Cubic spline interpolation

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Description

A fast, FORTRAN based function for cubic spline interpolation.

Usage

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splint(x, y, xgrid, wt=NULL, derivative=0,lam=0, df=NA, lambda=NULL)

Arguments

x

The x values that define the curve or a two column matrix of x and y values.

y

The y values that are paired with the x's.

xgrid

The grid to evaluate the fitted cubic interpolating curve.

derivative

Indicates whether the function or a a first or second derivative should be evaluated.

wt

Weights for different obsrevations in the scale of reciprocal variance.

lam

Value for smoothing parameter. Default value is zero giving interpolation.

lambda

Same as lam just to make this easier to remember.

df

Effective degrees of freedom. Default is to use lambda =0 or a df equal to the number of observations.

Details

Fits a piecewise interpolating or smoothing cubic polynomial to the x and y values. This code is designed to be fast but does not many options in sreg or other more statistical implementations. To make the solution well posed the the second and third derivatives are set to zero at the limits of the x values. Extrapolation outside the range of the x values will be a linear function.

It is assumed that there are no repeated x values; use sreg followed by predict if you do have replicated data.

Value

A vector consisting of the spline evaluated at the grid values in xgrid.

References

See Additive Models by Hastie and Tibshriani.

See Also

sreg, Tps

Examples

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x<- seq( 0, 120,,200)

# an interpolation
splint(rat.diet$t, rat.diet$trt,x )-> y

plot( rat.diet$t, rat.diet$trt)
lines( x,y)
#( this is weird and not appropriate!)

# the following two smooths should be the same

splint( rat.diet$t, rat.diet$con,x, df= 7)-> y1

# sreg function has more flexibility than splint but will
# be slower for larger data sets. 

sreg( rat.diet$t, rat.diet$con, df= 7)-> obj
predict(obj, x)-> y2 

# in fact predict.sreg interpolates the predicted values using splint!

# the two predicted lines (should) coincide
lines( x,y1, col="red",lwd=2)
lines(x,y2, col="blue", lty=2,lwd=2)
 

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