# caps: Cook and Peters Smoothing Spline with User-Specified Rigidity... In dplR: Dendrochronology Program Library in R

 caps R Documentation

## Cook and Peters Smoothing Spline with User-Specified Rigidity and Frequency Cutoff

### Description

Applies a smoothing spline to `y` with rigidity determined by two parameters: frequency response `f` at a wavelength of `nyrs` years.

### Usage

``````caps(y, nyrs = length(y) * 2/3, f = 0.5)
``````

### Arguments

 `y` a `numeric` vector, typically a tree-ring series. `nyrs` a number greater than zero, affecting the rigidity of the spline. If `nyrs` is between zero and one it will be treated as percentage of the length of the series. E.g., a value of 0.667 would 0.667 * length(y) or what is often called a 2/3 spline in the tree-ring literature (this is the default). When `f` is kept constant, a larger `nyrs` produces a more rigid spline. `f` a number between 0 and 1 giving the frequency response at a wavelength of `nyrs` years. When `nyrs` is kept constant, a smaller `f` produces a more rigid spline: At one extreme, `f = 0` causes the function to return the least-squares straight line fit to the data. At the other extreme, as `f` approaches 1 the result approaches the natural spline, i.e. the function outputs `y`. The default value is 0.5 and shouldn't be changed without a good reason.

### Details

This applies the classic smoothing spline from Cook and Peters (1981). The rigidity of the spline has a frequency response of 50% at a wavelength of `nyrs`. The references, of course, have more information.

This funciton was introduced to `dplR` in version 1.7.3 and essentially replaces `ffcsaps` for most uses. Where `ffcsaps` is written entirely in R, `caps` is a wrapper for a Fortran subroutine from Ed Cook's ARSTAN program that is thousands of times faster.

Note: like `ffcsaps`, `caps` returns `NA` if there are any `NA` values in `y`. See examples.

### Value

A filtered vector.

### Author(s)

Fotran code provided by Ed Cook and adapted for dplR by Andy Bunn.

### References

Cook, E. R. and Kairiukstis, L. A., editors (1990) Methods of Dendrochronology: Applications in the Environmental Sciences. Springer. ISBN-13: 978-0-7923-0586-6.

Cook, E. R. and Peters, K. (1981) The Smoothing Spline: A New Approach to Standardizing Forest Interior Tree-Ring Width Series for Dendroclimatic Studies. Tree-Ring Bulletin, 41, 45-53.

`ffcsaps`, `ads`

### Examples

``````library(graphics)
library(utils)

## Use first series from the Mesa Verde data set
data(co021)
series <- co021[, 1]
series <- series[!is.na(series)]
plot(series, type = "l", ylab = "Ring Width (mm)", col = "grey")
lines(caps(series, nyrs = 10), col = "red", lwd = 2)
lines(caps(series, nyrs = 100), col = "green", lwd = 2)
# A 2/3 spline, the default, 462.6667 yrs here
lines(caps(series), col = "blue", lwd = 2)
legend("topright",
c("Series", "nyrs=10", "nyrs=100",
paste("Default nyrs (", floor(length(series) * 2/3), ")", sep="")),
fill=c("grey", "red", "green", "blue"))

## Note behavior when NA is encountered and
## take appropriate measures as demonstrated above
y <- c(NA,NA,rnorm(100))
caps(y)

``````

dplR documentation built on June 22, 2024, 9:59 a.m.