wpmf {wsyn}

Wavelet phasor mean field

Description

Computes the wavelet phasor mean field from a matrix of spatiotemporal data. Also the creator function for the wpmf class. The wpmf class inherits from the tts class, which inherits from the list class.

Usage

wpmf(
  dat,
  times,
  scale.min = 2,
  scale.max.input = NULL,
  sigma = 1.05,
  f0 = 1,
  sigmethod = "none",
  nrand = 1000
)

Arguments

dat

A locations (rows) x time (columns) matrix

times

A vector of time step values, spacing 1

scale.min

The smallest scale of fluctuation that will be examined. At least 2.

scale.max.input

The largest scale of fluctuation guaranteed to be examined

sigma

The ratio of each time scale examined relative to the next timescale. Should be greater than 1.

f0

The ratio of the period of fluctuation to the width of the envelop

sigmethod

Method for significance testing the wmpf, one of quick, fft, aaft (see details)

nrand

The number of randomizations to be used for significance testing

Details

For sigmethod equal to quick, the empirical wpmf is compared to a distribution of magnitudes of sums of random phasors, using the same number of phasors as there are time series. The signif output is a list with first element "quick" and second element a vector of nrand magnitudes of sums of random phasors. For sigmethod equal to fft, the empirical wpmf is compared to wmpfs of Fourier surrogate datasets. The signif output is a list with first element "fft", second element equal to nrand, and third element the fraction of surrogate-based wpmf magnitudes that the empirical wpmf magnitude is greater than (times by timescales matrix). For sigmethod equal to aaft, aaft surrogates are used instead. Output has similar format to the fft case. Values other than quick, fft, and aaft for sigmethod result in no significance testing.

Value

wpmf returns an object of class wpmf. Slots are:

values

A matrix of complex numbers containing the wavelet phasor mean field, of dimensions length(times) by the number of timescales. Entries not considered reliable (longer timescales, near the edges of the time span) are set to NA.

times

The times associated with the data and the wpmf

timescales

The timescales associated with the wpmf

signif

A list with information from the significance testing. Format depends on sigmethod (see details).

dat

The data matrix (locations by time) from which the wpmf was computed

wtopt

The inputted wavelet transform options scale.min, scale.max.input, sigma, f0 in a list

Author(s)

Thomas Anderson, [e-mail], Jon Walter, [e-mail]; Lawrence Sheppard, [e-mail]; Daniel Reuman, [e-mail]

References

Sheppard, L.W., et al. (2016) Changes in large-scale climate alter spatial synchrony of aphid pests. Nature Climate Change. DOI: 10.1038/nclimate2881

See Also

wpmf_methods, wmf, tts, plotmag, browseVignettes("wsyn")

Examples

times<-1:30 #generate time steps
#generate fake count data for 20 locations
dat<-matrix(rpois(20*length(times),20),nrow=20,ncol=length(times)) 
dat<-cleandat(dat=dat,times=times,clev=2)$cdat #detrend and demean
res<-wpmf(dat,times)