Package jline.util.ode

Class Rodas

java.lang.Object

jline.util.ode.Rodas

public final class Rodas
extends Object

RODAS -- Rosenbrock method of order (3)4 for stiff and differential-algebraic systems M y' = f(x,y), including a SINGULAR mass matrix (index-1 DAE).

PORTED THIRD-PARTY CODE -- do not edit to fix a LINE bug; fix the caller.

Source: E. Hairer and G. Wanner, rodas.f / dc_decsol.f / decsol.f, version of October 28, 1996, as published with "Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems", Springer Series in Computational Mathematics 14. Licence in matlab/lib/thirdparty/rodas/LICENSE, which covers every port of it in this repository.

WHY THIS EXISTS IN THE JAR. The fluid solver integrates with LSODA (LSODAExt), which solves y' = f and cannot carry a mass matrix at all -- let alone a singular one. The dae method writes population conservation as an ALGEBRAIC row, one per closed chain, so its transient is an index-1 DAE with a singular M and has no LSODA route. RODAS is a fixed sequence of six linear solves against one real matrix rather than an iteration with a convergence policy, so a port has no iteration history to diverge on -- which is what lets MATLAB, C++, native Python and this agree in the last digits on that route. See _kb/06-solver-catalog.md.

THE TRANSLATION IS INDEX-FOR-INDEX. Every array here is allocated one longer than it needs to be and addressed from 1, exactly as the Fortran does, and the loop bounds are the Fortran's own. That is deliberate: a 0-based rewrite of 2000 lines of Fortran is where an off-by-one hides, and it would be invisible until it changed an answer nobody has a reference for. Index 0 of every internal array is unused. The CALLBACKS are the exception and are 0-based, because they are the boundary a Java caller actually writes; the copy at that boundary is O(n) against the O(n^3) factorisation it sits next to.

EVERY REDUCTION IS A SEQUENTIAL LOOP, as the Fortran accumulates it -- the error norm and the inner sums of DECOMR and SLVROD. Reassociating them would change the last bits, which is enough to move a step-size decision and desynchronise the whole trajectory from the other three codebases.

Reachable IJOB values are 1..5 (and 11..15 when m1 > 0, the second order form); RODAS itself never selects 6 or 7, which belong to RADAU5's Hessenberg option and are absent here rather than transliterated dead.

Java 8: no var, no List.of, no switch expressions.

See Also:

• DaeAnalyzer

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Rodas.Dense	CONTRO: the third-order interpolant RODAS carries over the step just accepted.
static interface	Rodas.Dfx	df/dx, for a non-autonomous system.
static interface	Rodas.Fcn	The right hand side f(x,y).
static interface	Rodas.Jac	df/dy.
static interface	Rodas.Mas	The mass matrix.
static final class	Rodas.Options	The Fortran switches, with rodas.f's own defaults.
static final class	Rodas.Result	Where the integration ended, and what it cost.
static class	Rodas.RodasInputException	Raised for an input rodas.f itself rejects before integrating.
static interface	Rodas.Solout	Called after each accepted step when iout != 0; negative stops.

Field Summary

Fields

Modifier and Type	Field	Description
static final int	IDID_NMAX	IDID: more than NMAX steps were needed.
static final int	IDID_SINGULAR	IDID: the matrix was repeatedly singular.
static final int	IDID_SOLOUT_STOP	IDID: SOLOUT asked for the integration to stop.
static final int	IDID_STEP_TOO_SMALL	IDID: the step size became too small.
static final int	IDID_SUCCESS	IDID: the integration reached XEND.

Method Summary

Modifier and Type	Method	Description
static Rodas.Result	integrate(int n, Rodas.Fcn fcn, double x, double[] y, double xend, double h, double[] rtol, double[] atol, int itol, Rodas.Options opt)	Integrate M y' = f(x,y) from x to xend.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

IDID_SUCCESS

public static final int IDID_SUCCESS

IDID: the integration reached XEND.

See Also:

• Constant Field Values

IDID_SOLOUT_STOP

public static final int IDID_SOLOUT_STOP

IDID: SOLOUT asked for the integration to stop.

See Also:

• Constant Field Values

IDID_NMAX

public static final int IDID_NMAX

IDID: more than NMAX steps were needed.

See Also:

• Constant Field Values

IDID_STEP_TOO_SMALL

public static final int IDID_STEP_TOO_SMALL

IDID: the step size became too small.

See Also:

• Constant Field Values

IDID_SINGULAR

public static final int IDID_SINGULAR

IDID: the matrix was repeatedly singular.

See Also:

• Constant Field Values

Method Details

integrate

public static Rodas.Result integrate(int n,
 Rodas.Fcn fcn,
 double x,
 double[] y,
 double xend,
 double h,
 double[] rtol,
 double[] atol,
 int itol,
 Rodas.Options opt)

Integrate M y' = f(x,y) from x to xend.

Parameters:

n - dimension of the system

fcn - the right hand side

x - initial abscissa

y - initial state, length n, 0-based; modified in place

xend - final abscissa

h - initial step size guess (0 means 1e-6)

rtol - relative tolerance, length 1 (itol 0) or n (itol 1)

atol - absolute tolerance, same shape as rtol

itol - 0 scalar tolerances, 1 one per equation

opt - the Fortran switches; null for all defaults

Returns:

where the integration ended and what it cost