAR(47), maximum number of Newton iterations per
Jacobian or preconditioner evaluation. (> 0)
IPAR(48), maximum number of Jacobian or preconditioner
evaluations. (> 0)
IPAR(49), maximum number of values of the artificial
stepsize parameter H to be tried if IPAR(38) = 1.
(> 0).
IPAR(50), flag to turn off the linesearch algorithm.
0 : ON
1 : OFF (default)
IPAR(138), number of convergence failures of the linear
iteration
IPAR(139), length of IWORK actually required.
IPAR(140), length of RWORK actually required.
IPAR(141), total number of nonlinear iterations.
IPAR(142), total number of linear (Krylov) iterations
IPAR(143), number of PSOL calls.
- DGELDA
IPAR(51), contains the strangeness index.
IPAR(52), number of differential components
IPAR(53), number of algebraic components
IPAR(54), number of undetermined components
IPAR(55), method used:
if 1 then uses the BDF solver
2 then uses the Runge-Kutta solver
IPAR(56), E(t) and A(t) are: 1 time dependent
0 constants
IPAR(57), Maximum index of the problem. ( .GE. 0 )
IPAR(58), Step size strategy:
0, Mod. predictive controlled of Gustafsson(safer)
1, classical step size control(faster)
RPAR (input/output) DOUBLE PRECISION array, dimension (201)
INPUT:
1..15 General
16..25 ODEPACK
26..35 RADAU5
36..50 DASSL/PK
51..60 GELDA
61..100 Reserved
OUTPUT:
101..110 General
111..125 ODEPACK
126..135 RADAU5
136..145 DASSL/PK
146..155 GELDA
156..200 Reserved
Any Mode:
201.. User Available
Common parameters for solvers:
RPAR(1), Initial step size guess.Obligatory in RADAU5.
RPAR(2), Maximum absolute step size allowed.
Common parameters for ODEPACK, DASSL, DASPK and DGELDA:
RPAR(111), Step size in t last used (successfully).
RPAR(112), Step size to be attempted on the next step.
RPAR(113), Current value of the independent variable
which the solver has actually reached
Common parameters for ODEPACK solver:
RPAR(16), Critical value of t which the solver is not
overshoot.
RPAR(17), Minimum absolute step size allowed.
RPAR(18), Tolerance scale factor, greater than 1.0.
Parameters for RADAU5 solver:
RPAR(26), The rounding unit, default 1E-16.
RPAR(27), The safety factor in step size prediction,
default 0.9D0.
RPAR(28), Decides whether the jacobian should be
recomputed, default 0.001D0.
Increase when jacobian evaluations are costly
For small systems should be smaller.
RPAR(29), Stopping criterion for Newton's method,
default MIN(0.03D0, RTOL(1)**0.5D0).
RPAR(30), RPAR(31): This saves, together with a
large RPAR(28), LU-decompositions and computing
time for large systems.
Small systems: RPAR(30)=1.D0, RPAR(31)=1.2D0
Large full systems: RPAR(30)=0.99D0, RPAR(31)=2.D0
might be good.
RPAR(32), RPAR(33), Parameters for step size
selection.Condition: RPAR(32)<=HNEW/HOLD<=RPAR(33)
Parameters for DASSL, DASPK and DGELDA solvers:
RPAR(36), Stopping point (Tstop)
- DASPK
RPAR(37), convergence test constant in SPIGMR
algorithm. (0 .LT. RPAR(37) .LT. 1.0)
RPAR(38), minimum scaled step in linesearch algorithm.
The default is = (unit roundoff)**(2/3). (> 0)
RPAR(39), swing factor in the Newton iteration
convergence test. (default 0.1) (> 0)
- DASPK
RPAR(40), safety factor used in step size prediction.
RPAR(41) and RPAR(42) restric the relation between the
new and old stepsize in step size selection.
1/RPAR(41) .LE. Hnew/Hold .LE. 1/RPAR(42)
RPAR(43), RPAR(44) QUOT1 and QUOT2 repectively.
If QUOT1 < Hnew/Hold < QUOT2 and A and E are
constants, the work can be saved by setting
Hnew=Hold and using the system matrix of the
previous step.</tt></pre>
<b>Tolerances</b>
<pre> RTOL DOUBLE PRECISION
Relative Tolerance.
ATOL DOUBLE PRECISION
Absolute Tolerance.</pre>
<b>Workspace</b>
<pre> IWORK INTEGER array, dimension (LIWORK)
LIWORK INTEGER
Minimum size of DWORK, depending on solver:
- LSODI, LSOIBT, DASSL
20 + NX
- RADAU5
3*N+20
DWORK DOUBLE PRECISION array, dimension (LDWORK)
LDWORK INTEGER
Size of DWORK, depending on solver:
- LSODI
22 + 9*NX + NX**2 , IPAR(3) = 1 or 10
22 + 10*NX + (2*ML + MU)*NX , IPAR(3) = 2 or 11
- LSOIBT
20 + nyh*(maxord + 1) + 3*NX + lenw where
nyh = Initial value of NX
maxord = Maximum order allowed(default or IPAR(13)
lenw = 3*mb*mb*nb + 2
- RADAU5
N*(LJAC+LMAS+3*LE+12)+20
where LJAC=N if (full jacobian)
LJAC=MLJAC+MUJAC+1 if (banded jacobian)
and LMAS=0 if (IPAR(9) = 10 or 11)
LMAS=N if (IPAR(9) = 1)
LMAS=MLMAS+MUMAS+1 if (IPAR(9) = 2)
and LE=N if (IPAR(9) = 1 or 10)
LE=2*MLJAC+MUJAC+1 if (IPAR(9) = 2 or 11)
- DASSL
>= 40 LRW .GE. 40+(MAXORD+4)*NEQ+NEQ**2, IPAR(3) = 1 or 10
>= 40+(MAXORD+4)*NEQ+(2*ML+MU+1)*NEQ, IPAR(3) = 2
>= 40+(MAXORD+4)*NEQ+(2*ML+MU+1)*NEQ
+2*(NEQ/(ML+MU+1)+1), IPAR(3) = 11</pre>
<b>Warning Indicator</b>
<pre> IWARN INTEGER
= 0: no warning;
= 1: LSODI/LSOIBT/RADAU5 do not use the input vector as argument;
= 2: LSODI/LSOIBT do not use the param vector as argument;
= 3: RTOL and ATOL are used as scalars;</pre>
<b>Error Indicator</b>
<pre> INFO INTEGER
= 0: Successful exit;
< 0: If INFO = -i, the i-th argument had an illegal
value;
= 1: Wrong tolerance mode;
= 2: Method (IPAR(9)) is not allowed for ODEPACK/RADAU5;
= 3: Method (IPAR(3)) is not allowed for LSODE/RADAU5/DASSL;
= 4: Option not allowed for IPAR(37);
= 5: Option not allowed for IPAR(38);
= 100+ERROR: RADAU5 returned -ERROR;
= 200+ERROR: DASSL returned -ERROR;
= 300+ERROR: DASPK returned -ERROR;
= 400+ERROR: DGELDA returned -ERROR.</pre>
<a NAME="Method"></a><b><font size=+1>Method</font></b>
<pre><tt><font color="#000000">Since the package integrates 8 different solvers, it is possible to solve differential
equations by means of Backward Differential Formulas, Runge-Kutta, using direct or
iterative methods (including preconditioning) for the linear system associated, differential
equations with time-varying coefficients or of order higher than one. The interface facilitates
the user the work of changing the integrator and testing the results, thus leading a more robust
and efficient integrated package.</font></tt></pre>
<a NAME="References"></a><b><font size=+1>References</font></b>
<pre> [1] A.C. Hindmarsh, Brief Description of ODEPACK: A Systematized Collection
of ODE Solvers, http://www.netlib.org/odepack/doc
[2] L.R. Petzold DASSL Library Documentation, http://www.netlib.org/ode/
[3] P.N. Brown, A.C. Hindmarsh, L.R. Petzold, DASPK Package 1995 Revision
[4] R.S. Maier, Using DASPK on the TMC CM5. Experiences with Two Programming
Models, Minesota Supercomputer Center, Technical Report.
[5] E. Hairer, G. Wanner, Solving Ordinary Dirential Equations II. Stiánd
Dirential- Algebraic Problems., Springer Seried in Computational
Mathermatics 14, Springer-Verlag 1991, Second Edition 1996.
[6] P. Kunkel, V. Mehrmann, W. Rath und J. Weickert, `GELDA: A Software
Package for the Solution of General Linear Dirential Algebraic
equations', SIAM Journal Scienti^Lc Computing, Vol. 18, 1997, pp.
115 - 138.
[7] M. Otter, DSblock: A neutral description of dynamic systems.
Version 3.3, http://www.netlib.org/odepack/doc
[8] M. Otter, H. Elmqvist, The DSblock model interface for exchanging model
components, Proceedings of EUROSIM 95, ed. F.Brenenecker, Vienna, Sep.
11-15, 1995
[9] M. Otter, The DSblock model interface, version 4.0, Incomplete Draft,
http://dv.op.dlr.de/~otter7dsblock/dsblock4.0a.html
[10] Ch. Lubich, U. Novak, U. Pohle, Ch. Engstler, MEXX - Numerical
Software for the Integration of Constrained Mechanical Multibody
Systems, http://www.netlib.org/odepack/doc
[11] Working Group on Software (WGS), SLICOT Implementation and Documentation
Standards (version 1.0), WGS-Report 90-1, Eindhoven University of
Technology, May 1990.
[12] P. Kunkel and V. Mehrmann, Canonical forms for linear differential-
algebraic equations with variable coeÆcients., J. Comput. Appl.
Math., 56:225{259, 1994.
[13] Working Group on Software (WGS), SLICOT Implementation and Documentation
Standards, WGS-Report 96-1, Eindhoven University of Technology, updated:
Feb. 1998, ../../REPORTS/rep96-1.ps.Z.
[14] A. Varga, Standarization of Interface for Nonlinear Systems Software
in SLICOT, Deutsches Zentrum ur Luft un Raumfahrt, DLR. SLICOT-Working
Note 1998-4, 1998, Available at
../../REPORTS/SLWN1998-4.ps.Z.
[15] D. Kirk, Optimal Control Theory: An Introduction, Prentice-Hall.
Englewood Cli, NJ, 1970.
[16] F.L. Lewis and V.L. Syrmos, Optimal Control, Addison-Wesley.
New York, 1995.
[17] W.M.Lioen, J.J.B de Swart, Test Set for Initial Value Problem Solvers,
Technical Report NM-R9615, CWI, Amsterdam, 1996.
http://www.cwi.nl/cwi/projects/IVPTestset/.
[18] V.Hernandez, I.Blanquer, E.Arias, and P.Ruiz,
Definition and Implementation of a SLICOT Standard Interface and the
associated MATLAB Gateway for the Solution of Nonlinear Control Systems
by using ODE and DAE Packages}, Universidad Politecnica de Valencia,
DSIC. SLICOT Working Note 2000-3: July 2000. Available at
../../REPORTS/SLWN2000-3.ps.Z.
[19] J.J.B. de Swart, W.M. Lioen, W.A. van der Veen, SIDE, November 25,
1998. Available at http://www.cwi.nl/cwi/projects/PSIDE/.
[20] Kim, H.Young, F.L.Lewis, D.M.Dawson, Intelligent optimal control of
robotic manipulators using neural networks.
[21] J.C.Fernandez, E.Arias, V.Hernandez, L.Penalver, High Performance
Algorithm for Tracking Trajectories of Robot Manipulators,
Preprints of the Proceedings of the 6th IFAC International Workshop on
Algorithms and Architectures for Real-Time Control (AARTC-2000),
pages 127-134.</pre>
<a NAME="Numerical Aspects"></a><b><font size=+1>Numerical Aspects</font></b>
<pre> The numerical aspects of the routine lie on the features of the
different packages integrated. Several packages are more robust
than others, and other packages simply cannot deal with problems
that others do. For a detailed description of the numerical aspects
of each method is recommended to check the references above.</pre>
<a NAME="Comments"></a><b><font size=+1>Further Comments</font></b>
<pre> Several packages (LSODES, LSOIBT) deal only with sparse matrices.
The interface checks the suitability of the methods to the
parameters and show a warning message if problems could arise.</pre>
<a NAME="Example"></a><b><font size=+1>Example</font></b>
<p><b>Program Text</b>
<br>
<p><tt>* DAESOLVER EXAMPLE PROGRAM TEXT FOR LSODIX
PROBLEM</tt>
<br><tt>*</tt>
<br><tt>* .. Parameters ..</tt>
<br><tt> INTEGER
NIN, NOUT</tt>
<br><tt> PARAMETER
( NIN = 5, NOUT = 6 )</tt>
<br><tt> INTEGER LSODI_, LSOIBT_, RADAU5_,
DASSL_, DASPK_, GELDA_</tt>
<br><tt> PARAMETER (LSODI_ = 1, LSOIBT_
= 2)</tt>
<br><tt> PARAMETER (RADAU5_ = 3, DASSL_
= 4, DASPK_ = 5)</tt>
<br><tt> PARAMETER (GELDA_ = 6)</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt>*</tt>
<br><tt> EXTERNAL IARGC_</tt>
<br><tt> INTEGER IARGC_</tt>
<br><tt> INTEGER NUMARGS</tt>
<br><tt> CHARACTER*80 NAME</tt>
<br><tt> CHARACTER*80 SOLVER</tt>
<br><tt>*</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt>*</tt>
<br><tt> WRITE ( NOUT, FMT = 99999 )</tt>
<br><tt>*</tt>
<br><tt> NUMARGS = IARGC_()</tt>
<br><tt>*</tt>
<br><tt> CALL GETARG_(0, NAME)</tt>
<br><tt> IF (NUMARGS .NE. 1) THEN</tt>
<br><tt> WRITE (*,*) 'Syntax
Error: ',NAME(1:8),' <solver>'</tt>
<br><tt> WRITE (*,*) 'Solvers
: LSODI, LSOIBT, RADAU5, DASSL, DASPK, GELD</tt>
<br><tt> &A'</tt>
<br><tt> ELSE</tt>
<br><tt>*</tt>
<br><tt> CALL GETARG_(1, SOLVER)</tt>
<br><tt>*</tt>
<br><tt> WRITE (*,*) 'Problem:
LSODIX Solver: ',SOLVER(1:7)</tt>
<br><tt>*</tt>
<br><tt> IF (SOLVER(1:5) .EQ.
'LSODI') THEN</tt>
<br><tt> CALL TEST(LSODI_)</tt>
<br><tt> ELSEIF (SOLVER(1:6)
.EQ. 'LSOIBT') THEN</tt>
<br><tt> CALL TEST(LSOIBT_)</tt>
<br><tt> ELSEIF (SOLVER(1:6)
.EQ. 'RADAU5') THEN</tt>
<br><tt> CALL TEST(RADAU5_)</tt>
<br><tt> ELSEIF (SOLVER(1:5)
.EQ. 'GELDA') THEN</tt>
<br><tt> CALL TEST(GELDA_)</tt>
<br><tt> ELSEIF (SOLVER(1:5)
.EQ. 'DASSL') THEN</tt>
<br><tt> CALL TEST(DASSL_)</tt>
<br><tt> ELSEIF (SOLVER(1:5)
.EQ. 'DASPK') THEN</tt>
<br><tt> CALL TEST(DASPK_)</tt>
<br><tt> ELSE</tt>
<br><tt> WRITE (*,*)
'Error: Solver: ', SOLVER,' unknown'</tt>
<br><tt> ENDIF</tt>
<br><tt> ENDIF</tt>
<br><tt>*</tt>
<br><tt>99999 FORMAT (' DAESOLVER EXAMPLE PROGRAM RESULTS FOR LSODIX PROBLEM'</tt>
<br><tt> .
,/1X)</tt>
<br><tt> END</tt>
<br>
<br>
<br>
<p><tt> SUBROUTINE TEST( ISOLVER )</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* PURPOSE</tt>
<br><tt>*</tt>
<br><tt>* Testing subroutine DAESolver</tt>
<br><tt>*</tt>
<br><tt>* ARGUMENTS</tt>
<br><tt>*</tt>
<br><tt>* Input/Output Parameters</tt>
<br><tt>*</tt>
<br><tt>* ISOLVER (input) INTEGER</tt>
<br><tt>*
Indicates the nonlinear solver package to be used:</tt>
<br><tt>*
= 1: LSODI,</tt>
<br><tt>*
= 2: LSOIBT,</tt>
<br><tt>*
= 3: RADAU5,</tt>
<br><tt>*
= 4: DASSL,</tt>
<br><tt>*
= 5: DASPK,</tt>
<br><tt>*
= 6: DGELDA.</tt>
<br><tt>*</tt>
<br><tt>* METHOD</tt>
<br><tt>*</tt>
<br><tt>* REFERENCES</tt>
<br><tt>*</tt>
<br><tt>* CONTRIBUTORS</tt>
<br><tt>*</tt>
<br><tt>* REVISIONS</tt>
<br><tt>*</tt>
<br><tt>* -</tt>
<br><tt>*</tt>
<br><tt>* KEYWORDS</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* ******************************************************************</tt>
<br><tt>* .. Parameters ..</tt>
<br><tt> INTEGER LSODI_, LSOIBT_, RADAU5_,
DASSL_, DASPK_, GELDA_</tt>
<br><tt> PARAMETER (LSODI_ = 1, LSOIBT_
= 2)</tt>
<br><tt> PARAMETER (RADAU5_ = 3, DASSL_
= 4, DASPK_ = 5)</tt>
<br><tt> PARAMETER (GELDA_ = 6)</tt>
<br><tt> INTEGER
NIN, NOUT</tt>
<br><tt> PARAMETER
( NIN = 5, NOUT = 6 )</tt>
<br><tt> INTEGER
MD, ND, LPAR, LWORK</tt>
<br><tt> PARAMETER
( MD = 400, ND = 100, LPAR = 201,</tt>
<br><tt> $
LWORK = 10000 )</tt>
<br><tt>* .. Common variables ..</tt>
<br><tt> COMMON /TESTING/ ISOLVER2</tt>
<br><tt> INTEGER ISOLVER2</tt>
<br><tt>* .. Scalar Arguments ..</tt>
<br><tt> INTEGER ISOLVER</tt>
<br><tt>* .. Local Scalars ..</tt>
<br><tt> INTEGER
NEQN, NDISC, MLJAC, MUJAC, MLMAS, MUMAS</tt>
<br><tt> INTEGER
IWARN, INFO</tt>
<br><tt> DOUBLE PRECISION ATOL, RTOL, NORM</tt>
<br><tt> LOGICAL
NUMJAC, NUMMAS, CONSIS</tt>
<br><tt>* .. Local Arrays ..</tt>
<br><tt> CHARACTER FULLNM*40, PROBLM*8, TYPE*3</tt>
<br><tt> CHARACTER*9 CDAEDF,CDAEDA,CDAEDE,CDAEOUT,</tt>
<br><tt> $
CJACFX,CJACFU,CJACFP,CJACFXDOT</tt>
<br><tt> INTEGER
IND(MD), IPAR(LPAR), IWORK(LWORK)</tt>
<br><tt> DOUBLE PRECISION T(0:ND), RPAR(LPAR),
DWORK(LWORK)</tt>
<br><tt> DOUBLE PRECISION X(MD), XPRIME(MD),
Y(MD), U(MD), P(MD), SOLU(MD)</tt>
<br><tt>* .. External Functions ..</tt>
<br><tt> DOUBLE PRECISION DNRM2</tt>
<br><tt> EXTERNAL
DNRM2</tt>
<br><tt>* .. External Subroutines ..</tt>
<br><tt> EXTERNAL
PLSODIX, ILSODIX, SLSODIX</tt>
<br><tt> EXTERNAL
DAXPY</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt>*</tt>
<br><tt> ISOLVER2 = ISOLVER</tt>
<br><tt> DO 20 I=1,NEQN</tt>
<br><tt> Y(I)=0D0</tt>
<br><tt> U(I)=0D0</tt>
<br><tt> P(I)=0D0</tt>
<br><tt> 20 CONTINUE</tt>
<br><tt> DO 40 I=1,LPAR</tt>
<br><tt> IPAR(I)=0</tt>
<br><tt> RPAR(I)=0D0</tt>
<br><tt> 40 CONTINUE</tt>
<br><tt> DO 60 I=1,LWORK</tt>
<br><tt> IWORK(I)=0</tt>
<br><tt> DWORK(I)=0D0</tt>
<br><tt> 60 CONTINUE</tt>
<br><tt>* Get the problem dependent parameters.</tt>
<br><tt> RTOL=1D-4</tt>
<br><tt> ATOL=1D-6</tt>
<br><tt> IPAR(1)=0</tt>
<br><tt> IPAR(2)=1</tt>
<br><tt> IPAR(3)=1</tt>
<br><tt> IPAR(12)= 10000</tt>
<br><tt> IF (ISOLVER .EQ. LSODI_ .OR. ISOLVER
.EQ. RADAU5_) THEN</tt>
<br><tt> IPAR(9)=1</tt>
<br><tt> IPAR(16)=1</tt>
<br><tt>C IPAR(17)=0</tt>
<br><tt> RPAR(1)=1D-3</tt>
<br><tt> ELSE</tt>
<br><tt>C (ISOLVER
.EQ. DASSL_ .OR. ISOLVER .EQ. DASPK_)</tt>
<br><tt>C IPAR(36)=0</tt>
<br><tt>C IPAR(37)=0</tt>
<br><tt>C IPAR(38)=0</tt>
<br><tt> IPAR(39)=1</tt>
<br><tt> END IF</tt>
<br><tt> CALL PLSODIX(FULLNM,PROBLM,TYPE,NEQN,NDISC,T,NUMJAC,MLJAC,</tt>
<br><tt> $
MUJAC,NUMMAS,MLMAS,MUMAS,IND)</tt>
<br><tt> CALL ILSODIX(NEQN,T(0),X,XPRIME,CONSIS)</tt>
<br><tt> x(1) = 1.0d0</tt>
<br><tt> x(2) = 0.0d0</tt>
<br><tt> x(3) = 0.0d0</tt>
<br><tt> xprime(1) = -0.04D0</tt>
<br><tt> xprime(2) = 0.04D0</tt>
<br><tt> xprime(3) = 0.0D0</tt>
<br><tt> CALL SLSODIX(NEQN,T(1),SOLU)</tt>
<p><tt> IF ( TYPE.NE.'DAE' ) THEN</tt>
<br><tt> WRITE ( NOUT,
FMT = 99998 )</tt>
<br><tt> ELSE</tt>
<br><tt> WRITE ( NOUT,
FMT = 99997 ) FULLNM, PROBLM, TYPE, ISOLVER</tt>
<br><tt> CDAEDF=''</tt>
<br><tt> CDAEDA=''</tt>
<br><tt> CDAEDE=''</tt>
<br><tt> CDAEOUT=''</tt>
<br><tt> CJACFX=''</tt>
<br><tt> CJACFU=''</tt>
<br><tt> CJACFP=''</tt>
<br><tt> CJACFXDOT=''</tt>
<p><tt> CALL DAESolver(
ISOLVER, CDAEDF, CDAEDA, CDAEDE, CDAEOUT,</tt>
<br><tt> $
CJACFX, CJACFU, CJACFP, CJACFXDOT,</tt>
<br><tt> $
NEQN, NEQN, NEQN, NEQN, T(0), T(1),</tt>
<br><tt> $
X, XPRIME, Y, U, P,</tt>
<br><tt> $
IPAR, RPAR, RTOL, ATOL,</tt>
<br><tt> $
IWORK, LWORK, DWORK, LWORK, IWARN, INFO )</tt>
<br><tt> IF ( INFO.NE.0
) THEN</tt>
<br><tt>
WRITE ( NOUT, FMT = 99996 ) INFO</tt>
<br><tt> ELSE</tt>
<br><tt>
IF ( IWARN.NE.0 ) THEN</tt>
<br><tt>
WRITE ( NOUT, FMT = 99995 ) IWARN</tt>
<br><tt>
ENDIF</tt>
<br><tt>
IF ( NEQN .LE. 30 ) THEN</tt>
<br><tt>
WRITE ( NOUT, FMT = 99994 )</tt>
<br><tt>
DO 80 I=1,NEQN</tt>
<br><tt>
WRITE ( NOUT, FMT = 99993 ) I, X(I), SOLU(I)</tt>
<br><tt> 80
CONTINUE</tt>
<br><tt>
END IF</tt>
<br><tt>
NORM=DNRM2(NEQN,SOLU,1)</tt>
<br><tt>
IF ( NORM.EQ.0D0 ) THEN</tt>
<br><tt>
NORM=1D0</tt>
<br><tt>
END IF</tt>
<br><tt>
CALL DAXPY(NEQN,-1D0,X,1,SOLU,1)</tt>
<br><tt>
NORM=DNRM2(NEQN,SOLU,1)/NORM</tt>
<br><tt>
WRITE ( NOUT, FMT = 99992 ) NORM</tt>
<br><tt> END IF</tt>
<br><tt> END IF</tt>
<br><tt>*</tt>
<br><tt>99998 FORMAT (' ERROR: This test is only intended for DAE problems')</tt>
<br><tt>99997 FORMAT (' ',A,' (',A,' , ',A,') with SOLVER ',I2)</tt>
<br><tt>99996 FORMAT (' INFO on exit from DAESolver = ',I3)</tt>
<br><tt>99995 FORMAT (' IWARN on exit from DAESolver = ',I3)</tt>
<br><tt>99994 FORMAT (' Solution: (calculated) (reference)')</tt>
<br><tt>99993 FORMAT (I,F,F)</tt>
<br><tt>99992 FORMAT (' Relative error comparing with the reference solution:'</tt>
<br><tt> $
,E,/1X)</tt>
<br><tt>* *** Last line of TEST ***</tt>
<br><tt> END</tt>
<br>
<br>
<br>
<p><tt> SUBROUTINE DAEDA_( RPAR, NRP, IPAR,
NIP, X, NX, U, NU, P, NP,</tt>
<br><tt> $
F, LDF, T, INFO )</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* PURPOSE</tt>
<br><tt>*</tt>
<br><tt>* Interface routine between DAESolver and
the problem function FEVAL</tt>
<br><tt>*</tt>
<br><tt>* ARGUMENTS</tt>
<br><tt>*</tt>
<br><tt>* Input/Output Parameters</tt>
<br><tt>*</tt>
<br><tt>* RPAR (input/output)
DOUBLE PRECISION array, dimension (NRP)</tt>
<br><tt>*
Array for communication between the driver and FEVAL.</tt>
<br><tt>*</tt>
<br><tt>* NRP (input)
INTEGER</tt>
<br><tt>*
Dimension of RPAR array.</tt>
<br><tt>*</tt>
<br><tt>* IPAR (input/output)
INTEGER array, dimension (NIP)</tt>
<br><tt>*
Array for communication between the driver and FEVAL.</tt>
<br><tt>*</tt>
<br><tt>* NIP (input)
INTEGER</tt>
<br><tt>*
Dimension of IPAR array.</tt>
<br><tt>*</tt>
<br><tt>* X
(input) DOUBLE PRECISION array, dimension (NX)</tt>
<br><tt>*
Array containing the state variables.</tt>
<br><tt>*</tt>
<br><tt>* NX
(input) INTEGER</tt>
<br><tt>*
Dimension of the state vector.</tt>
<br><tt>*</tt>
<br><tt>* U
(input) DOUBLE PRECISION array, dimension (NU)</tt>
<br><tt>*
Array containing the input values.</tt>
<br><tt>*</tt>
<br><tt>* NU
(input) INTEGER</tt>
<br><tt>*
Dimension of the input vector.</tt>
<br><tt>*</tt>
<br><tt>* P
(input) DOUBLE PRECISION array, dimension (NP)</tt>
<br><tt>*
Array containing the parameter values.</tt>
<br><tt>*</tt>
<br><tt>* NP
(input) INTEGER</tt>
<br><tt>*
Dimension of the parameter vector.</tt>
<br><tt>*</tt>
<br><tt>* F
(output) DOUBLE PRECISION array, dimension (LDF,NX)</tt>
<br><tt>*
The resulting function value f(T,X).</tt>
<br><tt>*</tt>
<br><tt>* LDF (input)
INTEGER</tt>
<br><tt>*
The leading dimension of F.</tt>
<br><tt>*</tt>
<br><tt>* T
(input) INTEGER</tt>
<br><tt>*
The time point where the function is evaluated.</tt>
<br><tt>*</tt>
<br><tt>* Error Indicator</tt>
<br><tt>*</tt>
<br><tt>* INFO INTEGER</tt>
<br><tt>*
Returns values of error from FEVAL or 100 in case</tt>
<br><tt>*
a bad problem was choosen.</tt>
<br><tt>*</tt>
<br><tt>* METHOD</tt>
<br><tt>*</tt>
<br><tt>* REFERENCES</tt>
<br><tt>*</tt>
<br><tt>* CONTRIBUTORS</tt>
<br><tt>*</tt>
<br><tt>* REVISIONS</tt>
<br><tt>*</tt>
<br><tt>* -</tt>
<br><tt>*</tt>
<br><tt>* KEYWORDS</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* ******************************************************************</tt>
<br><tt>*</tt>
<br><tt>* .. Common variables ..</tt>
<br><tt> COMMON /TESTING/ ISOLVER</tt>
<br><tt> INTEGER LSODI_, LSOIBT_, RADAU5_,
DASSL_, DASPK_, GELDA_</tt>
<br><tt> PARAMETER (LSODI_ = 1, LSOIBT_
= 2)</tt>
<br><tt> PARAMETER (RADAU5_ = 3, DASSL_
= 4, DASPK_ = 5)</tt>
<br><tt> PARAMETER (GELDA_ = 6)</tt>
<br><tt>* .. Scalar Arguments ..</tt>
<br><tt> INTEGER
NRP, NIP, NX, NU, NP, LDF, INFO</tt>
<br><tt> DOUBLE PRECISION T</tt>
<br><tt>* .. Array Arguments ..</tt>
<br><tt> INTEGER
IPAR(NIP)</tt>
<br><tt> DOUBLE PRECISION RPAR(NRP), X(NX),
U(NU), P(NP),</tt>
<br><tt> $ F(LDF,NX)</tt>
<br><tt>* .. External Subroutines ..</tt>
<br><tt> EXTERNAL
FLSODIX</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt> CALL FLSODIX(NX,T,X,X,F,INFO,RPAR,IPAR)</tt>
<br><tt>* *** Last line of DAEDA_ ***</tt>
<br><tt> END</tt>
<br>
<br>
<br>
<p><tt> SUBROUTINE DAEDF_( RPAR, NRP, IPAR,
NIP, X, XPRIME, NX,</tt>
<br><tt> $
U, NU, P, NP, T, F, LDF, INFO )</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* PURPOSE</tt>
<br><tt>*</tt>
<br><tt>* Interface routine between DAESolver and
the problem function MEVAL</tt>
<br><tt>*</tt>
<br><tt>* ARGUMENTS</tt>
<br><tt>*</tt>
<br><tt>* Input/Output Parameters</tt>
<br><tt>*</tt>
<br><tt>* RPAR (input/output)
DOUBLE PRECISION array, dimension (NRP)</tt>
<br><tt>*
Array for communication between the driver and MEVAL.</tt>
<br><tt>*</tt>
<br><tt>* NRP (input)
INTEGER</tt>
<br><tt>*
Dimension of RPAR array.</tt>
<br><tt>*</tt>
<br><tt>* IPAR (input/output)
INTEGER array, dimension (NIP)</tt>
<br><tt>*
Array for communication between the driver and MEVAL.</tt>
<br><tt>*</tt>
<br><tt>* NIP (input)
INTEGER</tt>
<br><tt>*
Dimension of IPAR array.</tt>
<br><tt>*</tt>
<br><tt>* X
(input) DOUBLE PRECISION array, dimension (NX)</tt>
<br><tt>*
Array containing the state variables.</tt>
<br><tt>*</tt>
<br><tt>* XPRIME (input) DOUBLE PRECISION
array, dimension (NX)</tt>
<br><tt>*
Array containing the state variables derivative.</tt>
<br><tt>*</tt>
<br><tt>* NX
(input) INTEGER</tt>
<br><tt>*
Dimension of the state vector.</tt>
<br><tt>*</tt>
<br><tt>* U
(input) DOUBLE PRECISION array, dimension (NU)</tt>
<br><tt>*
Array containing the input values.</tt>
<br><tt>*</tt>
<br><tt>* NU
(input) INTEGER</tt>
<br><tt>*
Dimension of the input vector.</tt>
<br><tt>*</tt>
<br><tt>* P
(input) DOUBLE PRECISION array, dimension (NP)</tt>
<br><tt>*
Array containing the parameter values.</tt>
<br><tt>*</tt>
<br><tt>* NP
(input) INTEGER</tt>
<br><tt>*
Dimension of the parameter vector.</tt>
<br><tt>*</tt>
<br><tt>* T
(input) INTEGER</tt>
<br><tt>*
The time point where the function is evaluated.</tt>
<br><tt>*</tt>
<br><tt>* F
(output) DOUBLE PRECISION array, dimension (LDF,NX)</tt>
<br><tt>*
The resulting function value f(T,X).</tt>
<br><tt>*</tt>
<br><tt>* LDF (input)
INTEGER</tt>
<br><tt>*
The leading dimension of F.</tt>
<br><tt>*</tt>
<br><tt>* Error Indicator</tt>
<br><tt>*</tt>
<br><tt>* INFO INTEGER</tt>
<br><tt>*
Returns values of error from MEVAL or 100 in case</tt>
<br><tt>*
a bad problem was choosen.</tt>
<br><tt>*</tt>
<br><tt>* METHOD</tt>
<br><tt>*</tt>
<br><tt>* REFERENCES</tt>
<br><tt>*</tt>
<br><tt>* CONTRIBUTORS</tt>
<br><tt>*</tt>
<br><tt>* REVISIONS</tt>
<br><tt>*</tt>
<br><tt>* -</tt>
<br><tt>*</tt>
<br><tt>* KEYWORDS</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* ******************************************************************</tt>
<br><tt>*</tt>
<br><tt>* .. Common variables ..</tt>
<br><tt> COMMON /TESTING/ ISOLVER</tt>
<br><tt> INTEGER ISOLVER</tt>
<br><tt> INTEGER LSODI_, LSOIBT_, RADAU5_,
DASSL_, DASPK_, GELDA_</tt>
<br><tt> PARAMETER (LSODI_ = 1, LSOIBT_
= 2)</tt>
<br><tt> PARAMETER (RADAU5_ = 3, DASSL_
= 4, DASPK_ = 5)</tt>
<br><tt> PARAMETER (GELDA_ = 6)</tt>
<br><tt>* .. Scalar Arguments ..</tt>
<br><tt> INTEGER
NRP, NIP, NX, NU, NP, LDF, INFO</tt>
<br><tt> DOUBLE PRECISION T</tt>
<br><tt>* .. Array Arguments ..</tt>
<br><tt> INTEGER
IPAR(NIP)</tt>
<br><tt> DOUBLE PRECISION RPAR(NRP), X(NX),
XPRIME(NX), U(NU), P(NP),</tt>
<br><tt> $ F(LDF,NX)</tt>
<br><tt>* .. Local Scalars ..</tt>
<br><tt> INTEGER
I</tt>
<br><tt>* .. External Subroutines ..</tt>
<br><tt> EXTERNAL
MLSODIX, RLSODIX</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt> IF (ISOLVER .EQ. DASSL_ .OR. ISOLVER
.EQ. DASPK_) THEN</tt>
<br><tt> CALL RLSODIX(LDF,NX,T,X,XPRIME,F,INFO,RPAR,IPAR)</tt>
<br><tt> ELSE</tt>
<br><tt> CALL MLSODIX(LDF,NX,T,X,XPRIME,F,INFO,RPAR,IPAR)</tt>
<br><tt> ENDIF</tt>
<br><tt>* *** Last line of DAEDF_ ***</tt>
<br><tt> END</tt>
<br>
<br>
<br>
<p><tt> SUBROUTINE JACFX_( NRP, NIP,
RPAR, IPAR, NX, NU,</tt>
<br><tt> $
NP, X, U, P, T, FX, LDFX,</tt>
<br><tt> $
INFO )</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* PURPOSE</tt>
<br><tt>*</tt>
<br><tt>* Interface routine between DAESolver and
the problem function JEVAL</tt>
<br><tt>*</tt>
<br><tt>* ARGUMENTS</tt>
<br><tt>*</tt>
<br><tt>* Input/Output Parameters</tt>
<br><tt>*</tt>
<br><tt>* NRP (input)
INTEGER</tt>
<br><tt>*
Dimension of RPAR array.</tt>
<br><tt>*</tt>
<br><tt>* NIP (input)
INTEGER</tt>
<br><tt>*
Dimension of IPAR array.</tt>
<br><tt>*</tt>
<br><tt>* RPAR (input/output)
DOUBLE PRECISION array</tt>
<br><tt>*
Array for communication between the driver and JEVAL.</tt>
<br><tt>*</tt>
<br><tt>* IPAR (input/output)
INTEGER array</tt>
<br><tt>*
Array for communication between the driver and JEVAL.</tt>
<br><tt>*</tt>
<br><tt>* NX
(input) INTEGER</tt>
<br><tt>*
Dimension of the state vector.</tt>
<br><tt>*</tt>
<br><tt>* NU
(input) INTEGER</tt>
<br><tt>*
Dimension of the input vector.</tt>
<br><tt>*</tt>
<br><tt>* NP
(input) INTEGER</tt>
<br><tt>*
Dimension of the parameter vector.</tt>
<br><tt>*</tt>
<br><tt>* X
(input) DOUBLE PRECISION array, dimension (NX)</tt>
<br><tt>*
Array containing the state variables.</tt>
<br><tt>*</tt>
<br><tt>* U
(input) DOUBLE PRECISION array, dimension (NU)</tt>
<br><tt>*
Array containing the input values.</tt>
<br><tt>*</tt>
<br><tt>* P
(input) DOUBLE PRECISION array, dimension (NP)</tt>
<br><tt>*
Array containing the parameter values.</tt>
<br><tt>*</tt>
<br><tt>* T
(input) INTEGER</tt>
<br><tt>*
The time point where the derivative is evaluated.</tt>
<br><tt>*</tt>
<br><tt>* FX
(output) DOUBLE PRECISION array, dimension (LDFX,NX)</tt>
<br><tt>*
The array with the resulting Jacobian matrix.</tt>
<br><tt>*</tt>
<br><tt>* LDFX (input)
INTEGER</tt>
<br><tt>*
The leading dimension of the array FX.</tt>
<br><tt>*</tt>
<br><tt>* Error Indicator</tt>
<br><tt>*</tt>
<br><tt>* INFO INTEGER</tt>
<br><tt>*
Returns values of error from JEVAL or 100 in case</tt>
<br><tt>*
a bad problem was choosen.</tt>
<br><tt>*</tt>
<br><tt>* METHOD</tt>
<br><tt>*</tt>
<br><tt>* REFERENCES</tt>
<br><tt>*</tt>
<br><tt>* CONTRIBUTORS</tt>
<br><tt>*</tt>
<br><tt>* REVISIONS</tt>
<br><tt>*</tt>
<br><tt>* -</tt>
<br><tt>*</tt>
<br><tt>* KEYWORDS</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* ******************************************************************</tt>
<br><tt>*</tt>
<br><tt>* .. Common variables ..</tt>
<br><tt> COMMON /TESTING/ ISOLVER</tt>
<br><tt> INTEGER LSODI_, LSOIBT_, RADAU5_,
DASSL_, DASPK_, GELDA_</tt>
<br><tt> PARAMETER (LSODI_ = 1, LSOIBT_
= 2)</tt>
<br><tt> PARAMETER (RADAU5_ = 3, DASSL_
= 4, DASPK_ = 5)</tt>
<br><tt> PARAMETER (GELDA_ = 6)</tt>
<br><tt>* .. Scalar Arguments ..</tt>
<br><tt> INTEGER
NRP, NIP, NX, NU, NP, LDFX, INFO</tt>
<br><tt> DOUBLE PRECISION T</tt>
<br><tt>* .. Array Arguments ..</tt>
<br><tt> INTEGER
IPAR(NIP)</tt>
<br><tt> DOUBLE PRECISION X(NX), U(NU), P(NP),
RPAR(NRP), FX(LDFX,NX)</tt>
<br><tt>* .. External Subroutines ..</tt>
<br><tt> EXTERNAL
JLSODIX</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt> CALL JLSODIX(LDFX,NX,T,X,X,FX,INFO,RPAR,IPAR)</tt>
<br><tt>* *** Last line of JACFX_ ***</tt>
<br><tt> END</tt>
<br>
<br>
<p><tt> SUBROUTINE JACFXDOT_( NRP, NIP, RPAR,
IPAR,</tt>
<br><tt> $
NX, NU, NP, XPRIME, U, P, T, J, LDJ, INFO )</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* PURPOSE</tt>
<br><tt>*</tt>
<br><tt>* MATJACFXDOT routine for TRANSAMP problem</tt>
<br><tt>*</tt>
<br><tt>* ARGUMENTS</tt>
<br><tt>*</tt>
<br><tt>* Input/Output Parameters</tt>
<br><tt>*</tt>
<br><tt>* NRP (input)
INTEGER</tt>
<br><tt>*
Dimension of RPAR array.</tt>
<br><tt>*</tt>
<br><tt>* NIP (input)
INTEGER</tt>
<br><tt>*
Dimension of IPAR array.</tt>
<br><tt>*</tt>
<br><tt>* RPAR (input/output)
DOUBLE PRECISION array</tt>
<br><tt>*
Array for communication with the driver.</tt>
<br><tt>*</tt>
<br><tt>* IPAR (input/output)
INTEGER array</tt>
<br><tt>*
Array for communication with the driver.</tt>
<br><tt>*</tt>
<br><tt>* NX
(input) INTEGER</tt>
<br><tt>*
Dimension of the state vector.</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* NU
(input) INTEGER</tt>
<br><tt>*
Dimension of the input vector.</tt>
<br><tt>*</tt>
<br><tt>* NP
(input) INTEGER</tt>
<br><tt>*
Dimension of the parameter vector.</tt>
<br><tt>*</tt>
<br><tt>* XPRIME (input) DOUBLE PRECISION
array, dimension (NX)</tt>
<br><tt>*
Array containing the derivative of the state variables.</tt>
<br><tt>*</tt>
<br><tt>* U
(input) DOUBLE PRECISION array, dimension (NU)</tt>
<br><tt>*
Array containing the input values.</tt>
<br><tt>*</tt>
<br><tt>* P
(input) DOUBLE PRECISION array, dimension (NP)</tt>
<br><tt>*
Array containing the parameter values.</tt>
<br><tt>*</tt>
<br><tt>* T
(input) INTEGER</tt>
<br><tt>*
The time point where the derivative is evaluated.</tt>
<br><tt>*</tt>
<br><tt>* J
(output) DOUBLE PRECISION array, dimension (LDJ,NX)</tt>
<br><tt>*
The array with the resulting derivative matrix.</tt>
<br><tt>*</tt>
<br><tt>* LDJ (input)
INTEGER</tt>
<br><tt>*
The leading dimension of the array J.</tt>
<br><tt>*</tt>
<br><tt>* Error Indicator</tt>
<br><tt>*</tt>
<br><tt>* INFO INTEGER</tt>
<br><tt>*
Returns 1 in case a bad problem was choosen.</tt>
<br><tt>*</tt>
<br><tt>* METHOD</tt>
<br><tt>*</tt>
<br><tt>* REFERENCES</tt>
<br><tt>*</tt>
<br><tt>* CONTRIBUTORS</tt>
<br><tt>*</tt>
<br><tt>* REVISIONS</tt>
<br><tt>*</tt>
<br><tt>* -</tt>
<br><tt>*</tt>
<br><tt>* KEYWORDS</tt>
<br><tt>*</tt>
<br><tt>*</tt>
<br><tt>* ******************************************************************</tt>
<br><tt>*</tt>
<br><tt>* .. Common variables ..</tt>
<br><tt> COMMON /TESTING/ ISOLVER</tt>
<br><tt> INTEGER LSODI_, LSOIBT_, RADAU5_,
DASSL_, DASPK_, GELDA_</tt>
<br><tt> PARAMETER (LSODI_ = 1, LSOIBT_
= 2)</tt>
<br><tt> PARAMETER (RADAU5_ = 3, DASSL_
= 4, DASPK_ = 5)</tt>
<br><tt> PARAMETER (GELDA_ = 6)</tt>
<br><tt>* .. Scalar Arguments ..</tt>
<br><tt> INTEGER
NRP, NIP, NX, NU, NP, LDJ, INFO</tt>
<br><tt> DOUBLE PRECISION T</tt>
<br><tt>* .. Array Arguments ..</tt>
<br><tt> INTEGER
IPAR(NIP)</tt>
<br><tt> DOUBLE PRECISION XPRIME(NX), U(NU),
P(NP), RPAR(NRP), J(LDJ,NX)</tt>
<br><tt>* .. Executable Statements ..</tt>
<br><tt>*</tt>
<br><tt> CALL JDOTLSODIX(LDJ,NX,T,XPRIME,XPRIME,J,INFO,RPAR,IPAR)</tt>
<br><tt> ENDIF</tt>
<br><tt>* *** Last line of JACFXDOT_ ***</tt>
<br><tt> END</tt>
<br><tt></tt>
<p><b>Program Data</b>
<pre>No data required</pre>
<b>Program Results</b>
<pre> DAESOLVER EXAMPLE PROGRAM RESULTS
Problem: LSODIX Solver: LSODI
lsodix (lsodix , DAE) with SOLVER 1
IWARN on exit from DAESolver = 2
Solution: (calculated) (reference)
6.462112224297606E-07
1.255974374648338E-10
6.117680951077711E-07
Relative error comparing with the reference solution: .8898590685949503E-06</pre>
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