RTMB (version 1.6)

Interpolation: Interpolation

Description

Some interpolation methods are available to be used as part of 'RTMB' objective functions.

Usage

interpol1Dfun(z, xlim = c(1, length(z)), ...)
interpol2Dfun(z, xlim = c(1, nrow(z)), ylim = c(1, ncol(z)), ...)
# S4 method for ANY,advector,ANY,missing
splinefun(x, y, method = c("fmm", "periodic", "natural"))
# S4 method for advector,missing,ANY,missing
splinefun(x, method = c("fmm", "periodic", "natural"))

Value

function of x.

function of x and y.

Arguments

z

Matrix to be interpolated

xlim

Domain of x

...

Configuration parameters

ylim

Domain of y

x

spline x coordinates

y

spline y coordinates

method

Same as for the stats version, however only the three first are available.

Functions

• interpol1Dfun(): Construct a kernel smoothed representation of a vector.

• interpol2Dfun(): Construct a kernel smoothed representation of a matrix.

• splinefun(x = ANY, y = advector, method = ANY, ties = missing): Construct a spline function.

• splinefun(x = advector, y = missing, method = ANY, ties = missing): Construct a spline function.

Details

interpol1Dfun and interpol2Dfun are kernel smoothers useful in the case where you need a 3rd order smooth representation of a data vector or matrix. A typical use case is when a high-resolution map needs to be accessed along a random effect trajectory. Both 1D and 2D cases accept an 'interpolation radius' parameter (default R=2) controlling the degree of smoothness. Note, that only the value R=1 will match the data exactly, while higher radius trades accuracy for smoothness. Note also that these smoothers do not attempt to extrapolate: The returned value will be NaN outside the valid range (xlim / ylim).

splinefun imitates the corresponding stats function. The AD implementation (in contrast to interpol1Dfun) works for parameter dependent y-coordinates.

Examples

## ======= interpol1D
## R=1 => exact match of observations
f <- interpol1Dfun(sin(1:10), R=1)
layout(t(1:2))
plot(sin(1:10))
plot(f, 1, 10, add=TRUE)
title("R=1")
F <- MakeTape(f, 0)
F3 <- F$jacfun()$jacfun()$jacfun()
plot(Vectorize(F3), 1, 10)
title("3rd derivative")
## ======= interpol2D
## R=1 => exact match of observations
f <- interpol2Dfun(volcano, xlim=c(0,1), ylim=c(0,1), R=1)
f(0,0) == volcano[1,1]   ## Top-left corner
f(1,1) == volcano[87,61] ## Bottom-right corner
## R=2 => trades accuracy for smoothness
f <- interpol2Dfun(volcano, xlim=c(0,1), ylim=c(0,1), R=2)
f(0,0) - volcano[1,1]    ## Error Top-left corner
F <- MakeTape(function(x) f(x[1],x[2]), c(.5,.5))
## ======= splinefun
T <- MakeTape(function(x){
   S <- splinefun(sin(x))
   S(4:6)
}, 1:10)