# Prediction matrix for soap film smooth Creates a prediction matrix for a soap film smooth object, mapping the coefficients of the smooth to the linear predictor component for the smooth. This is the `Predict.matrix` method function required by `gam`. ```r ## S3 method for class 'soap.film' Predict.matrix(object,data) ## S3 method for class 'sw' Predict.matrix(object,data) ## S3 method for class 'sf' Predict.matrix(object,data) ``` ## Arguments - `object`: A class `"soap.film"`, `"sf"` or `"sw"` object. - `data`: A list list or data frame containing the arguments of the smooth at which predictions are required. ## Details The smooth object will be largely what is returned from `smooth.construct.so.smooth.spec`, although elements `X` and `S` are not needed, and need not be present, of course. ## Returns A matrix. This may have an `"offset"` attribute corresponding to the contribution from any known boundary conditions on the smooth. ## References [https://www.maths.ed.ac.uk/~swood34/](https://www.maths.ed.ac.uk/~swood34/) ## Author(s) Simon N. Wood s.wood@bath.ac.uk ## See Also `smooth.construct.so.smooth.spec` ## Examples ```r ## This is a lower level example. The basis and ## penalties are obtained explicitly ## and `magic' is used as the fitting routine... require(mgcv) set.seed(66) ## create a boundary... fsb <- list(fs.boundary()) ## create some internal knots... knots <- data.frame(x=rep(seq(-.5,3,by=.5),4), y=rep(c(-.6,-.3,.3,.6),rep(8,4))) ## Simulate some fitting data, inside boundary... n<-1000 x <- runif(n)*5-1;y<-runif(n)*2-1 z <- fs.test(x,y,b=1) ind <- inSide(fsb,x,y) ## remove outsiders z <- z[ind];x <- x[ind]; y <- y[ind] n <- length(z) z <- z + rnorm(n)*.3 ## add noise ## plot boundary with knot and data locations plot(fsb[[1]]$x,fsb[[1]]$y,type="l");points(knots$x,knots$y,pch=20,col=2) points(x,y,pch=".",col=3); ## set up the basis and penalties... sob <- smooth.construct2(s(x,y,bs="so",k=40,xt=list(bnd=fsb,nmax=100)), data=data.frame(x=x,y=y),knots=knots) ## ... model matrix is element `X' of sob, penalties matrices ## are in list element `S'. ## fit using `magic' um <- magic(z,sob$X,sp=c(-1,-1),sob$S,off=c(1,1)) beta <- um$b ## produce plots... par(mfrow=c(2,2),mar=c(4,4,1,1)) m<-100;n<-50 xm <- seq(-1,3.5,length=m);yn<-seq(-1,1,length=n) xx <- rep(xm,n);yy<-rep(yn,rep(m,n)) ## plot truth... tru <- matrix(fs.test(xx,yy),m,n) ## truth image(xm,yn,tru,col=heat.colors(100),xlab="x",ylab="y") lines(fsb[[1]]$x,fsb[[1]]$y,lwd=3) contour(xm,yn,tru,levels=seq(-5,5,by=.25),add=TRUE) ## Plot soap, by first predicting on a fine grid... ## First get prediction matrix... X <- Predict.matrix2(sob,data=list(x=xx,y=yy)) ## Now the predictions... fv <- X%*%beta ## Plot the estimated function... image(xm,yn,matrix(fv,m,n),col=heat.colors(100),xlab="x",ylab="y") lines(fsb[[1]]$x,fsb[[1]]$y,lwd=3) points(x,y,pch=".") contour(xm,yn,matrix(fv,m,n),levels=seq(-5,5,by=.25),add=TRUE) ## Plot TPRS... b <- gam(z~s(x,y,k=100)) fv.gam <- predict(b,newdata=data.frame(x=xx,y=yy)) names(sob$sd$bnd[[1]]) <- c("xx","yy","d") ind <- inSide(sob$sd$bnd,xx,yy) fv.gam[!ind]<-NA image(xm,yn,matrix(fv.gam,m,n),col=heat.colors(100),xlab="x",ylab="y") lines(fsb[[1]]$x,fsb[[1]]$y,lwd=3) points(x,y,pch=".") contour(xm,yn,matrix(fv.gam,m,n),levels=seq(-5,5,by=.25),add=TRUE) ```

Predict.matrix.soap.film function