vode {deSolve} | R Documentation |
Solves the initial value problem for stiff or nonstiff systems of ordinary differential equations (ODE) in the form:
dy/dt = f(t,y)
The R function vode
provides an interface to the
Fortran ODE solver of the same name, written by Peter N. Brown, Alan C. Hindmarsh and George D. Byrne.
The system of ODE's is written as an R function or be defined in compiled code that has been dynamically loaded.
In contrast to lsoda
, the user has to specify whether or not the problem is stiff
and choose the appropriate solution method.
vode
is very similar to lsode
, but uses a variable-coefficient method
rather than the fixed-step-interpolate methods in lsode
.
In addition, in vode it is possible to choose whether or not a copy
of the Jacobian is saved for reuse in the corrector iteration algorithm;
In lsode
, a copy is not kept.
vode(y, times, func, parms, rtol=1e-6, atol=1e-8, jacfunc=NULL, jactype="fullint", mf=NULL, verbose=FALSE, tcrit=NULL, hmin=0, hmax=NULL, hini=0, ynames=TRUE, maxord=NULL, bandup=NULL, banddown=NULL, maxsteps=5000, dllname=NULL, initfunc=dllname, initpar=parms, rpar=NULL, ipar=NULL, nout=0, outnames=NULL, ...)
y |
the initial (state) values for the ODE system. If y has a name attribute, the names will be used to label the output matrix. |
times |
time sequence for which output is wanted; the first value of times must be the initial time; if only one step is to be taken; set times = NULL |
func |
either an R-function that computes the values of the
derivatives in the ODE system (the model definition) at time
t, or a character string giving the name of a compiled function in a dynamically loaded
shared library.
If func is an R-function, it must be defined as:
yprime = func(t, y, parms,...) . t is the current time point
in the integration, y is the current estimate of the variables
in the ODE system. If the initial values y has a names
attribute, the names will be available inside func . parms is
a vector or list of parameters; ... (optional) are any other arguments passed to the function.
The return value of func should be a list, whose first element is a
vector containing the derivatives of y with respect to
time , and whose next elements are global values that are required at
each point in times .
If func is a string, then dllname must give the name
of the shared library (without extension) which must be loaded
before vode() is called. See package vignette for more details.
|
parms |
vector or list of parameters used in func or jacfunc . |
rtol |
relative error tolerance, either a scalar or an array as
long as y . See details. |
atol |
absolute error tolerance, either a scalar or an array as
long as y . See details. |
jacfunc |
if not NULL , an R function that computes
the jacobian of the system of differential equations
dydot(i)/dy(j), or a string giving the name of a function or
subroutine in ‘dllname’ that computes the jacobian (see Details
below for more about this option). In some circumstances, supplying
jacfunc can speed up the computations, if the system is stiff. The R calling sequence for
jacfunc is identical to that of func .
If the jacobian is a full matrix, jacfunc should return a matrix dydot/dy, where the ith
row contains the derivative of dy_i/dt with respect to y_j,
or a vector containing the matrix elements by columns (the way R and Fortran store matrices).
If the jacobian is banded, jacfunc should return a matrix containing only the
nonzero bands of the jacobian, rotated row-wise. See first example of lsode. |
jactype |
the structure of the jacobian, one of "fullint", "fullusr", "bandusr" or "bandint" - either full or banded and estimated internally or by user; overruled if mf is not NULL |
mf |
the "method flag" passed to function vode - overrules jactype - provides more options than jactype - see details |
verbose |
if TRUE: full output to the screen, e.g. will output the settings of vectors *istate* and *rstate* - see details |
tcrit |
if not NULL , then vode cannot integrate past tcrit . The Fortran routine dvode overshoots its targets (times points in the vector times ), and interpolates values
for the desired time points. If there is a time beyond which integration should not proceed (perhaps because of a singularity),
that should be provided in tcrit . |
hmin |
an optional minimum value of the integration stepsize. In special situations this parameter may speed up computations with the cost of precision. Don't use hmin if you don't know why! |
hmax |
an optional maximum value of the integration stepsize. If not specified, hmax is set to the largest difference in times , to avoid that the simulation possibly ignores short-term events. If 0, no maximal size is specified |
hini |
initial step size to be attempted; if 0, initial step size is determined by the solver |
ynames |
if FALSE: names of state variables are not passed to function func ; this may speed up the simulation especially for multi-D models |
maxord |
the maximum order to be allowed. NULL uses the default, i.e. order 12 if implicit Adams method (meth=1), order 5 if BDF method (meth=2). Reduce maxord to save storage space |
bandup |
number of non-zero bands above the diagonal, in case the Jacobian is banded |
banddown |
number of non-zero bands below the diagonal, in case the Jacobian is banded |
maxsteps |
maximal number of steps during one call to the solver |
dllname |
a string giving the name of the shared library (without extension) that contains all the compiled function or subroutine definitions refered to in func and jacfunc . See package vignette |
initfunc |
if not NULL, the name of the initialisation function (which initialises values of parameters), as provided in ‘dllname’. See package vignette |
initpar |
only when ‘dllname’ is specified and an initialisation function initfunc is in the dll: the parameters passed to the initialiser, to initialise the common blocks (fortran) or global variables (C, C++) |
rpar |
only when ‘dllname’ is specified: a vector with double precision values passed to the dll-functions whose names are specified by func and jacfunc |
ipar |
only when ‘dllname’ is specified: a vector with integer values passed to the dll-functions whose names are specified by func and jacfunc |
nout |
only used if dllname is specified and the model is defined in compiled code: the number of output variables calculated in the compiled function func , present in the shared library. Note:
it is not automatically checked whether this is indeed the number of output variables calculed in the dll - you have to perform this check in the code - See package vignette |
outnames |
only used if ‘dllname’ is specified and nout > 0: the names of output variables calculated in the compiled function func , present in the shared library |
... |
additional arguments passed to func and jacfunc allowing this to be a generic function |
Before using the integrator vode
, the user has to decide whether or not the problem is stiff.
If the problem is nonstiff, use method flag mf
= 10, which selects a nonstiff (Adams) method, no Jacobian used.
If the problem is stiff, there are four standard choices
which can be specified with jactype
or mf
.
The options for jactype are
mf
=22
jacfunc
, corresponds to mf
=21
jacfunc
; the size of the bands specified by bandup
and banddown
, corresponds to mf
=24
bandup
and banddown
, corresponds to mf
=25
More options are available when specifying mf directly.
The legal values of mf
are 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, -11, -12, -14, -15, -21, -22, -24, -25.
mf
is a signed two-digit integer, mf
= JSV*(10*METH + MITER),where
func
per df/dy value).
MITER = 3 means chord iteration with an internally generated diagonal Jacobian approximation
(using 1 extra call to func
per df/dy evaluation).
MITER = 4 means chord iteration with a user-supplied banded Jacobian.
MITER = 5 means chord iteration with an internally generated banded Jacobian (using ML+MU+1 extra calls to func
per df/dy evaluation).
If MITER = 1 or 4, the user must supply a subroutine jacfunc
.
The example for integrator lsode
demonstrates how to specify both a banded and full jacobian.
The input parameters rtol
, and atol
determine the error
control performed by the solver.
If the request for precision exceeds the capabilities of the machine,
vode will return an error code. See lsoda
for details.
Models may be defined in compiled C or Fortran code, as well as in an R-function. See package vignette for details.
The output will have the attributes *istate*, and *rstate*, two vectors with several useful elements.
if verbose
= TRUE, the settings of istate and rstate will be written to the screen.
the following elements of istate are meaningful:
rstate contains the following:
For more information, see the comments in the original code dvode.f
A matrix with up to as many rows as elements in times and as many columns as elements in y
plus the number of "global" values returned
in the next elements of the return from func
, plus an additional column (the first) for the time value.
There will be one row for each element in times
unless the Fortran routine `vode' returns with an unrecoverable error.
If y
has a names attribute, it will be used to label the columns of the output value.
The output will have the attributes istate
, and rstate
, two vectors with several useful elements.
See details.
The first element of istate returns the conditions under which the last call to lsoda returned. Normal is istate[1] = 2
.
If verbose
= TRUE, the settings of istate and rstate will be written to the screen
Karline Soetaert <k.soetaert@nioo.knaw.nl>
Netlib: http://www.netlib.org
ode
, lsoda
, lsode
, lsodes
,
lsodar
, daspk
, rk
.
# The famous Lorenz equations: chaos in the earth's atmosphere # Lorenz 1963. J. Atmos. Sci. 20, 130-141. chaos<-function(t,state,parameters) { with(as.list(c(state)),{ dx <- -8/3*x+y*z dy <- -10*(y-z) dz <- -x*y+28*y-z list(c(dx,dy,dz)) }) } # end of model state <-c(x=1, y=1, z=1) times <-seq(0,100,0.01) out <-as.data.frame(vode(state,times,chaos,0)) plot(out$x,out$y,type="l",main="Lorenz butterfly")