##  R routines for the package mgcv (c) Simon Wood 2000-2016
##  With contributions from Henric Nilsson

Rrank <- function(R,tol=.Machine$double.eps^.9) {
## Finds rank of upper triangular matrix R, by estimating condition
## number of upper rank by rank block, and reducing rank until this is 
## acceptably low... assumes R pivoted 
 m <- nrow(R)
 rank <- min(m,ncol(R))
 ok <- TRUE
  while (ok) {
    Rcond <- .C(C_R_cond,R=as.double(R),r=as.integer(m),c=as.integer(rank),
             work=as.double(rep(0,4*m)),Rcond=as.double(1))$Rcond
    if (Rcond*tol<1) ok <- FALSE else rank <- rank - 1  
  }
  rank
}
 
slanczos <- function(A,k=10,kl=-1,tol=.Machine$double.eps^.5,nt=1) {
## Computes truncated eigen decomposition of symmetric A by 
## Lanczos iteration. If kl < 0 then k largest magnitude
## eigenvalues returned, otherwise k highest and kl lowest.
## Eigenvectors are always returned too.
## set.seed(1);n <- 1000;A <- matrix(runif(n*n),n,n);A <- A+t(A);er <- slanczos(A,10)
## um <- eigen(A,symmetric=TRUE);ind <- c(1:5,(n-5+1):n)
## range(er$values-um$values[ind]);range(abs(er$vectors)-abs(um$vectors[,ind]))
## It seems that when k (or k+kl) is beyond 10-15% of n
## then you might as well use eigen(A,symmetric=TRUE), but the
## extra cost is the expensive accumulation of eigenvectors.
## Should re-write whole thing using LAPACK routines for eigenvectors. 
   if (tol<=0||tol>.01) stop("silly tolerance supplied")
   k <- round(k);kl <- round(kl)
   if (k<0) stop("argument k must be positive.")
   m <- k + max(0,kl) 
   n <- nrow(A) 
   if (m<1) return(list(values=rep(0,0),vectors=matrix(0,n,0),iter=0)) 
   if (n != ncol(A)) stop("A not square")
   if (m>n) stop("Can not have more eigenvalues than nrow(A)")
   oo <- .C(C_Rlanczos,A=as.double(A),U=as.double(rep(0,n*m)),D=as.double(rep(0,m)),
            n=as.integer(n),m=as.integer(k),ml=as.integer(kl),tol=as.double(tol),nt=as.integer(nt))
   list(values = oo$D,vectors = matrix(oo$U,n,m),iter=oo$n) 
}

rig <- function(n,mean,scale) {
## inverse gaussian deviates generated by algorithm 5.7 of
## Gentle, 2003. scale = 1/lambda. 
  if (length(n)>1) n <- length(n)
  x <- y <- rnorm(n)^2
  mys <- mean*scale*y
  mu <- 0*y + mean ## y is there to ensure mu is a vector
  mu2 <- mu^2;
  ind <- mys < .Machine$double.eps^-.5 ## cut off for tail computation
  x[ind] <- mu[ind]*(1 + 0.5*(mys[ind] - sqrt(mys[ind]*4+mys[ind]^2)))
  x[!ind] <- mu[!ind]/mys[!ind] ## tail term (derived from Taylor of sqrt(1+eps) etc)
  #my <- mean*y; sc <- 0*y + scale
  #ind <- my > 1 ## cancellation error can be severe, without splitting
  #x[!ind] <- mu[!ind]*(1 + 0.5*sc[!ind]*(my[!ind] - sqrt(4*my[!ind]/sc[!ind] + my[!ind]^2)))
  ## really the sqrt in the next term should be expanded beyond first order and then
  ## worked on - otherwise too many exact zeros?
  #x[ind] <- pmax(0,mu[ind]*(1+my[ind]*.5*sc[ind]*(1-sqrt(1+ 4/(sc[ind]*my[ind])))))
  ind <- runif(n) > mean/(mean+x)
  x[ind] <- mu2[ind]/x[ind]
  x ## E(x) = mean; var(x) = scale*mean^3
}

strip.offset <- function(x) {
# sole purpose is to take a model frame and rename any "offset(a.name)"
# columns "a.name"
  na <- names(x)
  for (i in 1:length(na)) {
    if (substr(na[i],1,7)=="offset(") 
      na[i] <- substr(na[i],8,nchar(na[i])-1)
  }
  names(x) <- na
  x
}

lp <- function(c,A,b,C=NULL,d=NULL,Bi=NULL,maxit=max(1000,nrow(A)*10),phase1=FALSE) {
## Solves linear program min c'x s.t. Ax = b x>=0 given m initial
## active indices Bi, where A is m by p. The condition on Bi is that
## The solution to A[,Bi] x* = b must exist and x* >= 0.
## If Bi not supplied then a phase 1 LP is used to find it.
## Alternatively if both C and d are non-NULL then solves
## min  c'x s.t. Ax>b Cx=d, x otherwise unrestricted. (C and d
## can have no rows without counting as NULL.)
 
  sf <- is.null(C)||is.null(d) ## standard form
  if (!sf) { ## re-write in standard form
    pa <- ncol(A);ma <- nrow(A)
    A <- rbind(A,C)
    m <- nrow(A)
    A <- if (ma) cbind(A,-A,-diag(1,m)[,1:ma]) else cbind(A,-A)
    b <- c(b,d)
    c <- c(c,-c,rep(0,ma))
    if (!is.null(Bi)) {
      warning("Bi ignored when LP not in standard form")
      Bi <- NULL
    }
  }
  p <- ncol(A);m <- nrow(A)
  if (is.null(Bi)) { ## find Bi
    x <- feasible(A,b)
    Bi <- which(x!=0)
  }
  Ni <- (1:p)[-Bi] ## currently excluded
  conv <- FALSE
  B <- A[,Bi];
  qrb <- qr(t(B)); Q <- qr.Q(qrb); R <- qr.R(qrb)
  for (i in 1:maxit) {  
    N <- A[,Ni]
    # equivalent to xb <- solve(B,b)...
    xb <- Q%*%forwardsolve(R,b,upper.tri=TRUE,transpose=TRUE)
    # equivalent to sn <- c[Ni] - drop(t(N)%*%solve(t(B),c[Bi]))...
    v <- drop(c[Bi]%*%Q)
    sn <- c[Ni] - drop(t(N)%*%backsolve(R,v))
    eps <- kappa(R)*max(abs(v))*norm(N,"M")*.Machine$double.eps^.9
    if (phase1) {
      conv <- sum(c[Bi]*xb)==0 ## in phase 1, objective should end up at zero
      if (conv||all(sn>=0)) break
    } else if (all(sn >= -eps)) { conv <- TRUE; break }
    Nk <- which(sn==min(sn))[1] ## index of k within Ni
    k <- Ni[Nk] ## index in Ni to include
    # equivalent to w <- solve(B,A[,k])...
    w <- Q%*%forwardsolve(R,A[,k],upper.tri=TRUE,transpose=TRUE)
    if (all(w<=0)) stop("unbounded")
    ii <- w>0; xbd.min <- min(xb[ii]/w[ii])
    Bq <- which(xb/w==xbd.min&ii)[1] ## index (in Bi) to exclude
    q <- Bi[Bq] ## col of A to exclude
    ## now update Bi and Ni
    Ni[Nk] <- q; Bi[Bq] <- k
    .Call(C_QRdrop,Q,R,as.integer(Bq-1))
    .Call(C_QRadd,Q,R,A[,k])
    if (Bq<m) { Qm <- Q[m,]; Q[(Bq+1):m,] <- Q[Bq:(m-1),];Q[Bq,] <- Qm} 
  }
  if (!conv) stop("not converged")
  xb[xb<0] <- 0
  x <- rep(0,p)
  x[Bi] <- xb;
  if (!sf) x <- x[1:pa] - x[1:pa+pa] ## assemble +ve and negative parts of solution
  #cat(sum(c[Bi]*xb),"\n")  ## final objective 
  x
} ## lp

feasible <- function(A,b,C=NULL,d=NULL,maxit=max(1000,nrow(A)*10)) {
## Finds feasible initial parameter vector x, satisfying
## C x = d and A x >= b. First re-writes in standard form...
## [ A -A I ] [x'] = [b]  x' >= 0, z >= 0
## [ C -C 0 ] [z ]   [d]
## ... using slack variables and +/- parts of x in x'. Then constructs
## phase I LP to solve to find feasible x', and hence x.
## If C or d are NULL then it is assumed that the problem is already
## in standard form Ax=b x>=0. A 0-row C matrix is not NULL!
  sf <- is.null(C)||is.null(d)
  if (sf) { ## already in standard form Ax=b, x>=0 
    A1 <- A;b1 <- b; m <- nrow(A1); p <- ncol(A1)
  } else { ## in C x = d and A x >= b form
    ma <- nrow(A)
    A1 <- rbind(A,C)
    m <- nrow(A1);p <- ncol(A)
    A1 <- if (ma) cbind(A1,-A1,-diag(1,m)[,1:ma]) else cbind(A1,-A1) 
    b1 <- c(b,d)
  }  
  ## A1 is first matrix in above standard form, and b1 is r.h.s. vector
  ## Now form the phase 1 problem...
  Bi <- 1:m + ncol(A1);c1 <- c(rep(0,ncol(A1)),rep(1,m))
  A1 <- cbind(A1,diag(1*(b1>=0)-1*(b1<0),m))
  x0 <- lp(c1,A1,b1,Bi=Bi,maxit=maxit,phase1=TRUE)
  x1 <- if (sf) x0[1:p] else x0[1:p] - x0[1:p+p] ## assemble +ve and negative parts of solution
} ## feasible


pcls <- function(M)
# Function to perform penalized constrained least squares.
# Problem to be solved is:
#
#  minimise      ||W^0.5 (y - Xp)||^2 + p'Bp
#  subject to    Ain p >= b  & C p = "constant"
#
# where B = \sum_{i=1}^m \theta_i S_i and W=diag(w)
# on entry this routine requires a list M, with the following elements:
# M$X - the design matrix for this problem.
# M$p - a feasible initial parameter vector - note that this should not be set up to
#       lie exactly on all the inequality constraints - which can easily happen if M$p=0!
# M$y - response variable
# M$w - weight vector: W= diag(M$w)
# M$Ain - matrix of inequality constraints
# M$bin - b above
# M$C  - fixed constraint matrix
# M$S  - List of (minimal) penalty matrices
# M$off - used for unpacking M$S
# M$sp - array of theta_i's
# M$active - currently active constraints - i.e. those for
#            which Ain p = bin. Must not be >= length(p)
#            - typically used when calling sequentially
# Ain, bin and p are not in the object needed to call mgcv....
#
{ nar<-c(length(M$y),length(M$p),dim(M$Ain)[1],dim(M$C)[1])
  ## sanity checking ...
  if (nrow(M$X)!=nar[1]) stop("nrow(M$X) != length(M$y)") 
  if (ncol(M$X)!=nar[2]) stop("ncol(M$X) != length(M$p)")
  if (length(M$w)!=nar[1]) stop("length(M$w) != length(M$y)")
  if (nar[3]!=length(M$bin)) stop("nrow(M$Ain) != length(M$bin)")
  if (nrow(M$Ain)>0) {
    if (ncol(M$Ain)!=nar[2]) stop("nrow(M$Ain) != length(M$p)") 
    res <- as.numeric(M$Ain%*%M$p) - as.numeric(M$bin)
    if (min(res)< -max(c(abs(M$bin),norm(M$Ain,"M")))*.Machine$double.eps^.8) stop("initial parameters not feasible")

    if (is.null(M$active)||length(M$active)==0||M$active[1]==0) {
      res <- abs(res)
      if (sum(res<.Machine$double.eps^.5)>0) 
        warning("initial point very close to some inequality constraints")
      res <- mean(res)
      if (res<.Machine$double.eps^.5) 
        warning("initial parameters very close to inequality constraints")
    }	
  } else { ## dummy constraint
    M$Ain <- numeric(nar[2])
    M$bin <- -1; nar[3] <- 1
  }
  
  if (nrow(M$C)>0) if (ncol(M$C)!=nar[2]) stop("ncol(M$C) != length(M$p)")  
  if (length(M$S)!=length(M$off)) stop("M$S and M$off have different lengths")
  if (length(M$S)!=length(M$sp)) stop("M$sp has different length to M$S and M$off")
  
  
  # pack the S array for mgcv call 
  m<-length(M$S)
  Sa<-array(0,0);df<-0
  if (m>0) for (i in 1:m)
  { Sa<-c(Sa,M$S[[i]])
    df[i]<-nrow(M$S[[i]])
    if (M$off[i]+df[i]-1>nar[2]) stop(gettextf("M$S[%d] is too large given M$off[%d]", i, i))
  }
  qra.exist <- FALSE
  if (ncol(M$X)>nrow(M$X)) { ## p>n branch
    if (m>0) stop("Penalized model matrix must have no more columns than rows") 
    else { ## absorb M$C constraints
      qra <- qr(t(M$C)) ## note only absorbed in p>n case
      j <- nrow(M$C);k <- ncol(M$X)
      M$X <- t(qr.qty(qra,t(M$X))[(j+1):k,])
      M$Ain <- t(qr.qty(qra,t(M$Ain))[(j+1):k,])
      M$C <- matrix(0,0,0)
      M$p <- rep(0,ncol(M$X)) 
      nar[2] <- length(M$p)
      qra.exist <- TRUE
      if  (ncol(M$X)>nrow(M$X)) stop("Model matrix not full column rank")
    }
  }
  active <- integer(length(M$p)+1)
  if (!is.null(M$active)&&length(M$active>0)&&M$active[1]>1) {
    active[1] <- length(M$active);active[1:length(M$active)+1] <- M$active
    if (active[1]>=length(M$p)) stop("too many active constraints!")
  }  
  o<-.C(C_RPCLS,as.double(M$X),as.double(M$p),as.double(M$y),as.double(M$w),as.double(M$Ain),as.double(M$bin)
        ,as.double(M$C),as.double(Sa),as.integer(M$off),as.integer(df),as.double(M$sp),
        as.integer(length(M$off)),as.integer(nar),active=active)
  p <- array(o[[2]],length(M$p))
  if (qra.exist) p <- qr.qy(qra,c(rep(0,j),p))
  attr(p,"active") <- if (o$active[1]>0) o$active[1:o$active[1]+1]+1 else integer(0) ## the active set
  p
} ## pcls

all_vars1 <- function(form) {
## version of all.vars that doesn't split up terms like x$y into x and y
  vars <- all.vars(form)
  vn <- all.names(form)
  vn <- vn[vn%in%c(vars,"$","[[")] ## actual variable related names
  if ("[["%in%vn) stop("can't handle [[ in formula")
  ii <- which(vn%in%"$") ## index of '$'
  if (length(ii)) { ## assemble variable names
    vn1 <- if (ii[1]>1) vn[1:(ii[1]-1)]
    go <- TRUE
    k <- 1
    while (go) {
      n <- 2; 
      while(k<length(ii) && ii[k]==ii[k+1]-1) { k <- k + 1;n <- n + 1 }
      vn1 <- c(vn1,paste(vn[ii[k]+1:n],collapse="$"))
      if (k==length(ii)) {
        go <- FALSE
	ind <- if (ii[k]+n<length(vn)) (ii[k]+n+1):length(vn) else rep(0,0) 
      } else {
        k <- k +  1
	ind <- if (ii[k-1]+n<ii[k]-1) (ii[k-1]+n+1):(ii[k]-1) else rep(0,0)
      }
      vn1 <- c(vn1,vn[ind])
    }
  } else vn1 <- vn
  vn1
} ## all_vars1

interpret.gam0 <- function(gf,textra=NULL,extra.special=NULL)
# interprets a gam formula of the generic form:
#   y~x0+x1+x3*x4 + s(x5)+ s(x6,x7) ....
# and returns:
# 1. a model formula for the parametric part: pf (and pfok indicating whether it has terms)
# 2. a list of descriptors for the smooths: smooth.spec
# this is function does the work, and is called by in interpret.gam
# 'textra' is optional text to add to term labels
# 'extra.special' is label of extra smooth within formula.
{ p.env <- environment(gf) # environment of formula
  tf <- terms.formula(gf,specials=c("s","te","ti","t2",extra.special)) # specials attribute indicates which terms are smooth
 
  terms <- attr(tf,"term.labels") # labels of the model terms 
  nt <- length(terms) # how many terms?
  
  if (attr(tf,"response") > 0) {  # start the replacement formulae
    response <- as.character(attr(tf,"variables")[2])
  } else { 
    response <- NULL
  }
  sp <- attr(tf,"specials")$s     # array of indices of smooth terms 
  tp <- attr(tf,"specials")$te    # indices of tensor product terms
  tip <- attr(tf,"specials")$ti   # indices of tensor product pure interaction terms
  t2p <- attr(tf,"specials")$t2   # indices of type 2 tensor product terms
  zp <- if (is.null(extra.special)) NULL else attr(tf,"specials")[[extra.special]]
  off <- attr(tf,"offset") # location of offset in formula

  ## have to translate sp, tp, tip, t2p (zp) so that they relate to terms,
  ## rather than elements of the formula...
  vtab <- attr(tf,"factors") # cross tabulation of vars to terms
  if (length(sp)>0) for (i in 1:length(sp)) {
    ind <- (1:nt)[as.logical(vtab[sp[i],])]
    sp[i] <- ind # the term that smooth relates to
  }
  if (length(tp)>0) for (i in 1:length(tp)) {
    ind <- (1:nt)[as.logical(vtab[tp[i],])]
    tp[i] <- ind # the term that smooth relates to
  } 
  if (length(tip)>0) for (i in 1:length(tip)) {
    ind <- (1:nt)[as.logical(vtab[tip[i],])]
    tip[i] <- ind # the term that smooth relates to
  } 
  if (length(t2p)>0) for (i in 1:length(t2p)) {
    ind <- (1:nt)[as.logical(vtab[t2p[i],])]
    t2p[i] <- ind # the term that smooth relates to
  }
  if (length(zp)>0) for (i in 1:length(zp)) {
    ind <- (1:nt)[as.logical(vtab[zp[i],])]
    zp[i] <- ind # the term that smooth relates to
  } ## re-referencing is complete

  k <- kt <- kti <- kt2 <- ks <- kz <- kp <- 1 # counters for terms in the 2 formulae
  len.sp <- length(sp)
  len.tp <- length(tp)
  len.tip <- length(tip)
  len.t2p <- length(t2p)
  len.zp <- length(zp)
  ns <- len.sp + len.tp + len.tip + len.t2p + len.zp# number of smooths
  pav <- av <- rep("",0)
  smooth.spec <- list()
  #mgcvat <- "package:mgcv" %in% search() ## is mgcv in search path?
  mgcvns <- loadNamespace('mgcv')
  if (nt) for (i in 1:nt) { # work through all terms
    if (k <= ns&&((ks<=len.sp&&sp[ks]==i)||(kt<=len.tp&&tp[kt]==i)||(kz<=len.zp&&zp[kz]==i)||
                  (kti<=len.tip&&tip[kti]==i)||(kt2<=len.t2p&&t2p[kt2]==i))) { # it's a smooth
      ## have to evaluate in the environment of the formula or you can't find variables 
      ## supplied as smooth arguments, e.g. k <- 5;gam(y~s(x,k=k)), fails,
      ## but if you don't specify namespace of mgcv then stuff like 
      ## loadNamespace('mgcv'); k <- 10; mgcv::interpret.gam(y~s(x,k=k)) fails (can't find s)
      ## eval(parse(text=terms[i]),envir=p.env,enclos=loadNamespace('mgcv')) fails??
      ## following may supply namespace of mgcv explicitly if not on search path...
      ## If 's' etc are masked then we can fail even if mgcv on search path, hence paste
      ## of explicit mgcv reference into first attempt...
    
      st <- try(eval(parse(text=paste("mgcv::",terms[i],sep="")),envir=p.env),silent=TRUE)
      if (inherits(st,"try-error")) st <- 
            eval(parse(text=terms[i]),enclos=p.env,envir=mgcvns)
     
      if (!is.null(textra)) { ## modify the labels on smooths with textra
        pos <- regexpr("(",st$lab,fixed=TRUE)[1]
        st$label <- paste(substr(st$label,start=1,stop=pos-1),textra,
                    substr(st$label,start=pos,stop=nchar(st$label)),sep="")
      }
      smooth.spec[[k]] <- smooth.info(st) ## smooth.info supplies any extra specification info for class
      if (ks<=len.sp&&sp[ks]==i) ks <- ks + 1 else # counts s() terms
      if (kt<=len.tp&&tp[kt]==i) kt <- kt + 1 else # counts te() terms
      if (kti<=len.tip&&tip[kti]==i) kti <- kti + 1 else # counts ti() terms
      if (kt2<=len.t2p&&t2p[kt2]==i) kt2 <- kt2 + 1 # counts t2() terms
      else kz <- kz + 1
      k <- k + 1      # counts smooth terms 
    } else {          # parametric
      av[kp] <- terms[i] ## element kp on rhs of parametric
      kp <- kp+1    # counts parametric terms
    }
  }    
  if (!is.null(off)) { ## deal with offset 
    av[kp] <- as.character(attr(tf,"variables")[1+off])
    kp <- kp+1          
  }

  pf <- paste(response,"~",paste(av,collapse=" + "))
  if (attr(tf,"intercept")==0) {
    pf <- paste(pf,"-1",sep="")
    if (kp>1) pfok <- 1 else pfok <- 0
  } else { 
    pfok <- 1;if (kp==1) { 
      pf <- paste(pf,"1"); 
    }
  }

  fake.formula <- pf

  if (length(smooth.spec)>0) 
  for (i in 1:length(smooth.spec)) {
    nt <- length(smooth.spec[[i]]$term)
    ff1 <- paste(smooth.spec[[i]]$term[1:nt],collapse="+")
    fake.formula <- paste(fake.formula,"+",ff1)
    if (smooth.spec[[i]]$by!="NA") {
      fake.formula <- paste(fake.formula,"+",smooth.spec[[i]]$by)
      av <- c(av,smooth.spec[[i]]$term,smooth.spec[[i]]$by)
    } else av <- c(av,smooth.spec[[i]]$term)
  }
  fake.formula <- as.formula(fake.formula,p.env)
  if (length(av)) {
    ## need original variable names (without any transforms) for checking purposes
    ## when predicting. This facilitates...
    pred.formula <- as.formula(paste("~",paste(av,collapse="+")))
    pav <- all.vars(pred.formula) ## trick to strip out 'offset(x)' etc...
    pred.formula <- reformulate(pav,env=p.env) 
  } else  pred.formula <- ~1
  ret <- list(pf=as.formula(pf,p.env),pfok=pfok,smooth.spec=smooth.spec,
            fake.formula=fake.formula,response=response,fake.names=av,
            pred.names=pav,pred.formula=pred.formula)
  #environment(ret$fake.formula)  <- environment(ret$pred.formula) <- p.env	    
  class(ret) <- "split.gam.formula"
  ret
} ## interpret.gam0

interpret.gam <- function(gf,extra.special=NULL) {
## wrapper to allow gf to be a list of formulae or 
## a single formula. This facilitates general penalized 
## likelihood models in which several linear predictors 
## may be involved...
##
## The list syntax is as follows. The first formula must have a response on
## the lhs, rather than labels. For m linear predictors, there 
## must be m 'base formulae' in linear predictor order. lhs labels will 
## be ignored in a base formula. Empty base formulae have '-1' on rhs.
## Further formulae have labels up to m labels 1,...,m on the lhs, in a 
## syntax like this: 3 + 5 ~ s(x), which indicates that the same s(x) 
## should be added to both linear predictors 3 and 5. 
## e.g. A bivariate normal model with common expected values might be
## list(y1~-1,y2~-1,1+2~s(x)), whereas if the second component was contaminated 
## by something else we might have list(y1~-1,y2~s(v)-1,1+2~s(x)) 
## 
## For a list argument, this routine returns a list of split.formula objects 
## with an extra field "lpi" indicating the linear predictors to which each 
## contributes...
  if (is.list(gf)) {
    d <- length(gf)
    p.env <- environment(gf[[1]])
    ## make sure all formulae have a response, to avoid
    ## problems with parametric sub formulae of the form ~1
    #if (length(gf[[1]])<3) stop("first formula must specify a response")
    resp <- gf[[1]][2]
    
    ret <- list()
    pav <- av <- rep("",0)
    nlp <- 0 ## count number of linear predictors (may be different from number of formulae)
    for (i in 1:d) {
      textra <- if (i==1) NULL else paste(".",i-1,sep="") ## modify smooth labels to identify to predictor  

      lpi <- getNumericResponse(gf[[i]]) ## get linear predictors to which this applies, if explicit
      if (length(lpi)==1) warning("single linear predictor indices are ignored")
      if (length(lpi)>0) gf[[i]][[2]] <- NULL else { ## delete l.p. labels from formula response 
        nlp <- nlp + 1;lpi <- nlp ## this is base formula for l.p. number nlp       
      }
      ret[[i]] <- interpret.gam0(gf[[i]],textra,extra.special=extra.special)
      ret[[i]]$lpi <- lpi ## record of the linear predictors to which this applies
      
      ## make sure all parametric formulae have a response, to avoid
      ## problems with parametric sub formulae of the form ~1
      respi <- rep("",0) ## no extra response terms
      if (length(ret[[i]]$pf)==2) { 
        ret[[i]]$pf[3] <- ret[[i]]$pf[2];ret[[i]]$pf[2] <- resp
        respi <- rep("",0)
      } else if (i>1) respi <- ret[[i]]$response ## extra response terms
      av <- c(av,ret[[i]]$fake.names,respi) ## accumulate all required variable names 
      pav <- c(pav,ret[[i]]$pred.names) ## predictors only 
    } 
    av <- unique(av) ## strip out duplicate variable names
    pav <- unique(pav)
    if (length(av)>0) {
      ## work around - reformulate with response = "log(x)" will treat log(x) as a name,
      ## not the call it should be... 
      fff <- formula(paste(ret[[1]]$response,"~ ."))
      ret$fake.formula <- reformulate(av,response=ret[[1]]$response,env=p.env) 
      ret$fake.formula[[2]] <- fff[[2]] ## fix messed up response
    } else ret$fake.formula <- ret[[1]]$fake.formula ## create fake formula containing all variables
    ret$pred.formula <- if (length(pav)>0) reformulate(pav) else ~1 ## predictor only formula
    environment(ret$pred.formula) <- p.env
    ret$response <- ret[[1]]$response 
    ret$nlp <- nlp ## number of linear predictors
    for (i in 1:d) if (max(ret[[i]]$lpi)>nlp||min(ret[[i]]$lpi)<1) stop("linear predictor labels out of range")
    class(ret) <- "split.gam.formula"
    return(ret)
  } else interpret.gam0(gf,extra.special=extra.special)  
} ## interpret.gam


fixDependence <- function(X1,X2,tol=.Machine$double.eps^.5,rank.def=0,strict=FALSE)
# model matrix X2 may be linearly dependent on X1. This 
# routine finds which columns of X2 should be zeroed to 
# fix this. If rank.def>0 then it is taken as the known degree 
# of dependence of X2 on X1 and tol is ignored.
{ qr1 <- qr(X1,LAPACK=TRUE)
  R11 <- abs(qr.R(qr1)[1,1])
  r<-ncol(X1);n<-nrow(X1)
  if (strict) { ## only delete columns of X2 individually dependent on X1
    ## Project columns of X2 into space of X1 and look at difference
    ## to orignal X2 to check for deficiency...  
    QtX2 <- qr.qty(qr1,X2)
    QtX2[-(1:r),] <- 0
    mdiff <- colMeans(abs(X2 - qr.qy(qr1,QtX2)))
    if (rank.def>0) ind <- (1:ncol(X2))[rank(mdiff) <= rank.def] else
    ind <- (1:ncol(X2))[mdiff < R11*tol]
    if (length(ind)<1) ind <- NULL
  } else { ## make X2 full rank given X1
    QtX2 <- qr.qty(qr1,X2)[(r+1):n,] # Q'X2
    qr2 <- qr(QtX2,LAPACK=TRUE)
    R <- qr.R(qr2)
    # now final diagonal block of R may be zero, indicating rank 
    # deficiency.
    r0 <- r <- nrow(R)
    if (rank.def > 0 && rank.def <= nrow(R)) r0 <- r - rank.def else ## degree of rank def known
      while (r0>0 && mean(abs(R[r0:r,r0:r]))< R11*tol) r0 <- r0 -1 ## compute rank def
    r0 <- r0 + 1
    if (r0>r) return(NULL) else
    ind <- qr2$pivot[r0:r] # the columns of X2 to zero in order to get independence
  }
  ind
} ## fixDependence


augment.smX <- function(sm,nobs,np,nc) {
## augments a smooth model matrix with a square root penalty matrix for
## identifiability constraint purposes.
  ns <- length(sm$S) ## number of penalty matrices
  nco <- if (is.null(sm$C)||!is.matrix(sm$C)) 0 else nrow(sm$C)
  if (ns==0&&nc==0) { ## nothing to do
    return(rbind(sm$X,matrix(0,np,ncol(sm$X))))
  }
  if (ns) {
    ind <- colMeans(abs(sm$S[[1]]))!=0
    sqrmaX  <- mean(abs(sm$X[,ind]))^2
    alpha <- sqrmaX/mean(abs(sm$S[[1]][ind,ind]))
    St <- sm$S[[1]]*alpha
    if (ns>1) for (i in 2:ns) { 
      ind <- colMeans(abs(sm$S[[i]]))!=0
      alpha <- sqrmaX/mean(abs(sm$S[[i]][ind,ind]))
      St <- St +  sm$S[[i]]*alpha
    }
    rS <- mroot(St,rank=ncol(St)) ## get sqrt of penalty
    X <- rbind(sm$X,matrix(0,np+nc,ncol(sm$X))) ## create augmented model matrix
    X[nobs+sm$p.ind,] <- t(rS) ## add in
  }
  if (nco) {
    X[nobs+np+1:nco,] <- sm$C/norm(sm$C)
  }
  X ## scaled augmented model matrix
} ## augment.smX

gam.side <- function(sm,Xp,tol=.Machine$double.eps^.5,with.pen=TRUE)
# works through a list of smooths, sm, aiming to identify nested or partially
# nested terms, and impose identifiability constraints on them.
# Xp is the parametric model matrix. It is needed in order to check whether
# there is a constant (or equivalent) in the model. If there is, then this needs 
# to be included when working out side constraints, otherwise dependencies can be 
# missed. 
# Note that with.pen is quite extreme, since you then pretty much only pick
# up dependencies in the null spaces
{ if (!with.pen) { ## check that's possible and reset if not!
    with.pen <- nrow(Xp) < ncol(Xp) + sum(unlist(lapply(sm,function(x) ncol(x$X))))
  }
  m <- length(sm)
  if (m==0) return(sm)
  v.names<-array("",0);maxDim<-1
  for (i in 1:m) { ## collect all term names and max smooth `dim'
    vn <- sm[[i]]$term
    ## need to include by variables in names
    if (sm[[i]]$by!="NA") vn <- paste(vn,sm[[i]]$by,sep="")
    ## need to distinguish levels of factor by variables...
    if (!is.null(sm[[i]]$by.level))  vn <- paste(vn,sm[[i]]$by.level,sep="")
    sm[[i]]$vn <- vn ## use this record to identify variables from now
    v.names <- c(v.names,vn)
    if (sm[[i]]$dim > maxDim) maxDim <- sm[[i]]$dim
  } 
  lv <- length(v.names)   
  v.names <- unique(v.names)
  if (lv == length(v.names)) return(sm) ## no repeats => no nesting

  ## Only get this far if there is nesting.
  ## Need to test for intercept or equivalent in Xp
  intercept <- FALSE
  if (ncol(Xp)) {
    ## first check columns directly...
    if (sum(apply(Xp,2,sd)<.Machine$double.eps^.75)>0) intercept <- TRUE else {
      ## no constant column, so need to check span of Xp...
      f <- rep(1,nrow(Xp))
      ff <- qr.fitted(qr(Xp),f)
      if (max(abs(ff-f))<.Machine$double.eps^.75) intercept <- TRUE 
    }
  }

  sm.id <- as.list(v.names)
  names(sm.id) <- v.names
  for (i in 1:length(sm.id)) sm.id[[i]]<-array(0,0)
  sm.dim <- sm.id
  for (d in 1:maxDim) {
    for (i in 1:m) {
      if (sm[[i]]$dim==d&&sm[[i]]$side.constrain) for (j in 1:d) { ## work through terms
        term<-sm[[i]]$vn[j]
        a <- sm.id[[term]]
        la <- length(a)+1
        sm.id[[term]][la] <- i   ## record smooth i.d. for this variable
        sm.dim[[term]][la] <- d  ## ... and smooth dim.
      }
    }
  }
  ## so now each unique variable name has an associated array of 
  ## the smooths of which it is an argument, arranged in ascending 
  ## order of dimension. Smooths for which side.constrain==FALSE are excluded.
  if (maxDim==1) warning("model has repeated 1-d smooths of same variable.")

  ## Now set things up to enable term specific model matrices to be
  ## augmented with square root penalties, on the fly...
  if (with.pen) {
    k <- 1; nc <- 0
    for (i in 1:m) { ## create parameter indices for each term
      k1 <- k + ncol(sm[[i]]$X) - 1
      sm[[i]]$p.ind <- k:k1
      k <- k1 + 1
      if (!is.null(sm[[i]]$C)&&is.matrix(sm[[i]]$C)) nc <- max(nrow(sm[[i]]$C),nc) ## largest constraint
    }
    np <- k-1 ## number of penalized parameters
  }
  nobs <- nrow(sm[[1]]$X) ## number of observations
  
  for (d in 1:maxDim) { ## work up through dimensions 
    for (i in 1:m) { ## work through smooths
      if (sm[[i]]$dim == d&&sm[[i]]$side.constrain) { ## check for nesting
        if (with.pen) {
	  X1 <- if (intercept) matrix(c(rep(1,nobs),rep(0,np+nc)),nobs+np+nc,1) else
	                       matrix(0,nobs+np+nc,0)
	} else X1 <- matrix(1,nobs,as.integer(intercept))
	X1comp <- rep(0,0) ## list of components of X1 to avoid duplication
        for (j in 1:d) { ## work through variables
          b <- sm.id[[sm[[i]]$vn[j]]] # list of smooths dependent on this variable
          k <- (1:length(b))[b==i] ## locate current smooth in list 
          if (k>1) for (l in 1:(k-1)) if (!b[l] %in% X1comp) { ## collect X columns
           X1comp <- c(X1comp,b[l]) ## keep track of components to avoid adding same one twice
           if (with.pen) { ## need to use augmented model matrix in testing 
              if (is.null(sm[[b[l]]]$Xa)) sm[[b[l]]]$Xa <- augment.smX(sm[[b[l]]],nobs,np,nc)
              X1 <- cbind(X1,sm[[b[l]]]$Xa)
            } else X1 <- cbind(X1,sm[[b[l]]]$X) ## penalties not considered
          }
        } ## Now X1 contains columns for all lower dimensional terms
        if (ncol(X1)==as.integer(intercept)) ind <- NULL else {
          if (with.pen) {
             if (is.null(sm[[i]]$Xa)) sm[[i]]$Xa <- augment.smX(sm[[i]],nobs,np,nc)
             ind <- fixDependence(X1,sm[[i]]$Xa,tol=tol) 
          } else ind <- fixDependence(X1,sm[[i]]$X,tol=tol)        
        }
        ## ... the columns to zero to ensure independence
        if (!is.null(ind)) { 
          sm[[i]]$X <- sm[[i]]$X[,-ind,drop=FALSE]
          ## work through list of penalty matrices, applying constraints...
          nsmS <- length(sm[[i]]$S)
          if (nsmS>0) for (j in nsmS:1) { ## working down so that dropping is painless
            sm[[i]]$S[[j]] <- sm[[i]]$S[[j]][-ind,-ind,drop=FALSE]
            if (sum(sm[[i]]$S[[j]]!=0)==0) rank <- 0 else
            rank <- qr(sm[[i]]$S[[j]],tol=tol,LAPACK=FALSE)$rank
            sm[[i]]$rank[j] <- rank ## replace previous rank with new rank
            if (rank == 0) { ## drop the penalty
              sm[[i]]$rank <- sm[[i]]$rank[-j]
              sm[[i]]$S[[j]] <- NULL
              sm[[i]]$S.scale <- sm[[i]]$S.scale[-j]
              if (!is.null(sm[[i]]$L)) sm[[i]]$L <- sm[[i]]$L[-j,,drop=FALSE]
            }
          } ## penalty matrices finished
          ## Now we need to establish null space rank for the term
          mi <- length(sm[[i]]$S)
          if (mi>0) {
            St <- sm[[i]]$S[[1]]/norm(sm[[i]]$S[[1]],type="F")
            if (mi>1) for (j in 1:mi) St <- St + 
                  sm[[i]]$S[[j]]/norm(sm[[i]]$S[[j]],type="F")
            es <- eigen(St,symmetric=TRUE,only.values=TRUE)
            sm[[i]]$null.space.dim <- sum(es$values<max(es$values)*.Machine$double.eps^.75) 
          } ## rank found

          ## deal with any constraints (e.g. when not pre-absorbed)
	  if (!is.null(sm[[i]]$C)) sm[[i]]$C <- sm[[i]]$C[,-ind,drop=FALSE]
	  if (!is.null(sm[[i]]$Ain)) sm[[i]]$Ain <- sm[[i]]$Ain[,-ind,drop=FALSE]

          if (!is.null(sm[[i]]$L)) {
            ind <- as.numeric(colSums(sm[[i]]$L!=0))!=0
            sm[[i]]$L <- sm[[i]]$L[,ind,drop=FALSE] ## retain only those sps that influence something!
          }

          sm[[i]]$df <- ncol(sm[[i]]$X)
	  ind0 <- attr(sm[[i]],"del.index")
          attr(sm[[i]],"del.index") <- c(ind0,ind)
          ## Now deal with case in which prediction constraints differ from fit constraints
          if (!is.null(sm[[i]]$Xp)) { ## need to get deletion indices under prediction parameterization
            ## Note that: i) it doesn't matter what the identifiability con on X1 is
            ##            ii) the degree of rank deficiency can't be changed by an identifiability con
            if (with.pen) { 
              smi <- sm[[i]]  ## clone smooth 
              smi$X <- smi$Xp ## copy prediction Xp to X slot.
              smi$S <- smi$Sp ## and make sure penalty parameterization matches. 
              Xpa <- augment.smX(smi,nobs,np,nc)
              ind <- fixDependence(X1,Xpa,rank.def=length(ind)) 
            } else ind <- fixDependence(X1,sm[[i]]$Xp,rank.def=length(ind)) 
            sm[[i]]$Xp <- sm[[i]]$Xp[,-ind,drop=FALSE]
            attr(sm[[i]],"del.index") <- c(ind0,ind) ## over-writes original
          }
        }
        sm[[i]]$vn <- NULL
      } ## end if (sm[[i]]$dim == d)
    } ## end i in 1:m loop
  }  
  if (with.pen) for (i in 1:m) { ## remove working variables that were added
    sm[[i]]$p.ind <- NULL
    if (!is.null(sm[[i]]$Xa)) sm[[i]]$Xa <- NULL
  }
  sm
} ## gam.side

clone.smooth.spec <- function(specb,spec) {
## produces a version of base smooth.spec, `specb', but with 
## the variables relating to `spec'. Used by `gam.setup' in handling 
## of linked smooths.
 ## check dimensions same...
 if (specb$dim!=spec$dim) stop("`id' linked smooths must have same number of arguments") 
 ## Now start cloning...
 if (inherits(specb,c("tensor.smooth.spec","t2.smooth.spec"))) { ##`te' or `t2' generated base smooth.spec
    specb$term <- spec$term
    specb$label <- spec$label 
    specb$by <- spec$by
    k <- 1
    for (i in 1:length(specb$margin)) {
      if (is.null(spec$margin)) { ## sloppy user -- have to construct margin info...
         for (j in 1:length(specb$margin[[i]]$term)) {
           specb$margin[[i]]$term[j] <- spec$term[k]
           k <- k + 1
         }
         specb$margin[[i]]$label <- ""
 
      } else { ## second term was at least `te'/`t2', so margin cloning is easy
        specb$margin[[i]]$term <- spec$margin[[i]]$term
        specb$margin[[i]]$label <- spec$margin[[i]]$label
        specb$margin[[i]]$xt <- spec$margin[[i]]$xt
      }
    }

  } else { ## `s' generated case
    specb$term <- spec$term
    specb$label <- spec$label 
    specb$by <- spec$by
    specb$xt <- spec$xt ## don't generally know what's in here => don't clone
  }
  specb ## return clone
} ## clone.smooth.spec


parametricPenalty <- function(pterms,assign,paraPen,sp0) {
## routine to process any penalties on the parametric part of the model.
## paraPen is a list whose items have names corresponding to the 
## term.labels in pterms. Each list item may have named elements 
## L, rank and sp. All other elements should be penalty coefficient matrices.
  S <- list()     ## penalty matrix list
  off <- rep(0,0) ## offset array
  rank <- rep(0,0) ## rank array
  sp <- rep(0,0)    ## smoothing param array
  full.sp.names <- rep("",0) ## names for sp's multiplying penalties (not underlying)
  L <- matrix(0,0,0) 
  k <- 0
  tind <- unique(assign) ## unique term indices
  n.t <- length(tind)
  if (n.t>0) for (j in 1:n.t) if (tind[j]>0) {
    term.label <- attr(pterms[tind[j]],"term.label")
    P <- paraPen[[term.label]] ## get any penalty information for this term
    if (!is.null(P)) { ## then there is information
      ind <- (1:length(assign))[assign==tind[j]] ## index of coefs involved here
      Li <- P$L;P$L <- NULL
      spi <- P$sp;P$sp <- NULL
      ranki <- P$rank;P$rank <- NULL
      ## remaining terms should be penalty matrices...
      np <- length(P)

      if (!is.null(ranki)&&length(ranki)!=np) stop("`rank' has wrong length in `paraPen'") 
      if (np) for (i in 1:np) { ## unpack penalty matrices, offsets and ranks
        k <- k + 1
        S[[k]] <- P[[i]]
        off[k] <- min(ind) ## index of first coef penalized by this term
        if ( ncol(P[[i]])!=nrow(P[[i]])||nrow(P[[i]])!=length(ind)) stop(" a parametric penalty has wrong dimension")
        if (is.null(ranki)) {
          ev <- eigen(S[[k]],symmetric=TRUE,only.values=TRUE)$values
          rank[k] <- sum(ev>max(ev)*.Machine$double.eps*10) ## estimate rank
        } else rank[k] <- ranki[i]
      }
      ## now deal with L matrices
      if (np) { ## only do this stuff if there are any penalties!
        if (is.null(Li)) Li <- diag(np)
        if (nrow(Li)!=np) stop("L has wrong dimension in `paraPen'")
        L <- rbind(cbind(L,matrix(0,nrow(L),ncol(Li))),
                   cbind(matrix(0,nrow(Li),ncol(L)),Li))
        ind <- (length(sp)+1):(length(sp)+ncol(Li))
        ind2 <- (length(sp)+1):(length(sp)+nrow(Li)) ## used to produce names for full sp array
        if (is.null(spi)) {
          sp[ind] <- -1 ## auto-initialize
        } else {
          if (length(spi)!=ncol(Li)) stop("`sp' dimension wrong in `paraPen'")
          sp[ind] <- spi
        }
        ## add smoothing parameter names....
        if (length(ind)>1) names(sp)[ind] <- paste(term.label,ind-ind[1]+1,sep="") 
        else names(sp)[ind] <- term.label
        
        if (length(ind2)>1) full.sp.names[ind2] <- paste(term.label,ind2-ind2[1]+1,sep="") 
        else full.sp.names[ind2] <- term.label
      }
    } ## end !is.null(P)  
  } ## looped through all terms
  if (k==0) return(NULL)
  if (!is.null(sp0)) {
    if (length(sp0)<length(sp)) stop("`sp' too short")
    sp0 <- sp0[1:length(sp)]
    sp[sp<0] <- sp0[sp<0]
  }
  ## S is list of penalty matrices, off[i] is index of first coefficient penalized by each S[[i]]
  ## sp is array of underlying smoothing parameter (-ve to estimate), L is matrix mapping log
  ## underlying smoothing parameters to log smoothing parameters, rank[i] is the rank of S[[i]].
  list(S=S,off=off,sp=sp,L=L,rank=rank,full.sp.names=full.sp.names)
} ## parametricPenalty

getNumericResponse <- function(form) {
## takes a formula for which the lhs contains numbers, but no variable 
## names, and returns an array of those numbers. For example if 'form' 
## is '1+26~s(x)', this will return the numeric vector c(1,26). 
## A zero length vector is returned if the lhs contains no numbers,
## or contains variable names.  
## This is useful for setting up models in which
## multiple linear predictors share terms. The lhs numbers can then 
## indicate which linear predictors the rhs will contribute to.

  ## if the response contains variables or there is no
  ## response then return nothing...

  if (length(form)==2||length(all.vars(form[[2]]))>0) return(rep(0,0))

  ## deparse turns lhs into a string; strsplit extracts the characters 
  ## corresponding to numbers; unlist deals with the fact that deparse 
  ## will split long lines resulting in multiple list items from 
  ## strsplit; as.numeric converts the numbers; na.omit drops NAs
  ## resulting from "" elements; unique & round are obvious... 

  round(unique(na.omit(as.numeric(unlist(strsplit(deparse(form[[2]]), "[^0-9]+"))))))  

} ## getNumericResponse

olid <- function(X,nsdf,pstart,flpi,lpi) {
## X is a model matrix, made up of nf=length(nsdf) column blocks.
## The ith block starts at column pstart[i] and its first nsdf[i]
## columns are unpenalized. X is used to define nlp=length(lpi)
## linear predictors. lpi[[i]] gives the columns of X used in the 
## ith linear predictor. flpi[j] gives the linear predictor(s)
## to which the jth block of X belongs. The problem is that the 
## unpenalized blocks need not be identifiable when used in combination. 
## This function returns a vector dind of columns of X to drop for 
## identifiability, along with modified lpi, pstart and nsdf vectors.
  nlp <- length(lpi) ## number of linear predictors
  n <- nrow(X) 
  nf <- length(nsdf) ## number of formulae blocks
  Xp <- matrix(0,n*nlp,sum(nsdf))
  start <- 1
  ii <- 1:n
  tind <- rep(0,0) ## complete index of all parametric columns in X
  ## create a block matrix, Xp, with the same identifiability properties as
  ## unpenalized part of model...
  for (i in 1:nf) {
    stop <- start - 1 + nsdf[i]
    if (stop>=start) {
      ind <- pstart[i] + 1:nsdf[i] - 1
      for (k in flpi[[i]]) {
        Xp[ii+(k-1)*n,start:stop] <- X[,ind]
      }
      tind <- c(tind,ind)
      start <- start + nsdf[i]
    }
  }
  ## rank deficiency of Xp will reveal number of redundant parametric 
  ## terms, and a pivoted QR will reveal which to drop to restore
  ## full rank...
  qrx <- qr(Xp,LAPACK=TRUE,tol=0.0) ## unidentifiable columns get pivoted to final cols
  r <- Rrank(qr.R(qrx)) ## get rank from R factor of pivoted QR
  if (r==ncol(Xp)) { ## full rank, all fine, drop nothing
    dind <- rep(0,0)
  } else { ## reduced rank, drop some columns
    dind <- tind[sort(qrx$pivot[(r+1):ncol(X)],decreasing=TRUE)] ## columns to drop
    ## now we need to adjust nsdf, pstart and lpi
    for (d in dind) { ## working down through drop indices
      ## following commented out code is useful should it ever prove necessary to 
      ## adjust pstart and nsdf, but at present these are only used in prediction, 
      ## and it is cleaner to leave them unchanged, and simply drop using dind during prediction.
      #k <- if (d>=pstart[nf]) nlp else which(d >= pstart[1:(nf-1)] & d < pstart[2:nf])
      #nsdf[k] <- nsdf[k] - 1 ## one less unpenalized column in this block
      #if (k<nf) pstart[(k+1):nf] <-  pstart[(k+1):nf] - 1 ## later block starts move down 1 
      for (i in 1:nlp) { 
        k <- which(d == lpi[[i]])
        if (length(k)>0) lpi[[i]] <- lpi[[i]][-k] ## drop row
        k <- which(lpi[[i]]>d)
        if (length(k)>0) lpi[[i]][k] <- lpi[[i]][k] - 1 ## close up
      }
    } ## end of drop index loop
  }
  list(dind=dind,lpi=lpi) ##,pstart=pstart,nsdf=nsdf)
} ## olid


gam.setup.list <- function(formula,pterms,
                    data=stop("No data supplied to gam.setup"),knots=NULL,sp=NULL,
                    min.sp=NULL,H=NULL,absorb.cons=TRUE,sparse.cons=0,select=FALSE,idLinksBases=TRUE,
                    scale.penalty=TRUE,paraPen=NULL,gamm.call=FALSE,drop.intercept=NULL,apply.by=TRUE,modCon=0) {
## version of gam.setup for when gam is called with a list of formulae, 
## specifying several linear predictors...
## key difference to gam.setup is an attribute to the model matrix, "lpi", which is a list
## of column indices for each linear predictor 
  if (!is.null(paraPen)) stop("paraPen not supported for multi-formula models")
#  if (!absorb.cons) stop("absorb.cons must be TRUE for multi-formula models")
  d <- length(pterms) ## number of formulae
  if (is.null(drop.intercept)) drop.intercept <- rep(FALSE, d)
  if (length(drop.intercept) != d) stop("length(drop.intercept) should be equal to number of model formulas")

  lp.overlap <- if (formula$nlp<d) TRUE else FALSE ## predictors share terms

  G <- gam.setup(formula[[1]],pterms[[1]],
              data,knots,sp,min.sp,H,absorb.cons,sparse.cons,select,
              idLinksBases,scale.penalty,paraPen,gamm.call,drop.intercept[1],apply.by=apply.by,list.call=TRUE,modCon=modCon)
  G$pterms <- pterms
  
  G$offset <- list(G$offset)
  #G$contrasts <- list(G$contrasts)
  G$xlevels <- list(G$xlevels)
  G$assign <- list(G$assign)
  used.sp <- length(G$lsp0)
  if (!is.null(sp)&&used.sp>0) sp <- sp[-(1:used.sp)] ## need to strip off already used sp's
  if (!is.null(min.sp)&&nrow(G$L)>0) min.sp <- min.sp[-(1:nrow(G$L))]  

  ## formula[[1]] always relates to the base formula of the first linear predictor...

  flpi <- lpi <- list()
  for (i in 1:formula$nlp) lpi[[i]] <- rep(0,0)
  lpi[[1]] <- 1:ncol(G$X) ## lpi[[j]] is index of cols for jth linear predictor 
  flpi[[1]] <- formula[[1]]$lpi ## used in identifiability testing by olid, later  

  pof <- ncol(G$X) ## counts the model matrix columns produced so far
  pstart <- rep(0,d) ## indexes where parameteric columns start in each formula block of X
  pstart[1] <- 1
  if (d>1) for (i in 2:d) {
    if (is.null(formula[[i]]$response)) {  ## keep gam.setup happy
      formula[[i]]$response <- formula$response 
      mv.response <- FALSE
    } else mv.response <- TRUE
    #spind <- if (is.null(sp)) 1 else (length(G$S)+1):length(sp)
    formula[[i]]$pfok <- 1 ## empty formulae OK here!
    um <- gam.setup(formula[[i]],pterms[[i]],
              data,knots,sp,min.sp,#sp[spind],min.sp[spind],
	      H,absorb.cons,sparse.cons,select,
              idLinksBases,scale.penalty,paraPen,gamm.call,drop.intercept[i],apply.by=apply.by,list.call=TRUE,modCon=modCon)
    used.sp <- length(um$lsp0)	      
    if (!is.null(sp)&&used.sp>0) sp <- sp[-(1:used.sp)] ## need to strip off already used sp's
    if (!is.null(min.sp)&&nrow(um$L)>0) min.sp <- min.sp[-(1:nrow(um$L))]  

    flpi[[i]] <- formula[[i]]$lpi
    for (j in formula[[i]]$lpi) { ## loop through all l.p.s to which this term contributes
      lpi[[j]] <- c(lpi[[j]],pof + 1:ncol(um$X)) ## add these cols to lpi[[j]]
      ##lpi[[i]] <- pof + 1:ncol(um$X) ## old code
    }
    if (mv.response) G$y <- cbind(G$y,um$y)
    if (i>formula$nlp&&!is.null(um$offset)) {
      stop("shared offsets not allowed")
    }
    G$offset[[i]] <- um$offset
    #G$contrasts[[i]] <- um$contrasts
    if (!is.null(um$contrasts)) G$contrasts <- c(G$contrasts,um$contrasts)
    G$xlevels[[i]] <- um$xlevels
    G$assign[[i]] <- um$assign
    G$rank <- c(G$rank,um$rank)
    pstart[i] <- pof+1

    if (!is.null(um$C)||!is.null(G$C)) { ## extend any constraint matrix
      if (is.null(G$C)) {
        G$C <- matrix(0,0,ncol(G$X)); G$d <- numeric(0)
      }	
      if (is.null(um$C)) { 
        um$C <- matrix(0,0,ncol(um$X)); um$d <- numeric(0)
      }	
      G$C <- rbind(cbind(G$C,matrix(0,nrow(G$C),ncol(um$C))),
                   cbind(matrix(0,nrow(um$C),ncol(G$C)),um$C))
      G$d <- c(G$d,um$d)		   
    }
    
    G$X <- cbind(G$X,um$X) ## extend model matrix
    
    ## deal with the smooths...
    k <- G$m
    if (um$m) for (j in 1:um$m) {
      um$smooth[[j]]$first.para <- um$smooth[[j]]$first.para + pof
      um$smooth[[j]]$last.para <- um$smooth[[j]]$last.para + pof
      k <- k + 1 
      G$smooth[[k]] <- um$smooth[[j]]
    }
    ## L, S and off...
    ks <- length(G$S)
    M <- length(um$S)
 
    if (!is.null(um$L)||!is.null(G$L)) {
      if (is.null(G$L)) G$L <- diag(1,nrow=ks)
      if (is.null(um$L)) um$L <- diag(1,nrow=M)
      G$L <- rbind(cbind(G$L,matrix(0,nrow(G$L),ncol(um$L))),cbind(matrix(0,nrow(um$L),ncol(G$L)),um$L))
    }

 
    G$off <- c(G$off,um$off+pof)
    if (M) for (j in 1:M) {
      ks <- ks + 1
      G$S[[ks]] <- um$S[[j]]
    }
 
    G$m <- G$m + um$m ## number of smooths
    ##G$nsdf <- G$nsdf + um$nsdf ## or list??
    G$nsdf[i] <- um$nsdf
    if (!is.null(um$P)||!is.null(G$P)) {
      if (is.null(G$P)) G$P <- diag(1,nrow=pof)
      k <- ncol(um$X)
      if (is.null(um$P)) um$P <- diag(1,nrow=k)
      G$P <- rbind(cbind(G$P,matrix(0,pof,k)),cbind(matrix(0,k,pof),um$P))
    }
    G$cmX <- c(G$cmX,um$cmX)
    if (um$nsdf>0) um$term.names[1:um$nsdf] <- paste(um$term.names[1:um$nsdf],i-1,sep=".")
    G$term.names <- c(G$term.names,um$term.names)
    G$lsp0 <- c(G$lsp0,um$lsp0)
    G$sp <- c(G$sp,um$sp)
    pof <- ncol(G$X)
  } ## formula loop end

  ## If there is overlap then there is a danger of lack of identifiability of the 
  ## parameteric terms, especially if there are factors present in shared components. 
  ## The following code deals with this possibility... 
  if (lp.overlap) {
    rt <- olid(G$X,G$nsdf,pstart,flpi,lpi)
    if (length(rt$dind)>0) { ## then columns have to be dropped
      warning("dropping unidentifiable parametric terms from model",call.=FALSE)
      G$X <- G$X[,-rt$dind,drop=FALSE] ## drop cols
      if (!is.null(G$C)) G$C <- G$C[,-rt$dind,drop=FALSE]
      G$cmX <- G$cmX[-rt$dind]
      G$term.names <- G$term.names[-rt$dind]
      ## adjust indexing in smooth list, noting that coefs of smooths 
      ## are never dropped by dind 
      for (i in 1:length(G$smooth)) {
        k <- sum(rt$dind < G$smooth[[i]]$first.para)
        G$smooth[[i]]$first.para <- G$smooth[[i]]$first.para - k
        G$smooth[[i]]$last.para <- G$smooth[[i]]$last.para - k
      }
      for (i in 1:length(G$off)) G$off[i] <- G$off[i] - sum(rt$dind < G$off[i])
      ## replace various indices with updated versions...
      # pstart <- rt$pstart; G$nsdf <- rt$nsdf ## these two only needed in predict.gam - cleaner to leave unchanged
      lpi <- rt$lpi
      attr(G$nsdf,"drop.ind") <- rt$dind ## store drop index
    } 
  }
  attr(lpi,"overlap") <- lp.overlap
  attr(G$X,"lpi") <- lpi
  attr(G$nsdf,"pstart") <- pstart ##unlist(lapply(lpi,min))

  ## assemble a global indicator array for non-linear parameters... 
  G$g.index <- rep(FALSE,ncol(G$X))
  n.sp0 <- 0
  if (length(G$smooth)) for (i in 1:length(G$smooth)) {
    if (!is.null(G$smooth[[i]]$g.index)) G$g.index[G$smooth[[i]]$first.para:G$smooth[[i]]$last.para] <- G$smooth[[i]]$g.index
    n.sp <- length(G$smooth[[i]]$S)
    if (n.sp) {
      G$smooth[[i]]$first.sp <- n.sp0 + 1
      n.sp0 <- G$smooth[[i]]$last.sp <- n.sp0 + n.sp
    }
  }  
  if (!any(G$g.index)) G$g.index <- NULL  

  G
} ## gam.setup.list



gam.setup <- function(formula,pterms,
                     data=stop("No data supplied to gam.setup"),knots=NULL,sp=NULL,
                    min.sp=NULL,H=NULL,absorb.cons=TRUE,sparse.cons=0,select=FALSE,idLinksBases=TRUE,
                    scale.penalty=TRUE,paraPen=NULL,gamm.call=FALSE,drop.intercept=FALSE,
                    diagonal.penalty=FALSE,apply.by=TRUE,list.call=FALSE,modCon=0) 
## set up the model matrix, penalty matrices and auxilliary information about the smoothing bases
## needed for a gam fit.
## elements of returned object:
## * m - number of smooths
## * min.sp - minimum smoothing parameters
## * H supplied H matrix
## * pearson.extra, dev.extra, n.true --- entries to hold these quantities
## * pterms - terms object for parametric terms
## * intercept TRUE if intercept present
## * offset - the model offset
## * nsdf - number of strictly parameteric coefs
## * contrasts 
## * xlevels - records levels of factors
## * assign - indexes which parametric model matrix columns map to which term in pterms
## * smooth - list of smooths
## * S - penalties (non-zero block only)
## * off - first coef penalized by each element of S
## * cmX - col mean of X
## * P - maps parameters in fit constraint parameterization to those in prediction parameterization
## * X - model matrix
## * sp
## * rank
## * n.paraPen
## * L 
## * lsp0
## * y - response
## * C - constraint matrix - only if absorb.cons==FALSE
## * n - dim(y)
## * w - weights
## * term.names
## * nP
{ # split the formula if the object being passed is a formula, otherwise it's already split

  if (inherits(formula,"split.gam.formula")) split <- formula else
  if (inherits(formula,"formula")) split <- interpret.gam(formula) 
  else stop("First argument is no sort of formula!") 
  
  if (length(split$smooth.spec)==0) {
    if (split$pfok==0) stop("You've got no model....")
    m <- 0
  } else  m <- length(split$smooth.spec) # number of smooth terms
  
  G <- list(m=m,min.sp=min.sp,H=H,pearson.extra=0,
            dev.extra=0,n.true=-1,pterms=pterms) ## dev.extra gets added to deviance if REML/ML used in gam.fit3
  
  if (is.null(attr(data,"terms"))) # then data is not a model frame
  mf <- model.frame(split$pf,data,drop.unused.levels=FALSE) # must be false or can end up with wrong prediction matrix!
  else mf <- data # data is already a model frame

  G$intercept <-  attr(attr(mf,"terms"),"intercept")>0

  ## get any model offset. Complicated by possibility of offsets in multiple formulae...
  if (list.call) {
    offi <- attr(pterms,"offset")
    if (!is.null(offi)) {
      G$offset <- mf[[names(attr(pterms,"dataClasses"))[offi]]]
    }
  } else G$offset <- model.offset(mf)   # get any model offset including from offset argument
  
  if (!is.null(G$offset))  G$offset <- as.numeric(G$offset) 

  # construct strictly parametric model matrix.... 
  if (drop.intercept) attr(pterms,"intercept") <- 1 ## ensure there is an intercept to drop
  X <- model.matrix(pterms,mf)
  if (drop.intercept) { ## some extended families require intercept to be dropped 
    xat <- attributes(X);ind <- xat$assign>0 ## index of non intercept columns 
    X <- X[,ind,drop=FALSE] ## some extended families need to drop intercept
    xat$assign <- xat$assign[ind];xat$dimnames[[2]]<-xat$dimnames[[2]][ind];
    xat$dim[2] <- xat$dim[2]-1;attributes(X) <- xat
    G$intercept <- FALSE
  } 
  rownames(X) <- NULL ## save memory
  
  G$nsdf <- ncol(X)
  G$contrasts <- attr(X,"contrasts")
  G$xlevels <- .getXlevels(pterms,mf)
  G$assign <- attr(X,"assign") # used to tell which coeffs relate to which pterms

  ## now deal with any user supplied penalties on the parametric part of the model...
  PP <- parametricPenalty(pterms,G$assign,paraPen,sp)
  if (!is.null(PP)) { ## strip out supplied sps already used
    ind <- 1:length(PP$sp)
    if (!is.null(sp)) sp <- sp[-ind]
    if (!is.null(min.sp)) { 
      PP$min.sp <- min.sp[ind]
      min.sp <- min.sp[-ind]
    } 
  }
  
  # next work through smooth terms (if any) extending model matrix.....
  
  G$smooth <- list()
  G$S <- list()
 
  if (gamm.call) { ## flag that this is a call from gamm --- some smoothers need to know!
    if (m>0) for (i in 1:m) attr(split$smooth.spec[[i]],"gamm") <- TRUE
  }

  if (m>0 && idLinksBases) { ## search smooth.spec[[]] for terms linked by common id's
    id.list <- list() ## id information list
    for (i in 1:m) if (!is.null(split$smooth.spec[[i]]$id)) {
      id <- as.character(split$smooth.spec[[i]]$id)
      if (length(id.list)&&id%in%names(id.list)) { ## it's an existing id
        ni <- length(id.list[[id]]$sm.i) ## number of terms so far with this id
        id.list[[id]]$sm.i[ni+1] <- i    ## adding smooth.spec index to this id's list
        ## clone smooth.spec from base smooth spec....
        base.i <- id.list[[id]]$sm.i[1]
         
        split$smooth.spec[[i]] <- clone.smooth.spec(split$smooth.spec[[base.i]],
                                                      split$smooth.spec[[i]])
        
        ## add data for this term to the data list for basis setup...
        temp.term <- split$smooth.spec[[i]]$term
       
        ## note cbind deliberate in next line, as construction will handle matrix argument 
        ## correctly... 
        for (j in 1:length(temp.term)) id.list[[id]]$data[[j]] <- cbind(id.list[[id]]$data[[j]],
                                                          get.var(temp.term[j],data,vecMat=FALSE))
       
       } else { ## new id
        id.list[[id]] <- list(sm.i=i) ## start the array of indices of smooths with this id
        id.list[[id]]$data <- list()
        ## need to collect together all data for which this basis will be used,
        ## for basis setup...
        term <- split$smooth.spec[[i]]$term
        for (j in 1:length(term)) id.list[[id]]$data[[j]] <- get.var(term[j],data,vecMat=FALSE)
      } ## new id finished
    }
  } ## id.list complete

  G$off<-array(0,0)
  first.para<-G$nsdf+1
  sm <- list()
  newm <- 0
  if (m>0) for (i in 1:m) {
    # idea here is that terms are set up in accordance with information given in split$smooth.spec
    # appropriate basis constructor is called depending on the class of the smooth
    # constructor returns penalty matrices model matrix and basis specific information
  
    id <- split$smooth.spec[[i]]$id
    if (is.null(id)||!idLinksBases) { ## regular evaluation
      sml <- smoothCon(split$smooth.spec[[i]],data,knots,absorb.cons,scale.penalty=scale.penalty,
                       null.space.penalty=select,sparse.cons=sparse.cons,
                       diagonal.penalty=diagonal.penalty,apply.by=apply.by,modCon=modCon) 
    } else { ## it's a smooth with an id, so basis setup data differs from model matrix data
      names(id.list[[id]]$data) <- split$smooth.spec[[i]]$term ## give basis data suitable names
      sml <- smoothCon(split$smooth.spec[[i]],id.list[[id]]$data,knots,
                       absorb.cons,n=nrow(data),dataX=data,scale.penalty=scale.penalty,
                       null.space.penalty=select,sparse.cons=sparse.cons,
                       diagonal.penalty=diagonal.penalty,apply.by=apply.by,modCon=modCon)
    }
    #for (j in 1:length(sml)) {
    #  newm <- newm + 1
    #  sm[[newm]] <- sml[[j]]
    #}
    ind <- 1:length(sml)
    sm[ind+newm] <- sml[ind]
    newm <- newm + length(sml)
  }
  
  G$m <- m <- newm ## number of actual smooths

  ## at this stage, it is neccessary to impose any side conditions required
  ## for identifiability
  if (m>0) { 
    sm <- gam.side(sm,X,tol=.Machine$double.eps^.5)
    if (!apply.by) for (i in 1:length(sm)) { ## restore any by-free model matrices
      if (!is.null(sm[[i]]$X0)) { ## there is a by-free matrix to restore 
        ind <- attr(sm[[i]],"del.index") ## columns, if any to delete
        sm[[i]]$X <- if (is.null(ind)) sm[[i]]$X0 else sm[[i]]$X0[,-ind,drop=FALSE] 
      }
    }
  }

  ## The matrix, L, mapping the underlying log smoothing parameters to the
  ## log of the smoothing parameter multiplying the S[[i]] must be
  ## worked out...
  idx <- list() ## idx[[id]]$c contains index of first col in L relating to id
  L <- matrix(0,0,0)
  lsp.names <- sp.names <- rep("",0) ## need a list of names to identify sps in global sp array
  if (m>0) for (i in 1:m) {
    id <- sm[[i]]$id
    ## get the L matrix for this smooth...
    length.S <- if (is.null(sm[[i]]$updateS)) length(sm[[i]]$S) else sm[[i]]$n.sp ## deals with possibility of non-linear penalty
    Li <- if (is.null(sm[[i]]$L)) diag(length.S) else sm[[i]]$L 
     
    if (length.S > 0) { ## there are smoothing parameters to name
       if (length.S == 1) lspn <- sm[[i]]$label else {
          Sname <- names(sm[[i]]$S)
          lspn <- if (is.null(Sname)) paste(sm[[i]]$label,1:length.S,sep="") else
                  paste(sm[[i]]$label,Sname,sep="") ## names for all sp's
       }
       spn <- lspn[1:ncol(Li)] ## names for actual working sps
    }

    ## extend the global L matrix...
    if (is.null(id)||is.null(idx[[id]])) { ## new `id'     
      if (!is.null(id)) { ## create record in `idx'
        idx[[id]]$c <- ncol(L)+1   ## starting column in L for this `id'
        idx[[id]]$nc <- ncol(Li)   ## number of columns relating to this `id'
      }
      L <- rbind(cbind(L,matrix(0,nrow(L),ncol(Li))),
                 cbind(matrix(0,nrow(Li),ncol(L)),Li))
      if (length.S > 0) { ## there are smoothing parameters to name
        sp.names <- c(sp.names,spn) ## extend the sp name vector
        lsp.names <- c(lsp.names,lspn) ## extend full.sp name vector
      }
    } else { ## it's a repeat id => shares existing sp's
      L0 <- matrix(0,nrow(Li),ncol(L))
      if (ncol(Li)>idx[[id]]$nc) {
        stop("Later terms sharing an `id' can not have more smoothing parameters than the first such term")
      }
      L0[,idx[[id]]$c:(idx[[id]]$c+ncol(Li)-1)] <- Li
      L <- rbind(L,L0)
      if (length.S > 0) { ## there are smoothing parameters to name
        lsp.names <- c(lsp.names,lspn) ## extend full.sp name vector
      }
    }
  }

  ## create the model matrix...

  Xp <- NULL ## model matrix under prediction constraints, if given
  if (m>0) for (i in 1:m) {
    n.para <- ncol(sm[[i]]$X)
    # define which elements in the parameter vector this smooth relates to....
    sm[[i]]$first.para<-first.para     
    first.para <- first.para+n.para
    sm[[i]]$last.para <- first.para-1
    ## termwise offset handling ...
    Xoff <- attr(sm[[i]]$X,"offset")
    if (!is.null(Xoff)) { 
      if (is.null(G$offset)) G$offset <- Xoff
      else G$offset <- G$offset + Xoff
    }
    ## model matrix accumulation ...
    
    ## alternative version under alternative constraint first (prediction only)
    if (is.null(sm[[i]]$Xp)) {
      if (!is.null(Xp)) Xp <- cbind2(Xp,sm[[i]]$X)
    } else { 
      if (is.null(Xp)) Xp <- X
      Xp <- cbind2(Xp,sm[[i]]$Xp);sm[[i]]$Xp <- NULL
    }
    ## now version to use for fitting ...
    X <- cbind2(X,sm[[i]]$X);sm[[i]]$X<-NULL
   
    G$smooth[[i]] <- sm[[i]]   
  }

  if (is.null(Xp)) {
    G$cmX <- colMeans(X) ## useful for componentwise CI construction 
  } else {
    G$cmX <- colMeans(Xp)
    ## transform from fit params to prediction params...
    ## G$P <- qr.coef(qr(Xp),X) ## old code assumes always full rank!!
    
    qrx <- qr(Xp,LAPACK=TRUE)
    R <- qr.R(qrx)
    p <- ncol(R)
    rank <- Rrank(R) ## rank of Xp/R    
    QtX <- qr.qty(qrx,X)[1:rank,]
    if (rank<p) { ## rank deficient  
      R <- R[1:rank,]
      qrr <- qr(t(R),tol=0)
      R <- qr.R(qrr)
      G$P <- forwardsolve(t(R),QtX)
    } else {
      G$P <- backsolve(R,QtX)
    }
    if (rank<p) {
      G$P <- qr.qy(qrr,rbind(G$P,matrix(0,p-rank,p)))
    }
    G$P[qrx$pivot,] <- G$P
  }
  ## cmX relates to computation of CIs incorportating uncertainty about the mean
  ## It may make more sense to incorporate all uncertainty about the mean,
  ## rather than just the uncertainty in the fixed effects mean. This means
  ## incorporating the mean of random effects and unconstrained smooths. Hence
  ## comment out the following.
  #if (G$nsdf>0) G$cmX[-(1:G$nsdf)] <- 0 ## zero the smooth parts here 
  #else G$cmX <- G$cmX * 0
  G$X <- X;rm(X)
  n.p <- ncol(G$X) 
  # deal with penalties


  ## min.sp must be length nrow(L) to make sense
  ## sp must be length ncol(L) --- need to partition
  ## L into columns relating to free log smoothing parameters,
  ## and columns, L0, corresponding to values supplied in sp.
  ## lsp0 = L0%*%log(sp[sp>=0]) [need to fudge sp==0 case by
  ## setting log(0) to log(effective zero) computed case-by-case]

  ## following deals with supplied and estimated smoothing parameters...
  ## first process the `sp' array supplied to `gam'...
  
  if (!is.null(sp)) { # then user has supplied fixed smoothing parameters
   ok <- TRUE 
   if (length(sp) < ncol(L)) { 
      warning("Supplied smoothing parameter vector is too short - ignored.")
      ok <- FALSE
    }
    if (sum(is.na(sp))) { 
      warning("NA's in supplied smoothing parameter vector - ignoring.")
      ok <- FALSE
    }
  } else ok <- FALSE
  G$sp <- if (ok) sp[1:ncol(L)] else rep(-1,ncol(L))
  
  names(G$sp) <- sp.names

  ## now work through the smooths searching for any `sp' elements
  ## supplied in `s' or `te' terms.... This relies on `idx' created 
  ## above...
  
  k <- 1 ## current location in `sp' array
  if (m>0) for (i in 1:m) {
    id <- sm[[i]]$id
    if (is.null(sm[[i]]$L)) Li <- diag(length(sm[[i]]$S)) else Li <- sm[[i]]$L 
    if (is.null(id)) { ## it's a smooth without an id
      spi <- sm[[i]]$sp
      if (!is.null(spi)) { ## sp supplied in `s' or `te'
        if (length(spi)!=ncol(Li)) stop("incorrect number of smoothing parameters supplied for a smooth term")
        G$sp[k:(k+ncol(Li)-1)] <- spi
      }       
      k <- k + ncol(Li) 
    } else { ## smooth has an id
      spi <- sm[[i]]$sp
      if (is.null(idx[[id]]$sp.done)) { ## not already dealt with these sp's
        if (!is.null(spi)) { ## sp supplied in `s' or `te'
          if (length(spi)!=ncol(Li)) stop("incorrect number of smoothing parameters supplied for a smooth term")
          G$sp[idx[[id]]$c:(idx[[id]]$c+idx[[id]]$nc-1)] <- spi
        }
        idx[[id]]$sp.done <- TRUE ## only makes sense to use supplied `sp' from defining term
        k <- k + idx[[id]]$nc 
      }
    }
  } ## finished processing `sp' vectors supplied in `s' or `te' terms

  ## copy initial sp's back into smooth objects, so there is a record of
  ## fixed and free...
  k <- 1 
  if (length(idx)) for (i in 1:length(idx)) idx[[i]]$sp.done <- FALSE
  if (m>0) for (i in 1:m) { ## work through all smooths
    id <- sm[[i]]$id 
    if (!is.null(id)) { ## smooth with id
      if (idx[[id]]$nc>0) { ## only copy if there are sp's
        G$smooth[[i]]$sp <- G$sp[idx[[id]]$c:(idx[[id]]$c+idx[[id]]$nc-1)]
      }   
      if (!idx[[id]]$sp.done) { ## only update k on first encounter with this smooth
        idx[[id]]$sp.done <- TRUE
        k <- k + idx[[id]]$nc
      }
    
    } else { ## no id, just work through sp 
      if (is.null(sm[[i]]$L)) nc <- length(sm[[i]]$S) else nc <- ncol(sm[[i]]$L)
      if (nc>0) G$smooth[[i]]$sp <- G$sp[k:(k+nc-1)]
      k <- k + nc
    }
  } ## now all elements of G$smooth have a record of initial sp. 


  if (!is.null(min.sp)) { # then minimum s.p.'s supplied
    if (length(min.sp)<nrow(L)) stop("length of min.sp is wrong.")
    if (nrow(L)>0) min.sp <- min.sp[1:nrow(L)]
    if (sum(is.na(min.sp))) stop("NA's in min.sp.")
    if (sum(min.sp<0)) stop("elements of min.sp must be non negative.")
  }

  k.sp <- 0 # count through sp and S
  G$rank <- array(0,0)
  if (m>0) for (i in 1:m) {
    sm<-G$smooth[[i]]
    if (length(sm$S)>0)
    for (j in 1:length(sm$S)) {  # work through penalty matrices
      k.sp <- k.sp+1
      G$off[k.sp] <- sm$first.para 
      G$S[[k.sp]] <- sm$S[[j]]
      if (!is.null(sm$C)) attr(G$S[[k.sp]],"C") <- sm$C 
      G$rank[k.sp]<-sm$rank[j]
      if (!is.null(min.sp)) {
        if (is.null(H)) H<-matrix(0,n.p,n.p)
        H[sm$first.para:sm$last.para,sm$first.para:sm$last.para] <-
        H[sm$first.para:sm$last.para,sm$first.para:sm$last.para]+min.sp[k.sp]*sm$S[[j]] 
      }           
    } 
  }
 
  ## need to modify L, lsp.names, G$S, G$sp, G$rank and G$off to include any penalties
  ## on parametric stuff, at this point....
  if (!is.null(PP)) { ## deal with penalties on parametric terms
    L <- rbind(cbind(L,matrix(0,nrow(L),ncol(PP$L))),
                 cbind(matrix(0,nrow(PP$L),ncol(L)),PP$L))
    G$off <- c(PP$off,G$off)
    G$S <- c(PP$S,G$S)
    G$rank <- c(PP$rank,G$rank)
    G$sp <- c(PP$sp,G$sp)
    lsp.names <- c(PP$full.sp.names,lsp.names)
    G$n.paraPen <- length(PP$off)
    if (!is.null(PP$min.sp)) { ## deal with minimum sps
      if (is.null(H)) H <- matrix(0,n.p,n.p)
      for (i in 1:length(PP$S)) {
        ind <- PP$off[i]:(PP$off[i]+ncol(PP$S[[i]])-1)
        H[ind,ind] <- H[ind,ind] + PP$min.sp[i] * PP$S[[i]]
      }
    } ## min.sp stuff finished
  } else G$n.paraPen <- 0


  ## Now remove columns of L and rows of sp relating to fixed 
  ## smoothing parameters, and use removed elements to create lsp0

  fix.ind <- G$sp>=0

  if (sum(fix.ind)) {
    lsp0 <- G$sp[fix.ind]
    ind <- lsp0==0 ## find the zero s.p.s
    ef0 <- indi <- (1:length(ind))[ind]
    if (length(indi)>0) for (i in 1:length(indi)) {
      ## find "effective zero" to replace each zero s.p. with
      ii <- G$off[i]:(G$off[i]+ncol(G$S[[i]])-1) 
      ef0[i] <- norm(G$X[,ii],type="F")^2/norm(G$S[[i]],type="F")*.Machine$double.eps*.1
    }
    lsp0[!ind] <- log(lsp0[!ind])
    lsp0[ind] <- log(ef0) ##log(.Machine$double.xmin)*1000 ## zero fudge
    lsp0 <- as.numeric(L[,fix.ind,drop=FALSE]%*%lsp0)

    L <- L[,!fix.ind,drop=FALSE]  
    G$sp <- G$sp[!fix.ind]
  } else {lsp0 <- rep(0,nrow(L))}

  G$H <- H

  if (ncol(L)==nrow(L)&&!sum(L!=diag(ncol(L)))) L <- NULL ## it's just the identity

  G$L <- L;G$lsp0 <- lsp0
  names(G$lsp0) <- lsp.names ## names of all smoothing parameters (not just underlying)

  if (absorb.cons==FALSE) {  ## need to accumulate constraints 
    G$C <- matrix(0,0,n.p); G$d <- numeric(0)
    if (m>0) {
      for (i in 1:m) {
        n.con <- if (is.null(G$smooth[[i]]$C)) 0 else nrow(G$smooth[[i]]$C)
        C <- matrix(0,n.con,n.p)
        C[,G$smooth[[i]]$first.para:G$smooth[[i]]$last.para] <- G$smooth[[i]]$C
        G$C <- rbind(G$C,C)
	dd <- if (is.null(G$smooth[[i]]$d)) numeric(n.con) else G$smooth[[i]]$d
	G$d <- c(G$d,dd)
        G$smooth[[i]]$d <- G$smooth[[i]]$C <- NULL
      }
      rm(C)
    }
  } ## absorb.cons == FALSE
 
  G$y <- drop(data[[split$response]])
  ydim <- dim(G$y)
  if (!is.null(ydim)&&length(ydim)<2) dim(G$y) <- NULL
         
  ##data[[deparse(split$full.formula[[2]],backtick=TRUE)]]
  
  G$n <- nrow(data)

  if (is.null(data$"(weights)")) G$w <- rep(1,G$n)
  else G$w <- data$"(weights)"  

  ## Create names for model coefficients... 

  if (G$nsdf > 0) term.names <- colnames(G$X)[1:G$nsdf] else term.names<-array("",0)
  n.smooth <- length(G$smooth)
  ## create coef names, if smooth has any coefs, and create a global indicator of non-linear parameters
  ## g.index, if needed
  n.sp0 <- 0
  if (n.smooth) for (i in 1:n.smooth) {
    k <- 1
    jj <- G$smooth[[i]]$first.para:G$smooth[[i]]$last.para
    if (G$smooth[[i]]$df > 0) for (j in jj) {
      term.names[j] <- paste(G$smooth[[i]]$label,".",as.character(k),sep="")
      k <- k+1
    }
    n.sp <- length(G$smooth[[i]]$S)
    if (n.sp) { ## record sp this relates to in full sp vector
      G$smooth[[i]]$first.sp <- n.sp0 + 1
      n.sp0 <- G$smooth[[i]]$last.sp <- n.sp0 + n.sp
    }
    if (!is.null(G$smooth[[i]]$g.index)) {
      if (is.null(G$g.index)) G$g.index <- rep(FALSE,n.p)
      G$g.index[jj] <- G$smooth[[i]]$g.index
    }
    
  }
  G$term.names <- term.names

  ## Deal with non-linear parameterizations...
 

  G$pP <- PP ## return paraPen object, if present

  G
} ## gam.setup



formula.gam <- function(x, ...)
# formula.lm and formula.glm reconstruct the formula from x$terms, this is 
# problematic because of the way mgcv handles s() and te() terms 
{ x$formula
}

BC <- function(y,lambda=1) {
  y <- if (lambda==0) log(y) else (y^lambda-1)/lambda
}

corBC <- function(lambda,y,mu) {
  n <- length(y)
  qn <- qnorm((1:n-.5)/n)
  -cor(qn,sort(BC(y,lambda)-BC(mu,lambda)))
}


pdef <- function(V,eps = .Machine$double.eps^.9) {
## find nearest pdf matrix to symmetric matrix V
  ev <- eigen(V,symmetric=TRUE)
  thresh <- max(abs(ev$values))*eps
  ii <- ev$values<thresh
  if (any(ii)) {
    ev$values[ii] <- thresh
    V <- ev$vectors %*% (ev$values*t(ev$vectors))
  }
  V
} ## pdef

gam.outer <- function(lsp,fscale,family,control,method,optimizer,criterion,scale,gamma,G,start=NULL,nei=NULL,...)
# function for smoothing parameter estimation by outer optimization. i.e.
# P-IRLS scheme iterated to convergence for each trial set of smoothing
# parameters.
# MAJOR STEPS:
#  1. Call appropriate smoothing parameter optimizer, and extract fitted model
#    `object'
#  2. Call `gam.fit3.post.proc' to get parameter covariance matrices, edf etc to
#     add to `object' 
{ if (is.na(optimizer[2])) optimizer[2] <- "newton"
  if (!optimizer[2]%in%c("newton","bfgs","nlm","optim")) stop("unknown outer optimization method.")

  if (length(lsp)==0) { ## no sp estimation to do -- run a fit instead
    optimizer[2] <- "no.sps" ## will cause gam2objective to be called, below
  }
  nbGetTheta <- substr(family$family[1],1,17)=="Negative Binomial" && length(family$getTheta())>1
  if (nbGetTheta) stop("Please provide a single value for theta or use nb to estimate it")
 
  ## some preparations for the other methods, which all use gam.fit3...
 
  family <- fix.family.link(family)
  family <- fix.family.var(family)
  if (method%in%c("REML","ML","P-REML","P-ML")) family <- fix.family.ls(family)
  
  if (optimizer[1]=="efs"&& optimizer[2] != "no.sps" ) { ## experimental extended efs
    ##warning("efs is still experimental!")
    if (inherits(family,"general.family")) {
      object <- efsud(x=G$X,y=G$y,lsp=lsp,Sl=G$Sl,weights=G$w,offset=G$offxset,family=family,
                     control=control,Mp=G$Mp,start=start)
    } else {
      family <- fix.family.ls(family)
      object <- efsudr(x=G$X,y=G$y,lsp=lsp,Eb=G$Eb,UrS=G$UrS,weights=G$w,family=family,offset=G$offset,
                       start=start,
                       U1=G$U1, intercept = TRUE,scale=scale,Mp=G$Mp,control=control,n.true=G$n.true,...)
    }
    object$gcv.ubre <- object$REML
  } else if (optimizer[2]=="newton"||optimizer[2]=="bfgs"){ ## the gam.fit3 method 
    if (optimizer[2]=="bfgs") 
    b <- bfgs(lsp=lsp,X=G$X,y=G$y,Eb=G$Eb,UrS=G$UrS,L=G$L,lsp0=G$lsp0,offset=G$offset,U1=G$U1,Mp = G$Mp,
                family=family,weights=G$w,control=control,gamma=gamma,scale=scale,conv.tol=control$newton$conv.tol,
                maxNstep= control$newton$maxNstep,maxSstep=control$newton$maxSstep,maxHalf=control$newton$maxHalf, 
                printWarn=FALSE,scoreType=criterion,null.coef=G$null.coef,start=start,
                pearson.extra=G$pearson.extra,dev.extra=G$dev.extra,n.true=G$n.true,Sl=G$Sl,nei=nei,...) else
    b <- newton(lsp=lsp,X=G$X,y=G$y,Eb=G$Eb,UrS=G$UrS,L=G$L,lsp0=G$lsp0,offset=G$offset,U1=G$U1,Mp=G$Mp,
                family=family,weights=G$w,control=control,gamma=gamma,scale=scale,conv.tol=control$newton$conv.tol,
                maxNstep= control$newton$maxNstep,maxSstep=control$newton$maxSstep,maxHalf=control$newton$maxHalf, 
                printWarn=FALSE,scoreType=criterion,null.coef=G$null.coef,start=start,
                pearson.extra=G$pearson.extra,dev.extra=G$dev.extra,n.true=G$n.true,Sl=G$Sl,
		edge.correct=control$edge.correct,,nei=nei,...)                
                
    object <- b$object
    object$REML <- object$REML1 <- object$REML2 <-
    object$GACV <- object$D2 <- object$P2 <- object$UBRE2 <- object$trA2 <- 
    object$GACV1 <- object$GACV2 <- object$GCV2 <- object$D1 <- object$P1 <- NULL
    object$sp <- as.numeric(exp(b$lsp))
    object$gcv.ubre <- b$score
    b <- list(conv=b$conv,iter=b$iter,grad=b$grad,hess=b$hess,score.hist=b$score.hist) ## return info
    object$outer.info <- b   
  } else { ## methods calling gam.fit3 
    args <- list(X=G$X,y=G$y,Eb=G$Eb,UrS=G$UrS,offset=G$offset,U1=G$U1,Mp=G$Mp,family=family,
             weights=G$w,control=control,scoreType=criterion,gamma=gamma,scale=scale,
             L=G$L,lsp0=G$lsp0,null.coef=G$null.coef,n.true=G$n.true,Sl=G$Sl,start=start,nei=nei)
  
    if (optimizer[2]=="nlm") {
       b <- nlm(gam4objective, lsp, typsize = lsp, fscale = fscale, 
            stepmax = control$nlm$stepmax, ndigit = control$nlm$ndigit,
	    gradtol = control$nlm$gradtol, steptol = control$nlm$steptol, 
            iterlim = control$nlm$iterlim,
	    check.analyticals=control$nlm$check.analyticals,
            args=args,...)
      lsp <- b$estimate
      
    } else if (optimizer[2]=="optim") {
      b<-optim(par=lsp,fn=gam2objective,gr=gam2derivative,method="L-BFGS-B",control=
         list(fnscale=fscale,factr=control$optim$factr,lmm=min(5,length(lsp))),args=args,...)
      lsp <- b$par
    } else b <- NULL
    obj <- gam2objective(lsp,args,printWarn=TRUE,...) # final model fit, with warnings 
    object <- attr(obj,"full.fit")
    attr(obj,"full.fit") <- NULL
    object$gcv.ubre <- obj 
    object$outer.info <- b
    object$sp <- exp(lsp)
  } # end of methods calling gam.fit2
  
  
  if (scale>0) { 
    object$scale.estimated <- FALSE; object$scale <- scale} else {
    object$scale <- object$scale.est;object$scale.estimated <- TRUE
  } 
  
  object$control <- control
  object$method <- method
  if (inherits(family,"general.family")) {
    mv <- gam.fit5.post.proc(object,G$Sl,G$L,G$lsp0,G$S,G$off,gamma)
    ## object$coefficients <- Sl.initial.repara(G$Sl,object$coefficients,inverse=TRUE)
  } else mv <- gam.fit3.post.proc(G$X,G$L,G$lsp0,G$S,G$off,object,gamma)

  object[names(mv)] <- mv
  if (!is.null(nei)) {
    if (isTRUE(all.equal(sort(nei$d),1:nrow(G$X))) && length(nei$md)==nrow(G$X) && criterion=="NCV") { ## each point predicted on its own
      loocv <- length(nei$a)==length(nei$d) && isTRUE(all.equal(nei$d,nei$a)) && length(nei$ma) == length(nei$a) ## leave one out CV,
      if (is.logical(nei$jackknife)&&nei$jackknife) loocv <- TRUE ## straight jackknife requested
      if (nei$jackknife < 0) nei$jackknife <- TRUE ## signal cov matrix calc
    } else {
      loocv <- FALSE
      if (nei$jackknife < 0) nei$jackknife <- FALSE
    }  
  }
  if (!is.null(nei)&&(criterion!="NCV"||nei$jackknife)) { ## returning NCV when other criterion used for sp selection, or computing perturbations
    if (!is.null(nei$QNCV)&&nei$GNCV) family$qapprox <- TRUE
    if (is.null(family$qapprox)) family$qapprox <- FALSE
    lsp <- if (is.null(G$L)) log(object$sp) + G$lsp0 else G$L%*%log(object$sp)+G$lsp0
    if (object$scale.estimated && criterion %in% c("REML","ML","EFS")) lsp <- lsp[-length(lsp)] ## drop log scale estimate
    if (is.null(nei$gamma)) nei$gamma <- 1 ## a major application of this NCV is to select gamma - so it must not itself change with gamma!
    if (criterion!="NCV") nei$jackknife <- FALSE ## no cov matrix stuff.
    if (nei$jackknife) {
      n <- length(nei$d)
      nei1 <- if (loocv) nei else list(d=1:n,md=1:n,ma=1:n,a=1:n) ## set up for LOO CV or requested straight jackknife
      nei1$jackknife <- 10 ## signal that cross-validated beta perturbations are required
    } else nei1 <- nei ## called with another criteria
    b <- gam.fit3(x=G$X, y=G$y, sp=lsp,Eb=G$Eb,UrS=G$UrS,
                 offset = G$offset,U1=G$U1,Mp=G$Mp,family = family,weights=G$w,deriv=0,
                 control=control,gamma=nei$gamma, 
		 scale=scale,printWarn=FALSE,start=start,scoreType="NCV",null.coef=G$null.coef,
                 pearson.extra=G$pearson.extra,dev.extra=G$dev.extra,n.true=G$n.true,Sl=G$Sl,nei=nei1,...)
    object$NCV <- as.numeric(b$NCV)
    if (nei$jackknife) { ## need to compute direct cov matrix estimate
      dd <- attr(b$NCV,"dd") ## leave-one-out parameter perturbations
      if (!loocv) { ## need to account for assumed independence structure
        rsd0 <- residuals.gam(object)
        ## compute cross validated residuals...
        eta.cv <- attr(object$gcv.ubre,"eta.cv")
        fitted0 <- object$fitted.values 
        if (inherits(object$family,"general.family")) {
          for (j in 1:ncol(eta.cv)) {
            object$fitted.values[,j] <-
	      if (j <= length(G$offset)&&!is.null(G$offset[[j]])) family$linfo[[j]]$linkinv(eta.cv[,j]+G$offset[[j]]) else 
                family$linfo[[j]]$linkinv(eta.cv[,j])
          }	
        } else {
          object$fitted.values <- object$family$linkinv(eta.cv+G$offset) 
        }
        rsd1 <- residuals.gam(object) ## CV residuals
	ii <- !is.finite(rsd1);if (any(ii)) rsd1[ii] <- rsd0[ii]

        if (FALSE) {
	## version based on estimating correction factors for Vj. Not as well founded as current version.
        ## adaptive weighting to avoid underestimating mu error, while accounting for higher variance in
	## cv mu relative to mu...
        alpha <- 0.4 ## half way between full shrinkage compensation (.3) and none (.5)  
      
	mu.err <- (1-alpha)*(rsd0-rsd1)
	#rsd <- alpha*rsd0 + (1-alpha)*rsd1
        object$fitted.values <- fitted0

        V0 <- neicov(dd,nei=nei)    ## direct V (too small)
	dd0 <- dd*mu.err/rsd0
	
        V0 <- V0 - neicov(dd,dd0,nei)-neicov(dd0,dd,nei)
        #dd0 <- dd*(rsd0-rsd)/rsd0
        V0 <- V0+neicov(dd0,dd0,nei)
        Vj <- V0
	## get nearest +ve def matrix
        ev <- eigen(Vj)
        mev <- mean(ev$values)
        ev$values[ev$values<0] <- 0
	#if (mev>0) ev$values <- ev$values*mev/mean(ev$values)
	V0 <- sqrt(ev$values)*t(ev$vectors);
	Vj <- crossprod(V0) *n/(n-sum(object$edf))
        }
	
        Vj <- neicov(dd,nei=nei)*n/(n-sum(object$edf)) ## estimate based on raw residuals
        rat <- rsd1/rsd0; rat[!is.finite(rat)] <- 1
        Vcv <- neicov(dd*rat,nei=nei)*n/(n-sum(object$edf)) ## based on cross validated resdiduals
	ev <- eigen(Vj,symmetric=TRUE,only.values=TRUE)$values 
        trVj <- sum(ev[ev>0]) # trace of closest pdef matrix if Vj not pdef
	alpha <- max(trVj/sum(diag(object$Ve)),1) ## inverse learning rate (conservative Vj)
	#alpha1 <- sum(Vj*object$Ve)/sum(object$Ve^2) ## LS version - little difference
	Vj <- Vcv + (object$Vp-object$Ve)*alpha ## bias correct conservative (too large)
	#Vj <- Vj + (object$Vp-object$Ve)*alpha ## bias correct
	ev <- eigen(Vj,symmetric=TRUE)
	if (any(ev$values<0)) { ## find closest pdef matrix
	  ev$values[ev$values<0] <- 0
	  Vj <- crossprod(sqrt(ev$values)*t(ev$vectors))
	}
	#attr(Vj,"Vcv") <- Vcv ## conservative as attribute
      } else { ## LOO or straight jackknife requested
        Vj <- pdef(crossprod(dd)) ## straight jackknife is fine.
	alpha <- sum(diag(Vj))/sum(diag(object$Ve)) ## inverse learning rate (do not impose lower limit)
	Vj <- Vj + (object$Vp-object$Ve)*alpha ## bias correct
      }
      attr(object$Ve,"Vp") <- object$Vp ## keep original
      attr(object$Ve,"inv.learn") <- alpha
      object$Vp <- Vj     
    }
  }
  ## note: use of the following (Vc) in place of Vp appears to mess up p-values for smooths,
  ##       but doesn't change r.e. p-values of course. 
  #if (!is.null(mv$Vc)) object$Vc <- mv$Vc 
  #if (!is.null(mv$edf2)) object$edf2 <- mv$edf2
  #object$Vp <- mv$Vb
  #object$V.sp <- mv$V.sp
  #object$hat<-mv$hat
  #object$Ve <- mv$Ve
  #object$edf<-mv$edf
  #object$edf1 <- mv$edf1
  ##object$F <- mv$F ## DoF matrix --- probably not needed
  #object$R <- mv$R ## qr.R(sqrt(W)X)
  object$aic <- object$aic + 2*sum(object$edf)
  object$nsdf <- G$nsdf
  object$K <-  object$D1 <-  object$D2 <-  object$P <-  object$P1 <-  object$P2 <- object$dw.drho <-  
  object$GACV <-  object$GACV1 <-  object$GACV2 <-  object$REML <-  object$REML1 <-  object$REML2 <-  
  object$GCV<-object$GCV1<- object$GCV2 <- object$UBRE <-object$UBRE1 <- object$UBRE2 <- object$trA <-
  object$trA1<- object$trA2 <- object$alpha <- object$alpha1 <- object$scale.est <- NULL
  object$sig2 <- object$scale
  
  object
} ## gam.outer

get.null.coef <- function(G,start=NULL,etastart=NULL,mustart=NULL,...) {
## Get an estimate of the coefs corresponding to maximum reasonable deviance...
  y <- G$y
  weights <- G$w
  nobs <- G$n ## ignore codetools warning!!
  ##start <- etastart <- mustart <- NULL
  family <- G$family
  eval(family$initialize) ## have to do this to ensure y numeric
  #y <- as.numeric(y)
  mum <- mean(y)+0*y
  etam <- family$linkfun(mum)
  null.coef <- qr.coef(qr(G$X),etam)
  null.coef[is.na(null.coef)] <- 0;
  ## get a suitable function scale for optimization routines
  null.scale <- sum(family$dev.resids(y,mum,weights))/nrow(G$X) 
  list(null.coef=null.coef,null.scale=null.scale)
}

estimate.gam <- function (G,method,optimizer,control,in.out,scale,gamma,start=NULL,nei=NULL,...) {
## Do gam estimation and smoothness selection...

  if (!is.null(G$family$method) && !method %in% G$family$method) method <- G$family$method[1] 

  if (method %in% c("QNCV","NCV")||!is.null(nei)) {
    optimizer <- c("outer","bfgs")
    if (method=="QNCV") { method <- "NCV";G$family$qapprox <- TRUE } else G$family$qapprox <- FALSE
    if (is.null(nei)) nei <- list(d=1:G$n,md=1:G$n,ma=1:G$n,a=1:G$n) ## LOOCV
    if (is.null(nei$a)||is.null(nei$ma)) nei$a <- nei$ma <- nei$md <- nei$d <- 1:G$n 
    if (is.null(nei$d)) if (length(nei$ma)==G$n) nei$md <- nei$d <- 1:G$n else stop("unclear which points NCV neighbourhoods belong to")
    if (length(nei$md)!=length(nei$ma)) stop("for NCV number of dropped and predicted neighbourhoods must match")
    nei$ma <- round(nei$ma); nei$md <- round(nei$md); nei$a <- round(nei$a); nei$d <- round(nei$d); 
    if (min(nei$d)<1||max(nei$d>G$n)||min(nei$a)<1||max(nei$a>G$n)) stop("nei indexes non-existent points")
    if (nei$ma[1]<1||max(nei$ma)>length(nei$a)||length(nei$ma)<2||any(diff(nei$ma)<1)) stop('nei$ma faulty')
    if (nei$md[1]<1||max(nei$md)>length(nei$d)||length(nei$md)<2||any(diff(nei$md)<1)) stop('nei$md faulty')
    if (is.null(nei$jackknife)) nei$jackknife <- -1
  }  

  if (inherits(G$family,"extended.family")) { ## then there are some restrictions...
    if (!(method%in%c("REML","ML","NCV"))) method <- "REML"
    if (inherits(G$family,"general.family")) {
       if (!(method%in%c("REML","NCV"))||optimizer[1]=="efs") method <- "REML"
       if (method=="NCV"&&is.null(G$family$ncv)) {
         warning("family lacks a Neighbourhood Cross Validation method")
         method <- "REML"
       }	 
       G$Sl <- Sl.setup(G) ## prepare penalty sequence
      
       G$X <- Sl.initial.repara(G$Sl,G$X,both.sides=FALSE) ## re-parameterize accordingly
 
       if (!is.null(start)) start <- Sl.initial.repara(G$Sl,start,inverse=FALSE,both.sides=FALSE)

       ## make sure optimizer appropriate for available derivatives
       if (!is.null(G$family$available.derivs)) {
         if (G$family$available.deriv==1 && optimizer[1]!="efs")  optimizer <- c("outer","bfgs")
	 if (G$family$available.derivs==0) optimizer <- "efs"
       }	 
    }
  }

  if (!optimizer[1]%in%c("outer","efs")) stop("unknown optimizer")
  if (optimizer[1]=="efs") method <- "REML"
  if (!method%in%c("GCV.Cp","GACV.Cp","REML","P-REML","ML","P-ML","NCV")) stop("unknown smoothness selection criterion") 
  G$family <- fix.family(G$family)
  G$rS <- mini.roots(G$S,G$off,ncol(G$X),G$rank)
 
  reml <- method%in%c("REML","P-REML","ML","P-ML","NCV")
  
  Ssp <- totalPenaltySpace(G$S,G$H,G$off,ncol(G$X))
  G$Eb <- Ssp$E       ## balanced penalty square root for rank determination purposes 
  G$U1 <- cbind(Ssp$Y,Ssp$Z) ## eigen space basis
  G$Mp <- ncol(Ssp$Z) ## null space dimension
  G$UrS <- list()     ## need penalty matrices in overall penalty range space...
  if (length(G$S)>0) for (i in 1:length(G$S)) G$UrS[[i]] <- t(Ssp$Y)%*%G$rS[[i]] else i <- 0
  if (!is.null(G$H)) { ## then the sqrt fixed penalty matrix H is needed for (RE)ML 
      G$UrS[[i+1]] <- t(Ssp$Y)%*%mroot(G$H)
  }


  # is outer looping needed ?
  outer.looping <- (!G$am ||reml||method=="GACV.Cp"||method=="NCV"||!is.null(nei)) 

  ## sort out exact sp selection criterion to use

  fam.name <- G$family$family[1]

  if (scale==0) { ## choose criterion for performance iteration
    if (fam.name == "binomial"||fam.name == "poisson") G$sig2<-1 #ubre
      else G$sig2 <- -1 #gcv
  } else {G$sig2 <- scale}


  if (reml||method=="NCV") { ## then RE(ML) selection, but which variant?
   criterion <- method
   if (fam.name == "binomial"||fam.name == "poisson") scale <- 1
   if (inherits(G$family,"extended.family") && scale <=0) {
     scale <- if (is.null(G$family$scale)) 1 else G$family$scale
   }
  } else {
    if (scale==0) { 
      if (fam.name=="binomial"||fam.name=="poisson") scale <- 1 #ubre
      else scale <- -1 #gcv
    }
    if (scale > 0) criterion <- "UBRE"
    else {
      if (method=="GCV.Cp") criterion <- "GCV" else criterion <- "GACV"
    }
  }


  if (substr(fam.name,1,17)=="Negative Binomial") { 
    scale <- 1; ## no choice
    if (method%in%c("GCV.Cp","GACV.Cp")) criterion <- "UBRE"
  }
  ## Reset P-ML or P-REML in known scale parameter cases
  if (scale>0) {
    if (method=="P-ML") criterion <- method <- "ML" else 
    if (method=="P-REML")  criterion <- method <- "REML"
  } 

  family <- G$family; nb.fam.reset <- FALSE
  
  if (substr(G$family$family[1],1,17)=="Negative Binomial") { ## initialize sensibly
      scale <- G$sig2 <- 1
      G$family <- negbin(max(family$getTheta()),link=family$link)
      nb.fam.reset <- TRUE
  }
  
  ## extended family may need to manipulate G...
    
  if (!is.null(G$family$preinitialize)) {
    if (inherits(G$family,"general.family")) {
      Gmod <- G$family$preinitialize(G) ## modifies some elements of G
      for (gnam in names(Gmod)) G[[gnam]] <- Gmod[[gnam]] ## copy these into G  
    } else {
      ## extended family - usually just initializes theta and possibly y
      if (!is.null(attr(G$family$preinitialize,"needG"))) attr(G$family,"G") <- G ## more complicated
      pini <- G$family$preinitialize(G$y,G$family)
      attr(G$family,"G") <- NULL
      if (!is.null(pini$family)) G$family <- pini$family
      if (!is.null(pini$Theta)) G$family$putTheta(pini$Theta)
      if (!is.null(pini$y)) G$y <- pini$y
    }
  }

  lsp2 <- if (length(G$sp)>0) log(initial.spg(G$X,G$y,G$w,G$family,G$S,G$rank,G$off,
                       offset=G$offset,L=G$L,lsp0=G$lsp0,E=G$Eb,...))  else rep(0,0)

  if (!outer.looping) { ## additive GCV/UBRE
    object <- am.fit(G,control=control,gamma=gamma,...)
    lsp <- log(object$sp) 
  } else {
    if (!is.null(in.out)) { # initial s.p.s and scale provided
      ok <- TRUE ## run a few basic checks
      if (is.null(in.out$sp)||is.null(in.out$scale)) ok <- FALSE
      if (length(in.out$sp)!=length(G$sp)) ok <- FALSE
      if (!ok) stop("in.out incorrect: see documentation")
      lsp <- log(in.out$sp) 
    } else { 
      lsp <- lsp2
    } 

    if (nb.fam.reset) G$family <- family ## restore, in case manipulated for negative binomial 
       
    ## Get an estimate of the coefs corresponding to maximum reasonable deviance,
    ## and an estimate of the function scale, suitable for optimizers that need this.
    ## Doesn't make sense for general families that have to initialize coefs directly.
  
    null.stuff  <- if (inherits(G$family,"general.family")) list() else { 
      if (is.null(G$family$get.null.coef)) get.null.coef(G,...) else G$family$get.null.coef(G,...)
    }

    scale.as.sp <- (criterion%in%c("REML","ML")||(criterion=="NCV"&&inherits(G$family,"extended.family")))&&scale<=0
 
    if (scale.as.sp) { ## log(scale) to be estimated as a smoothing parameter
      if (is.null(in.out)) {
          log.scale <- log(null.stuff$null.scale/10)
      } else {
          log.scale <- log(in.out$scale)
      }
      lsp <- c(lsp,log.scale) ## append log initial scale estimate to lsp
      ## extend G$L, if present...
      if (!is.null(G$L)) { 
        G$L <- cbind(rbind(G$L,rep(0,ncol(G$L))),c(rep(0,nrow(G$L)),1))
      }
      if (!is.null(G$lsp0)) G$lsp0 <- c(G$lsp0,0)
    } 
    ## check if there are extra parameters to estimate
    if (inherits(G$family,"extended.family")&&!inherits(G$family,"general.family")&&G$family$n.theta>0) {
      th0 <- G$family$getTheta() ## additional (initial) parameters of likelihood 
      nth <- length(th0)
      nlsp <- length(lsp)
      ind <- 1:nlsp + nth ## only used if nlsp>0
      lsp <- c(th0,lsp) ## append to start of lsp
      ## extend G$L, G$lsp0 if present...
      if (!is.null(G$L)&&nth>0) { 
        L <- rbind(cbind(diag(nth),matrix(0,nth,ncol(G$L))),
                   cbind(matrix(0,nrow(G$L),nth),G$L))
        #sat <- attr(G$L,"scale")
        G$L <- L
        #attr(G$L,"scale") <- sat
        #attr(G$L,"not.sp") <- nth ## first not.sp params are not smoothing params
      }
      if (!is.null(G$lsp0)) G$lsp0 <- c(th0*0,G$lsp0)
    } else nth <- 0

   
    G$null.coef <- null.stuff$null.coef

    object <- gam.outer(lsp,fscale=null.stuff$null.scale, ##abs(object$gcv.ubre)+object$sig2/length(G$y),
                        family=G$family,control=control,criterion=criterion,method=method,
                        optimizer=optimizer,scale=scale,gamma=gamma,G=G,start=start,nei=nei,...)
    
    if (scale.as.sp)  object$sp <- object$sp[-length(object$sp)] ## drop scale estimate from sp array
    
    if (inherits(G$family,"extended.family")&&nth>0) object$sp <- object$sp[-(1:nth)] ## drop theta params
 
  } ## finished outer looping

  ## correct null deviance if there's an offset [Why not correct calc in gam.fit/3???]....

  if (!inherits(G$family,"extended.family")&&G$intercept&&any(G$offset!=0)) object$null.deviance <-
         glm(object$y~offset(G$offset),family=object$family,weights=object$prior.weights)$deviance

  object$method <- if (method=="NCV"&&G$family$qapprox) "QNCV" else criterion

  object$smooth<-G$smooth

  names(object$edf) <- G$term.names
  names(object$edf1) <- G$term.names

  if (inherits(family,"general.family")) {
    object$coefficients <- Sl.initial.repara(G$Sl,object$coefficients,inverse=TRUE)
  }
  
  ## extended family may need to manipulate fit object. Code
  ## will need to include the following line if G$X used...
  ## G$X <- Sl.initial.repara(G$Sl,G$X,inverse=TRUE,cov=FALSE,both.sides=FALSE)
  if (!is.null(G$family$postproc)) {
    if (inherits(G$family,"general.family")) eval(G$family$postproc) else {
      posr <- G$family$postproc(family=object$family,y=G$y,prior.weights=object$prior.weights,
              fitted=object$fitted.values,linear.predictors=object$linear.predictors,offset=G$offset,
	      intercept=G$intercept)
      if (!is.null(posr$family)) object$family$family <- posr$family
      if (!is.null(posr$deviance)) object$deviance <- posr$deviance
      if (!is.null(posr$null.deviance)) object$null.deviance <- posr$null.deviance	      
    }
  } 

  if (!is.null(G$P)) { ## matrix transforming from fit to prediction parameterization
    object$coefficients <- as.numeric(G$P %*% object$coefficients)
    object$Vp <- G$P %*% object$Vp %*% t(G$P)
    object$Ve <- G$P %*% object$Ve %*% t(G$P)
    rownames(object$Vp) <- colnames(object$Vp) <- G$term.names
    rownames(object$Ve) <- colnames(object$Ve) <- G$term.names
  }
  names(object$coefficients) <- G$term.names 
  
  object
} ## end estimate.gam

variable.summary <- function(pf,dl,n) {
## routine to summarize all the variables in dl, which is a list
## containing raw input variables to a model (i.e. no functions applied)
## pf is a formula containing the strictly parametric part of the
## model for the variables in dl. A list is returned, with names given by 
## the variables. For variables in the parametric part, then the list elements
## may be:
## * a 1 column matrix with elements set to the column medians, if variable 
##   is a matrix.
## * a 3 figure summary (min,median,max) for a numeric variable.
## * a factor variable, with the most commonly occuring factor (all levels)
## --- classes are as original data type, but anything not numeric, factor or matrix
## is coerced to numeric. 
## For non-parametric variables, any matrices are coerced to numeric, otherwise as 
## parametric.      
## medians in the above are always observed values (to deal with variables coerced to 
## factors in the model formulae in a nice way).
## variables with less than `n' entries are discarded
   v.n <- length(dl)
   ## if (v.n) for (i in 1:v.n) if (length(dl[[i]])<n) dl[[i]] <- NULL 
   
   v.name <- v.name1 <- names(dl)
   if (v.n) ## need to strip out names of any variables that are too short.
   { k <- 0 ## counter for retained variables
     for (i in 1:v.n) if (length(dl[[i]])>=n) { 
       k <- k+1
       v.name[k] <- v.name1[i] ## save names of variables of correct length
     }
     if (k>0) v.name <- v.name[1:k] else v.name <- rep("",k)
   }

   ## v.name <- names(dl)    ## the variable names
   p.name <- all.vars(pf[-2]) ## variables in parametric part (not response)
   vs <- list()
   v.n <- length(v.name)
   if (v.n>0) for (i in 1:v.n) {
     if (v.name[i]%in%p.name) para <- TRUE else para <- FALSE ## is variable in the parametric part?

     if (para&&is.matrix(dl[[v.name[i]]])&&ncol(dl[[v.name[i]]])>1) { ## parametric matrix --- a special case
       x <- matrix(apply(dl[[v.name[i]]],2,quantile,probs=0.5,type=3,na.rm=TRUE),1,ncol(dl[[v.name[i]]])) ## nearest to median entries
     } else { ## anything else
       x <- dl[[v.name[i]]]
       if (is.character(x)) x <- as.factor(x)
       if (is.factor(x)) {
         x <- x[!is.na(x)]
         lx <- levels(x)
         freq <- tabulate(x)
         ii <- min((1:length(lx))[freq==max(freq)])
         x <- factor(lx[ii],levels=lx) 
       } else {
         x <- as.numeric(x)
         x <- c(min(x,na.rm=TRUE),as.numeric(quantile(x,probs=.5,type=3,na.rm=TRUE)) ,max(x,na.rm=TRUE)) ## 3 figure summary
       }
     }
     vs[[v.name[i]]] <- x
   }
   vs
} ## end variable.summary


nanei <- function(nb,k) {
## nb is an NCV neighbourhood defining list, k an array of points to drop.
## this function adjusts nb to remove the dropped points and adjust the
## indices accordingly, so that the structure works with a data frame
## from which rows in k have been dropped.
## A problem is that if a whole prediction/omission fold is dropped then
## the corresponding omission/prediction fold must be dropped too. 
  if (!length(k)) return()
  if (is.null(nb$a)||is.null(nb$ma)||is.null(nb$md)||is.null(nb$d)) stop("full nei list needed if data incomplete")

  ## first work on drop-folds...
  kk <- which(nb$a %in% k) ## position of omitted in nb$a
  ## adjust ma for the fact that points are to be omitted...
  m <- nb$ma - cumsum(tabulate(findInterval(kk-1,nb$ma)+1,nbins=length(nb$ma)))
  mdi <- which(diff(c(0,m))==0) ## identify zero length folds to omit entirely

  ## now get elements of nb$d to omit from pred-folds because some drop-folds omitted entirely from k...
  mm <- nb$md
  i0 <- if (length(mdi)) unlist(apply(array(mdi),1,function(mdi) (c(0,mm)[mdi]+1):c(0,mm)[mdi+1] ,simplify=TRUE)) else rep(0,0)

  ## now the pred-folds...
  ii <- unique(c(i0,which(nb$d %in% k))) ## position of omitted in nb$i
  ## adjust mi for the fact that points are to be omitted...
  mi <- nb$md - cumsum(tabulate(findInterval(ii-1,nb$md)+1,nbins=length(nb$ma)))
  midi <- which(diff(c(0,mi))==0) ## identify zero length folds

  ## Now once more through drop-folds folds to omit because pred-fold omitted
  mm <- nb$ma
  k0 <- if (length(midi)) unlist(apply(array(midi),1,function(mdi) (c(0,mm)[mdi]+1):c(0,mm)[mdi+1] ,simplify=TRUE)) else rep(0,0)
  kk <- unique(c(k0,kk)) ## all points to omit from drop-folds
  m <- nb$ma - cumsum(tabulate(findInterval(kk-1,nb$ma)+1,nbins=length(nb$ma)))
  mdi <- which(diff(c(0,m))==0) ## identify zero length folds to omit entirely

  
  if (length(mdi)) nb$ma <- m[-mdi] ## omit zero length folds
  nb$a <- nb$a[-kk] ## omit the elements of k
  nb$a <- nb$a - findInterval(nb$a,sort(k)) ## and shift indices to account for omitted

  if (length(midi)) nb$md <- mi[-midi] ## omit zero length folds
  nb$d <- nb$d[-ii] ## omit the elements of i
  nb$d <- nb$d - findInterval(nb$d,sort(k)) ## and shift indices to account for omitted
  nb 
} ## nanei


onei <- function(nb,cbase=FALSE) {
## orders the neighbourhood indices into ascending order within each neighbourhood.
## this makes some matching tasks easier especially for bam.
  if (is.null(nb$a)||is.null(nb$ma)) return() ## LOOCV - nothing to do
  nn <- length(nb$ma) ## number of neighbourhoods
  b <- rep(1:nn,times=diff(c(0,nb$ma))) ## neighbourhood indices/labels
  nb$a <- nb$a[order(b,nb$a)] ## order drop indices within neighbourhood.
  if (!is.null(nb$md)) {
    b <- rep(1:nn,times=diff(c(0,nb$md))) ## neighbourhood indices/labels
    nb$d <- nb$d[order(b,nb$d)] ## order predict indices within neighbourhood.
  }
  if (cbase) {
    nb$a <- as.integer(nb$a) - 1L; nb$d <-  as.integer(nb$d) - 1L
    nb$ma <-  as.integer(nb$ma) - 1L; nb$md <-  as.integer(nb$md) - 1L
  }
  nb
} ## onei

## don't be tempted to change to control=list(...) --- messes up passing on other stuff via ...

gam <- function(formula,family=gaussian(),data=list(),weights=NULL,subset=NULL,na.action,offset=NULL,
                method="GCV.Cp",optimizer=c("outer","newton"),control=list(),#gam.control(),
                scale=0,select=FALSE,knots=NULL,sp=NULL,min.sp=NULL,H=NULL,gamma=1,fit=TRUE,
                paraPen=NULL,G=NULL,in.out=NULL,drop.unused.levels=TRUE,drop.intercept=NULL,
		nei=NULL,discrete=FALSE,...) {
## Routine to fit a GAM to some data. The model is stated in the formula, which is then 
## interpreted to figure out which bits relate to smooth terms and which to parametric terms.
## Basic steps:
## 1. Formula is split up into parametric and non-parametric parts,
##    and a fake formula constructed to be used to pick up data for
##    model frame. pterms "terms" object(s) created for parametric 
##    components, model frame created along with terms object.
## 2. 'gam.setup' called to do most of basis construction and other
##    elements of model setup.
## 3. 'estimate.gam' is called to estimate the model. This performs further 
##    pre- and post- fitting steps and calls either 'gam.fit' (performance
##    iteration) or 'gam.outer' (default method). 'gam.outer' calls the actual 
##    smoothing parameter optimizer ('newton' by default) and then any post 
##    processing. The optimizer calls 'gam.fit3/4/5' to estimate the model 
##    coefficients and obtain derivatives w.r.t. the smoothing parameters.
## 4. Finished 'gam' object assembled.
   control <- do.call("gam.control",control)
   if (is.null(G) && discrete) { ## get bam to do the setup
     cl <- match.call() ## NOTE: check all arguments more carefully
     cl[[1]] <- quote(bam)
     cl$fit = FALSE
     G <- eval(cl,parent.frame()) ## NOTE: cl probaby needs modifying in G to work properly (with fit=FALSE reset?? also below??)
   }
   if (is.null(G)) {
    ## create model frame..... 
    gp <- interpret.gam(formula) # interpret the formula 
    cl <- match.call() # call needed in gam object for update to work
    mf <- match.call(expand.dots=FALSE)
    mf$formula <- gp$fake.formula 
    mf$family <- mf$control<-mf$scale<-mf$knots<-mf$sp<-mf$min.sp<-mf$H<-mf$select <- mf$drop.intercept <- mf$nei <-
                 mf$gamma<-mf$method<-mf$fit<-mf$paraPen<-mf$G<-mf$optimizer <- mf$in.out <- mf$discrete <- mf$...<-NULL
    mf$drop.unused.levels <- drop.unused.levels
    mf[[1]] <- quote(stats::model.frame) ## as.name("model.frame")
    pmf <- mf
    mf <- eval(mf, parent.frame()) # the model frame now contains all the data 
    if (nrow(mf)<2) stop("Not enough (non-NA) data to do anything meaningful")
    terms <- attr(mf,"terms")

    if (!is.null(nei)) { ## check if data dropped
      k <- attr(mf,"na.action")
      if (!is.null(k)) { ## need to adjust nei for dropped data
        nei <- nanei(nei,as.numeric(k))
      }
    }
    ## summarize the *raw* input variables
    ## note can't use get_all_vars here -- buggy with matrices
    vars <- all_vars1(gp$fake.formula[-2]) ## drop response here
    inp <- parse(text = paste("list(", paste(vars, collapse = ","),")"))

    ## allow a bit of extra flexibility in what `data' is allowed to be (as model.frame actually does)
    if (!is.list(data)&&!is.data.frame(data)) data <- as.data.frame(data) 

    dl <- eval(inp, data, parent.frame())
    names(dl) <- vars ## list of all variables needed
    var.summary <- variable.summary(gp$pf,dl,nrow(mf)) ## summarize the input data
    rm(dl) ## save space    

    ## pterms are terms objects for the parametric model components used in 
    ## model setup - don't try obtaining by evaluating pf in mf - doesn't
    ## work in general (e.g. with offset)...

    if (is.list(formula)) { ## then there are several linear predictors
      environment(formula) <- environment(formula[[1]]) ## e.g. termplots needs this
      pterms <- list()
      tlab <- rep("",0)
      for (i in 1:length(formula)) {
        pmf$formula <- gp[[i]]$pf 
        pterms[[i]] <- attr(eval(pmf, parent.frame()),"terms")
        tlabi <- attr(pterms[[i]],"term.labels")
        if (i>1&&length(tlabi)>0) tlabi <- paste(tlabi,i-1,sep=".")
        tlab <- c(tlab,tlabi)
      }
      attr(pterms,"term.labels") <- tlab ## labels for all parametric terms, distinguished by predictor
    } else { ## single linear predictor case
      pmf$formula <- gp$pf
      pmf <- eval(pmf, parent.frame()) # pmf contains all data for parametric part
      pterms <- attr(pmf,"terms") ## pmf only used for this
    }

    if (is.character(family)) family <- eval(parse(text=family))
    if (is.function(family)) family <- family()
    if (is.null(family$family)) stop("family not recognized")
  
    if (family$family[1]=="gaussian" && family$link=="identity") am <- TRUE
    else am <- FALSE
    
    if (!control$keepData) rm(data) ## save space

    ## check whether family requires intercept to be dropped...
    # drop.intercept <- if (is.null(family$drop.intercept) || !family$drop.intercept) FALSE else TRUE
    # drop.intercept <- as.logical(family$drop.intercept)
    if (is.null(family$drop.intercept)) { ## family does not provide information
      lengthf <- if (is.list(formula)) length(formula) else 1
      if (is.null(drop.intercept)) drop.intercept <- rep(FALSE, lengthf) else {
        drop.intercept <- rep(drop.intercept,length=lengthf) ## force drop.intercept to correct length
	if (sum(drop.intercept)) family$drop.intercept <- drop.intercept ## ensure prediction works
      }
    } else drop.intercept <- as.logical(family$drop.intercept) ## family overrides argument
    
    if (inherits(family,"general.family")&&!is.null(family$presetup)) eval(family$presetup)

    gsname <- if (is.list(formula)) "gam.setup.list" else "gam.setup" 

    G <- do.call(gsname,list(formula=gp,pterms=pterms,
                 data=mf,knots=knots,sp=sp,min.sp=min.sp,
                 H=H,absorb.cons=TRUE,sparse.cons=0,select=select,
                 idLinksBases=control$idLinksBases,scale.penalty=control$scalePenalty,
                 paraPen=paraPen,drop.intercept=drop.intercept))
    
    G$var.summary <- var.summary
    G$family <- family
   
    if ((is.list(formula)&&(is.null(family$nlp)||family$nlp!=gp$nlp))||
        (!is.list(formula)&&!is.null(family$npl)&&(family$npl>1))) stop("incorrect number of linear predictors for family")
       
    G$terms<-terms;
    G$mf<-mf;G$cl<-cl;
    G$am <- am

    if (is.null(G$offset)) G$offset<-rep(0,G$n)
     
    G$min.edf <- G$nsdf ## -dim(G$C)[1]
    if (G$m) for (i in 1:G$m) G$min.edf<-G$min.edf+G$smooth[[i]]$null.space.dim

    G$formula <- formula
    G$pred.formula <- gp$pred.formula
    environment(G$formula)<-environment(formula)
  } else { ## G not null
    if (!is.null(sp)&&any(sp>=0)) { ## request to modify smoothing parameters
      if (is.null(G$L)) G$L <- diag(length(G$sp))
      if (length(sp)!=ncol(G$L)) stop('length of sp must be number of free smoothing parameters in original model')
      ind <- sp>=0 ## which smoothing parameters are now fixed
      spind <- log(sp[ind]); 
      spind[!is.finite(spind)] <- -30 ## set any zero parameters to effective zero
      G$lsp0 <- G$lsp0 + drop(G$L[,ind,drop=FALSE] %*% spind) ## add fix to lsp0
      G$L <- G$L[,!ind,drop=FALSE] ## drop the cols of G
      G$sp <- rep(-1,ncol(G$L))
    }
  }

  if (!fit) {
    class(G) <- "gam.prefit"
    return(G)
  }  


  ## if (ncol(G$X)>nrow(G$X)) warning("Model has more coefficients than data") ##stop("Model has more coefficients than data") 

  G$conv.tol <- control$mgcv.tol      # tolerence for mgcv
  G$max.half <- control$mgcv.half # max step halving in Newton update mgcv

  object <- estimate.gam(G,method,optimizer,control,in.out,scale,gamma,nei=nei,...)

  
  if (!is.null(G$L)) { 
    object$full.sp <- as.numeric(exp(G$L%*%log(object$sp)+G$lsp0))
    names(object$full.sp) <- names(G$lsp0)
  }
  names(object$sp) <- names(G$sp)
  object$paraPen <- G$pP
  object$formula <- G$formula
  ## store any lpi attribute of G$X for use in predict.gam...
  if (is.list(object$formula)) attr(object$formula,"lpi") <- attr(G$X,"lpi")
  object$var.summary <- G$var.summary 
  object$cmX <- G$cmX ## column means of model matrix --- useful for CIs
  object$model<-G$mf # store the model frame
  object$na.action <- attr(G$mf,"na.action") # how to deal with NA's
  object$control <- control
  object$terms <- G$terms
  object$pred.formula <- G$pred.formula

  attr(object$pred.formula,"full") <- reformulate(all.vars(object$terms))
  
  object$pterms <- G$pterms
  object$assign <- G$assign # applies only to pterms
  object$contrasts <- G$contrasts
  object$xlevels <- G$xlevels
  object$offset <- G$offset
  if (!is.null(G$Xcentre)) object$Xcentre <- G$Xcentre
  if (control$keepData) object$data <- data
  object$df.residual <- nrow(G$X) - sum(object$edf)
  object$min.edf <- G$min.edf
  if (G$am&&!(method%in%c("REML","ML","P-ML","P-REML"))) object$optimizer <- "magic" else object$optimizer <- optimizer
  object$call <- G$cl # needed for update() to work
  class(object) <- c("gam","glm","lm")
  if (is.null(object$deviance)) object$deviance <- sum(residuals(object,"deviance")^2)
  names(object$gcv.ubre) <- method
  ## The following lines avoid potentially very large objects in hidden environments being stored
  ## with fitted gam objects. The downside is that functions like 'termplot' that rely on searching in
  ## the environment of the formula can fail...
  environment(object$formula) <- environment(object$pred.formula) <-
  environment(object$terms) <- environment(object$pterms) <- .GlobalEnv
  if (!is.null(object$model))  environment(attr(object$model,"terms"))  <- .GlobalEnv
  if (!is.null(attr(object$pred.formula,"full"))) environment(attr(object$pred.formula,"full")) <- .GlobalEnv
  object
} ## gam



print.gam<-function (x,...) 
# default print function for gam objects
{ print(x$family)
  cat("Formula:\n")
  if (is.list(x$formula)) for (i in 1:length(x$formula)) print(x$formula[[i]]) else
     print(x$formula)
  n.smooth<-length(x$smooth)
  if (n.smooth==0)
  cat("Total model degrees of freedom",sum(x$edf),"\n")
  else
  { edf<-0
    cat("\nEstimated degrees of freedom:\n")
    for (i in 1:n.smooth)
    edf[i]<-sum(x$edf[x$smooth[[i]]$first.para:x$smooth[[i]]$last.para])
    edf.str <- format(round(edf,digits=4),digits=3,scientific=FALSE)
    for (i in 1:n.smooth) {   
    cat(edf.str[i]," ",sep="")
      if (i%%7==0) cat("\n")
    }
    cat(" total =",round(sum(x$edf),digits=2),"\n")
  }
  if (!is.null(x$method)&&!(x$method%in%c("PQL","lme.ML","lme.REML")))  
  cat("\n",x$method," score: ",x$gcv.ubre,"     ",sep="")
  if (!is.null(x$rank) && x$rank< length(x$coefficients)) cat("rank: ",x$rank,"/",length(x$coefficients),sep="") 
  cat("\n")
  invisible(x)
} ## print.gam

gam.control <- function (nthreads=1,ncv.threads=1,irls.reg=0.0,epsilon = 1e-7, maxit = 200,
                         mgcv.tol=1e-7,mgcv.half=15,trace =FALSE,
                         rank.tol=.Machine$double.eps^0.5,
                         nlm=list(),optim=list(),newton=list(),#outerPIsteps=0,
                         idLinksBases=TRUE,scalePenalty=TRUE,efs.lspmax=15,efs.tol=.1,
                         keepData=FALSE,scale.est="fletcher",edge.correct=FALSE) 
# Control structure for a gam. 
# irls.reg is the regularization parameter to use in the GAM fitting IRLS loop.
# epsilon is the tolerance to use in the IRLS MLE loop. maxit is the number 
# of IRLS iterations to use. mgcv.tol is the tolerance to use in the mgcv call within each IRLS. mgcv.half is the 
# number of step halvings to employ in the mgcv search for the optimal GCV score, before giving up 
# on a search direction. trace turns on or off some de-bugging information.
# rank.tol is the tolerance to use for rank determination
# outerPIsteps was the number of performance iteration steps used to intialize
#                         outer iteration (unused for a while) 
{   scale.est <- match.arg(scale.est,c("fletcher","pearson","deviance"))
    if (!is.logical(edge.correct)&&(!is.numeric(edge.correct)||edge.correct<0)) stop(
        "edge.correct must be logical or a positive number")
    if (!is.numeric(nthreads) || nthreads <1) stop("nthreads must be a positive integer")
    if (!is.numeric(ncv.threads) || ncv.threads <1) stop("ncv.threads must be a positive integer") 
    if (!is.numeric(irls.reg) || irls.reg <0.0) stop("IRLS regularizing parameter must be a non-negative number.")
    if (!is.numeric(epsilon) || epsilon <= 0) 
        stop("value of epsilon must be > 0")
    if (!is.numeric(maxit) || maxit <= 0) 
        stop("maximum number of iterations must be > 0")
    if (rank.tol<0||rank.tol>1) 
    { rank.tol=.Machine$double.eps^0.5
      warning("silly value supplied for rank.tol: reset to square root of machine precision.")
    }
    # work through nlm defaults
    if (is.null(nlm$ndigit)||nlm$ndigit<2) nlm$ndigit <- max(2,ceiling(-log10(epsilon)))
    nlm$ndigit <- round(nlm$ndigit)
    ndigit <- floor(-log10(.Machine$double.eps))
    if (nlm$ndigit>ndigit) nlm$ndigit <- ndigit
    if (is.null(nlm$gradtol)) nlm$gradtol <- epsilon*10
    nlm$gradtol <- abs(nlm$gradtol)
    ## note that nlm will stop after hitting stepmax 5 consecutive times
    ## hence should not be set too small ... 
    if (is.null(nlm$stepmax)||nlm$stepmax==0) nlm$stepmax <- 2
    nlm$stepmax <- abs(nlm$stepmax)
    if (is.null(nlm$steptol)) nlm$steptol <- 1e-4
    nlm$steptol <- abs(nlm$steptol)
    if (is.null(nlm$iterlim)) nlm$iterlim <- 200
    nlm$iterlim <- abs(nlm$iterlim)
    ## Should be reset for a while anytime derivative code altered...
    if (is.null(nlm$check.analyticals)) nlm$check.analyticals <- FALSE
    nlm$check.analyticals <- as.logical(nlm$check.analyticals) 

    # and newton defaults
    if (is.null(newton$conv.tol)) newton$conv.tol <- 1e-6
    if (is.null(newton$maxNstep)) newton$maxNstep <- 5
    if (is.null(newton$maxSstep)) newton$maxSstep <- 2
    if (is.null(newton$maxHalf)) newton$maxHalf <- 30
    if (is.null(newton$use.svd)) newton$use.svd <- FALSE

    # and optim defaults
    if (is.null(optim$factr)) optim$factr <- 1e7
    optim$factr <- abs(optim$factr)
    if (efs.tol<=0) efs.tol <- .1

    list(nthreads=round(nthreads),ncv.threads=round(ncv.threads),irls.reg=irls.reg,epsilon = epsilon, maxit = maxit,
         trace = trace, mgcv.tol=mgcv.tol,mgcv.half=mgcv.half,
         rank.tol=rank.tol,nlm=nlm,
         optim=optim,newton=newton,#outerPIsteps=outerPIsteps,
         idLinksBases=idLinksBases,scalePenalty=scalePenalty,efs.lspmax=efs.lspmax,efs.tol=efs.tol,
         keepData=as.logical(keepData[1]),scale.est=scale.est,edge.correct=edge.correct)
    
} ## gam.control



mgcv.get.scale<-function(Theta,weights,good,mu,mu.eta.val,G)
# Get scale implied by current fit and trial -ve binom Theta, I've used
# mu and mu.eta.val used in fit rather than implied by it....
{ variance<- negbin(Theta)$variance
  w<-sqrt(weights[good]*mu.eta.val[good]^2/variance(mu)[good])
  wres<-w*(G$y-G$X%*%G$p)
  sum(wres^2)/(G$n-sum(G$edf))
}


mgcv.find.theta<-function(Theta,T.max,T.min,weights,good,mu,mu.eta.val,G,tol)
# searches for -ve binomial theta between given limits to get scale=1 
{ scale<-mgcv.get.scale(Theta,weights,good,mu,mu.eta.val,G)
  T.hi<-T.low<-Theta
  while (scale<1&&T.hi<T.max) 
  { T.hi<-T.hi*2
    T.hi<-min(T.hi,T.max)
    scale<-mgcv.get.scale(T.hi,weights,good,mu,mu.eta.val,G)
  } 
  if (all.equal(T.hi,T.max)==TRUE && scale<1) return(T.hi)
  T.low<-T.hi
  while (scale>=1&&T.low>T.min)
  { T.low<-T.low/2 
    T.low<-max(T.low,T.min)
    scale<-mgcv.get.scale(T.low,weights,good,mu,mu.eta.val,G)
  } 
  if (all.equal(T.low,T.min)==TRUE && scale>1) return(T.low)
  # (T.low,T.hi) now brackets scale=1. 
  while (abs(scale-1)>tol)
  { Theta<-(T.low+T.hi)/2
    scale<-mgcv.get.scale(Theta,weights,good,mu,mu.eta.val,G)
    if (scale<1) T.low<-Theta
    else T.hi<-Theta
  }
  Theta
}


full.score <- function(sp,G,family,control,gamma,...)
# function suitable for calling from nlm in order to polish gam fit
# so that actual minimum of score is found in generalized cases
{ .Deprecated(msg="Internal mgcv function full.score is no longer used and will be removed soon.")
  if (is.null(G$L)) {
    G$sp<-exp(sp);
  } else {
    G$sp <- as.numeric(exp(G$L%*%sp + G$lsp0))
  }
  # set up single fixed penalty....
  q<-NCOL(G$X)
  if (is.null(G$H)) G$H<-matrix(0,q,q)
  for (i in 1:length(G$S))
  { j<-ncol(G$S[[i]])
    off1<-G$off[i];off2<-off1+j-1
    G$H[off1:off2,off1:off2]<-G$H[off1:off2,off1:off2]+G$sp[i]*G$S[[i]]
  }
  G$S<-list() # have to reset since length of this is used as number of penalties
  G$L <- NULL
  xx<-gam.fit(G,family=family,control=control,gamma=gamma,...)
  res <- xx$gcv.ubre.dev
  attr(res,"full.gam.object")<-xx
  res
} ## full.score

am.fit <- function (G, #start = NULL, etastart = NULL, 
    #mustart = NULL,# family = gaussian(), 
    control = gam.control(),gamma=1,...) {
    ## fit additive model using 'magic' returning gam type object.

    family <- gaussian()
    intercept<-G$intercept
    n <- nobs <- NROW(G$y) ## n just there to keep codetools happy
    y <- G$y # original data
    X <- G$X # original design matrix
    if (ncol(G$X) == 0) stop("Model seems to contain no terms")
    olm <- G$am   # only need 1 iteration as it's a pure additive model.
    
    # obtain average element sizes for the penalties
    n.S <- length(G$S)
    if (n.S>0) {
      S.size <- rep(0,n.S)
      for (i in 1:n.S) S.size[i] <- mean(abs(G$S[[i]])) 
    }
    weights<-G$w # original weights

    n.score <- sum(weights!=0) ## n to use in GCV score (i.e. don't count points with no influence)   

    offset<-G$offset 

    variance <- family$variance;dev.resids <- family$dev.resids
    aic <- family$aic
    if (NCOL(y) > 1) stop("y must be univariate unless binomial")
    
    scale <- G$sig2

    msp <- G$sp
    magic.control<-list(tol=G$conv.tol,step.half=G$max.half,#maxit=control$maxit+control$globit,
                          rank.tol=control$rank.tol)

    ## solve the penalized LS problem ...
    good <- weights > 0
    G$y <- y[good] - offset[good]
    G$X <- X[good,,drop=FALSE]
    G$w <- sqrt(weights[good]) ## note magic assumes sqrt weights
    mr <- magic(G$y,G$X,msp,G$S,G$off,L=G$L,lsp0=G$lsp0,G$rank,G$H,matrix(0,0,ncol(G$X)),
                G$w,gamma=gamma,G$sig2,G$sig2<0,
                ridge.parameter=control$irls.reg,control=magic.control,n.score=n.score,nthreads=control$nthreads)
    coef <- mr$b;msp <- mr$sp;G$sig2 <- mr$scale;G$gcv.ubre <- mr$score;

    if (any(!is.finite(coef))) warning(gettextf("Non-finite coefficients at iteration"))
  
    mu <- eta <- drop(X %*% coef + offset) 
    dev <- sum(dev.resids(y, mu, weights))
    
    residuals <- rep(NA, nobs)
    residuals[good] <- G$y - (mu - offset)[good]
       
    wtdmu <- if (intercept) sum(weights * y)/sum(weights) else offset
    nulldev <- sum(dev.resids(y, wtdmu, weights))
    n.ok <- nobs - sum(weights == 0)
    nulldf <- n.ok - as.integer(intercept)
    
    ## Extract a little more information from the fit....

    mv <- magic.post.proc(G$X,mr,w=G$w^2)
    G$Vp<-mv$Vb;G$hat<-mv$hat;
    G$Ve <- mv$Ve # frequentist cov. matrix
    G$edf<-mv$edf
    G$conv<-mr$gcv.info
    G$sp<-msp
    rank<-G$conv$rank

    ## use MLE of scale in Gaussian case - best estimate otherwise. 
    dev1 <- if (scale>0) scale*sum(weights) else dev 

    aic.model <- aic(y, n, mu, weights, dev1) + 2 * sum(G$edf)
    if (scale < 0) { ## deviance based GCV
      gcv.ubre.dev <- n.score*dev/(n.score-gamma*sum(G$edf))^2
    } else { # deviance based UBRE, which is just AIC
      gcv.ubre.dev <- dev/n.score + 2 * gamma * sum(G$edf)/n.score - G$sig2
    }

    list(coefficients = as.vector(coef), residuals = residuals, fitted.values = mu, 
        family = family,linear.predictors = eta, deviance = dev,
        null.deviance = nulldev, iter = 1, weights = weights, prior.weights = weights,  
        df.null = nulldf, y = y, converged = TRUE,sig2=G$sig2,edf=G$edf,edf1=mv$edf1,hat=G$hat,
        R=mr$R,
        boundary = FALSE,sp = G$sp,nsdf=G$nsdf,Ve=G$Ve,Vp=G$Vp,rV=mr$rV,mgcv.conv=G$conv,
        gcv.ubre=G$gcv.ubre,aic=aic.model,rank=rank,gcv.ubre.dev=gcv.ubre.dev,scale.estimated = (scale < 0))
} ## am.fit


gam.fit <- function (G, start = NULL, etastart = NULL, 
    mustart = NULL, family = gaussian(), 
    control = gam.control(),gamma=1,
    fixedSteps=(control$maxit+1),...) 
# fitting function for a gam, modified from glm.fit.
# note that smoothing parameter estimates from one irls iterate are carried over to the next irls iterate
# unless the range of s.p.s is large enough that numerical problems might be encountered (want to avoid 
# completely flat parts of gcv/ubre score). In the latter case autoinitialization is requested.
# fixedSteps < its default causes at most fixedSteps iterations to be taken,
# without warning if convergence has not been achieved. This is useful for
# obtaining starting values for outer iteration.
{   .Deprecated(msg="Internal mgcv function gam.fit is no longer used - see gam.fit3.")
    intercept<-G$intercept
    conv <- FALSE
    n <- nobs <- NROW(G$y) ## n just there to keep codetools happy
    nvars <- NCOL(G$X) # check this needed
    y<-G$y # original data
    X<-G$X # original design matrix
    if (nvars == 0) stop("Model seems to contain no terms")
    olm <- G$am   # only need 1 iteration as it's a pure additive model.
    if (!olm)  .Deprecated(msg="performance iteration with gam is deprecated, use bam instead")
    find.theta<-FALSE # any supplied -ve binomial theta treated as known, G$sig2 is scale parameter
    if (substr(family$family[1],1,17)=="Negative Binomial")
    { Theta <- family$getTheta()
      if (length(Theta)==1) { ## Theta fixed
        find.theta <- FALSE
        G$sig2 <- 1
      } else {
        if (length(Theta)>2)
        warning("Discrete Theta search not available with performance iteration")
        Theta <- range(Theta)
        T.max <- Theta[2]          ## upper search limit
        T.min <- Theta[1]          ## lower search limit
        Theta <- sqrt(T.max*T.min) ## initial value
        find.theta <- TRUE
      }
      nb.link<-family$link # negative.binomial family, there's a choise of links
    }

    
    # obtain average element sizes for the penalties
    n.S<-length(G$S)
    if (n.S>0)
    { S.size<-0
      for (i in 1:n.S) S.size[i]<-mean(abs(G$S[[i]])) 
    }
    weights<-G$w # original weights

    n.score <- sum(weights!=0) ## n to use in GCV score (i.e. don't count points with no influence)   

    offset<-G$offset 

    variance <- family$variance;dev.resids <- family$dev.resids
    aic <- family$aic
    linkinv <- family$linkinv;linkfun <- family$linkfun;mu.eta <- family$mu.eta
    if (!is.function(variance) || !is.function(linkinv)) 
        stop("illegal `family' argument")
    valideta <- family$valideta
    if (is.null(valideta)) 
        valideta <- function(eta) TRUE
    validmu <- family$validmu
    if (is.null(validmu)) 
        validmu <- function(mu) TRUE
    if (is.null(mustart))   # new from version 1.5.0 
    { eval(family$initialize)}
    else 
    { mukeep <- mustart
      eval(family$initialize)
      mustart <- mukeep
    }
    if (NCOL(y) > 1) 
        stop("y must be univariate unless binomial")
    
    coefold <- NULL                 # 1.5.0
    eta <- if (!is.null(etastart))  # 1.5.0
        etastart

    else if (!is.null(start)) 
    if (length(start) != nvars) 
    stop(gettextf("Length of start should equal %d and correspond to initial coefs.",nvars)) 
    else 
    { coefold<-start                        #1.5.0
      offset+as.vector(if (NCOL(G$X) == 1)
       G$X * start
       else G$X %*% start)
    }
    else family$linkfun(mustart)
    mu <- linkinv(eta)
    if (!(validmu(mu) && valideta(eta))) 
        stop("Can't find valid starting values: please specify some")
    devold <- sum(dev.resids(y, mu, weights))
   
    boundary <- FALSE
    scale <- G$sig2

    msp <- G$sp
    magic.control<-list(tol=G$conv.tol,step.half=G$max.half,#maxit=control$maxit+control$globit,
                          rank.tol=control$rank.tol)

    for (iter in 1:(control$maxit)) 
    {
        good <- weights > 0
        varmu <- variance(mu)[good]
        if (any(is.na(varmu))) 
            stop("NAs in V(mu)")
        if (any(varmu == 0)) 
            stop("0s in V(mu)")
        mu.eta.val <- mu.eta(eta)
        if (any(is.na(mu.eta.val[good]))) 
            stop("NAs in d(mu)/d(eta)")
        good <- (weights > 0) & (mu.eta.val != 0) # note good modified here => must re-calc each iter
        if (all(!good)) {
            conv <- FALSE
            warning(gettextf("No observations informative at iteration %d", 
                iter))
            break
        }
   
        mevg <- mu.eta.val[good];mug <- mu[good];yg <- y[good]
        weg <- weights[good];##etag <- eta[good]
        var.mug<-variance(mug)

        G$y <- z <- (eta - offset)[good] + (yg - mug)/mevg
        w <- sqrt((weg * mevg^2)/var.mug)
        
        G$w<-w
        G$X<-X[good,,drop=FALSE]  # truncated design matrix       
     
        # must set G$sig2 to scale parameter or -1 here....
        G$sig2 <- scale


        if (sum(!is.finite(G$y))+sum(!is.finite(G$w))>0) 
        stop("iterative weights or data non-finite in gam.fit - regularization may help. See ?gam.control.")

        ## solve the working weighted penalized LS problem ...

        mr <- magic(G$y,G$X,msp,G$S,G$off,L=G$L,lsp0=G$lsp0,G$rank,G$H,matrix(0,0,ncol(G$X)),  #G$C,
                    G$w,gamma=gamma,G$sig2,G$sig2<0,
                    ridge.parameter=control$irls.reg,control=magic.control,n.score=n.score,nthreads=control$nthreads)
        G$p<-mr$b;msp<-mr$sp;G$sig2<-mr$scale;G$gcv.ubre<-mr$score;

        if (find.theta) {# then family is negative binomial with unknown theta - estimate it here from G$sig2
            ##  need to get edf array
          mv <- magic.post.proc(G$X,mr,w=G$w^2)
          G$edf <- mv$edf

          Theta<-mgcv.find.theta(Theta,T.max,T.min,weights,good,mu,mu.eta.val,G,.Machine$double.eps^0.5)
          family<-do.call("negbin",list(theta=Theta,link=nb.link))
          variance <- family$variance;dev.resids <- family$dev.resids
          aic <- family$aic
          family$Theta <- Theta ## save Theta estimate in family
        }

        if (any(!is.finite(G$p))) {
            conv <- FALSE   
            warning(gettextf("Non-finite coefficients at iteration %d",iter))
            break
        }

		
        start <- G$p
        eta <- drop(X %*% start) # 1.5.0
        mu <- linkinv(eta <- eta + offset)
        eta <- linkfun(mu) # force eta/mu consistency even if linkinv truncates
        dev <- sum(dev.resids(y, mu, weights))
        if (control$trace) 
            message(gettextf("Deviance = %s Iterations - %d", dev, iter, domain = "R-mgcv"))
        boundary <- FALSE
        if (!is.finite(dev)) {
            if (is.null(coefold))
            stop("no valid set of coefficients has been found:please supply starting values",
            call. = FALSE)
            warning("Step size truncated due to divergence",call.=FALSE)
            ii <- 1
            while (!is.finite(dev)) {
                if (ii > control$maxit) 
                  stop("inner loop 1; can't correct step size")
                ii <- ii + 1
                start <- (start + coefold)/2
                eta<-drop(X %*% start)
                mu <- linkinv(eta <- eta + offset)
                eta <- linkfun(mu) 
                dev <- sum(dev.resids(y, mu, weights))
            }
            boundary <- TRUE
            if (control$trace) 
                cat("Step halved: new deviance =", dev, "\n")
        }
        if (!(valideta(eta) && validmu(mu))) {
            warning("Step size truncated: out of bounds.",call.=FALSE)
            ii <- 1
            while (!(valideta(eta) && validmu(mu))) {
                if (ii > control$maxit) 
                  stop("inner loop 2; can't correct step size")
                ii <- ii + 1
                start <- (start + coefold)/2
                eta<-drop(X %*% start)
                mu <- linkinv(eta <- eta + offset)
                eta<-linkfun(mu)
            }
            boundary <- TRUE
            dev <- sum(dev.resids(y, mu, weights))
            if (control$trace) 
                cat("Step halved: new deviance =", dev, "\n")
        }

        ## Test for convergence here ...

        if (abs(dev - devold)/(0.1 + abs(dev)) < control$epsilon || olm ||
            iter >= fixedSteps) {
            conv <- TRUE
            coef <- start #1.5.0
            break
        }
        else {
            devold <- dev
            coefold <- coef<-start
        }
    }
    if (!conv) 
    { warning("Algorithm did not converge") 
    }
    if (boundary) 
        warning("Algorithm stopped at boundary value")
    eps <- 10 * .Machine$double.eps
    if (family$family[1] == "binomial") {
        if (any(mu > 1 - eps) || any(mu < eps)) 
            warning("fitted probabilities numerically 0 or 1 occurred")
    }
    if (family$family[1] == "poisson") {
        if (any(mu < eps)) 
            warning("fitted rates numerically 0 occurred")
    }
    
    residuals <- rep(NA, nobs)
    residuals[good] <- z - (eta - offset)[good]
    
    wt <- rep(0, nobs)
    wt[good] <- w^2
   
    wtdmu <- if (intercept) sum(weights * y)/sum(weights) else linkinv(offset)
    nulldev <- sum(dev.resids(y, wtdmu, weights))
    n.ok <- nobs - sum(weights == 0)
    nulldf <- n.ok - as.integer(intercept)
    
    ## Extract a little more information from the fit....

    mv <- magic.post.proc(G$X,mr,w=G$w^2)
    G$Vp<-mv$Vb;G$hat<-mv$hat;
    G$Ve <- mv$Ve # frequentist cov. matrix
    G$edf<-mv$edf
    G$conv<-mr$gcv.info
    G$sp<-msp
    rank<-G$conv$rank

    ## use MLE of scale in Gaussian case - best estimate otherwise. 
    dev1 <- if (scale>0) scale*sum(weights) else if (family$family=="gaussian") dev else G$sig2*sum(weights)  

    aic.model <- aic(y, n, mu, weights, dev1) + 2 * sum(G$edf)
    if (scale < 0) { ## deviance based GCV
      gcv.ubre.dev <- n.score*dev/(n.score-gamma*sum(G$edf))^2
    } else { # deviance based UBRE, which is just AIC
      gcv.ubre.dev <- dev/n.score + 2 * gamma * sum(G$edf)/n.score - G$sig2
    }
  
	list(coefficients = as.vector(coef), residuals = residuals, fitted.values = mu, 
        family = family,linear.predictors = eta, deviance = dev,
        null.deviance = nulldev, iter = iter, weights = wt, prior.weights = weights,  
        df.null = nulldf, y = y, converged = conv,sig2=G$sig2,edf=G$edf,edf1=mv$edf1,hat=G$hat,
        ##F=mv$F,
        R=mr$R,
        boundary = boundary,sp = G$sp,nsdf=G$nsdf,Ve=G$Ve,Vp=G$Vp,rV=mr$rV,mgcv.conv=G$conv,
        gcv.ubre=G$gcv.ubre,aic=aic.model,rank=rank,gcv.ubre.dev=gcv.ubre.dev,scale.estimated = (scale < 0))
} ## gam.fit


model.matrix.gam <- function(object,...)
{ if (!inherits(object,"gam")) stop("`object' is not of class \"gam\"")
  predict(object,type="lpmatrix",...)
}

get.na.action <- function(na.action) {
## get the name of the na.action whether function or text string.
## avoids deparse(substitute(na.action)) which is easily broken by 
## nested calls.
  if (is.character(na.action)) {
    if (na.action%in%c("na.omit","na.exclude","na.pass","na.fail")) 
      return(na.action) else stop("unrecognised na.action")
  } 
  if (!is.function(na.action)) stop("na.action not character or function")
  a <- try(na.action(c(0,NA)),silent=TRUE)
  if (inherits(a,"try-error")) return("na.fail")
  if (inherits((attr(a,"na.action")),"omit")) return("na.omit")
  if (inherits((attr(a,"na.action")),"exclude")) return("na.exclude")
  return("na.pass")
} ## get.na.action


predict.gam <- function(object,newdata,type="link",se.fit=FALSE,terms=NULL,exclude=NULL,
                       block.size=NULL,newdata.guaranteed=FALSE,na.action=na.pass,
                       unconditional=FALSE,iterms.type=NULL,...) {

# This function is used for predicting from a GAM. 'object' is a gam object, newdata a dataframe to
# be used in prediction......
#
# Type == "link"     - for linear predictor (may be several for extended case)
#      == "response" - for fitted values: may be several if several linear predictors,
#                      and may return something other than inverse link of l.p. for some families
#      == "terms"    - for individual terms on scale of linear predictor 
#      == "iterms"   - exactly as "terms" except that se's include uncertainty about mean  
#      == "lpmatrix" - for matrix mapping parameters to l.p. - has "lpi" attribute if multiple l.p.s
#      == "newdata"  - returns newdata after pre-processing 
# Steps are:
#  1. Set newdata to object$model if no newdata supplied
#  2. split up newdata into manageable blocks if too large
#  3. Obtain parametric model matrix (safely!)
#  4. Work through smooths calling prediction.matrix constructors for each term
#  5. Work out required quantities
# 
# The splitting into blocks enables blocks of compiled code to be called efficiently
# using smooth class specific prediction matrix constructors, without having to 
# build up potentially enormous prediction matrices.
# if newdata.guaranteed == TRUE then the data.frame is assumed complete and
# ready to go, so that only factor levels are checked for sanity.
# 
# if `terms' is non null then it should be a list of terms to be returned 
# when type=="terms" or "iterms". 
# if `object' has an attribute `para.only' then only parametric terms of order
# 1 are returned for type=="terms"/"iterms" : i.e. only what termplot can handle.
#
# if no new data is supplied then na.action does nothing, otherwise 
# if na.action == "na.pass" then NA predictors result in NA predictions (as lm
#                   or glm)
#              == "na.omit" or "na.exclude" then NA predictors result in
#                       dropping
# if GC is TRUE then gc() is called after each block is processed

  ## para acts by adding all smooths to the exclude list. 
  ## it also causes any lp matrix to be smaller than it would otherwise have been.
  #if (para) exclude <- c(exclude,unlist(lapply(object$smooth,function(x) x$label)))

  if (unconditional) {
    if (is.null(object$Vc)) warning("Smoothness uncertainty corrected covariance not available") else 
    object$Vp <- object$Vc
  }

  if (type!="link"&&type!="terms"&&type!="iterms"&&type!="response"&&type!="lpmatrix"&&type!="newdata")  { 
    warning("Unknown type, reset to terms.")
    type<-"terms"
  }
  if (!inherits(object,"gam")) stop("predict.gam can only be used to predict from gam objects")

  ## to mimic behaviour of predict.lm, some resetting is required ...
  if (missing(newdata)) na.act <- object$na.action else {
    if (is.null(na.action)) na.act <- NULL 
    else {
      na.txt <- if (is.character(na.action)||is.function(na.action)) get.na.action(na.action) else "na.pass"
      #if (is.character(na.action))
      #na.txt <- na.action else ## substitute(na.action) else
      #if (is.function(na.action)) na.txt <- deparse(substitute(na.action))
      if (na.txt=="na.pass") na.act <- "na.exclude" else
      if (na.txt=="na.exclude") na.act <- "na.omit" else
      na.act <- na.action
    }
  } ## ... done

  # get data from which to predict.....  
  nd.is.mf <- FALSE # need to flag if supplied newdata is already a model frame 
  ## get name of response...
  # yname <- all.vars(object$terms)[attr(object$terms,"response")]
  yname <- attr(attr(object$terms,"dataClasses"),"names")[attr(object$terms,"response")]
  if (newdata.guaranteed==FALSE) {
    if (missing(newdata)) { # then "fake" an object suitable for prediction 
      newdata <- object$model
      new.data.ok <- FALSE
      nd.is.mf <- TRUE
      response <- newdata[[yname]] ## ok even with "cbind(foo,bar)" as yname 
    } else {  # do an R ``standard'' evaluation to pick up data
      new.data.ok <- TRUE
      if (is.data.frame(newdata)&&!is.null(attr(newdata,"terms"))) { # it's a model frame
        if (sum(!(names(object$model)%in%names(newdata)))) stop(
        "newdata is a model.frame: it should contain all required variables\n")
         nd.is.mf <- TRUE
	 response <- newdata[[yname]]
      } else {
        ## Following is non-standard to allow convenient splitting into blocks
        ## below, and to allow checking that all variables are in newdata ...

        ## get names of required variables, less response, but including offset variable
        ## see ?terms.object and ?terms for more information on terms objects
        # yname <- all.vars(object$terms)[attr(object$terms,"response")] ## redundant
        resp <- get.var(yname,newdata,FALSE)
        naresp <- FALSE
        #if (!is.null(object$family$predict)&&!is.null(newdata[[yname]])) {
	if (!is.null(object$family$predict)&&!is.null(resp)) {
          ## response provided, and potentially needed for prediction (e.g. Cox PH family)
          if (!is.null(object$pred.formula)) object$pred.formula <- attr(object$pred.formula,"full")
          response <- TRUE
          Terms <- terms(object)
          #resp <- newdata[[yname]]
	  if (is.matrix(resp)) {
            if (sum(is.na(rowSums(resp)))>0) stop("no NAs allowed in response data for this model")
          } else { ## vector response
            if (sum(is.na(resp))>0) {
              naresp <- TRUE ## there are NAs in supplied response
              ## replace them with a numeric code, so that rows are not dropped below
              rar <- range(resp,na.rm=TRUE)
              thresh <- rar[1]*1.01-rar[2]*.01
              resp[is.na(resp)] <- thresh
              newdata[[yname]] <- thresh 
            }
	  }  
        } else { ## response not provided
          response <- FALSE 
          Terms <- delete.response(terms(object))
        }
        allNames <- if (is.null(object$pred.formula)) all.vars(Terms) else all.vars(object$pred.formula)
        if (length(allNames) > 0) { 
          ff <- if (is.null(object$pred.formula)) reformulate(allNames) else  object$pred.formula
          if (sum(!(allNames%in%names(newdata)))) { 
            warning("not all required variables have been supplied in  newdata!\n")
          }
          ## note that `xlev' argument not used here, otherwise `as.factor' in 
          ## formula can cause a problem ... levels reset later.
          newdata <- eval(model.frame(ff,data=newdata,na.action=na.act),parent.frame())
          if (naresp) newdata[[yname]][newdata[[yname]]<=thresh] <- NA ## reinstate as NA  
        } ## otherwise it's intercept only and newdata can be left alone
        na.act <- attr(newdata,"na.action")
        #response <- if (response) newdata[[yname]] else NULL
	response <- if (response) get.var(yname,newdata,FALSE) else NULL
      }
    }
  } else { ## newdata.guaranteed == TRUE
    na.act <- NULL
    new.data.ok=TRUE ## it's guaranteed!
    if (!is.null(attr(newdata,"terms"))) nd.is.mf <- TRUE
    #response <- newdata[[yname]]
    response <- get.var(yname,newdata,FALSE)
  }


  ## now check the factor levels and split into blocks...

  if (new.data.ok) {
    ## check factor levels are right ...
    names(newdata) -> nn # new data names
    colnames(object$model) -> mn # original names
    for (i in 1:length(newdata)) 
    if (nn[i]%in%mn && is.factor(object$model[,nn[i]])) { # then so should newdata[[i]] be 
      levm <- levels(object$model[,nn[i]]) ## original levels
      ## need to avoid dropping NAs if they are a factor level in original model
      levn <- if (any(is.na(levm))) levels(factor(newdata[[i]],exclude=NULL)) else levels(factor(newdata[[i]])) ## new levels
      if (sum(!levn%in%levm)>0) { ## check not trying to sneak in new levels 
        msg <- paste("factor levels",paste(levn[!levn%in%levm],collapse=", "),"not in original fit",collapse="")
        warning(msg)
	xlev <- !(newdata[[i]] %in% levm) & !is.na(newdata[[i]]) ## attribute marking extra (non-NA) levels in factor 
      } else xlev <- NULL
      ## set prediction levels to fit levels...
      if (is.matrix(newdata[[i]])) {
        dum <- factor(newdata[[i]],levels=levm,exclude=NULL)
	dim(dum) <- dim(newdata[[i]])
	newdata[[i]] <- dum
	if (!is.null(xlev)) {
	  dim(xlev) <- dim(dum)
	  attr(newdata[[i]],"xlev") <- xlev
	}  
      } else {
        newdata[[i]] <- factor(newdata[[i]],levels=levm,exclude=NULL)
	if (!is.null(xlev)) attr(newdata[[i]],"xlev") <- xlev ## not used in this routine
      }
    }
    if (type=="newdata") return(newdata)

    # split prediction into blocks, to avoid running out of memory
    if (length(newdata)==1) newdata[[2]] <- newdata[[1]] # avoids data frame losing its labels and dimensions below!
    if (is.null(dim(newdata[[1]]))) np <- length(newdata[[1]]) 
    else np <- dim(newdata[[1]])[1] 
    nb <- length(object$coefficients)
    if (is.null(block.size)) block.size <- 1000
    if (block.size < 1) block.size <- np
  } else { # no new data, just use object$model
    np <- nrow(object$model)
    nb <- length(object$coefficients)
  }
  
  if (type=="lpmatrix") block.size <- NULL ## nothing gained by blocking in this case - and offset handling easier this way

  ## split prediction into blocks, to avoid running out of memory
  if (is.null(block.size)) { 
    ## use one block as predicting using model frame
    ## and no block size supplied... 
    n.blocks <- 1
    b.size <- array(np,1)
  } else {
    n.blocks <- np %/% block.size
    b.size <- rep(block.size,n.blocks)
    last.block <- np-sum(b.size)
    if (last.block>0) {
      n.blocks <- n.blocks+1  
      b.size[n.blocks] <- last.block
    }
  }


  # setup prediction arrays...
  ## in multi-linear predictor models, lpi[[i]][j] is the column of model matrix contributing the jth col to lp i 
  lpi <- if (is.list(object$formula)) attr(object$formula,"lpi") else NULL
  nlp <- if (is.null(lpi)) 1 else length(lpi)  ## number of linear predictors
  n.smooth<-length(object$smooth)
  if (type=="lpmatrix") {
    H <- matrix(0,np,nb)
  } else if (type=="terms"||type=="iterms") { 
    term.labels <- attr(object$pterms,"term.labels")
    para.only <- attr(object,"para.only")
    if (is.null(para.only)) para.only <- FALSE  # if TRUE then only return information on parametric part
    n.pterms <- length(term.labels)
    fit <- array(0,c(np,n.pterms+as.numeric(para.only==0)*n.smooth))
    if (se.fit) se <- fit
    ColNames <- term.labels
  } else { ## "response" or "link"
    ## get number of linear predictors, in case it's more than 1...
    #if (is.list(object$formula)) {
    #  nlp <- length(lpi) ## number of linear predictors
    #} else nlp <- 1 
   
    fit <- if (nlp>1) matrix(0,np,nlp) else array(0,np)
    if (se.fit) se <- fit
    fit1 <- NULL ## "response" returned by fam$fv can be non-vector 
  }
  stop <- 0
  if (is.list(object$pterms)) { ## multiple linear predictors
    if (type=="iterms") {
      warning("type iterms not available for multiple predictor cases")
      type <- "terms"
    }
    pstart <- attr(object$nsdf,"pstart") ## starts of parametric blocks in coef vector
    pind <- rep(0,0) ## index of parametric coefs
    Terms <- list();pterms <- object$pterms
    for (i in 1:length(object$nsdf)) {
      Terms[[i]] <- delete.response(object$pterms[[i]])
      if (object$nsdf[i]>0) pind <- c(pind,pstart[i]-1+1:object$nsdf[i])
    }
  } else { ## normal single predictor case
    Terms <- list(delete.response(object$pterms)) ## make into a list anyway
    pterms <- list(object$pterms)
    pstart <- 1
    pind <- 1:object$nsdf ## index of parameteric coefficients
  }

  ## check if extended family required intercept to be dropped...
  #drop.intercept <- FALSE 
  #if (!is.null(object$family$drop.intercept)&&object$family$drop.intercept) {
  #  drop.intercept <- TRUE;
  #  ## make sure intercept explicitly included, so it can be cleanly dropped...
  #  for (i in 1:length(Terms)) attr(Terms[[i]],"intercept") <- 1 
  #} 
  drop.intercept <- object$family$drop.intercept
  if (is.null(drop.intercept)) {
    drop.intercept <- rep(FALSE, length(Terms))
  } else {
    ## make sure intercept explicitly included, so it can be cleanly dropped...
    for (i in 1:length(Terms)) {
      if (drop.intercept[i] == TRUE) attr(Terms[[i]],"intercept") <- 1 
    }
  }
  ## index of any parametric terms that have to be dropped
  ## this is used to help with identifiability in multi-
  ## formula models...

  drop.ind <- attr(object$nsdf,"drop.ind") 

  ####################################
  ## Actual prediction starts here...
  ####################################

  s.offset <- NULL # to accumulate any smooth term specific offset
  any.soff <- FALSE # indicator of term specific offset existence
  if (n.blocks > 0) for (b in 1:n.blocks) { # work through prediction blocks
    start <- stop+1
    stop <- start + b.size[b] - 1
    if (n.blocks==1) data <- newdata else data <- newdata[start:stop,]
    X <- matrix(0,b.size[b],nb+length(drop.ind))
    Xoff <- matrix(0,b.size[b],n.smooth) ## term specific offsets 
    offs <- list()
    for (i in 1:length(Terms)) { ## loop for parametric components (1 per lp)
      ## implements safe prediction for parametric part as described in
      ## http://developer.r-project.org/model-fitting-functions.txt
      if (new.data.ok) {
        if (nd.is.mf) mf <- model.frame(data,xlev=object$xlevels) else {
          mf <- model.frame(Terms[[i]],data,xlev=object$xlevels)
          if (!is.null(cl <- attr(pterms[[i]],"dataClasses"))) .checkMFClasses(cl,mf)
        }
	## next line is just a work around to prevent a spurious warning (e.g. R 3.6) from
	## model.matrix if contrast relates to a term in mf which is not
	## part of Terms[[i]] (model.matrix doc actually defines contrast w.r.t. mf,
	## not Terms[[i]])...
	oc <- if (length(object$contrasts)==0) object$contrasts else
	      object$contrasts[names(object$contrasts)%in%attr(Terms[[i]],"term.labels")]
        Xp <- model.matrix(Terms[[i]],mf,contrasts=oc) 
      } else { 
        Xp <- model.matrix(Terms[[i]],object$model)
        mf <- newdata # needed in case of offset, below
      }
      if (!is.null(terms)||!is.null(exclude)) { ## work out which parts of Xp to zero
        assign <- attr(Xp,"assign") ## assign[i] is the term to which Xp[,i] relates
	if (min(assign)==0&&("(Intercept)"%in%exclude||(!is.null(terms)&&!"(Intercept)"%in%terms))) Xp[,which(assign==0)] <- 0
	tlab <- attr(Terms[[i]],"term.labels")
	ii <- which(assign%in%which(tlab%in%exclude))
	if (length(ii)) Xp[,ii] <- 0
	if (!is.null(terms)) {
	  ii <- which(assign%in%which(!tlab%in%terms))
	  if (length(ii)) Xp[,ii] <- 0
	}   
      }
      offi <- attr(Terms[[i]],"offset")
      if (is.null(offi)) offs[[i]] <- 0 else { ## extract offset
        offs[[i]] <- mf[[names(attr(Terms[[i]],"dataClasses"))[offi+1]]]
      }
      if (drop.intercept[i]) { 
        xat <- attributes(Xp);ind <- xat$assign>0 
        Xp <- Xp[,xat$assign>0,drop=FALSE] ## some extended families need to drop intercept
        xat$assign <- xat$assign[ind];xat$dimnames[[2]]<-xat$dimnames[[2]][ind];
        xat$dim[2] <- xat$dim[2]-1;attributes(Xp) <- xat 
      }
      if (object$nsdf[i]>0) X[,pstart[i]-1 + 1:object$nsdf[i]] <- Xp
    } ## end of parametric loop
 ##   if (length(offs)==1) offs <- offs[[1]] ## messes up later handling
     
    if (!is.null(drop.ind)) X <- X[,-drop.ind]

    if (n.smooth) for (k in 1:n.smooth) { ## loop through smooths
      klab <- object$smooth[[k]]$label
      if ((is.null(terms)||(klab%in%terms))&&(is.null(exclude)||!(klab%in%exclude))) {
        Xfrag <- PredictMat(object$smooth[[k]],data)		 
        X[,object$smooth[[k]]$first.para:object$smooth[[k]]$last.para] <- Xfrag
        Xfrag.off <- attr(Xfrag,"offset") ## any term specific offsets?
        if (!is.null(Xfrag.off)) { Xoff[,k] <- Xfrag.off; any.soff <- TRUE }
      }
      if (type=="terms"||type=="iterms") ColNames[n.pterms+k] <- klab
    } ## smooths done

    

    if (!is.null(object$Xcentre)) { ## Apply any column centering
      X <- sweep(X,2,object$Xcentre)
    }

    # Now have prediction matrix, X, for this block, need to do something with it...

    if (type=="lpmatrix") { 
      H[start:stop,] <- X
      if (any.soff) s.offset <- rbind(s.offset,Xoff)
    } else if (type=="terms"||type=="iterms") { ## split results into terms
      lass <- if (is.list(object$assign)) object$assign else list(object$assign)
      k <- 0
      for (j in 1:length(lass)) if (length(lass[[j]])) { ## work through assign list
        ind <- 1:length(lass[[j]]) ## index vector for coefs involved
        nptj <- max(lass[[j]]) ## number of terms involved here
        if (nptj>0) for (i in 1:nptj) { ## work through parametric part
          k <- k + 1 ## counts total number of parametric terms
          ii <- ind[lass[[j]]==i] + pstart[j] - 1 
          fit[start:stop,k] <- X[,ii,drop=FALSE]%*%object$coefficients[ii]
          if (se.fit) se[start:stop,k] <-
          sqrt(pmax(0,rowSums((X[,ii,drop=FALSE]%*%object$Vp[ii,ii])*X[,ii,drop=FALSE])))
        }
      } ## assign list done
      if (n.smooth&&!para.only) {
        for (k in 1:n.smooth) # work through the smooth terms 
        { first <- object$smooth[[k]]$first.para; last <- object$smooth[[k]]$last.para
          fit[start:stop,n.pterms+k] <- X[,first:last,drop=FALSE] %*% object$coefficients[first:last] + Xoff[,k]
          if (se.fit) { # diag(Z%*%V%*%t(Z))^0.5; Z=X[,first:last]; V is sub-matrix of Vp
            if (type=="iterms"&& attr(object$smooth[[k]],"nCons")>0) { ## termwise se to "carry the intercept
              ## some general families, add parameters after cmX created, which are irrelevant to cmX... 
              if (length(object$cmX) < ncol(X)) object$cmX <- c(object$cmX,rep(0,ncol(X)-length(object$cmX)))
              if (!is.null(iterms.type)&&iterms.type==2) object$cmX[-(1:object$nsdf)] <- 0 ## variability of fixed effects mean only
              X1 <- matrix(object$cmX,nrow(X),ncol(X),byrow=TRUE)
              meanL1 <- object$smooth[[k]]$meanL1
              if (!is.null(meanL1)) X1 <- X1 / meanL1              
              X1[,first:last] <- X[,first:last]
              se[start:stop,n.pterms+k] <- sqrt(pmax(0,rowSums((X1%*%object$Vp)*X1)))
            } else se[start:stop,n.pterms+k] <- ## terms strictly centred
            sqrt(pmax(0,rowSums((X[,first:last,drop=FALSE]%*%
                          object$Vp[first:last,first:last,drop=FALSE])*X[,first:last,drop=FALSE])))
          } ## end if (se.fit)
        } 
        colnames(fit) <- ColNames
        if (se.fit) colnames(se) <- ColNames
      } else {
        if (para.only&&is.list(object$pterms)) { 
          ## have to use term labels that match original data, or termplot fails 
          ## to plot. This only applies for 'para.only==1' calls which are 
          ## designed for use from termplot called from plot.gam
          term.labels <- unlist(lapply(object$pterms,attr,"term.labels"))
        }
        colnames(fit) <- term.labels
        if (se.fit) colnames(se) <- term.labels
        if (para.only) { 
          # retain only terms of order 1 - this is to make termplot work
          order <- if (is.list(object$pterms)) unlist(lapply(object$pterms,attr,"order")) else attr(object$pterms,"order")
          term.labels <- term.labels[order==1]
          ## fit <- as.matrix(as.matrix(fit)[,order==1])
          fit <- fit[,order==1,drop=FALSE]
          colnames(fit) <- term.labels
          if (se.fit) { ## se <- as.matrix(as.matrix(se)[,order==1])
            se <- se[,order==1,drop=FALSE]
            colnames(se) <- term.labels 
          }
        } 
      } 
    } else { ## "link" or "response" case
      fam <- object$family
      if (!is.null(object$family$setInd)) object$family$setInd(start:stop) ## family may need to know subset index - e.g gfam
      k <- attr(attr(object$model,"terms"),"offset")
      if (nlp>1) { ## multiple linear predictor case
        if (is.null(fam$predict)||type=="link") {
          ##pstart <- c(pstart,ncol(X)+1)
          ## get index of smooths with an offset...
          off.ind <- (1:n.smooth)[as.logical(colSums(abs(Xoff)))]
          for (j in 1:nlp) { ## looping over the model formulae
            ind <- lpi[[j]] ##pstart[j]:(pstart[j+1]-1)
            fit[start:stop,j] <- X[,ind,drop=FALSE]%*%object$coefficients[ind] + offs[[j]]
            if (length(off.ind)) for (i in off.ind) { ## add any term specific offsets
              if (object$smooth[[i]]$first.para%in%ind)  fit[start:stop,j] <- fit[start:stop,j] + Xoff[,i]
            }
            if (se.fit) se[start:stop,j] <- 
            sqrt(pmax(0,rowSums((X[,ind,drop=FALSE]%*%object$Vp[ind,ind,drop=FALSE])*X[,ind,drop=FALSE])))
            ## model offset only handled for first predictor... fixed
            ##if (j==1&&!is.null(k))  fit[start:stop,j] <- fit[start:stop,j] + model.offset(mf)
            if (type=="response") { ## need to transform lp to response scale
              linfo <- object$family$linfo[[j]] ## link information
              if (se.fit) se[start:stop,j] <- se[start:stop,j]*abs(linfo$mu.eta(fit[start:stop,j]))
              fit[start:stop,j] <- linfo$linkinv(fit[start:stop,j])
            }
          } ## end of lp loop
        } else { ## response case with own predict code
          #lpi <- list();pst <- c(pstart,ncol(X)+1)
          #for (i in 1:(length(pst)-1)) lpi[[i]] <- pst[i]:(pst[i+1]-1)
          attr(X,"lpi") <- lpi  
          ffv <- fam$predict(fam,se.fit,y= if (is.matrix(response)) response[start:stop,] else response[start:stop],
                             X=X,beta=object$coefficients,off=offs,Vb=object$Vp)
          if (is.matrix(fit)&&!is.matrix(ffv[[1]])) {
            fit <- fit[,1]; if (se.fit) se <- se[,1]
          }
          if (is.matrix(ffv[[1]])&&(!is.matrix(fit)||ncol(ffv[[1]])!=ncol(fit))) {
            fit <- matrix(0,np,ncol(ffv[[1]])); if (se.fit) se <- fit
          }
          if (is.matrix(fit)) {
            fit[start:stop,] <- ffv[[1]]
            if (se.fit) se[start:stop,] <- ffv[[2]]
          } else {
            fit[start:stop] <- ffv[[1]]
            if (se.fit) se[start:stop] <- ffv[[2]]
          }
        } ## end of own response prediction code
      } else { ## single linear predictor
        offs <- if (is.null(k)) rowSums(Xoff) else rowSums(Xoff) + model.offset(mf)
        fit[start:stop] <- X%*%object$coefficients + offs
        if (se.fit) se[start:stop] <- sqrt(pmax(0,rowSums((X%*%object$Vp)*X)))
        if (type=="response") { # transform    
          linkinv <- fam$linkinv
          if (is.null(fam$predict)) {
            dmu.deta <- fam$mu.eta  
            if (se.fit) se[start:stop]<-se[start:stop]*abs(dmu.deta(fit[start:stop])) 
            fit[start:stop] <- linkinv(fit[start:stop])
          } else { ## family has its own prediction code for response case
            ffv <- fam$predict(fam,se.fit,y= if (is.matrix(response)) response[start:stop,] else response[start:stop],
                               X=X,beta=object$coefficients,off=offs,Vb=object$Vp)
            if (is.null(fit1)&&is.matrix(ffv[[1]])) {
              fit1 <- matrix(0,np,ncol(ffv[[1]]))
              if (se.fit) se1 <- fit1
            }
            if (is.null(fit1)) {
              fit[start:stop] <- ffv[[1]]
              if (se.fit) se[start:stop] <- ffv[[2]]
            } else {
              fit1[start:stop,] <- ffv[[1]]
              if (se.fit) se1[start:stop,] <- ffv[[2]]
            }
          }
        }
      } ## single lp done
    } ## end of link or response case 
    rm(X)
  } ## end of prediction block loop
 
  if (!is.null(object$family$setInd)) object$family$setInd(NULL) ## reset any set subset index
  
  if ((type=="terms"||type=="iterms")&&(!is.null(terms)||!is.null(exclude))) { # return only terms requested via `terms'
    cnames <- colnames(fit)
    if (!is.null(terms)) {
      if (sum(!(terms %in%cnames))) 
        warning("non-existent terms requested - ignoring")
      else { 
        fit <- fit[,terms,drop=FALSE]
        if (se.fit) {
           se <- se[,terms,drop=FALSE]
        }
      }
    }
    if (!is.null(exclude)) {
      if (sum(!(exclude %in%cnames))) 
        warning("non-existent exclude terms requested - ignoring")
      else { 
        exclude <- which(cnames%in%exclude) ## convert to numeric column index
        fit <- fit[,-exclude,drop=FALSE]
        if (se.fit) {
          se <- se[,-exclude,drop=FALSE]
        }
      }
    }
  }

  if (type=="response"&&!is.null(fit1)) {
    fit <- fit1
    if (se.fit) se <- se1
  }

  rn <- rownames(newdata)
  if (type=="lpmatrix") { 
    colnames(H) <- names(object$coefficients);rownames(H)<-rn
    if (!is.null(s.offset)) { 
      s.offset <- napredict(na.act,s.offset)
      attr(H,"offset") <- s.offset ## term specific offsets...
    }
    #if (!is.null(attr(attr(object$model,"terms"),"offset"))) {
    #  attr(H,"model.offset") <- napredict(na.act,model.offset(mf)) 
    #}
    if (!is.null(offs)) {
      offs <- offs[1:nlp]
      for (i in 1:nlp) offs[[i]] <- napredict(na.act,offs[[i]])
      attr(H,"model.offset") <- if (nlp==1) offs[[1]] else offs
    }
    H <- napredict(na.act,H)
    if (length(object$nsdf)>1) { ## add "lpi" attribute if more than one l.p.
      #lpi <- list();pst <- c(pstart,ncol(H)+1)
      #for (i in 1:(length(pst)-1)) lpi[[i]] <- pst[i]:(pst[i+1]-1)  
      attr(H,"lpi") <- lpi
    }
  } else { 
    if (se.fit) { 
      if (is.null(nrow(fit))) {
        names(fit) <- rn
        names(se) <- rn
        fit <- napredict(na.act,fit)
        se <- napredict(na.act,se) 
      } else { 
        rownames(fit)<-rn
        rownames(se)<-rn
        fit <- napredict(na.act,fit)
        se <- napredict(na.act,se)
      }
      H<-list(fit=fit,se.fit=se) 
    } else { 
      H <- fit
      if (is.null(nrow(H))) names(H) <- rn else
      rownames(H)<-rn
      H <- napredict(na.act,H)
    }
  }
  if ((type=="terms"||type=="iterms")&&attr(object$terms,"intercept")==1) attr(H,"constant") <- object$coefficients[1]
  H # ... and return
} ## end of predict.gam



concurvity <- function(b,full=TRUE) {
## b is a gam object
## full==TRUE means that dependence of each term on rest of model 
##            is considered.
## full==FALSE => pairwise comparison.
  if (!inherits(b,"gam")) stop("requires an object of class gam")
  m <- length(b$smooth)
  if (m<1) stop("nothing to do for this model")
  X <- model.matrix(b)
  X <- X[rowSums(is.na(X))==0,]
  ## this step speeds up remaining computation...
  X <- qr.R(qr(X,tol=0,LAPACK=FALSE)) 
  stop <- start <- rep(1,m)
  lab <- rep("",m)
  for (i in 1:m) { ## loop through smooths
    start[i] <- b$smooth[[i]]$first.para
    stop[i] <- b$smooth[[i]]$last.para
    lab[i] <- b$smooth[[i]]$label
  }
  if (min(start)>1) { ## append parametric terms
    start <- c(1,start)
    stop <- c(min(start)-1,stop)
    lab <- c("para",lab)
    m <- m + 1
  }

  n.measures <- 3
  measure.names <- c("worst","observed","estimate")

  ##n <- nrow(X)
  if (full) { ## get dependence of each smooth on all the rest...
    conc <- matrix(0,n.measures,m)
    for (i in 1:m) {
      Xi <- X[,-(start[i]:stop[i]),drop=FALSE]
      Xj <- X[,start[i]:stop[i],drop=FALSE]
      r <- ncol(Xi) 
      R <- qr.R(qr(cbind(Xi,Xj),LAPACK=FALSE,tol=0))[,-(1:r),drop=FALSE] ## No pivoting!!  
       
      ##u worst case...
      Rt <- qr.R(qr(R,tol=0)) 
      conc[1,i] <- svd(forwardsolve(t(Rt),t(R[1:r,,drop=FALSE])))$d[1]^2
       
      ## observed...
      beta <- b$coef[start[i]:stop[i]]
      conc[2,i] <- sum((R[1:r,,drop=FALSE]%*%beta)^2)/sum((Rt%*%beta)^2)

      ## less pessimistic...
      conc[3,i] <- sum(R[1:r,]^2)/sum(R^2)
    }
    colnames(conc) <- lab
    rownames(conc) <- measure.names
  } else { ## pairwise measures
    conc <- list()
    for (i in 1:n.measures) conc[[i]] <- matrix(1,m,m) ## concurvity matrix
    for (i in 1:m) { ## concurvity calculation loop
      Xi <- X[,start[i]:stop[i],drop=FALSE]
      r <- ncol(Xi)
      for (j in 1:m) if (i!=j) { 
        Xj <- X[,start[j]:stop[j],drop=FALSE]
        R <- qr.R(qr(cbind(Xi,Xj),LAPACK=FALSE,tol=0))[,-(1:r),drop=FALSE] ## No pivoting!!  
        
        ## worst case...
        Rt <- qr.R(qr(R,tol=0)) 
        conc[[1]][i,j] <- svd(forwardsolve(t(Rt),t(R[1:r,,drop=FALSE])))$d[1]^2
       
        ## observed...
        beta <- b$coef[start[j]:stop[j]]
        conc[[2]][i,j] <- sum((R[1:r,,drop=FALSE]%*%beta)^2)/sum((Rt%*%beta)^2)

        ## less pessimistic...
        conc[[3]][i,j] <- sum(R[1:r,]^2)/sum(R^2)
        
        ## Alternative less pessimistic
       # log.det.R <- sum(log(abs(diag(R[(r+1):nrow(R),,drop=FALSE]))))
       # log.det.Rt <- sum(log(abs(diag(Rt))))
       # conc[[4]][i,j] <- 1 - exp(log.det.R-log.det.Rt) 
        rm(Xj,R,Rt)
      }
    } ## end of conc loop
    for (i in 1:n.measures) rownames(conc[[i]]) <- colnames(conc[[i]]) <- lab
    names(conc) <- measure.names
  } ## end of pairwise
  conc ## 
} ## end of concurvity


residuals.gam <-function(object, type = "deviance",...)
## calculates residuals for gam object 
{ ## if family has its own residual function, then use that...
  if (!is.null(object$family$residuals)) {
    res <- object$family$residuals(object,type,...)
    res <- naresid(object$na.action,res)
    return(res)
  }
  type <- match.arg(type,c("deviance", "pearson","scaled.pearson", "working", "response"))
  #if (sum(type %in% c("deviance", "pearson","scaled.pearson", "working", "response") )==0) 
  #      stop(paste(type," residuals not available"))
  ## default computations...
  y <- object$y
  mu <- object$fitted.values
  wts <- object$prior.weights
  if (type == "working") { 
    res <- object$residuals 
  } else if (type == "response") {
    res <- y - mu 
  } else if (type == "deviance") {
    res <- object$family$dev.resids(y,mu,wts)
    s <- attr(res,"sign")
    if (is.null(s)) s <- sign(y-mu)
    res <- sqrt(pmax(res,0)) * s 
  } else { ## some sort of Pearson
    var <- object$family$variance
    if (is.null(var)) {
      warning("Pearson residuals not available for this family - returning deviance residuals")
      return(residuals.gam(object))
    }
    res <- (y-mu)*sqrt(wts)/sqrt(var(mu))
    if (type == "scaled.pearson") res <- res/sqrt(object$sig2)
  }
  res <- naresid(object$na.action,res)
  res
} ## residuals.gam


## Start of anova and summary (with contributions from Henric Nilsson) ....

psum.chisq <- function(q,lb,df=rep(1,length(lb)),nc=rep(0,length(lb)),sigz=0,
                            lower.tail=FALSE,tol=2e-5,nlim=100000,trace=FALSE) {
## compute Pr(q>\sum_j lb[j] X_j + sigz Z) where X_j ~ chisq(df[j],nc[j]), Z~N(0,1) and nc is
## a vector of non-centrality parameters. lb can be either sign. df should be integer. 
  p <- q
  r <- length(lb)
  if (length(df)==1) df <- rep(df,r)
  if (length(nc)==1) nc <- rep(nc,r)
  if (length(df)!=r||length(nc)!=r) stop("lengths of lb, df and nc must match")
  df <- round(df)
  if (any(df<1)) stop("df must be positive integers")
  if (all(lb==0)) stop("at least one element of lb must be non-zero")
  if (sigz<0) sigz <- 0
  for (i in 1:length(q)) {  
    oo <- .C(C_davies,as.double(lb),as.double(nc),as.integer(df),as.integer(r),as.double(sigz),
             c=as.double(q[i]),as.integer(nlim),as.double(tol),trace=as.double(rep(0,7)),
             ifault=as.integer(0))
    if (oo$ifault!=0) {
      if (oo$ifault==2) { 
        warning("danger of round-off error")
        p[i] <- if (lower.tail) oo$c else 1 - oo$c
      } else { 
        warning("failure of Davies method, falling back on Liu et al approximtion")
        p[i] <- if (all(nc==0)) liu2(q[i],lb,h=df) else NA
      }
    } else p[i] <- if (lower.tail) oo$c else 1 - oo$c
  } 
  if (trace) {
    attr(p,"trace") <- oo$trace
    attr(p,"ifault") <- oo$ifault
  }
  p
} ##psum.chisq

liu2 <- function(x, lambda, h = rep(1,length(lambda)),lower.tail=FALSE) {
# Evaluate Pr[sum_i \lambda_i \chi^2_h_i < x] approximately.
# Code adapted from CompQuadForm package of Pierre Lafaye de Micheaux 
# and directly from....
# H. Liu, Y. Tang, H.H. Zhang, A new chi-square approximation to the 
# distribution of non-negative definite quadratic forms in non-central 
# normal variables, Computational Statistics and Data Analysis, Volume 53, 
# (2009), 853-856. Actually, this is just Pearson (1959) given that
# the chi^2 variables are central. 
# Note that this can be rubbish in lower tail (e.g. lambda=c(1.2,.3), x = .15)
  
#  if (FALSE) { ## use Davies exact method in place of Liu et al/ Pearson approx.
#    require(CompQuadForm)
#    r <- x
#    for (i in 1:length(x)) r[i] <- davies(x[i],lambda,h)$Qq
#    return(pmin(r,1))
#  }

  if (length(h) != length(lambda)) stop("lambda and h should have the same length!")
 
  lh <- lambda*h
  muQ <- sum(lh)
  
  lh <- lh*lambda
  c2 <- sum(lh)
  
  lh <- lh*lambda
  c3 <- sum(lh)
  
  xpos <- x > 0
  res <- 1 + 0 * x
  if (sum(xpos)==0 || c2 <= 0) return(res)

  s1 <- c3/c2^1.5
  s2 <- sum(lh*lambda)/c2^2

  sigQ <- sqrt(2*c2)

  t <- (x[xpos]-muQ)/sigQ

  if (s1^2>s2) {
    a <- 1/(s1-sqrt(s1^2-s2))
    delta <- s1*a^3-a^2
    l <- a^2-2*delta
  } else {
    a <- 1/s1
    delta <- 0
    if (c3==0) return(res)
    l <- c2^3/c3^2
  }

  muX <- l+delta
  sigX <- sqrt(2)*a
  res[xpos] <- pchisq(t*sigX+muX,df=l,ncp=delta,lower.tail=lower.tail)
  res
} ## liu2



simf <- function(x,a,df,nq=50) {
## suppose T = sum(a_i \chi^2_1)/(chi^2_df/df). We need
## Pr[T>x] = Pr(sum(a_i \chi^2_1) > x *chi^2_df/df). Quadrature 
## used here. So, e.g.
## 1-pf(4/3,3,40);simf(4,rep(1,3),40);1-pchisq(4,3)
## DEPRECATED in favour of psum.chisq...
  p <- (1:nq-.5)/nq
  q <- qchisq(p,df)
  x <- x*q/df
  pr <- sum(liu2(x,a)) ## Pearson/Liu approx to chi^2 mixture
  pr/nq 
}

packing.ind <- function(first,last,p,n) {
## Let A be a matrix with n rows, and B be a p by p matrix.
## A[first:last,first:last] is to be filled using B. If
## B is of the corect dimension then A[first:last,first:last] <-B
## but if p is a submultiple of (last-first+1) then the leading
## block diagonal of the block is to be filled repeatedly with
## B. In either case this routine returns an index ii such that
## A[ii] <- B fills the block appropriately
  if (last-first == p-1) {
    ii <- first:last
    return(rep(ii,p) + n*rep(ii-1,each=p))
  } else {
    k <- round((last-first+1)/p)
    if (k*p!=last-first+1) stop("incorrect sub-block size")
    ii <- rep(1:p,p) + n*rep(1:p-1,each=p)
    p2 <- p*p
    ind <- rep(0,p2*k)
    jj <- 1:(p2)
    for (i in 1:k) {
      bs <- first + (i-1)*p -1 
      ind[jj] <- ii + bs + bs*n
      jj <- jj + p2
    }
    return(ind)
  }
} ## packing.ind

recov <- function(b,re=rep(0,0),m=0) {
## b is a fitted gam object. re is an array of indices of 
## smooth terms to be treated as fully random....
## Returns frequentist Cov matrix based on the given
## mapping from data to params, but with dist of data
## corresponding to that implied by treating terms indexed
## by re as random effects... (would be usual frequentist 
## if nothing treated as random)
## if m>0, then this indexes a term, not in re, whose
## unpenalized cov matrix is required, with the elements of re
## dropped.
  if (!inherits(b,"gam")) stop("recov works with fitted gam objects only") 
  if (is.null(b$full.sp)) sp <- b$sp else sp <- b$full.sp
  if (length(re)<1) { 
    if (m>0) {
      ## annoyingly, need total penalty  
      np <- length(coef(b))
      k <- 1;S1 <- matrix(0,np,np)
      for (i in 1:length(b$smooth)) { 
        ns <- length(b$smooth[[i]]$S)
        #ind <- b$smooth[[i]]$first.para:b$smooth[[i]]$last.para
        if (ns>0) {
          ii <- packing.ind(b$smooth[[i]]$first.para,b$smooth[[i]]$last.para,ncol(b$smooth[[i]]$S[[1]]),np) 
          for (j in 1:ns) {
            #S1[ind,ind] <- S1[ind,ind] + sp[k]*b$smooth[[i]]$S[[j]]
            S1[ii] <- S1[ii] + sp[k]*as.numeric(b$smooth[[i]]$S[[j]])
            k <- k + 1
          }
        }
      }
      LRB <- rbind(b$R,t(mroot(S1)))
      ii <- b$smooth[[m]]$first.para:b$smooth[[m]]$last.para 
      ## ii is cols of LRB related to smooth m, which need 
      ## to be moved to the end...
      LRB <- cbind(LRB[,-ii],LRB[,ii])
      ii <- (ncol(LRB)-length(ii)+1):ncol(LRB)
      Rm <- qr.R(qr(LRB,tol=0,LAPACK=FALSE))[ii,ii] ## unpivoted QR
    } else Rm <- NULL
    return(list(Ve=(t(b$Ve)+b$Ve)*.5,Rm=Rm)) 
  }

  if (m%in%re) stop("m can't be in re")
  ## partition R into R1 ("fixed") and R2 ("random"), with S1 and S2
  p <- length(b$coefficients)
  rind <- rep(FALSE,p) ## random coefficient index
  for (i in 1:length(re)) {
    rind[b$smooth[[re[i]]]$first.para:b$smooth[[re[i]]]$last.para] <- TRUE
  }
  p2 <- sum(rind) ## number random
  p1 <- p - p2 ## number fixed
  map <- rep(0,p) ## remaps param indices to indices in split version
  map[rind] <- 1:p2 ## random
  map[!rind] <- 1:p1 ## fixed
  
  ## split R...
  R1 <- b$R[,!rind]  ## fixed effect columns
  R2 <- b$R[,rind]   ## random effect columns
  ## seitdem ich dich kennen, hab ich ein probleme,

  ## assemble S1 and S2
  S1 <- matrix(0,p1,p1);S2 <- matrix(0,p2,p2)
 
  k <- 1
  for (i in 1:length(b$smooth)) { 
    ns <- length(b$smooth[[i]]$S)
    #ind <- map[b$smooth[[i]]$first.para:b$smooth[[i]]$last.para]
    is.random <- i%in%re
    if (ns>0) { 
     ii <- packing.ind(map[b$smooth[[i]]$first.para],map[b$smooth[[i]]$last.para],ncol(b$smooth[[i]]$S[[1]]),if (is.random) p2 else p1)
     for (j in 1:ns) {
        #if (is.random) S2[ind,ind] <- S2[ind,ind] +  sp[k]*b$smooth[[i]]$S[[j]] else
        #   S1[ind,ind] <- S1[ind,ind] + sp[k]*b$smooth[[i]]$S[[j]]
        if (is.random) S2[ii] <- S2[ii] +  sp[k]*as.numeric(b$smooth[[i]]$S[[j]]) else
           S1[ii] <- S1[ii] + sp[k]*as.numeric(b$smooth[[i]]$S[[j]])
        k <- k + 1
      }
    }
  }
  ## pseudoinvert S2
  if (nrow(S2)==1) {
    S2[1,1] <- 1/sqrt(S2[1,1])
  } else if (max(abs(diag(diag(S2))-S2))==0) {
    ds2 <- diag(S2)
    ind <- ds2 > max(ds2)*.Machine$double.eps^.8
    ds2[ind] <- 1/ds2[ind];ds2[!ind] <- 0
    diag(S2) <- sqrt(ds2)
  } else {
    ev <- eigen((S2+t(S2))/2,symmetric=TRUE)
    ind <- ev$values > max(ev$values)*.Machine$double.eps^.8
    ev$values[ind] <- 1/ev$values[ind];ev$values[!ind] <- 0 
    ## S2 <- ev$vectors%*%(ev$values*t(ev$vectors))
    S2 <- sqrt(ev$values)*t(ev$vectors)
  }
  ## choleski of cov matrix....
  ## L <- chol(diag(p)+R2%*%S2%*%t(R2)) ## L'L = I + R2 S2^- R2'
  L <- chol(diag(p) + crossprod(S2%*%t(R2)))  

  ## now we need the square root of the unpenalized
  ## cov matrix for m
  if (m>0) {
      ## llr version
      LRB <- rbind(L%*%R1,t(mroot(S1)))
      ii <- map[b$smooth[[m]]$first.para:b$smooth[[m]]$last.para] 
      ## ii is cols of LRB related to smooth m, which need 
      ## to be moved to the end...
      LRB <- cbind(LRB[,-ii],LRB[,ii])
      ii <- (ncol(LRB)-length(ii)+1):ncol(LRB) ## need to pick up final block
      Rm <- qr.R(qr(LRB,tol=0,LAPACK=FALSE))[ii,ii,drop=FALSE] ## unpivoted QR
  } else Rm <- NULL

  list(Ve= crossprod(L%*%b$R%*%b$Vp)/b$sig2, ## Frequentist cov matrix
       Rm=Rm)
 # mapi <- (1:p)[!rind] ## indexes mapi[j] is index of total coef vector to which jth row/col of Vb/e relates
  
} ## end of recov


reTest <- function(b,m) {
## Test the mth smooth for equality to zero
## and accounting for all random effects in model 
  
  ## check that smooth penalty matrices are full size.  
  ## e.g. "fs" type smooths estimated by gamm do not 
  ## have full sized S matrices, and we can't compute 
  ## p-values here - actually we can see recov!
  #if (ncol(b$smooth[[m]]$S[[1]]) != b$smooth[[m]]$last.para-b$smooth[[m]]$first.para+1) {
  #  return(list(stat=NA,pval=NA,rank=NA)) 
  #}

  ## find indices of random effects other than m
  rind <- rep(0,0)
  for (i in 1:length(b$smooth)) if (!is.null(b$smooth[[i]]$random)&&b$smooth[[i]]$random&&i!=m) rind <- c(rind,i)
  ## get frequentist cov matrix of effects treating smooth terms in rind as random
  rc <- recov(b,rind,m) 
  Ve <- rc$Ve
  ind <- b$smooth[[m]]$first.para:b$smooth[[m]]$last.para
  B <- mroot(Ve[ind,ind,drop=FALSE]) ## BB'=Ve
 
  Rm <- rc$Rm
  
  b.hat <- coef(b)[ind]
  d <- Rm%*%b.hat
  stat <- sum(d^2)/b$sig2
  ev <- eigen(crossprod(Rm%*%B)/b$sig2,symmetric=TRUE,only.values=TRUE)$values
  ev[ev<0] <- 0
  rank <- sum(ev>max(ev)*.Machine$double.eps^.8)
  
  if (b$scale.estimated) {
    #pval <- simf(stat,ev,b$df.residual)
    k <- max(1,round(b$df.residual))
    pval <- psum.chisq(0,c(ev,-stat/k),df=c(rep(1,length(ev)),k))
  } else { 
    #pval <- liu2(stat,ev)
    pval <- psum.chisq(stat,ev) 
  }
  list(stat=stat,pval=pval,rank=rank)
} ## end reTest



testStat <- function(p,X,V,rank=NULL,type=0,res.df= -1) {
## Implements Wood (2013) Biometrika 100(1), 221-228
## The type argument specifies the type of truncation to use.
## on entry `rank' should be an edf estimate
## 0. Default using the fractionally truncated pinv.
## 1. Round down to k if k<= rank < k+0.05, otherwise up.
## res.df is residual dof used to estimate scale. <=0 implies
## fixed scale.

  qrx <- qr(X,tol=0)
  R <- qr.R(qrx)
  V <- R%*%V[qrx$pivot,qrx$pivot,drop=FALSE]%*%t(R)
  V <- (V + t(V))/2
  ed <- eigen(V,symmetric=TRUE)
  ## remove possible ambiguity from statistic...
  siv <- sign(ed$vectors[1,]);siv[siv==0] <- 1
  ed$vectors <- sweep(ed$vectors,2,siv,"*")

  k <- max(0,floor(rank)) 
  nu <- abs(rank - k)     ## fractional part of supplied edf
  if (type==1) { ## round up is more than .05 above lower
    if (rank > k + .05||k==0) k <- k + 1
    nu <- 0;rank <- k
  }

  if (nu>0) k1 <- k+1 else k1 <- k

  ## check that actual rank is not below supplied rank+1
  r.est <- sum(ed$values > max(ed$values)*.Machine$double.eps^.9)
  if (r.est<k1) {k1 <- k <- r.est;nu <- 0;rank <- r.est}

  ## Get the eigenvectors...
  # vec <- qr.qy(qrx,rbind(ed$vectors,matrix(0,nrow(X)-ncol(X),ncol(X))))
  vec <- ed$vectors
  if (k1<ncol(vec)) vec <- vec[,1:k1,drop=FALSE]

  ## deal with the fractional part of the pinv...
  if (nu>0&&k>0) {
     if (k>1) vec[,1:(k-1)] <- t(t(vec[,1:(k-1)])/sqrt(ed$val[1:(k-1)]))
     b12 <- .5*nu*(1-nu)
     if (b12<0) b12 <- 0
     b12 <- sqrt(b12)
     B <- matrix(c(1,b12,b12,nu),2,2)
     ev <- diag(ed$values[k:k1]^-.5,nrow=k1-k+1)
     B <- ev%*%B%*%ev
     eb <- eigen(B,symmetric=TRUE)
     rB <- eb$vectors%*%diag(sqrt(eb$values))%*%t(eb$vectors)
     vec1 <- vec
     vec1[,k:k1] <- t(rB%*%diag(c(-1,1))%*%t(vec[,k:k1]))
     vec[,k:k1] <- t(rB%*%t(vec[,k:k1]))
  } else {
    vec1 <- vec <- if (k==0) t(t(vec)*sqrt(1/ed$val[1])) else
            t(t(vec)/sqrt(ed$val[1:k]))
    if (k==1) rank <- 1
  }
  ## there is an ambiguity in the choise of test statistic, leading to slight
  ## differences in the p-value computation depending on which of 2 alternatives 
  ## is arbitrarily selected. Following allows both to be computed and p-values
  ## averaged (can't average test stat as dist then unknown) 
  d <- t(vec)%*%(R%*%p)
  d <- sum(d^2) 
  d1 <- t(vec1)%*%(R%*%p)
  d1 <- sum(d1^2)
  ##d <- d1 ## uncomment to avoid averaging

  rank1 <- rank ## rank for lower tail pval computation below

  ## note that for <1 edf then d is not weighted by EDF, and instead is 
  ## simply refered to a chi-squared 1

  if (nu>0) { ## mixture of chi^2 ref dist
     if (k1==1) rank1 <- val <- 1 else { 
       val <- rep(1,k1) ##ed$val[1:k1]
       rp <- nu+1
       val[k] <- (rp + sqrt(rp*(2-rp)))/2
       val[k1] <- (rp - val[k])
     }
   
     if (res.df <= 0) pval <- (psum.chisq(d,val)+psum.chisq(d1,val))/2 else {  ## (liu2(d,val) + liu2(d1,val))/2 else
       k0 <- max(1,round(res.df))
       pval <- (psum.chisq(0,c(val,-d/k0),df=c(rep(1,length(val)),k0)) + psum.chisq(0,c(val,-d1/k0),df=c(rep(1,length(val)),k0)) )/2 
       #pval <- (simf(d,val,res.df) + simf(d1,val,res.df))/2
     }
  } else { pval <- 2 }
  ## integer case still needs computing, 
  ## OLD: also liu/pearson approx only good in 
  ## upper tail. In lower tail, 2 moment approximation is better (Can check this 
  ## by simply plotting the whole interesting range as a contour plot!)
  ##if (pval > .5) 
  if (pval > 1) { 
    if (res.df <= 0) pval <- (pchisq(d,df=rank1,lower.tail=FALSE)+pchisq(d1,df=rank1,lower.tail=FALSE))/2 else
    pval <- (pf(d/rank1,rank1,res.df,lower.tail=FALSE)+pf(d1/rank1,rank1,res.df,lower.tail=FALSE))/2
  }
  list(stat=d,pval=min(1,pval),rank=rank)
} ## end of testStat




summary.gam <- function (object, dispersion = NULL, freq = FALSE,re.test = TRUE, ...) {
## summary method for gam object - provides approximate p values 
## for terms + other diagnostics
## Improved by Henric Nilsson
## * freq determines whether a frequentist or Bayesian cov matrix is 
##   used for parametric terms. Usually the default TRUE will result
##   in reasonable results with paraPen.
## If a smooth has a field 'random' and it is set to TRUE then 
## it is treated as a random effect for some p-value dist calcs 


  pinv<-function(V,M,rank.tol=1e-6) {
  ## a local pseudoinverse function
    D <- eigen(V,symmetric=TRUE)
    M1<-length(D$values[D$values>rank.tol*D$values[1]])
    if (M>M1) M<-M1 # avoid problems with zero eigen-values
  
    if (M+1<=length(D$values)) D$values[(M+1):length(D$values)]<-1
    D$values<- 1/D$values
    if (M+1<=length(D$values)) D$values[(M+1):length(D$values)]<-0
    res <- D$vectors%*%(D$values*t(D$vectors))  ##D$u%*%diag(D$d)%*%D$v
    attr(res,"rank") <- M
    res
  } ## end of pinv
  
  if (is.null(object$R)) { ## Factor from QR decomp of sqrt(W)X
    warning("p-values for any terms that can be penalized to zero will be unreliable: refit model to fix this.")
    useR <- FALSE
  } else useR <- TRUE

  p.table <- pTerms.table <- s.table <- NULL

  if (freq) covmat <- object$Ve else covmat <- object$Vp
  name <- names(object$edf)
  dimnames(covmat) <- list(name, name)
  covmat.unscaled <- covmat/object$sig2
  est.disp <- object$scale.estimated
  if (!is.null(dispersion)) { 
    covmat <- dispersion * covmat.unscaled
    object$Ve <- object$Ve*dispersion/object$sig2 ## freq
    object$Vp <- object$Vp*dispersion/object$sig2 ## Bayes
    est.disp <- FALSE
  } else dispersion <- object$sig2
 

  ## Now the individual parameteric coefficient p-values...

  se <- diag(covmat)^0.5
  residual.df<-length(object$y)-sum(object$edf)
  if (sum(object$nsdf) > 0) { # individual parameters
    if (length(object$nsdf)>1) { ## several linear predictors 
      pstart <- attr(object$nsdf,"pstart")
      ind <- rep(0,0)
      for (i in 1:length(object$nsdf)) if (object$nsdf[i]>0) ind <- 
          c(ind,pstart[i]:(pstart[i]+object$nsdf[i]-1))
    } else { pstart <- 1;ind <- 1:object$nsdf} ## only one lp
    p.coeff <- object$coefficients[ind]
    p.se <- se[ind]
    p.t<-p.coeff/p.se
    if (!est.disp) {
      p.pv <- 2*pnorm(abs(p.t),lower.tail=FALSE)
      p.table <- cbind(p.coeff, p.se, p.t, p.pv)   
      dimnames(p.table) <- list(names(p.coeff), c("Estimate", "Std. Error", "z value", "Pr(>|z|)"))
    } else {
      p.pv <- 2*pt(abs(p.t),df=residual.df,lower.tail=FALSE)
      p.table <- cbind(p.coeff, p.se, p.t, p.pv)
      dimnames(p.table) <- list(names(p.coeff), c("Estimate", "Std. Error", "t value", "Pr(>|t|)"))
    }    
  } else {p.coeff <- p.t <- p.pv <- array(0,0)}

  ## Next the p-values for parametric terms, so that factors are treated whole... 
  
  pterms <- if (is.list(object$pterms)) object$pterms else list(object$pterms)
  if (!is.list(object$assign)) object$assign <- list(object$assign)
  npt <- length(unlist(lapply(pterms,attr,"term.labels")))
  if (npt>0)  pTerms.df <- pTerms.chi.sq <- pTerms.pv <- array(0,npt)
  term.labels <- rep("",0)
  k <- 0 ## total term counter
  for (j in 1:length(pterms)) {
    tlj <- attr(pterms[[j]],"term.labels") 
    nt <- length(tlj)
    if (j>1 && nt>0) tlj <- paste(tlj,j-1,sep=".")
    term.labels <- c(term.labels,tlj)
    if (nt>0) { # individual parametric terms
      np <- length(object$assign[[j]])
      ind <- pstart[j] - 1 + 1:np 
      Vb <- covmat[ind,ind,drop=FALSE]
      bp <- array(object$coefficients[ind],np)
    
      for (i in 1:nt) { 
        k <- k + 1
        ind <- object$assign[[j]]==i
        b <- bp[ind];V <- Vb[ind,ind]
        ## pseudo-inverse needed in case of truncation of parametric space 
        if (length(b)==1) { 
          V <- 1/V 
          pTerms.df[k] <- nb <- 1      
          pTerms.chi.sq[k] <- V*b*b
        } else {
          V <- pinv(V,length(b),rank.tol=.Machine$double.eps^.5)
          pTerms.df[k] <- nb <- attr(V,"rank")      
          pTerms.chi.sq[k] <- t(b)%*%V%*%b
        }
        if (!est.disp)
        pTerms.pv[k] <- pchisq(pTerms.chi.sq[k],df=nb,lower.tail=FALSE)
        else
        pTerms.pv[k] <- pf(pTerms.chi.sq[k]/nb,df1=nb,df2=residual.df,lower.tail=FALSE)      
      } ## for (i in 1:nt)
    } ## if (nt>0)
  }

  if (npt) {
    attr(pTerms.pv,"names") <- term.labels
    if (!est.disp) {      
      pTerms.table <- cbind(pTerms.df, pTerms.chi.sq, pTerms.pv)   
      dimnames(pTerms.table) <- list(term.labels, c("df", "Chi.sq", "p-value"))
    } else {
      pTerms.table <- cbind(pTerms.df, pTerms.chi.sq/pTerms.df, pTerms.pv)   
      dimnames(pTerms.table) <- list(term.labels, c("df", "F", "p-value"))
    }
  } else { pTerms.df<-pTerms.chi.sq<-pTerms.pv<-array(0,0)}

  ## Now deal with the smooth terms....

  m <- length(object$smooth) # number of smooth terms
  
  df <- edf1 <- edf <- s.pv <- chi.sq <- array(0, m)
  if (m>0) { # form test statistics for each smooth
    ## Bayesian p-values required 
    if (useR)  X <- object$R else {
      sub.samp <- max(1000,2*length(object$coefficients)) 
      if (nrow(object$model)>sub.samp) { ## subsample to get X for p-values calc.
        kind <- temp.seed(11)
        #seed <- try(get(".Random.seed",envir=.GlobalEnv),silent=TRUE) ## store RNG seed
        #if (inherits(seed,"try-error")) {
        #  runif(1)
        #  seed <- get(".Random.seed",envir=.GlobalEnv)
        #}
        #kind <- RNGkind(NULL)
        #RNGkind("default","default")
        #set.seed(11) ## ensure repeatability
        ind <- sample(1:nrow(object$model),sub.samp,replace=FALSE)  ## sample these rows from X
        X <- predict(object,object$model[ind,],type="lpmatrix")
        #RNGkind(kind[1],kind[2])
        #assign(".Random.seed",seed,envir=.GlobalEnv) ## RNG behaves as if it had not been used
        temp.seed(kind)
      } else { ## don't need to subsample 
        X <- model.matrix(object)
      }
      X <- X[!is.na(rowSums(X)),] ## exclude NA's (possible under na.exclude)    
    } ## end if (m>0)
    ii <- 0
    for (i in 1:m) { ## loop through smooths

      start <- object$smooth[[i]]$first.para;stop <- object$smooth[[i]]$last.para

      V <- object$Vp[start:stop,start:stop,drop=FALSE] ## Bayesian
      
      p <- object$coefficients[start:stop]  # params for smooth
      edf1i <- edfi <- sum(object$edf[start:stop]) # edf for this smooth
      ## extract alternative edf estimate for this smooth, if possible...
      if (!is.null(object$edf1)) edf1i <-  sum(object$edf1[start:stop])
      Xt <- X[,start:stop,drop=FALSE]  
      fx <- if (inherits(object$smooth[[i]],"tensor.smooth")&&
                !is.null(object$smooth[[i]]$fx)) all(object$smooth[[i]]$fx) else object$smooth[[i]]$fixed
      if (!fx&&object$smooth[[i]]$null.space.dim==0&&!is.null(object$R)) { ## random effect or fully penalized term
        res <- if (re.test) reTest(object,i) else NULL
      } else { ## Inverted Nychka interval statistics
        if (est.disp) rdf <- residual.df else rdf <- -1
        res <- testStat(p,Xt,V,min(ncol(Xt),edf1i),type=0,res.df = rdf)
      }
      if (!is.null(res)) {
        ii <- ii + 1
        df[ii] <- res$rank
        chi.sq[ii] <- res$stat
        s.pv[ii] <- res$pval 
        edf1[ii] <- edf1i 
        edf[ii] <- edfi 
        names(chi.sq)[ii]<- object$smooth[[i]]$label
      }
    } 
    if (ii==0) df <- edf1 <- edf <- s.pv <- chi.sq <- array(0, 0) else {
      df <- df[1:ii];chi.sq <- chi.sq[1:ii];edf1 <- edf1[1:ii]
      edf <- edf[1:ii];s.pv <- s.pv[1:ii]
    }
    if (!est.disp) {
      s.table <- cbind(edf, df, chi.sq, s.pv)      
      dimnames(s.table) <- list(names(chi.sq), c("edf", "Ref.df", "Chi.sq", "p-value"))
    } else {
      s.table <- cbind(edf, df, chi.sq/df, s.pv)      
      dimnames(s.table) <- list(names(chi.sq), c("edf", "Ref.df", "F", "p-value"))
    }
  }
  w <- as.numeric(object$prior.weights)
  mean.y <- sum(w*object$y)/sum(w)
  w <- sqrt(w)
  nobs <- nrow(object$model)
  r.sq <- if (inherits(object$family,"general.family")||!is.null(object$family$no.r.sq)) NULL else  
          1 - var(w*(as.numeric(object$y)-object$fitted.values))*(nobs-1)/(var(w*(as.numeric(object$y)-mean.y))*residual.df) 
  dev.expl<-(object$null.deviance-object$deviance)/object$null.deviance
  if (object$method%in%c("REML","ML")) object$method <- paste("-",object$method,sep="")
  ret<-list(p.coeff=p.coeff,se=se,p.t=p.t,p.pv=p.pv,residual.df=residual.df,m=m,chi.sq=chi.sq,
       s.pv=s.pv,scale=dispersion,r.sq=r.sq,family=object$family,formula=object$formula,n=nobs,
       dev.expl=dev.expl,edf=edf,dispersion=dispersion,pTerms.pv=pTerms.pv,pTerms.chi.sq=pTerms.chi.sq,
       pTerms.df = pTerms.df, cov.unscaled = covmat.unscaled, cov.scaled = covmat, p.table = p.table,
       pTerms.table = pTerms.table, s.table = s.table,method=object$method,sp.criterion=object$gcv.ubre,
       rank=object$rank,np=length(object$coefficients))
 
  class(ret)<-"summary.gam"
  ret
} ## end summary.gam

print.summary.gam <- function(x, digits = max(3, getOption("digits") - 3), 
                              signif.stars = getOption("show.signif.stars"), ...)
# print method for gam summary method. Improved by Henric Nilsson
{ print(x$family)
  cat("Formula:\n") 

  if (is.list(x$formula)) for (i in 1:length(x$formula)) print(x$formula[[i]]) else
     print(x$formula)

  if (length(x$p.coeff)>0)
  { cat("\nParametric coefficients:\n")
    printCoefmat(x$p.table, digits = digits, signif.stars = signif.stars, na.print = "NA", ...)
  }
  cat("\n")
  if(x$m>0)
  { cat("Approximate significance of smooth terms:\n")
    printCoefmat(x$s.table, digits = digits, signif.stars = signif.stars, has.Pvalue = TRUE, na.print = "NA",cs.ind=1, ...)
  }
  cat("\n")
  if (!is.null(x$rank) && x$rank< x$np) cat("Rank: ",x$rank,"/",x$np,"\n",sep="") 
  if (!is.null(x$r.sq)) cat("R-sq.(adj) = ",formatC(x$r.sq,digits=3,width=5),"  ")
  if (length(x$dev.expl)>0) cat("Deviance explained = ",formatC(x$dev.expl*100,digits=3,width=4),"%",sep="")
  cat("\n")
  if ((!is.null(x$sp.criterion)&&!is.na(x$sp.criterion)) &&
      !is.null(x$method) && !(x$method%in%c("PQL","lme.ML","lme.REML")))  
    cat(x$method," = ",formatC(x$sp.criterion,digits=5),sep="")
 
  cat("  Scale est. = ",formatC(x$scale,digits=5,width=8,flag="-"),"  n = ",x$n,"\n",sep="")
  invisible(x)
} ## print.summary.gam


anova.gam <- function (object, ..., dispersion = NULL, test = NULL,  freq=FALSE)
# improved by Henric Nilsson
{   # adapted from anova.glm: R stats package
    dotargs <- list(...)
    named <- if (is.null(names(dotargs)))
        rep(FALSE, length(dotargs))
    else (names(dotargs) != "")
    if (any(named))
        warning("The following arguments to anova.glm(..) are invalid and dropped: ",
            paste(deparse(dotargs[named]), collapse = ", "))
    dotargs <- dotargs[!named]
    is.glm <- unlist(lapply(dotargs, function(x) inherits(x,
        "glm")))
    dotargs <- dotargs[is.glm]
    if (length(dotargs) > 0) {
      if (!is.null(test)&&!test%in%c("Chisq","LRT","F")) stop("un-supported test")
      ## check for multiple formulae to avoid problems...
      if (is.list(object$formula)) object$formula <- object$formula[[1]]
      ## reset df.residual to value appropriate for GLRT...
      n <- if (is.matrix(object$y)) nrow(object$y) else length(object$y)
      dfc <- if (is.null(object$edf2)) 0 else sum(object$edf2) - sum(object$edf) 
      object$df.residual <- n - sum(object$edf1) - dfc
      ## reset the deviance to -2*logLik for general families...
      if (inherits(object$family,"extended.family")) {  
        min.df <- object$df.residual
        disp <- if (is.null(dispersion)) object$sig2 else dispersion
        object$deviance <- -2 * as.numeric(logLik(object)) ## deviance returned is not always suitable for e.g. F test
        if (!is.null(test)) test <- "Chisq"
      }
      ## repeat above 3 steps for each element of dotargs...
      for (i in 1:length(dotargs)) {
        if (is.list(dotargs[[i]]$formula)) dotargs[[i]]$formula <- dotargs[[i]]$formula[[1]]
        dfc <- if (is.null(dotargs[[i]]$edf2)) 0 else sum(dotargs[[i]]$edf2) - sum(dotargs[[i]]$edf) 
        dotargs[[i]]$df.residual <- n - sum(dotargs[[i]]$edf1) - dfc
        if (inherits(dotargs[[i]]$family,"extended.family")) {
          if (object$df.residual < min.df) {
            object$df.residual -> min.df
            disp <- if (is.null(dispersion))  dotargs[[i]]$sig2 else dispersion
          }
          dotargs[[i]]$deviance <- -2 * as.numeric(logLik(dotargs[[i]]))
        } 
      } 
      if (inherits(object$family,"extended.family")) { ## multiply by dispersion as anova.glm will divide by it!
         object$deviance <- object$deviance * disp
         for (i in 1:length(dotargs)) dotargs[[i]]$deviance <- dotargs[[i]]$deviance * disp
      } 
      return(anova(structure(c(list(object), dotargs), class="glmlist"), 
            dispersion = dispersion, test = test))
    } 
    if (!is.null(test)) warning("test argument ignored")
    if (!inherits(object,"gam")) stop("anova.gam called with non gam object")
    sg <- summary(object, dispersion = dispersion, freq = freq)
    class(sg) <- "anova.gam"
    sg
} ## anova.gam


print.anova.gam <- function(x, digits = max(3, getOption("digits") - 3), ...)
{ # print method for class anova.gam resulting from single
  # gam model calls to anova. Improved by Henric Nilsson.
  print(x$family)
  cat("Formula:\n") 
  if (is.list(x$formula)) for (i in 1:length(x$formula)) print(x$formula[[i]]) else
  print(x$formula)
  if (length(x$pTerms.pv)>0)
  { cat("\nParametric Terms:\n")
    printCoefmat(x$pTerms.table, digits = digits, signif.stars = FALSE, has.Pvalue = TRUE, na.print = "NA", ...)
  }
  cat("\n")
  if(x$m>0)
  { cat("Approximate significance of smooth terms:\n")
    printCoefmat(x$s.table, digits = digits, signif.stars = FALSE, has.Pvalue = TRUE, na.print = "NA", ...)
  }
  invisible(x)
} ## print.anova.gam

## End of improved anova and summary code. 


pen.edf <- function(x) {
## obtains the edf associated with each penalty. That is the edf 
## of the group of coefficients penalized by each penalty.
## hard to interpret for overlapping penalties. brilliant for t2
## smooths!
  if (!inherits(x,"gam")) stop("not a gam object")
  if (length(x$smooth)==0) return(NULL)
  k <- 0 ## penalty counter
  edf <- rep(0,0)
  edf.name <- rep("",0)
  for (i in 1:length(x$smooth)) { ## work through smooths
    if (length(x$smooth[[i]]$S)>0) {
      pind <- x$smooth[[i]]$first.para:x$smooth[[i]]$last.para ## range of coefs relating to this term
      Snames <- names(x$smooth[[i]]$S)
      if (is.null(Snames)) Snames <- as.character(1:length(x$smooth[[i]]$S))
      if (length(Snames)==1) Snames <- ""
      for (j in 1:length(x$smooth[[i]]$S)) {
        ind <- rowSums(x$smooth[[i]]$S[[j]]!=0)!=0 ## index of penalized coefs (within pind)
        k <- k+1
        edf[k] <- sum(x$edf[pind[ind]]) 
        edf.name[k] <- paste(x$smooth[[i]]$label,Snames[j],sep="")
      }    
    }
  } ## finished all penalties
  names(edf) <- edf.name
  if (k==0) return(NULL)
  edf
} ## end of pen.edf



cooks.distance.gam <- function(model,...)
{ res <- residuals(model,type="pearson")
  dispersion <- model$sig2
  hat <- model$hat
  p <- sum(model$edf)
  (res/(1 - hat))^2 * hat/(dispersion * p)
}


sp.vcov <- function(x,edge.correct=TRUE,reg=1e-3) {
## get cov matrix of smoothing parameters, if available
  if (!inherits(x,"gam")) stop("argument is not a gam object")
  if (x$method%in%c("ML","P-ML","REML","P-REML","fREML")&&!is.null(x$outer.info$hess)) {
    hess <- x$outer.info$hess
    p <- ncol(hess)
    if (edge.correct&&!is.null(attr(hess,"hess1"))) {
      V <- solve(attr(hess,"hess1")+diag(p)*reg) 
      attr(V,"lsp") <- attr(hess,"lsp1")
      return(V)
    } else return(solve(hess+reg))
  } else return(NULL)
}

gam.vcomp <- function(x,rescale=TRUE,conf.lev=.95) {
## Routine to convert smoothing parameters to variance components
## in a fitted `gam' object.
  if (!inherits(x,"gam")) stop("requires an object of class gam")
  if (!is.null(x$reml.scale)&&is.finite(x$reml.scale)) scale <- x$reml.scale else scale <- x$sig2
  if (length(x$sp)==0) return()
  if (rescale) { ## undo any rescaling of S[[i]] that may have been done
    m <- length(x$smooth)
    if (is.null(x$paraPen)) { 
      k <- 1;
      if (is.null(x$full.sp)) kf <- -1 else kf <- 1 ## place holder in full sp vector
    } else { ## don't rescale paraPen related stuff
      k <- sum(x$paraPen$sp<0)+1 ## count free sp's for paraPen
      if (is.null(x$full.sp)) kf <- -1 else kf <- length(x$paraPen$full.sp.names)+1
    }
    idx <- rep("",0) ## vector of ids used
    idxi <- rep(0,0) ## indexes ids in smooth list
    if (m>0) for (i in 1:m) { ## loop through all smooths
      if (!is.null(x$smooth[[i]]$id)) { ## smooth has an id
        if (x$smooth[[i]]$id%in%idx) { 
          ok <- FALSE ## id already dealt with --- ignore smooth
        } else {
          idx <- c(idx,x$smooth[[i]]$id) ## add id to id list
          idxi <- c(idxi,i) ## so smooth[[idxi[k]]] is prototype for idx[k]
          ok <- TRUE
        } 
      } else { ok <- TRUE} ## no id so proceed
      if (ok) { 
       if (length(x$smooth[[i]]$S.scale)!=length(x$smooth[[i]]$S))
         warning("S.scale vector doesn't match S list - please report to maintainer")
	n.s <- length(x$smooth[[i]]$S.scale)
        if (n.s>0) for (j in 1:n.s) {
          if (x$smooth[[i]]$sp[j]<0) { ## sp not supplied
            x$sp[k] <- x$sp[k] / x$smooth[[i]]$S.scale[j]
            k <- k + 1
            if (kf>0) {
              x$full.sp[kf] <- x$full.sp[kf] / x$smooth[[i]]$S.scale[j]
              kf <- kf + 1
            }
          } else { ## sp supplied
            x$full.sp[kf] <- x$full.sp[kf] / x$smooth[[i]]$S.scale[j]
            kf <- kf + 1
          } 
        }
      } else { ## this id already dealt with, but full.sp not scaled yet 
        ii <- idxi[idx%in%x$smooth[[i]]$id] ## smooth prototype
	n.s <- length(x$smooth[[ii]]$S.scale)
        for (j in 1:n.s) {
          x$full.sp[kf] <- x$full.sp[kf] / x$smooth[[ii]]$S.scale[j]
          kf <- kf + 1
        }
      } 
    } ## finished rescaling
  }
  ## variance components (original scale)
  vc <-  scale/x$sp
  names(vc) <- names(x$sp)

  if (is.null(x$full.sp)) vc.full <- NULL else { 
    vc.full <- c(scale/x$full.sp)
    names(vc.full) <- names(x$full.sp)
  }
  ## If a Hessian exists, get CI's for variance components...

  if (x$method%in%c("ML","P-ML","REML","P-REML","fREML")&&!is.null(x$outer.info$hess)) {
    if (is.null(x$family$n.theta)||x$family$n.theta<=0||"perf" %in% x$optimizer) H <- x$outer.info$hess ## the hessian w.r.t. log sps and log scale
    else { ## first rows and cols of Hessian relate to extra log lik params
      ind <- 1:x$family$n.theta
      H <- x$outer.info$hess[-ind,-ind,drop=FALSE]
    }

    if (ncol(H)>length(x$sp)) scale.est <- TRUE else scale.est <- FALSE
    
    ## get derivs of log sqrt var comps wrt log sp and log scale....
    J <- matrix(0,nrow(H),ncol(H)) 
    if (scale.est) { 
      diag(J) <- -.5 # -2
      J[,ncol(J)] <- .5 # 2
      vc <- c(vc,scale);names(vc) <- c(names(x$sp),"scale")
    } else {
      diag(J) <- -0.5 #-2
    }
    #H <- t(J)%*%H%*%J ## hessian of log sqrt variances
    eh <- eigen(H,symmetric=TRUE)
    ind <- eh$values>max(eh$values)*.Machine$double.eps^75 ## index of non zero eigenvalues 
    rank <- sum(ind) ## rank of hessian
    iv <- eh$values*0;iv[ind] <- 1/eh$values[ind]
    V <- eh$vectors%*%(iv*t(eh$vectors)) ## cov matrix for sp's ## log sqrt variances
    V <- J%*%V%*%t(J) ## cov matrix for log sqrt variance
    lsd <- log(sqrt(vc)) ## log sqrt variances
    sd.lsd <- sqrt(diag(V))
    if (conf.lev<=0||conf.lev>=1) conf.lev <- 0.95
    crit <- qnorm(1-(1-conf.lev)/2)
    ll <- lsd - crit * sd.lsd
    ul <- lsd + crit * sd.lsd
    res <- cbind(exp(lsd),exp(ll),exp(ul))
    rownames(res) <- names(vc)
    colnames(res) <- c("std.dev","lower","upper")
    cat("\n")
    cat(paste("Standard deviations and",conf.lev,"confidence intervals:\n\n"))
    print(res)
    cat("\nRank: ");cat(rank);cat("/");cat(ncol(H));cat("\n")
    if (!is.null(vc.full)) { 
      cat("\nAll smooth components:\n")
      print(sqrt(vc.full))
      res <- list(all=sqrt(vc.full),vc=res)
    }
    invisible(res)
  } else {
    if (is.null(vc.full)) return(sqrt(vc)) else return(list(vc=sqrt(vc),all=sqrt(vc.full)))
  } 
} ## end of gam.vcomp


gam.sandwich <- function(b,freq=FALSE) {
## computes sandwich estimator of variance
  B2 <- if (freq) 0 else b$Vp - b$Ve ## Bayes squared bias estimate
  X <- model.matrix(b)
  m <- nrow(X); m <- m/(m-sum(b$edf))
  if (inherits(b$family,"extended.family")) {
    if (inherits(b$family,"general.family")) {
       if (is.null(b$family$sandwich)) stop("no sandwich estimate available for this model")
       Vs <- m*b$Vp%*%b$family$sandwich(b$y,X,b$coefficients,b$prior.weights,b$family,offset=attr(X,"offset"))%*%b$Vp + B2
    } else {
      dd <- dDeta(b$y,b$fitted.values,b$prior.weights,b$family$getTheta(),b$family,deriv=0)
      Vs <- m*b$Vp%*%crossprod(0.5/b$sig2*dd$Deta*X)%*%b$Vp + B2 
    }
  } else { ## exponential family
    mu <- b$fitted.values
    w <- b$family$mu.eta(b$linear.predictors)*(b$y - mu)/(b$sig2*b$family$variance(mu))
    Vs <- m*b$Vp%*%crossprod(w*X)%*%b$Vp + B2
  }
  Vs
} ## gam.sandwich


vcov.gam <- function(object, sandwich=FALSE, freq = FALSE, dispersion = NULL,unconditional=FALSE, ...)
## supplied by Henric Nilsson <henric.nilsson@statisticon.se> 
{ if (sandwich) vc <- gam.sandwich(object,freq) else { 
    if (freq)
      vc <- object$Ve
    else { 
      vc <- if (unconditional&&!is.null(object$Vc)) object$Vc else object$Vp
    }
  }
  if (!is.null(dispersion))
    vc <- dispersion * vc / object$sig2
  name <- names(object$edf)
  dimnames(vc) <- list(name, name)
  vc
}




influence.gam <- function(model,...) { model$hat }




logLik.gam <- function (object,...)
{  # based on logLik.glm - is ordering of p correction right???
   # if (length(list(...)))
   #     warning("extra arguments discarded")
   
    ##fam <- family(object)$family
    sc.p <- as.numeric(object$scale.estimated)
    p <- sum(object$edf) + sc.p
    val <- p - object$aic/2
    #if (fam %in% c("gaussian", "Gamma", "inverse.gaussian","Tweedie"))
    #    p <- p + 1
    if (!is.null(object$edf2)) p <- sum(object$edf2) + sc.p
    np <- length(object$coefficients) + sc.p 
    if (p > np) p <- np 
    if (inherits(object$family,"extended.family")&&!is.null(object$family$n.theta)) p <- p + object$family$n.theta 
    attr(val, "df") <- p
    class(val) <- "logLik"
    val
} ## logLik.gam



# From here on is the code for magic.....

mroot <- function(A,rank=NULL,method="chol")
# finds the smallest square root of A, or the best approximate square root of 
# given rank. B is returned where BB'=A. A assumed non-negative definite. 
# Current methods "chol", "svd". "svd" is slower, but much better at getting the 
# correct rank if it isn't known in advance. 
{ if (is.null(rank)) rank <- 0 
  if (!isTRUE(all.equal(A,t(A)))) stop("Supplied matrix not symmetric")
  if (method=="svd") { 
    um <- eigen(A,symmetric=TRUE) ## same as svd for +ve semi def, but faster
    if (rank<1) rank <- sum(um$values > max(um$values)*.Machine$double.eps)
    if (rank==0) stop("Something wrong - matrix probably not +ve semi definite")
    return(t(t(um$vectors[,1:rank])*sqrt(um$values[1:rank])))
  } else if (method=="chol") { 
    ## don't want to be warned it's not +ve def...
    L <- suppressWarnings(chol(A,pivot=TRUE,tol=0))
    piv <- order(attr(L,"pivot"))
    ## chol does not work as documented (reported), have to explicitly zero
    ## the trailing block...
    r <- attr(L,"rank")
    p <- ncol(L)
    if (r < p) L[(r+1):p,(r+1):p] <- 0
    if (rank < 1) rank <- r
    L <- L[,piv,drop=FALSE]; L <- t(L[1:rank,,drop=FALSE])
    return(L)
  } else
  stop("method not recognised.")
} ## mroot



magic.post.proc <- function(X,object,w=NULL)
# routine to take list returned by magic and extract:
# Vb the estimated bayesian parameter covariance matrix. rV%*%t(rV)*scale
# Ve the frequentist parameter estimator covariance matrix.
# edf the array of estimated degrees of freedom per parameter Vb%*%t(X)%*%W%*%X /scale
# hat the leading diagonal of the hat/influence matrix 
# NOTE: W=diag(w) if w non-matrix, otherwise w is a matrix square root. 
# flop count is O(nq^2) if X is n by q... this is why routine not part of magic
{ ## V<-object$rV%*%t(object$rV)
  V <- tcrossprod(object$rV)
  if (!is.null(w)) 
  { if (is.matrix(w)) WX <- X <- w%*%X else 
    WX <- as.vector(w)*X # use recycling rule to form diag(w)%*%X cheaply 
    
  } else {WX <- X}
  ##if (nthreads <= 1) M <- WX%*%V else M <- pmmult(WX,V,tA=FALSE,tB=FALSE,nt=nthreads)
  M <- WX%*%V  ## O(np^2) part
  ##Ve <- (V%*%t(X))%*%M*object$scale # frequentist cov. matrix
  XWX <- crossprod(object$R) #t(X)%*%WX
  F <- Ve <- V%*%XWX
  edf1 <- rowSums(t(Ve)*Ve) ## this is diag(FF), where F is edf matrix
  Ve <- Ve%*%V*object$scale ## frequentist cov matrix
  B <- X*M
  rm(M)
  hat <- rowSums(B) #apply(B,1,sum) # diag(X%*%V%*%t(WX))
  edf <- colSums(B) #apply(B,2,sum) # diag(V%*%t(X)%*%WX)
  Vb <- V*object$scale;rm(V)
  list(Ve=Ve,Vb=Vb,hat=hat,edf=edf,edf1=2*edf-edf1,F=F)
} ## magic.post.proc

single.sp <- function(X,S,target=.5,tol=.Machine$double.eps*100)
## function to find smoothing parameter corresponding to particular 
## target e.d.f. for a single smoothing parameter problem. 
## X is model matrix; S is penalty matrix; target is target 
## average e.d.f. per penalized term.
{ R <- qr.R(qr(X)) ### BUG? pivoting?
  te <- try(RS <- backsolve(R,S,transpose=TRUE),silent=TRUE)
  if (inherits(te,"try-error")) return(-1)
  te <- try(RSR <- backsolve(R,t(RS),transpose=TRUE),silent=TRUE)
  if (inherits(te,"try-error")) return(-1)
  RSR <- (RSR+t(RSR))/2
  d <- eigen(RSR,symmetric=TRUE)$values
  d <- d[d>max(d)*tol]
  ff <- function(lambda,d,target) { 
    mean(1/(1+exp(lambda)*d))-target
  }
  lower <- 0
  while (ff(lower,d,target) <= 0) lower <- lower - 1
  upper <- lower
  while (ff(upper,d,target) > 0) upper <- upper + 1
  exp(uniroot(ff,c(lower,upper),d=d,target=target)$root)
}


initial.spg <- function(x,y,weights,family,S,rank,off,offset=NULL,L=NULL,lsp0=NULL,type=1,
                        start=NULL,mustart=NULL,etastart=NULL,E=NULL,...) {
## initial smoothing parameter values based on approximate matching 
## of Frob norm of XWX and S. If L is non null then it is assumed
## that the sps multiplying S elements are given by L%*%sp+lsp0 and 
## an appropriate regression step is used to find `sp' itself.
## This routine evaluates initial guesses at W.
  ## Get the initial weights...
  if (length(S)==0) return(rep(0,0))
  ## start <- etastart <- mustart <- NULL
  nobs <- nrow(x) ## ignore codetools warning - required for initialization
  if (is.null(mustart)) mukeep <- NULL else mukeep <- mustart 
  eval(family$initialize) 
  if (inherits(family,"general.family")) { ## Cox, gamlss etc...   
    lbb <- family$ll(y,x,start,weights,family,offset=offset,deriv=1)$lbb ## initial Hessian
    lambda <- rep(0,length(S))
    if (TRUE) { ## experimental
      for (i in 1:length(S)) {
        ind <- off[i]:(off[i]+ncol(S[[i]])-1)
	if (rank[i]<ncol(S[[i]])) { ## find a basis for row/col space of S[[i]] and project into that.
          suppressWarnings(cs <- chol(S[[i]],pivot=TRUE))
          piv <- attr(cs,"pivot")
	  Z <- S[[i]][,piv[1:rank[i]],drop=FALSE] ## basis for the space of S[[i]]
          Z <- Z/norm(Z)
	  ZHZ <- -t(Z)%*%lbb[ind,ind]%*%Z
          ZSZ <- t(Z)%*%S[[i]]%*%Z
        } else { ZHZ <- -lbb[ind,ind];ZSZ <- S[[i]] }
	lambda[i] <- .3*norm(ZHZ,"M")/norm(ZSZ,"M")
      }
    } else { ## original
    ## initially work out the number of times that each coefficient is penalized
    pcount <- rep(0,ncol(lbb))
    for (i in 1:length(S)) {
      ind <- off[i]:(off[i]+ncol(S[[i]])-1)
      dlb <- -diag(lbb[ind,ind,drop=FALSE])
      indp <- rowSums(abs(S[[i]]))>max(S[[i]])*.Machine$double.eps^.75 & dlb!=0
      ind <- ind[indp] ## drop indices of unpenalized
      pcount[ind] <- pcount[ind] + 1 ## add up times penalized
    }
    ## choose lambda so that corresponding elements of lbb and S[[i]]
    ## are roughly in balance...
    for (i in 1:length(S)) {
      ind <- off[i]:(off[i]+ncol(S[[i]])-1)
      lami <- 1
      #dlb <- -diag(lbb[ind,ind])
      dlb <- abs(diag(lbb[ind,ind,drop=FALSE])) 
      dS <- diag(S[[i]])
      pc <- pcount[ind]
      ## get index of elements doing any actual penalization...
      ind <- rowSums(abs(S[[i]]))>max(S[[i]])*.Machine$double.eps^.75 & dlb!=0 ## dlb > 0
      ## drop elements that are not penalizing
      dlb <- dlb[ind]/pc[ind] ## idea is to share out between penalties
      dS <- dS[ind]
      rm <- max(length(dS)/rank[i],1) ## rough correction for rank deficiency in penalty
      #while (mean(dlb/(dlb + lami * dS * rm)) > 0.4) lami <- lami*5
      #while (mean(dlb/(dlb + lami * dS * rm )) < 0.4) lami <- lami/5 
      while (sqrt(mean(dlb/(dlb + lami * dS * rm))*mean(dlb)/mean(dlb+lami*dS*rm)) > 0.4) lami <- lami*5
      while (sqrt(mean(dlb/(dlb + lami * dS * rm))*mean(dlb)/mean(dlb+lami*dS*rm)) < 0.4) lami <- lami/5
      lambda[i] <- lami 
      ## norm(lbb[ind,ind])/norm(S[[i]])
    }
    }
  } else { ## some sort of conventional regression
    if (is.null(mukeep)) {
      if (!is.null(start)) etastart <- drop(x%*%start)
      if (!is.null(etastart)) mustart <- family$linkinv(etastart)
    } else mustart <- mukeep
    if (inherits(family,"extended.family")) {
      theta <- family$getTheta()
      ## use 'as.numeric' - 'drop' can leave result as 1D array...
      Ddo <- family$Dd(y,mustart,theta,weights)
      mu.eta2 <-family$mu.eta(family$linkfun(mustart))^2 
      w <- .5 * as.numeric(Ddo$Dmu2 * mu.eta2)
      if (any(w<0)) w <- .5 * as.numeric(Ddo$EDmu2 * mu.eta2) 
    } else w <- as.numeric(weights*family$mu.eta(family$linkfun(mustart))^2/family$variance(mustart))
    w <- sqrt(w)
    if (type==1) { ## what PI would have used
      lambda <-  initial.sp(w*x,S,off)
    } else { ## balance frobenius norms
      csX <- colSums((w*x)^2) 
      lambda <- rep(0,length(S))
      for (i in 1:length(S)) {
        ind <- off[i]:(off[i]+ncol(S[[i]])-1)
        lambda[i] <- sum(csX[ind])/sqrt(sum(S[[i]]^2))
      }
    }
  }
  if (!is.null(L)) {
    lsp <- log(lambda)
    if (is.null(lsp0)) lsp0 <- rep(0,nrow(L))
    lsp <- as.numeric(coef(lm(lsp~L-1+offset(lsp0))))
    lambda <- exp(lsp)
  }

  lambda ## initial values

} ## initial.spg

initial.sp <- function(X,S,off,expensive=FALSE,XX=FALSE)
# Find initial smoothing parameter guesstimates based on model matrix X 
# and penalty list S. off[i] is the index of the first parameter to
# which S[[i]] applies, since S[[i]]'s only store non-zero submatrix of 
# penalty coefficient matrix.
# if XX==TRUE then X contains X'X, not X!
{ n.p <- length(S) 
  if (XX) expensive <- FALSE 
  def.sp <- array(0,n.p)
  if (n.p) { 
    ldxx <- if (XX) diag(X) else colSums(X*X) # yields diag(t(X)%*%X)
    ldss <- ldxx*0       # storage for combined penalty l.d. 
    if (expensive) St <- matrix(0,ncol(X),ncol(X)) 
    pen <- rep(FALSE,length(ldxx)) # index of what actually gets penalized
    for (i in 1:n.p) { # loop over penalties
      maS <- max(abs(S[[i]])) 
      rsS <- rowMeans(abs(S[[i]]))
      csS <- colMeans(abs(S[[i]]))
      dS <- diag(abs(S[[i]])) ## new 1.8-4
      thresh <- .Machine$double.eps^.8 * maS ## .Machine$double.eps*maS*10
      ind <- rsS > thresh & csS > thresh & dS > thresh # only these columns really penalize
      ss <- diag(S[[i]])[ind] # non-zero elements of l.d. S[[i]]
      start <- off[i];finish <- start+ncol(S[[i]])-1
      xx <- ldxx[start:finish]
      xx <- xx[ind]
      pen[start:finish] <- pen[start:finish]|ind
      sizeXX <- mean(xx)
      sizeS <- mean(ss)
      if (sizeS <= 0) stop(gettextf("S[[%d]] matrix is not +ve definite.", i)) 
      def.sp[i] <- sizeXX/ sizeS # relative s.p. estimate
      ## accumulate leading diagonal of \sum sp[i]*S[[i]]
      ldss[start:finish] <- ldss[start:finish] + def.sp[i]*diag(S[[i]]) 
      
      if (expensive) St[start:finish,start:finish] <- 
                     St[start:finish,start:finish] + def.sp[i]*S[[i]]
    }
    if (expensive) { ## does full search for overall s.p.
      msp <- single.sp(X,St)           
      if (msp>0) def.sp <- def.sp*msp  
    } else {
      ind <- ldss > 0 & pen & ldxx > 0 # base following only on penalized terms
      ldxx<-ldxx[ind];ldss<-ldss[ind]
      while (mean(ldxx/(ldxx+ldss))>.4) { def.sp <- def.sp*10;ldss <- ldss*10 }
      while (mean(ldxx/(ldxx+ldss))<.4) { def.sp <- def.sp/10;ldss <- ldss/10 }
    }
  } 
  as.numeric(def.sp)
} ## initial.sp



 
magic <- function(y,X,sp,S,off,L=NULL,lsp0=NULL,rank=NULL,H=NULL,C=NULL,w=NULL,gamma=1,scale=1,gcv=TRUE,
                ridge.parameter=NULL,control=list(tol=1e-6,step.half=25,
                rank.tol=.Machine$double.eps^0.5),extra.rss=0,n.score=length(y),nthreads=1)
# Wrapper for C routine magic. Deals with constraints weights and square roots of 
# penalties. 
# y is data vector, X is model matrix, sp is array of smoothing parameters,
# S is list of penalty matrices stored as smallest square submatrix excluding no 
# non-zero entries, off[i] is the location on the leading diagonal of the
# total penalty matrix of element (1,1) of S[[i]], rank is an array of penalty 
# ranks, L is a matrix mapping the log underlying smoothing parameters to the 
# smoothing parameters that actually multiply the penalties. i.e. the 
# log smoothing parameters are L%*%sp + lsp0
# H is any fixed penalty, C is a linear constraint matrix and w is the 
# weight vector. gamma is the dof inflation factor, scale is the scale parameter, only 
# used with UBRE, gcv TRUE means use GCV, if false, use UBRE.  
# Return list includes rV such that cov(b)=rV%*%t(rV)*scale and the leading diagonal
# of rV%*%t(rV)%*%t(X)%*%X gives the edf for each parameter.
# NOTE: W is assumed to be square root of inverse of covariance matrix. i.e. if
# W=diag(w) RSS is ||W(y-Xb||^2  
# If `ridge.parameter' is a positive number then then it is assumed to be the multiplier
# for a ridge penalty to be applied during fitting. 
# `extra.rss' is an additive constant by which the RSS is modified in the
#  GCV/UBRE or scale calculations, n.score is the `n' to use in the GCV/UBRE
#  score calcualtions (Useful for dealing with huge datasets).
{ if (is.null(control)) control <- list()
  if (is.null(control$tol)) control$tol <- 1e-6
  if (is.null(control$step.half)) control$step.half <- 25
  if (is.null(control$rank.tol)) control$rank.tol <- .Machine$double.eps^0.5

  n.p<-length(S)
  n.b<-dim(X)[2] # number of parameters
  # get initial estimates of smoothing parameters, using better method than is
  # built in to C code. This must be done before application of general 
  # constraints.
  if (n.p) def.sp <- initial.sp(X,S,off) else def.sp <- sp

  if (!is.null(L)) { ## have to estimate appropriate starting coefs
    if (!inherits(L,"matrix")) stop("L must be a matrix.")
    if (nrow(L)<ncol(L)) stop("L must have at least as many rows as columns.")
    if (nrow(L)!=n.p||ncol(L)!=length(sp)) stop("L has inconsistent dimensions.")
    if (is.null(lsp0)) lsp0 <- rep(0,nrow(L))
    if (ncol(L)) def.sp <- exp(as.numeric(coef(lm(log(def.sp)~L-1+offset(lsp0)))))
  }

  # get square roots of penalties using supplied ranks or estimated 
  if (n.p>0)
  { for (i in 1:n.p) 
    { if (is.null(rank)) B <- mroot(S[[i]],method="svd") 
      else B <- mroot(S[[i]],rank=rank[i],method="chol")
      m <- dim(B)[2]
      R<-matrix(0,n.b,m)
      R[off[i]:(off[i]+dim(B)[1]-1),]<-B
      S[[i]]<-R
    }
    rm(B);rm(R)
  }
  # if there are constraints then need to form null space of constraints Z 
  # (from final columns of Q, from QR=C'). Then form XZ and Z'S_i^0.5 for all i 
  # and Z'HZ.
  # On return from mgcv2 set parameters to Zb (apply Q to [0,b']').   
  ##Xo<-X
  if (!is.null(C)) # then impose constraints 
   { n.con<-dim(C)[1]
    ns.qr<-qr(t(C)) # last n.b-n.con columns of Q are the null space of C
    X<-t(qr.qty(ns.qr,t(X)))[,(n.con+1):n.b,drop=FALSE] # last n.b-n.con cols of XQ (=(Q'X')')
    # need to work through penalties forming Z'S_i^0.5 's
    if (n.p>0) for (i in 1:n.p) { 
      S[[i]]<-qr.qty(ns.qr,S[[i]])[(n.con+1):n.b,,drop=FALSE]
      ## following essential given assumptions of the C code...
      if (ncol(S[[i]])>nrow(S[[i]])) { ## no longer have a min col square root.
        S[[i]] <- t(qr.R(qr(t(S[[i]])))) ## better!
      }
    }
    # and Z'HZ too
    if (!is.null(H))
    { H<-qr.qty(ns.qr,H)[(n.con+1):n.b,,drop=FALSE] # Z'H
      H<-t(qr.qty(ns.qr,t(H))[(n.con+1):n.b,,drop=FALSE]) # Z'HZ = (Z'[Z'H]')' 
    }
    full.rank=n.b-n.con
  } else full.rank=n.b
  # now deal with weights....
  if (!is.null(w))
  { if (is.matrix(w))
    { if (dim(w)[1]!=dim(w)[2]||dim(w)[2]!=dim(X)[1]) stop("dimensions of supplied w wrong.")
      y<-w%*%y
      X<-w%*%X
    } else
    { if (length(y)!=length(w)) stop("w different length from y!")
      y<-y*w
      X<-as.vector(w)*X # use recycling rule to form diag(w)%*%X cheaply
    }
  }
  if (is.null(dim(X))) { # lost dimensions as result of being single columned! 
    n <- length(y)
    if (n!=length(X)) stop("X lost dimensions in magic!!")
    dim(X) <- c(n,1)
  }
  # call real mgcv engine...
  Si<-array(0,0);cS<-0
  if (n.p>0) for (i in 1:n.p) { 
    Si <- c(Si,S[[i]]);
    cS[i] <- dim(S[[i]])[2]
  }
  rdef <- ncol(X) - nrow(X)
  if (rdef>0) { ## need to zero pad model matrix
    n.score <- n.score ## force evaluation *before* y lengthened
    X <- rbind(X,matrix(0,rdef,ncol(X)))
    y <- c(y,rep(0,rdef))
  }

  icontrol<-as.integer(gcv);icontrol[2]<-length(y);q<-icontrol[3]<-dim(X)[2];
  if (!is.null(ridge.parameter)&&ridge.parameter>0)
  { if(is.null(H)) H<-diag(ridge.parameter,q) else H<-H+diag(ridge.parameter,q)}
  icontrol[4]<-as.integer(!is.null(H));icontrol[5]<- n.p;icontrol[6]<-control$step.half
  if (is.null(L)) { icontrol[7] <- -1;L <- diag(n.p) } else icontrol[7]<-ncol(L)
  if (is.null(lsp0)) lsp0 <- rep(0,nrow(L))
 
  b<-array(0,icontrol[3])
  # argument names in call refer to returned values.
  if (nthreads<1) nthreads <- 1 ## can't set up storage without knowing nthreads
  if (nthreads>1) extra.x <- q^2 * nthreads else extra.x <- 0 
  um<-.C(C_magic,as.double(y),X=as.double(c(X,rep(0,extra.x))),sp=as.double(sp),as.double(def.sp),
          as.double(Si),as.double(H),as.double(L),
          lsp0=as.double(lsp0),score=as.double(gamma),scale=as.double(scale),info=as.integer(icontrol),as.integer(cS),
          as.double(control$rank.tol),rms.grad=as.double(control$tol),b=as.double(b),rV=double(q*q),
          as.double(extra.rss),as.integer(n.score),as.integer(nthreads))
  res<-list(b=um$b,scale=um$scale,score=um$score,sp=um$sp,sp.full=as.numeric(exp(L%*%log(um$sp))))
  res$R <- matrix(um$X[1:q^2],q,q)
  res$rV<-matrix(um$rV[1:(um$info[1]*q)],q,um$info[1])
  gcv.info<-list(full.rank=full.rank,rank=um$info[1],fully.converged=as.logical(um$info[2]),
      hess.pos.def=as.logical(um$info[3]),iter=um$info[4],score.calls=um$info[5],rms.grad=um$rms.grad)
  res$gcv.info<-gcv.info
  if (!is.null(C)) { # need image of constrained parameter vector in full space
    b <- c(rep(0,n.con),res$b)
    res$b <- qr.qy(ns.qr,b) # Zb 
    b <- matrix(0,n.b,dim(res$rV)[2])
    b[(n.con+1):n.b,] <- res$rV 
    res$rV <- qr.qy(ns.qr,b)# ZrV
  } 
  res
} ## magic


print.mgcv.version <- function()
{ library(help=mgcv)$info[[1]] -> version
  version <- version[pmatch("Version",version)]
  um <- strsplit(version," ")[[1]]
  version <- um[nchar(um)>0][2]
  hello <- paste("This is mgcv ",version,". For overview type 'help(\"mgcv-package\")'.",sep="")
  packageStartupMessage(hello)
}

set.mgcv.options <- function()
## function used to set optional value used in notLog
## and notExp...
{ ##runif(1) ## ensure there is a seed (can be removed by user!)
  options(mgcv.vc.logrange=25)
}

.onLoad <- function(...) {
  set.mgcv.options()
}

.onAttach <- function(...) { 
  print.mgcv.version()
  set.mgcv.options()
}

.onUnload <- function(libpath) library.dynam.unload("mgcv", libpath)



###############################################################################
### ISSUES.....
#
#* Could use R_CheckUserInterrupt() to allow user interupt of
#  mgcv code. (6.12) But then what about memory?#
#
#* predict.gam and plot.gam "iterms" and `seWithMean' options
#  don't deal properly with case in which centering constraints
#  are not conventional sum to zero ones.
#
# * add randomized residuals (see Mark B email)?
#
# * sort out all the different scale parameters floating around, and explain the 
#   sp variance link better.
