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Rev 61160 Rev 61168
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\dontshow{
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\dontshow{
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print.default(cars.spl)
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print.default(cars.spl)
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}
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}
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## "Proof" that the derivatives are okay, by comparing with approximation
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## "Proof" that the derivatives are okay, by comparing with approximation
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diff.quot <- function(x,y) {
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diff.quot <- function(x, y) {
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  ## Difference quotient (central differences where available)
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  ## Difference quotient (central differences where available)
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  n <- length(x); i1 <- 1:2; i2 <- (n-1):n
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  n <- length(x); i1 <- 1:2; i2 <- (n-1):n
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  c(diff(y[i1]) / diff(x[i1]), (y[-i1] - y[-i2]) / (x[-i1] - x[-i2]),
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  c(diff(y[i1]) / diff(x[i1]), (y[-i1] - y[-i2]) / (x[-i1] - x[-i2]),
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    diff(y[i2]) / diff(x[i2]))
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    diff(y[i2]) / diff(x[i2]))
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}
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}
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xx <- unique(sort(c(seq(0,30, by = .2), kn <- unique(speed))))
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xx <- unique(sort(c(seq(0, 30, by = .2), kn <- unique(speed))))
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i.kn <- match(kn, xx)# indices of knots within xx
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i.kn <- match(kn, xx)   # indices of knots within xx
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op <- par(mfrow = c(2,2))
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op <- par(mfrow = c(2,2))
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plot(speed, dist, xlim = range(xx), main = "Smooth.spline & derivatives")
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plot(speed, dist, xlim = range(xx), main = "Smooth.spline & derivatives")
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lines(pp <- predict(cars.spl, xx), col = "red")
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lines(pp <- predict(cars.spl, xx), col = "red")
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points(kn, pp$y[i.kn], pch = 3, col = "dark red")
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points(kn, pp$y[i.kn], pch = 3, col = "dark red")
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mtext("s(x)", col = "red")
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mtext("s(x)", col = "red")
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for(d in 1:3){
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for(d in 1:3){
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  n <- length(pp$x)
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  n <- length(pp$x)
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  plot(pp$x, diff.quot(pp$x,pp$y), type = 'l', xlab = "x", ylab = "",
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  plot(pp$x, diff.quot(pp$x,pp$y), type = "l", xlab = "x", ylab = "",
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       col = "blue", col.main = "red",
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       col = "blue", col.main = "red",
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       main= paste0("s" ,paste(rep("'",d), collapse = ""),"(x)"))
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       main = paste0("s" ,paste(rep("'", d), collapse = ""), "(x)"))
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  mtext("Difference quotient approx.(last)", col = "blue")
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  mtext("Difference quotient approx.(last)", col = "blue")
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  lines(pp <- predict(cars.spl, xx, deriv = d), col = "red")
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  lines(pp <- predict(cars.spl, xx, deriv = d), col = "red")
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\dontshow{
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\dontshow{
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  print(pp)
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  print(pp)
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}
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}