R/lsode.R

In deSolve: Solvers for Initial Value Problems of Differential Equations ('ODE', 'DAE', 'DDE')

### ============================================================================
### lsode -- solves ordinary differential equation systems
### The user has to specify whether or not
### the problem is stiff and choose the appropriate method.
### It is very similar to vode, except for some implementation details.
### More specifically, 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; this requires less memory but may be slightly
### slower.
###
### as from deSolve 1.7, lsode finds the root of at least one of a set
### of constraint functions g(i) of the independent and dependent variables.
### It finds only those roots for which some g(i), as a function
### of t, changes sign in the interval of integration.
### 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.

### ============================================================================

lsode <- function(y, times, func, parms, rtol=1e-6, atol=1e-6,
  jacfunc=NULL, jactype = "fullint", mf = NULL, rootfunc=NULL,
  verbose=FALSE, nroot = 0,
  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,forcings=NULL,
  initforc = NULL, fcontrol=NULL, events=NULL, lags = NULL, ...)
{

  if (is.list(func)) {            ### IF a list
      if (!is.null(jacfunc) & "jacfunc" %in% names(func))
         stop("If 'func' is a list that contains jacfunc, argument 'jacfunc' should be NULL")
      if (!is.null(rootfunc) & "rootfunc" %in% names(func))
         stop("If 'func' is a list that contains rootfunc, argument 'rootfunc' should be NULL")
      if (!is.null(initfunc) & "initfunc" %in% names(func))
         stop("If 'func' is a list that contains initfunc, argument 'initfunc' should be NULL")
      if (!is.null(dllname) & "dllname" %in% names(func))
         stop("If 'func' is a list that contains dllname, argument 'dllname' should be NULL")
      if (!is.null(initforc) & "initforc" %in% names(func))
         stop("If 'func' is a list that contains initforc, argument 'initforc' should be NULL")
      if (!is.null(events$func) & "eventfunc" %in% names(func))
         stop("If 'func' is a list that contains eventfunc, argument 'events$func' should be NULL")
      if ("eventfunc" %in% names(func)) {
         if (! is.null(events))
           events$func <- func$eventfunc
         else
           events <- list(func = func$eventfunc)
      }
     if (!is.null(func$jacfunc))  jacfunc <- func$jacfunc
     if (!is.null(func$rootfunc)) rootfunc <- func$rootfunc
     if (!is.null(func$initfunc)) initfunc <- func$initfunc
     if (!is.null(func$dllname))  dllname <- func$dllname
     if (!is.null(func$initforc)) initforc <- func$initforc
     func <- func$func
  }
### check input
  hmax <- checkInput (y, times, func, rtol, atol,
    jacfunc, tcrit, hmin, hmax, hini, dllname)

  n <- length(y)

  if (!is.null(maxord))
    if(maxord < 1) stop("`maxord' must be >1")

### Jacobian, method flag
  if (is.null(mf)){
    if (jactype == "fullint" ) imp <- 22 # full, calculated internally
    else if (jactype == "fullusr" ) imp <- 21 # full, specified by user function
    else if (jactype == "bandusr" ) imp <- 24 # banded, specified by user function
    else if (jactype == "bandint" ) imp <- 25 # banded, calculated internally
    else
     stop("'jactype' must be one of 'fullint', 'fullusr', 'bandusr' or 'bandint' if 'mf' not specified")
  } else imp <- mf

  if (! imp %in% c(10:15, 20:25))
    stop ("method flag 'mf' not allowed")

  # check other specifications depending on Jacobian
  miter <- imp%%10
  if (miter %in% c(1,4) & is.null(jacfunc))
    stop ("'jacfunc' NOT specified; either specify 'jacfunc' or change 'jactype' or 'mf'")
  meth <- abs(imp)%/%10                # basic linear multistep method

  if (is.null (maxord)) maxord <- if (meth==1) 12 else 5
  if (meth==1 && maxord > 12) stop ("'maxord' too large: should be <= 12")
  if (meth==2 && maxord > 5 ) stop ("'maxord' too large: should be <= 5")
  if (miter %in% c(4,5) && is.null(bandup))
    stop("'bandup' must be specified if banded Jacobian")
  if (miter %in% c(4,5) && is.null(banddown))
    stop("'banddown' must be specified if banded Jacobian")
  if (is.null(banddown)) banddown <-1
  if (is.null(bandup  )) bandup   <-1

### model and Jacobian function
  JacFunc   <- NULL
  Ynames    <- attr(y,"names")
  RootFunc <- NULL
  flist     <- list(fmat=0,tmat=0,imat=0,ModelForc=NULL)
  ModelInit <- NULL
  Eventfunc <- NULL
  events <- checkevents(events, times, Ynames, dllname,TRUE)
  if (! is.null(events$newTimes)) times <- events$newTimes

  ## if (miter == 4) Jacobian should have banddown empty rows
  if (miter == 4 && banddown>0)
    erow<-matrix(data=0, ncol=n, nrow=banddown) else erow<-NULL

  if (is.character(func) | inherits(func, "CFunc")) {   # function specified in a DLL or inline compiled
    DLL <- checkDLL(func,jacfunc,dllname,
                    initfunc,verbose,nout, outnames)

    ## Is there a root function?
    if (!is.null(rootfunc)) {
      if (!is.character(rootfunc) & !inherits(rootfunc, "CFunc"))
        stop("If 'func' is dynloaded, so must 'rootfunc' be")
      rootfuncname <- rootfunc
      if (inherits(rootfunc, "CFunc"))
        RootFunc <- body(rootfunc)[[2]]
      else if (is.loaded(rootfuncname, PACKAGE = dllname))  {
        RootFunc <- getNativeSymbolInfo(rootfuncname, PACKAGE = dllname)$address
      } else
        stop(paste("root function not loaded in DLL",rootfunc))
      if (nroot == 0)
        stop("if 'rootfunc' is specified in a DLL, then 'nroot' should be > 0")
    }

    ModelInit <- DLL$ModelInit
    Func    <- DLL$Func
    JacFunc <- DLL$JacFunc
    Nglobal <- DLL$Nglobal
    Nmtot   <- DLL$Nmtot

    if (! is.null(forcings))
      flist <- checkforcings(forcings,times,dllname,initforc,verbose,fcontrol)

    if (is.null(ipar)) ipar<-0
    if (is.null(rpar)) rpar<-0
    Eventfunc <- events$func
    if (is.function(Eventfunc))
      rho <- environment(Eventfunc)
    else
      rho <- NULL


  } else {

    if (is.null(initfunc))
      initpar <- NULL # parameter initialisation not needed if function is not a DLL

    rho <- environment(func)
    # func and jac are overruled, either including ynames, or not
    # This allows to pass the "..." arguments and the parameters

    if (ynames)  {
      Func    <- function(time,state) {
        attr(state,"names") <- Ynames
         unlist(func   (time,state,parms,...))
      }

      Func2   <- function(time,state)  {
        attr(state,"names") <- Ynames
        func   (time,state,parms,...)
      }

      JacFunc <- function(time,state) {
        attr(state,"names") <- Ynames
        rbind(jacfunc(time,state,parms,...),erow)
      }
      RootFunc <- function(time,state) {
        attr(state,"names") <- Ynames
        rootfunc(time,state,parms,...)
      }
      if (! is.null(events$Type))
       if (events$Type == 2)
         Eventfunc <- function(time,state) {
           attr(state,"names") <- Ynames
           events$func(time,state,parms,...)
         }
    } else {                          # no ynames...
      Func    <- function(time,state)
         unlist(func   (time,state,parms,...))

      Func2   <- function(time,state)
        func   (time,state,parms,...)

      JacFunc <- function(time,state)
        rbind(jacfunc(time,state,parms,...),erow)

      RootFunc <- function(time,state)
        rootfunc(time,state,parms,...)

      if (! is.null(events$Type))
       if (events$Type == 2)
         Eventfunc <- function(time,state)
           events$func(time,state,parms,...)

    }

    ## Check function and return the number of output variables +name
    FF <- checkFunc(Func2,times,y,rho)
    Nglobal<-FF$Nglobal
    Nmtot <- FF$Nmtot

    ## Check event function
    if (! is.null(events$Type))
      if (events$Type == 2)
        checkEventFunc(Eventfunc,times,y,rho)

    ## and for rootfunc
    if (! is.null(rootfunc))  {
      tmp2 <- eval(rootfunc(times[1],y,parms,...), rho)
      if (!is.vector(tmp2))
        stop("root function 'rootfunc' must return a vector\n")
      nroot <- length(tmp2)
    } else nroot = 0

    if (miter %in% c(1,4)) {
      tmp <- eval(JacFunc(times[1], y), rho)
      if (!is.matrix(tmp))
         stop("Jacobian function 'jacfunc' must return a matrix\n")
      dd <- dim(tmp)
      if ((miter == 4 && any(dd != c(bandup+banddown+banddown+1,n))) ||
          (miter == 1 && any(dd != c(n,n)))) # thpe add 'any' (2 times)
         stop("Jacobian dimension not ok")
     }
  }


### work arrays iwork, rwork
  # length of rwork and iwork
  lrw <- 20+n*(maxord+1)+3*n  +3*nroot
  if(miter %in% c(1,2) ) lrw <- lrw + 2*n*n+2
  if(miter ==3)          lrw <- lrw + n+2
  if(miter %in% c(4,5) ) lrw <- lrw + (2*banddown+ bandup+1)*n+2

  liw   <- if (miter %in% c(0,3)) 20 else 20+n

  # only first 20 elements passed; other will be allocated in C-code
  iwork <- vector("integer",20)
  rwork <- vector("double",20)
  rwork[] <- 0.
  iwork[] <- 0

  iwork[1] <- banddown
  iwork[2] <- bandup
  iwork[5] <- maxord
  iwork[6] <- maxsteps

  if(!is.null(tcrit)) rwork[1] <- tcrit
  rwork[5] <- hini
  rwork[6] <- hmax
  rwork[7] <- hmin

### the task to be performed.
  itask <- if (! is.null(times)) {
    if (is.null (tcrit)) 1 else 4
  } else  {                             # times specified
    if (is.null (tcrit)) 2 else 5       # only one step
  }
  if(is.null(times)) times<-c(0,1e8)

### print to screen...
  if (verbose) {
    printtask(itask,func,jacfunc)
    printM("\n--------------------")
    printM("Integration method")
    printM("--------------------")
    df   <- c("method flag,    =",
              "meth            =",
              "miter           =")
    vals <- c(imp,  meth, miter)
    txt  <- "; (note: mf = (10 * meth + miter))"

    if (meth==1)  txt <- c(txt,
     "; the basic linear multistep method: the implicit Adams method")  else
    if (meth==2)  txt <- c(txt,
     "; the basic linear multistep method:
     based on backward differentiation formulas")

    if (miter==0) txt <- c(txt,
     "; functional iteration (no Jacobian matrix is involved") else
    if (miter==1) txt <- c(txt,
     "; chord iteration with a user-supplied full (NEQ by NEQ) Jacobian") else
    if (miter==2) txt <- c(txt,
    "; chord iteration with an internally generated full Jacobian,
     (NEQ extra calls to F per df/dy value)") else
    if (miter==3) txt <- c(txt,
     "; chord iteration with an internally generated diagonal Jacobian
     (1 extra call to F per df/dy evaluation)") else
    if (miter==4) txt <- c(txt,
     "; chord iteration with a user-supplied banded Jacobian") else
    if (miter==5) txt <- c(txt,
     "; chord iteration with an internally generated banded Jacobian
     (using ML+MU+1 extra calls to F per df/dy evaluation)")
    printmessage(df, vals, txt)
  }

### calling solver
  storage.mode(y) <- storage.mode(times) <- "double"
  IN <-2
  if (!is.null(rootfunc)) IN <- 6

  lags <- checklags(lags, dllname)

  ## end time lags...
  on.exit(.C("unlock_solver"))
  out <- .Call("call_lsoda",y,times,Func,initpar,
               rtol, atol, rho, tcrit, JacFunc, ModelInit, Eventfunc,
               as.integer(verbose), as.integer(itask), as.double(rwork),
               as.integer(iwork), as.integer(imp),as.integer(Nglobal),
               as.integer(lrw),as.integer(liw),as.integer(IN),
               RootFunc, as.integer(nroot), as.double (rpar), as.integer(ipar),
               0L, flist, events, lags, PACKAGE="deSolve")

### saving results
  if (nroot>0) iroot  <- attr(out, "iroot")

  out <- saveOut(out, y, n, Nglobal, Nmtot, func, Func2,
                 iin=c(1,12:19), iout=c(1:3,14,5:9))

  if (nroot>0) attr(out, "iroot") <- iroot
  attr(out, "type") <- "lsode"
  if (verbose) diagnostics(out)
  return(out)
}