psd (version 2.1.2)

splineGrad: Numerical derivatives of a series based on its smooth-spline representation

Description

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

Usage

splineGrad(dseq, dsig, ...)
# S3 method for default
splineGrad(dseq, dsig, plot.derivs = FALSE, ...)

Value

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

Arguments

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?

Author

A.J. Barbour

Details

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

See Also

smooth.spline, constrain_tapers

Examples

if (FALSE) #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)

#REX