## code for soap film smoothing to deal with difficult boundary regions ## Copyright Simon Wood 2006-2012 unconstrain <- function(object,beta) { ## function to produce full version of constrained coefficients of ## smooth object. Returned vector may have an attribute "constant" ## to be subtraccted from results. ## NOTE: sum to zero on some parameters only branch is not fully ## tested (also unused at present)! del.index <- attr(object,"del.index") if (!is.null(del.index)) { beta.full <- rep(0,length(beta)+length(del.index)) k <- 1;j <- 1 for (i in 1:length(beta.full)) { if (j <= length(del.index) && i==del.index[j]) { beta.full[i] <- 0;j <- j + 1 } else { beta.full[i] <- beta[k];k <- k + 1 } } beta <- beta.full } ## end of del.index handling qrc <- attr(object,"qrc") if (!is.null(qrc)) { ## then smoothCon absorbed constraints j <- attr(object,"nCons") if (j>0) { ## there were constraints to absorb - need to untransform k <- length(beta) + j if (inherits(qrc,"qr")) { indi <- attr(object,"indi") ## index of constrained parameters if (is.null(indi)) { ## X <- t(qr.qty(qrc,t(X))[(j+1):k,,drop=FALSE]) ## XZ beta <- qr.qy(qrc,c(rep(0,j),beta)) } else { ## only some parameters are subject to constraint ## NOTE: this branch not fully tested ##nx <- length(indi) ##nc <- j;nz <- nx - nc Xbeta <- qr.qy(qrc,c(rep(0,j),beta[indi])) beta.full <- rep(0,length(beta)+j) ib <- 1;ii <- 1 for (i in 1:length(beta.full)) { if (i==indi[ii]) { beta.full[i] <- Xbeta[ii]; ii <- ii + 1 } else { beta.full[i] <- beta[ib]; ib <- ib + 1 } } ##X[,indi[1:nz]]<-t(qr.qty(qrc,t(X[,indi,drop=FALSE]))[(nc+1):nx,,drop=FALSE]) ## X <- X[,-indi[(nz+1):nx]] beta <- beta.full } } else if (inherits(qrc,"sweepDrop")) { ## Sweep and drop constraints. First element is index to drop. ## Remainder are constants to be swept out of remaining columns ## X <- sweep(X[,-qrc[1],drop=FALSE],2,qrc[-1]) #X <- X[,-qrc[1],drop=FALSE] - matrix(qrc[-1],nrow(X),ncol(X)-1,byrow=TRUE) cnst <- sum(beta*qrc[-1]) if (qrc[1]==1) beta <- c(0,beta) else if (qrc[1]==length(beta)+1) beta <- c(beta,0) else beta <- c(beta[1:(qrc[1]-1)],0,beta[qrc[1]:length(beta)]) attr(beta,"constant") <- cnst } else if (qrc>0) { ## simple set to zero constraint ##X <- X[,-qrc] if (qrc==1) beta <- c(0,beta) else if (qrc==length(beta)+1) beta <- c(beta,0) else beta <- c(beta[1:(qrc-1)],0,beta[qrc:length(beta)]) } else if (qrc<0) { ## params sum to zero # X <- t(diff(t(X))) beta <- t(diff(diag(length(beta)+1)))%*%beta } } ## end if (j>0) } ## end if qrc exists beta } ## end of unconstrain bnd2C <- function(bnd) { ## converts boundary loop list to form required in C code. n.loop <- 1 if (is.null(bnd$x)) { ## translate into form that C routine needs bn <- list(x=bnd[[1]]$x,y=bnd[[1]]$y) n.loop <- length(bnd) if (length(bnd)>1) for (i in 2:n.loop) { bn$x <- c(bn$x,NA,bnd[[i]]$x);bn$y <- c(bn$y,NA,bnd[[i]]$y) } bnd <- bn } ## replace NA segment separators with a numeric code lowLim <- min(c(bnd$x,bnd$y),na.rm=TRUE)-1 ind <- is.na(bnd$x)|is.na(bnd$y) bnd$x[ind] <- bnd$y[ind] <- lowLim - 1 bnd$n <- length(bnd$x) if (bnd$n != length(bnd$y)) stop("x and y must be same length") bnd$breakCode <-lowLim bnd$n.loop <- n.loop bnd } ## end bnd2C inSide <- function(bnd,x,y) ## tests whether each point x[i],y[i] is inside the boundary defined ## by bnd$x, bnd$y, or by multiple boundary loops in bnd[[1]]$x, ## bnd[[1]]$y, bnd[[2]]$x, ... etc. ## names in bnd must match those of x and y, but do not need to be "x" and "y" { ## match the names up first... xname <- deparse(substitute(x)) yname <- deparse(substitute(y)) bnd.name <- names(bnd) if (is.null(bnd.name)) for (i in 1:length(bnd)) { bnd.name <- names(bnd[[i]]) if (xname%in%bnd.name==FALSE||yname%in%bnd.name==FALSE) stop("variable names don't match boundary names") bnd.name[xname==bnd.name] <- "x" bnd.name[yname==bnd.name] <- "y" names(bnd[[i]]) <- bnd.name } else { if (xname%in%bnd.name==FALSE||yname%in%bnd.name==FALSE) stop("variable names don't match boundary names") bnd.name[xname==bnd.name] <- "x" bnd.name[yname==bnd.name] <- "y" names(bnd) <- bnd.name } ## now do the real stuff... bnd <- bnd2C(bnd) um <-.C(C_in_out,bx=as.double(bnd$x),by=as.double(bnd$y),break.code=as.double(bnd$breakCode), x=as.double(x),y=as.double(y),inside=as.integer(y*0),nb=as.integer(bnd$n), n=as.integer(length(x))) as.logical(um$inside) } ## end inSide process.boundary <- function(bnd) ## takes a list of boundary loops, makes sure that they join up ## and add a distance along loop array, d to each list element. { for (i in 1:length(bnd)) { x <- bnd[[i]]$x;y<-bnd[[i]]$y;n <- length(x) if (length(y)!=n) stop("x and y not same length") if (x[1]!=x[n]||y[1]!=y[n]) { ## then loop not closed, so close it n<-n+1;x[n] <- x[1];y[n] <- y[1] if (inherits(bnd[[i]],"data.frame")) bnd[[i]][n,] <-bnd[[i]][1,] else { ## hopefully a list! bnd[[i]]$x[n] <- x[1];bnd[[i]]$y[n] <- y[1] if (!is.null(bnd[[i]]$f)) bnd[[i]]$f[n] <- bnd[[i]]$f[1] } } len <- c(0,sqrt((x[1:(n-1)]-x[2:n])^2+(y[1:(n-1)]-y[2:n])^2)) ## seg lengths bnd[[i]]$d<-cumsum(len) ## distance along boundary } bnd } ## end process.boundary crunch.knots <- function(G,knots,x0,y0,dx,dy) ## finds indices of knot locations in solution grid ## the knot x,y locations are given in the `knots' argument. { nk <- length(knots$x) nx <- ncol(G);ny <- nrow(G) ki <- rep(0,nk) if (nk==0) return(ki) for (k in 1:nk) { i <- round((knots$x[k]-x0)/dx)+1 j <- round((knots$y[k]-y0)/dy)+1 if (i>1&&i<=nx&&j>1&&j<=ny) { ki[k] <- G[j,i] if (ki[k] <= 0) { str <- paste("knot",k,"is on or outside boundary") stop(str) } } } ## all knots done ki ## ki[k] indexes kth knot in solution grid } ## end crunch.knots setup.soap <- function(bnd,knots,nmax=100,k=10,bndSpec=NULL) { ## setup soap film smooth - nmax is number of grid cells for longest side ## it's important that grid cells are square! ## check boundary... if (!inherits(bnd,"list")) stop("bnd must be a list.") n.loops <- length(bnd) if (n.loops!=length(k)) { if (length(k)==1) k <- rep(k,n.loops) else stop("lengths of k and bnd are not compatible.") } bnd <- process.boundary(bnd) ## add distances and close any open loops ## create grid on which to solve Laplace equation ## Obtain grid limits from boundary 'bnd'.... x0 <- min(bnd[[1]]$x);x1 <- max(bnd[[1]]$x) y0 <- min(bnd[[1]]$y);y1 <- max(bnd[[1]]$y) if (length(bnd)>1) for (i in 2:length(bnd)) { x0 <- min(c(x0,bnd[[i]]$x)); x1 <- max(c(x1,bnd[[i]]$x)) y0 <- min(c(y0,bnd[[i]]$y)); y1 <- max(c(y1,bnd[[i]]$y)) } ## now got the grid limits, can set it up if (x1-x0>y1-y0) { ## x is longest side dy <- dx <- (x1-x0) /(nmax-1) nx <- nmax ny <- ceiling((y1-y0)/dy)+1 } else { ## y is longest side dy <- dx <- (y1-y0) /(nmax-1) ny <- nmax nx <- ceiling((x1-x0)/dy)+1 } ## so grid is now nx by ny, cell size is dx by dy (but dx=dy) ## x0, y0 is "lower left" cell centre ## Create grid index G bnc <- bnd2C(bnd) ## convert boundary to form required in C code G <- matrix(0,ny,nx) nb <- rep(0,bnc$n.loop) oo <- .C(C_boundary,G=as.integer(G), d=as.double(G), dto=as.double(G), x0=as.double(x0), y0 = as.double(y0), dx=as.double(dx), dy = as.double(dy), nx=as.integer(nx),as.integer(ny), x=as.double(bnc$x),y=as.double(bnc$y), breakCode=as.double(bnc$breakCode),n=as.integer(bnc$n),nb=as.integer(nb)) ret <- list(G=matrix(oo$G,ny,nx),nb=oo$nb,d=oo$d[oo$d >= 0],x0=x0,y0=y0,dx=dx,dy=dy,bnd=bnd) rm(oo) ## Now create the PDE coefficient matrix n.inside <- sum(ret$G > - nx*ny) xx <- rep(0,5*n.inside) o1 <- .C(C_pde_coeffs,as.integer(ret$G),xx=as.double(xx),ii=as.integer(xx),jj=as.integer(xx), n=as.integer(0),as.integer(nx),as.integer(ny),as.double(dx),as.double(dy)) ind <- 1:o1$n X <- sparseMatrix(i=o1$ii[ind]+1,j=o1$jj[ind]+1,x=o1$xx[ind]) er <- expand(lu(X)) ret$Q <- er$Q;ret$U <- er$U;ret$L <- er$L;ret$P <- er$P ret$ng <- n.inside ## the number of cells to solve for rm(er);rm(X) ## ... so the sparse LU decomposition of X can be used to solve PDE. ## X = PLUQ where P and Q are permuation matrices. ## now obtain location of knots in solution ... ret$ki <- crunch.knots(ret$G,knots,x0,y0,dx,dy) ## setup the boundary conditions/boundary splines bc <- list() ## to hold boundary conditions start <- 1 for (i in 1:length(bnd)) { stop <- start - 1 + ret$nb[i] ## ret$d[start:stop] = dist along boundary loop i if (is.null(bnd[[i]]$f)) { ## this boundary is free d <- c(ret$d[start:stop],0) # boundary gridpoint distances along smooth if (is.null(bndSpec)) { bsm <- smooth.construct(s(d,bs="cc",k=k[i]),data=data.frame(d=d),knots=NULL) } else if (bndSpec$bs=="cc"){ if (bndSpec$knot.space=="even") knots <- seq(min(d),max(d),length=k[i]) else knots <- quantile(unique(d),seq(0,1,length=k[i])) bsm <- smooth.construct(s(d,bs="cc",k=k[i]),data=data.frame(d=d),knots=NULL) } else { ## use "cp" P-spline bsm <- smooth.construct(s(d,bs="cp",k=k[i],m=bndSpec$m),data=data.frame(d=d),knots=NULL) } bc[[i]] <- list(bsm=bsm,X=bsm$X[1:ret$nb[i],],S=bsm$S[[1]],free.bound=TRUE) } else { ## boundary is fixed ## pmax/pmin needed to avoid rounding error induced NA's d <- pmax(pmin(ret$d[start:stop],max(bnd[[i]]$d)),min(bnd[[i]]$d)) ui <- !duplicated(bnd[[i]]$d) ff <- approx(bnd[[i]]$d[ui],bnd[[i]]$f[ui],d)$y ## fixed values for BC bc[[i]] <- list(f=ff,free.bound=FALSE) } start <- stop + 1 } ret$bc <- bc ret } ## end of setup.soap soap.basis <- function(sd,x=NA,y=NA,film=TRUE,wiggly=TRUE,penalty=TRUE,plot=FALSE,beta=1) { ## function to evaluate soap basis using soap definition object 'sd' ## returned by setup.soap. x and y are values at which to evaluate. ## If plot==TRUE then then data suitable for plotting are returned at the resolution ## of the solution grid. Then beta contains either the coefficients, or a single number ## representing the single basis function to return (0 for the offset). if (!plot) { indout <- inSide(sd$bnd,x,y); n <- length(x) } else { penalty <- FALSE ## Some constraints result in the need to add a constant ## to the field (e.g. sweep and drop) cnst <- attr(beta,"constant") if (is.null(cnst)) cnst <- 0 else cnst <- -cnst } offset.needed <- FALSE; nc <- length(sd$ki)*as.numeric(wiggly) ## number of interior knots nb <- 0 ## boundary basis dimension offset <- NULL if (film) { stop <- 0 for (i in 1:length(sd$bc)) { ## work through boundary loops start <- stop + 1;stop <- start - 1 + sd$nb[i] if (sd$bc[[i]]$free.bound) nb <- nb + ncol(sd$bc[[i]]$X) else { ## fixed boundary, so offset required if (!offset.needed) { bndOff <- rep(0,sd$ng) ## array for fixed boundary conditions offset.needed <- TRUE } bndOff[start:stop] <- sd$bc[[i]]$f } ## fixed boundary done } ## finished first pass through loops } ## finished first if film if (plot) { ## preliminaries for plotting info if (length(beta)==1) { ## just one basis function to be returned if (beta<0||beta>nc+nb||(beta==0&&!offset.needed)) stop("attempt to select non existent basis function") select.basis <- TRUE } else { ## whole smooth to be returned if (length(beta)!=nc+nb) stop("coefficient vector wrong length") select.basis <- FALSE } G <- sd$G ## solution grid G[G < - length(G)] <- NA ## exterior marked as NA ind <- !is.na(G) gind <- G[ind] <- abs(G[ind])+1 ## need to create the indices such that G[gind] <- g is correct... gind[G[ind]] <- (1:length(G))[ind] G[ind] <- cnst ## now clear interior of G } ## finished preliminary if (plot) if (film) { if (offset.needed) { ## solve for offset soap film bndOff <- solve(sd$Q,solve(sd$U,solve(sd$L,solve(t(sd$P),bndOff)))) if (plot) { ## grid is all that's needed if (select.basis&&beta==0||!select.basis) { G[gind] <- bndOff } } else { ## need full interpolation NAcode <- max(bndOff)*2 offset <- .C(C_gridder,z=as.double(x),as.double(x),as.double(y),as.integer(length(x)),as.double(bndOff), as.integer(sd$G),nx=as.integer(ncol(sd$G)),ny=as.integer(nrow(sd$G)),as.double(sd$x0), as.double(sd$y0),as.double(sd$dx),as.double(sd$dy),as.double(NAcode*2))$z offset[offset>NAcode] <- NA offset[!indout] <- NA } } } ## finished preliminary if (film) if (!plot) { X <- matrix(0,n,nb+nc) ## model matrix if (penalty) { S <- list();off <- 1;nS=0} else {off <- S <- NULL} } k <- 1 ## model matrix column if (film&&nb>0) { ## now work through boundary bases stop <- 0 for (i in 1:length(sd$bc)) { ## work through boundary loops start <- stop + 1;stop <- start - 1 + sd$nb[i] ind <- start:stop ## index of this loop in solution grid if (sd$bc[[i]]$free.bound) { if (penalty) { nS <- nS + 1 off[nS] <- k S[[nS]] <- sd$bc[[i]]$S } ## penalty done for (j in 1:ncol(sd$bc[[i]]$X)) { ## loop over loop basis cols z <- rep(0,sd$ng) z[ind] <- sd$bc[[i]]$X[,j] ## PDE rhs z <- solve(sd$Q,solve(sd$U,solve(sd$L,solve(t(sd$P),z)))) if (plot) { if (select.basis) { if (beta==k) G[gind] <- z } else G[gind] <- G[gind] + beta[k]*z } else { NAcode <- max(z)*2 Xj <- .C(C_gridder,z=as.double(x),as.double(x),as.double(y),as.integer(length(x)),as.double(z), as.integer(sd$G),nx=as.integer(ncol(sd$G)),ny=as.integer(nrow(sd$G)),as.double(sd$x0), as.double(sd$y0),as.double(sd$dx),as.double(sd$dy),as.double(NAcode*2))$z Xj[Xj>NAcode] <- NA;X[,k] <- Xj; } k <- k + 1 } ## basis done } ## end of free boundary } ## end of boundary loops } ## end of film processing if (wiggly) { ## interior basis functions required g <- matrix(0,sd$ng,nc) for (i in 1:nc) g[sd$ki[i],i] <- 1 g <- as(solve(sd$Q,solve(sd$U,solve(sd$L,solve(t(sd$P),g)))),"matrix") g <- sweep(g,2,apply(g,2,max),"/") ## normalize - not really needed if (penalty) { ## get soap penalty nS <- nS + 1;off[nS] <- k S[[nS]] <- crossprod(g) * sd$dx * sd$dy } g <- solve(sd$Q,solve(sd$U,solve(sd$L,solve(t(sd$P),g)))) NAcode <- max(g)*2 for (i in 1:nc) { if (plot) { if (select.basis) { if (k==beta) G[gind] <- g[,i] } else G[gind] <- G[gind] + beta[k]*g[,i] } else { Xj <- .C(C_gridder,z=as.double(x),as.double(x),as.double(y),as.integer(length(x)),as.double(g[,i]), as.integer(sd$G),nx=as.integer(ncol(sd$G)),ny=as.integer(nrow(sd$G)),as.double(sd$x0), as.double(sd$y0),as.double(sd$dx),as.double(sd$dy),as.double(NAcode*2))$z Xj[Xj>NAcode] <- NA;X[,k] <- Xj } k <- k + 1 } } if (plot) { return(t(G)) } else { X[!indout,] <- NA return(list(X=X,S=S,off=off,offset=offset)) } } ## end soap.basis smooth.construct.so.smooth.spec<-function(object,data,knots) ## a full soap film smooth constructor method function for ## integration with mgcv::gam { if (is.null(knots)) stop("knots must be specified for soap") if (object$dim!=2) stop("soap films are bivariate only") x <- data[[object$term[1]]] y <- data[[object$term[2]]] knt <- list(x=knots[[object$term[1]]],y=knots[[object$term[2]]]) if (length(knt$x)<1) stop("need at least one interior knot") bnd <- object$xt$bnd if (is.null(bnd)) stop("can't soap smooth without a boundary") if (!inherits(bnd,"list")) stop("bnd must be a list of boundary loops") ## check knots within boundary... kin <- in.out(bnd,cbind(knt[[1]],knt[[2]])) if (any(!kin)) warning("dropping soap knots not inside boundary - use 'in.out' to investigate.") knt[[1]] <- knt[[1]][kin];knt[[2]] <- knt[[2]][kin] for (i in 1:length(bnd)) { ## re-lable boundary nm <- names(bnd[[i]]) ind <- nm==object$term[1] if (sum(ind)!=1) stop("faulty bnd") names(bnd[[i]])[ind] <- "x" ind <- nm==object$term[2] if (sum(ind)!=1) stop("faulty bnd") names(bnd[[i]])[ind] <- "y" } if (length(object$bs.dim)==1) k <- rep(object$bs.dim,length(bnd)) else { if (length(object$bs.dim)==length(bnd)) k <- object$bs.dim else stop("k and bnd lengths are inconsistent") } if (is.null(object$xt$nmax)) nmax <- 200 else nmax <- object$xt$nmax ## setup the soap defining structures sd <- setup.soap(bnd,knots=knt,nmax=nmax,k=k,bndSpec=object$xt$bndSpec) b <- soap.basis(sd,x,y,film=TRUE,wiggly=TRUE,penalty=TRUE) if (sum(is.na(b$X))>0) stop("data outside soap boundary") # b <- soap.construct(x,y,bnd,knots=knt,k=k,n.grid=n.grid,basis.type=2, # depth=depth,rel.eps=rel.eps,abs.eps=abs.eps, # bndSpec=object$xt$bndSpec) ## get penalty null space for the term... ns.dim <- 0;n <- length(sd$bc) if (n>0) for (i in 1:n) if (sd$bc[[i]]$free.bound) ns.dim <- ns.dim + sd$bc[[i]]$bsm$null.space.dim object$null.space.dim <- ns.dim need.con <- TRUE for (i in 1:length(sd$bc)) if (!sd$bc[[i]]$free.bound) need.con <- FALSE ## rescale basis for nice conditioning.... irng <- 1/as.numeric(apply(b$X,2,max)-apply(b$X,2,min)) b$X <- t(t(b$X)*irng) ## now apply rescaling for (i in 1:length(b$S)) { a <- irng[b$off[i]:(b$off[i]+ncol(b$S[[i]])-1)] b$S[[i]] <- diag(a)%*%b$S[[i]]%*%diag(a) } object$irng <- irng ## the column scaling factor if (any(!is.finite(irng))) stop("soap basis ill-conditioned - changing 'xt$nmax' may help") object$X <- b$X ## model matrix attr(object$X,"offset") <- b$offset if (!object$fixed) { ## have to unpack a bit... S <- list();n <- ncol(object$X) for (i in 1:length(b$S)) { S[[i]] <- matrix(0,n,n) m <- ncol(b$S[[i]]) ind <- b$off[i]:(b$off[i]+m-1) S[[i]][ind,ind] <- b$S[[i]] } object$S <- S ## penalties } rr <- ncol(b$S[[1]])-1 if (length(b$S)>1) for (i in 2:length(b$S)) rr <- c(rr,ncol(b$S[[i]])-1) rr[length(rr)] <- rr[length(rr)]+1 object$rank <- rr # penalty ranks if (!need.con) object$C <- matrix(0,0,ncol(object$X)) ## no con object$df <- ncol(object$X) # -nrow(object$C) for (i in 1:length(sd$bc)) { sd$bc[[i]]$bsm <- sd$bc[[i]]$S <- NULL } object$sd <- sd class(object)<-"soap.film" # Give object a class object } ## end of full soap constructor smooth.construct.sf.smooth.spec<-function(object,data,knots) ## a soap film smooth boundary interpolating film only constructor ## method function for integration with mgcv::gam { if (is.null(knots)) stop("knots must be specified for soap") if (object$dim!=2) stop("soap films are bivariate only") x <- data[[object$term[1]]] y <- data[[object$term[2]]] knt <- list(x=knots[[object$term[1]]],y=knots[[object$term[2]]]) ## if (length(knt$x)<1) stop("need at least one interior knot") bnd <- object$xt$bnd if (is.null(bnd)) stop("can't soap smooth without a boundary") if (!inherits(bnd,"list")) stop("bnd must be a list of boundary loops") for (i in 1:length(bnd)) { ## re-lable boundary nm <- names(bnd[[i]]) ind <- nm==object$term[1] if (sum(ind)!=1) stop("faulty bnd") names(bnd[[i]])[ind] <- "x" ind <- nm==object$term[2] if (sum(ind)!=1) stop("faulty bnd") names(bnd[[i]])[ind] <- "y" } if (length(object$bs.dim)==1) k <- rep(object$bs.dim,length(bnd)) else { if (length(object$bs.dim)==length(bnd)) k <- object$bs.dim else stop("k and bnd lengths are inconsistent") } if (is.null(object$xt$nmax)) nmax <- 200 else nmax <- object$xt$nmax ## setup the soap defining structures sd <- setup.soap(bnd,knots=knt,nmax=nmax,k=k,bndSpec=object$xt$bndSpec) b <- soap.basis(sd,x,y,film=TRUE,wiggly=FALSE,penalty=TRUE) if (sum(is.na(b$X))>0) stop("data outside soap boundary") if (ncol(b$X)==0) stop("no free coefs in sf smooth") # b <- soap.construct(x,y,bnd,knots=knt,k=k,n.grid=n.grid,basis.type=2, # depth=depth,rel.eps=rel.eps,abs.eps=abs.eps,film=TRUE, # wiggly=FALSE,bndSpec=object$xt$bndSpec) ## get penalty null space for term ns.dim <- 0;n <- length(sd$bc) k <- 0 ## counter for b$S rr <- rep(0,length(b$S)) if (n>0) for (i in 1:n) if (sd$bc[[i]]$free.bound) { nsd <- sd$bc[[i]]$bsm$null.space.dim ns.dim <- ns.dim + nsd k <- k + 1 rr[k] <- ncol(b$S[[k]]) - nsd ## rank of b$S[[k]] } object$null.space.dim <- ns.dim object$rank <- rr # penalty ranks need.con <- TRUE for (i in 1:length(sd$bc)) if (!sd$bc[[i]]$free.bound) need.con <- FALSE ## rescale basis for nice conditioning.... irng <- 1/as.numeric(apply(b$X,2,max)-apply(b$X,2,min)) b$X <- t(t(b$X)*irng) ## now apply rescaling if (length(b$S)>0) for (i in 1:length(b$S)) { a <- irng[b$off[i]:(b$off[i]+ncol(b$S[[i]])-1)] b$S[[i]] <- diag(a)%*%b$S[[i]]%*%diag(a) } object$irng <- irng ## the column scaling factor object$X <- b$X ## model matrix attr(object$X,"offset") <- b$offset if (!object$fixed) { ## have to unpack a bit... S <- list();n <- ncol(object$X) if (length(b$S)>0) for (i in 1:length(b$S)) { S[[i]] <- matrix(0,n,n) m <- ncol(b$S[[i]]) ind <- b$off[i]:(b$off[i]+m-1) S[[i]][ind,ind] <- b$S[[i]] } object$S <- S ## penalties } if (!need.con) object$C <- matrix(0,0,ncol(object$X)) ## no con object$df <- ncol(object$X) # -nrow(object$C) for (i in 1:length(sd$bc)) { sd$bc[[i]]$bsm <- sd$bc[[i]]$S <- NULL } object$sd <- sd class(object)<-c("sf","soap.film") # Give object a class object } ## end of boundary film component soap constructor smooth.construct.sw.smooth.spec<-function(object,data,knots) ## a soap film smooth wiggly component only constructor method function for ## integration with mgcv::gam { if (is.null(knots)) stop("knots must be specified for soap") if (object$dim!=2) stop("soap films are bivariate only") x <- data[[object$term[1]]] y <- data[[object$term[2]]] knt <- list(x=knots[[object$term[1]]],y=knots[[object$term[2]]]) if (length(knt$x)<1) stop("need at least one interior knot") bnd <- object$xt$bnd if (is.null(bnd)) stop("can't soap smooth without a boundary") if (!inherits(bnd,"list")) stop("bnd must be a list of boundary loops") for (i in 1:length(bnd)) { ## re-lable boundary nm <- names(bnd[[i]]) ind <- nm==object$term[1] if (sum(ind)!=1) stop("faulty bnd") names(bnd[[i]])[ind] <- "x" ind <- nm==object$term[2] if (sum(ind)!=1) stop("faulty bnd") names(bnd[[i]])[ind] <- "y" } if (length(object$bs.dim)==1) k <- rep(object$bs.dim,length(bnd)) else { if (length(object$bs.dim)==length(bnd)) k <- object$bs.dim else stop("k and bnd lengths are inconsistent") } if (is.null(object$xt$nmax)) nmax <- 200 else nmax <- object$xt$nmax ## setup the soap defining structures sd <- setup.soap(bnd,knots=knt,nmax=nmax,k=k,bndSpec=object$xt$bndSpec) b <- soap.basis(sd,x,y,film=FALSE,wiggly=TRUE,penalty=TRUE) if (sum(is.na(b$X))>0) stop("data outside soap boundary") object$null.space.dim <- 0 ## penalty is full rank, for this case ## rescale basis for nice conditioning.... irng <- 1/as.numeric(apply(b$X,2,max)-apply(b$X,2,min)) b$X <- t(t(b$X)*irng) ## now apply rescaling for (i in 1:length(b$S)) { a <- irng[b$off[i]:(b$off[i]+ncol(b$S[[i]])-1)] b$S[[i]] <- diag(a)%*%b$S[[i]]%*%diag(a) } object$irng <- irng ## the column scaling factor object$X <- b$X ## model matrix if (!object$fixed) { ## have to unpack a bit... S <- list();n <- ncol(object$X) for (i in 1:length(b$S)) { S[[i]] <- matrix(0,n,n) m <- ncol(b$S[[i]]) ind <- b$off[i]:(b$off[i]+m-1) S[[i]][ind,ind] <- b$S[[i]] } object$S <- S ## penalties } rr <- ncol(b$S[[1]])-1 if (length(b$S)>1) for (i in 2:length(b$S)) rr <- c(rr,ncol(b$S[[i]])-1) rr[length(rr)] <- rr[length(rr)]+1 object$rank <- rr # penalty ranks object$df <- ncol(object$X) # -nrow(object$C) for (i in 1:length(sd$bc)) { sd$bc[[i]]$bsm <- sd$bc[[i]]$S <- NULL } object$sd <- sd object$C <- matrix(0,0,ncol(object$X)) ## this is tied to zero class(object)<-c("sw","soap.film") # Give object a class object } ## end of wiggly component of soap constructor Predict.matrix.soap.film<-function(object,data) # prediction method function for the soap.film smooth class { x <- get.var(object$term[1],data) y <- get.var(object$term[2],data) b <- soap.basis(object$sd,x,y,film=TRUE,wiggly=TRUE,penalty=FALSE) X <- t(object$irng*t(b$X)) attr(X,"offset") <- b$offset X } Predict.matrix.sf <- function(object,data) # prediction method function for the sf smooth class --- the boundary interpolating film # component of a soap film smooth { x <- get.var(object$term[1],data) y <- get.var(object$term[2],data) b <- soap.basis(object$sd,x,y,film=TRUE,wiggly=FALSE,penalty=FALSE) X <- t(object$irng*t(b$X)) attr(X,"offset") <- b$offset X } Predict.matrix.sw <- function(object,data) # prediction method function for the sw smooth class --- the wiggly # component of a soap film smooth { x <- get.var(object$term[1],data) y <- get.var(object$term[2],data) X <- soap.basis(object$sd,x,y,film=FALSE,wiggly=TRUE,penalty=FALSE)$X X <- t(object$irng*t(X)) X } plot.soap.film <- function(x,P=NULL,data=NULL,label="",se1.mult=1,se2.mult=2, partial.resids=FALSE,rug=TRUE,se=TRUE,scale=-1,n=100,n2=40,n3=3, theta=30,phi=30,jit=FALSE,xlab=NULL,ylab=NULL,main=NULL, ylim=NULL,xlim=NULL,too.far=0.1,shade=FALSE,shade.col="gray80", shift=0,trans=I,by.resids=FALSE,scheme=0,hcolors=heat.colors(100), contour.col=1,...) { ## plot method function for soap.smooth terms if (scheme==3) { if (is.null(P)) outline <- FALSE else outline <- TRUE if (is.null(xlim)) xlim <- c(x$sd$x0,x$sd$x0+ncol(x$sd$G)*x$sd$dx) if (is.null(ylim)) ylim <- c(x$sd$y0,x$sd$y0+nrow(x$sd$G)*x$sd$dy) P0 <- plot.mgcv.smooth(x=x,P=P,data=data,label=label,se1.mult=se1.mult,se2.mult=se2.mult, partial.resids=partial.resids,rug=rug,se=se,scale=scale,n=n,n2=n2, theta=theta,phi=phi,jit=jit,xlab=xlab,ylab=ylab,main=main, ylim=ylim,xlim=xlim,too.far=too.far,shade=shade,shade.col=shade.col, shift=shift,trans=trans,by.resids=by.resids,hcolors=hcolors, ## don't pass scheme!! contour.col=contour.col,...) if (outline) { if (is.null(names(P$bnd))) { for (i in 1:length(P$bnd)) lines(P$bnd[[i]],lwd=2) } else lines(P$bnd,lwd=2) } else { P0$bnd <- x$sd$bnd} return(P0) } if (is.null(P)) { ## get plotting information... if (!x$plot.me) return(NULL) ## shouldn't or can't plot ## get basic plot data beta <- unconstrain(x,attr(x,"coefficients"))*x$irng ## coefs raw <- data[x$term] film <- wiggly <- TRUE if (inherits(x,"sw")) film <- FALSE else if (inherits(x,"sf")) wiggly <- FALSE soap.basis(x$sd,film=film,wiggly=wiggly,plot=TRUE,beta=beta) -> G if (is.null(xlab)) xlabel<- x$term[1] else xlabel <- xlab if (is.null(ylab)) ylabel <- x$term[2] else ylabel <- ylab xscale <- x$sd$x0 + 0:(nrow(G)-1) * x$sd$dx yscale <- x$sd$y0 + 0:(ncol(G)-1) * x$sd$dy main <- if (is.null(main)) label return(list(fit=G,scale=FALSE,se=FALSE,raw=raw,xlab=xlabel,ylab=ylabel, xscale=xscale,yscale=yscale,main=main,bnd=x$sd$bnd)) } else { ## do plot if (scheme==0) { xlim <- range(P$xscale);dx = xlim[2] - xlim[1] ylim <- range(P$yscale);dy = ylim[2] - ylim[1] plot(P$xscale[1],P$yscale[1],xlab=P$xlab,ylab=P$ylab,main=P$main,xlim=xlim,ylim=ylim,...) rect(xlim[1]-dx,ylim[1]-dy,xlim[2]+dx,ylim[2]+dy,col="lightgrey") image(P$xscale,P$yscale,P$fit,add=TRUE,col=hcolors,...) contour(P$xscale,P$yscale,P$fit,add=TRUE,col=contour.col,...) } else if (scheme==1) { image(P$xscale,P$yscale,P$fit,col=grey(0:50/50),xlab=P$xlab, ylab=P$ylab,main=P$main,...) contour(P$xscale,P$yscale,P$fit,add=TRUE,col=contour.col,...) } else if (scheme==2) { contour(P$xscale,P$yscale,P$fit,xlab=P$xlab, ylab=P$ylab,main=P$main,col=contour.col,...) if (is.null(names(P$bnd))) { for (i in 1:length(P$bnd)) lines(P$bnd[[i]],lwd=2) } else lines(P$bnd,lwd=2) } } } ## end plot.soap.smooth fs.test <- function(x,y,r0=.1,r=.5,l=3,b=1,exclude=TRUE) ## test function based on Tim Ramsay (2002) J.R.Statist. Soc. B ## 64(2):307-319 "Spline smoothing over difficult regions" { q <- pi*r/2 ## 1/2 length of semi-circle part of centre curve a <- d <- x*0 ## along and distance to arrays ## convert x,y to along curve and distance to curve (a,d) ## co-ordinates. 0 distance along is at (x=-r,y=0) ind <- x>=0 & y>0 a[ind] <- q + x[ind] d[ind] <- y[ind]-r ind <- x>=0 & y<=0 a[ind] <- -q - x[ind] d[ind] <- -r - y[ind] ind <- x < 0 a[ind] <- -atan(y[ind]/x[ind])*r d[ind] <- sqrt(x[ind]^2+y[ind]^2) - r ## create exclusion index ind <- abs(d)>r-r0 | (x>l & (x-l)^2+d^2 > (r-r0)^2) # f <- a*b # the original f <- a*b+d^2 if (exclude) f[ind] <- NA attr(f,"exclude") <- ind f } fs.boundary <- function(r0=.1,r=.5,l=3,n.theta=20) ## produce boundary file for fs.test { rr <- r+(r-r0) theta <- seq(pi,pi/2,length=n.theta) x <- rr*cos(theta); y <- rr*sin(theta) theta <- seq(pi/2,-pi/2,length=2*n.theta) x <- c(x,(r-r0)*cos(theta)+l); y <- c(y,(r-r0)*sin(theta)+r) theta <- seq(pi/2,pi,length=n.theta) x <- c(x,r0*cos(theta)); y <- c(y,r0*sin(theta)) n<-length(x) x <- c(x,x[n:1]);y <- c(y,-y[n:1]) return(list(x=x,y=y)) }