lsodar {deSolve} | R Documentation |
Solving initial value problems for stiff or
non-stiff systems of first-order ordinary differential equations
(ODEs) and including root-finding.
The R function lsodar
provides an interface to the
Fortran ODE solver of the same name, written by Alan
C. Hindmarsh and Linda R. Petzold.
The system of ODE's is written as an R function or be defined in
compiled code that has been dynamically loaded. - see description of lsoda
for details.
lsodar
differs from lsode
in two respects.
lsodar(y, times, func, parms, rtol=1e-6, atol=1e-6, jacfunc=NULL, jactype="fullint", rootfunc=NULL, verbose=FALSE, nroot=0, tcrit=NULL, hmin=0, hmax=NULL, hini=0, ynames=TRUE, maxordn=12, maxords = 5, 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 |
times at which explicit estimates for y are desired. The first value in times must be the initial time. |
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 lsodar() 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 |
rootfunc |
if not NULL , an R function that computes
the function whose root has to be estimated or a string giving the name of a function or
subroutine in ‘dllname’ that computes the root function. The R calling sequence for
rootfunc is identical to that of func . rootfunc should
return a vector with the function values whose root is sought |
verbose |
a logical value that, when TRUE, triggers more verbose output from the ODE solver. Will output the settings of vectors *istate* and *rstate* - see details |
nroot |
only used if ‘dllname’ is specified: the number of constraint functions whose roots are desired during the integration; if rootfunc is an R-function, the solver estimates the number of roots |
tcrit |
if not NULL , then lsodar cannot integrate past tcrit . The Fortran routine lsodar 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, the 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 |
maxordn |
the maximum order to be allowed in case the method is non-stiff. Should be <=12. Reduce maxord to save storage space |
maxords |
the maximum order to be allowed in case the method is stiff. Should be <=5. 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 |
The work is done by the Fortran subroutine lsodar
,
whose documentation should be consulted for details (it is included as
comments in the source file ‘src/opkdmain.f’). The implementation is based on the
November, 2003 version of lsodar, from Netlib.
lsodar
switches automatically between stiff and nonstiff methods (similar as lsoda
).
This means that the user does not have to determine whether the
problem is stiff or not, and the solver will automatically choose the
appropriate method. It always starts with the nonstiff method.
It finds the root of at least one of a set of constraint functions g(i) of the independent and dependent variables. It then returns the solution at the root if that occurs sooner than the specified stop condition, and otherwise returns the solution according the specified stop condition.
The form of the jacobian can be specified by jactype
which can take the following values.
jacfunc
jacfunc
; the size of the bands specified by bandup
and banddown
bandup
and banddown
if jactype
= "fullusr" or "bandusr" then the user must supply a subroutine jacfunc
.
The input parameters rtol
, and atol
determine the error
control performed by the solver. 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.
Examples in Fortran are in the ‘dynload’ subdirectory of
the deSolve
package directory.
The output will have the attributes *istate*, *rstate*, and if a root was found iroot, three 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:
iroot
.
-1 if excess work done, -2 means excess accuracy requested. (Tolerances too small),
-3 means illegal input detected. (See printed message.), -4 means repeated error test failures. (Check all input),
-5 means repeated convergence failures. (Perhaps bad Jacobian supplied or wrong choice of MF or tolerances.),
-6 means error weight became zero during problem. (Solution component i vanished, and atol or atol(i) = 0.)
rstate contains the following:
iroot is a vector, its length equal to the number of constraint functions; it will have a value of 1 for the constraint function whose root that has been found and 0 otherwise.
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 and additional column for the time value. There will be a row
for each element in times
unless the Fortran routine `lsodar'
returns with an unrecoverable error or has found a root, in which case the last row will contain the function value at the root.
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
if a root has been found, the output will also have the attribute iroot
, an integer indicating which root has been found.
Karline Soetaert <k.soetaert@nioo.knaw.nl>
Netlib: http://www.netlib.org
\code{ode}, lsoda
, lsode
, lsodes
,
vode
, daspk
, rk
.
######################################### ### example 1: from lsodar source code ######################################### Fun <- function (t,y,parms) { ydot <- vector(len=3) ydot[1] <- -.04*y[1] + 1.e4*y[2]*y[3] ydot[3] <- 3.e7*y[2]*y[2] ydot[2] <- -ydot[1]-ydot[3] return(list(ydot,ytot = sum(y))) } rootFun <- function (t,y,parms) { yroot <- vector(len=2) yroot[1] <- y[1] - 1.e-4 yroot[2] <- y[3] - 1.e-2 return(yroot) } y <- c(1,0,0) times <- c(0,0.4*10^(0:8)) Out <- NULL ny <- length(y) out <- lsodar(y=y,times=times,fun=Fun,rootfun=rootFun, rtol=1e-4,atol=c(1e-6,1e-10,1e-6), parms=NULL) print(paste("root is found for eqn",which(attributes(out)$iroot==1))) print(out[nrow(out),]) ######################################### ### example 2: ### using lsodar to estimate steady-state conditions ######################################### # Bacteria (Bac) are growing on a substrate (Sub) model <- function(t,state,pars) { with (as.list(c(state,pars)), { # substrate uptake death respiration dBact = gmax*eff*Sub/(Sub+ks)*Bact - dB*Bact - rB*Bact dSub =-gmax *Sub/(Sub+ks)*Bact + dB*Bact +input return(list(c(dBact,dSub))) }) } # root is the condition where sum of |rates of change| # is very small rootfun <- function (t,state,pars) { dstate <- unlist(model(t,state,pars)) #rate of change vector return(sum(abs(dstate))-1e-10) } pars <- list(Bini=0.1,Sini=100,gmax =0.5,eff = 0.5, ks =0.5, rB =0.01, dB =0.01, input=0.1) tout <- c(0,1e10) state <- c(Bact=pars$Bini,Sub =pars$Sini) out <- lsodar(state,tout,model,pars,rootfun=rootfun) print(out)