splineGrad: Numerical derivatives of a series based on its smooth-spline...
In williamdeleo/psd: Adaptive, Sine-Multitaper Power Spectral Density Estimation

Description Usage Arguments Details Value Author(s) See Also Examples

This computes the numerical derivatives of a spline representation of the input series; differentiation of spline curves is numerically efficient.

splineGrad(dseq, dsig, ...)

## Default S3 method:
splineGrad(dseq, dsig, plot.derivs = FALSE, ...)

`dseq`	numeric; a vector of positions for `dsig`.
`dsig`	numeric; a vector of values (which will have a spline fit to them).
`...`	additional arguments passed to `smooth.spline`
`plot.derivs`	logical; should the derivatives be plotted?

With smoothing, the numerical instability for "noisy" data can be drastically reduced, since spline curves are inherently (at least) twice differentiable.

A matrix with columns representing x, f(x), f'(x), f''(x)

A.J. Barbour

smooth.spline, constrain_tapers

## Not run: #REX
library(psd)

##
## Spline gradient
##

set.seed(1234)
x <- seq(0,5*pi,by=pi/64)
y <- cos(x) #**2

splineGrad(x, y, TRUE)

# unfortunately, the presence of
# noise will affect numerical derivatives
y <- y + rnorm(length(y), sd=.1)
splineGrad(x, y, TRUE)

# so change the smoothing used in smooth.spline
splineGrad(x, y, TRUE, spar=0.2)
splineGrad(x, y, TRUE, spar=0.6)
splineGrad(x, y, TRUE, spar=1.0)


## End(Not run)#REX