# Predict.matrix.soap.film: Prediction matrix for soap film smooth In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

 Predict.matrix.soap.film 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)

## 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=".")

## 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=".")