polyfunc <- function(order,x) {
## the given data points
dat1<-array(c(0:0), dim = c(11,1))
dat2<-array(c(1:1), dim = c(10,1))
datapt <- c(dat1,dat2)

## the parts for the van matrix
data<-array(c(-10:10), dim = c(21,order))
power<-array(c(0:(order-1)), dim = c(order,21))
pnew<-t(power)

## the van matrix
u <- (data^pnew)

## take svd - returns d u v get element by saying out$u
out <- svd(u)

## assign to WVU convention
w<- out$d
V <- out$v
U<-out$u

## then to get coefficients one has to flip the diagonal W components and then test ##whether they are
## larger then a threshold
invw <- 1/w

## create a true fals mask to make those elements zero
mask <- (invw>0.0001)
invw <- invw*mask

## w need to be turned into matirx
W<-diag(invw)

##then multiply the inverse etc of VWU
res <- V %*% W %*% t(U)

## multiply result with the datapoint vector
##gives the coeficients
fin <- res %*% datapt



##plot(x,datapt)
##lines(x,5.846163e-01 + (1.341669e-01*x) + 
##(-3.652122e-03*x*x) + (-9.534706e-04*x*x*x) + (-4.522241e-05*x*x*x*x))

##fin
##plot(x,polyseries(x,fin,order))

##plot(x,datapt)
##plot(x,polyseries(x,fin,order))
##lines(x,polyseries(x,fin,order))
}


polyseries <- function(x,coeff,order) {
return <- c(0:(length(x)-1))
for (i in 1:length(x)) {
	pow <- c(0:(order-1))
	series <- array(c(x[i]), dim = c(1,order))
	pow <- series^pow
	return[i] <- sum(t(coeff) * pow)
 }
return
}