Predict.matrix.soap.film {mgcv} R Documentation

## Prediction matrix for soap film smooth

### Description

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.

### Usage

## 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.

### Value

A matrix. This may have an "offset" attribute corresponding to the contribution from any known boundary conditions on the smooth.

### Author(s)

Simon N. Wood s.wood@bath.ac.uk

### References

smooth.construct.so.smooth.spec

### Examples

## 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=".")