var.fd: Variance, Covariance, and Correlation Surfaces for Functional...

View source: R/var.fd.R

var.fdR Documentation

Variance, Covariance, and Correlation Surfaces for Functional Data Object(s)


Compute variance, covariance, and / or correlation functions for functional data.

These are two-argument functions and therefore define surfaces. If only one functional data object is supplied, its variance or correlation function is computed. If two are supplied, the covariance or correlation function between them is computed.


var.fd(fdobj1, fdobj2=fdobj1)


fdobj1, fdobj2

a functional data object.


a two-argument or bivariate functional data object representing the variance, covariance or correlation surface for a single functional data object or the covariance between two functional data objects or between different variables in a multivariate functional data object.


An list object of class bifd with the following components:


the coefficient array with dimensions fdobj1[["basis"]][["nbasis"]] by fdobj2[["basis"]][["nbasis"]] giving the coefficients of the covariance matrix in terms of the bases used by fdobj1 and fdobj2.






dimnames list for a 4-dimensional 'coefs' array. If length(dim(coefs)) is only 2 or 3, the last 2 or 1 component of bifdnames is not used with dimnames(coefs).

Examples below illustrate this structure in simple cases.


Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

mean.fd, sd.fd, std.fd stdev.fd


oldpar <- par(no.readonly=TRUE)
## Example with 2 different bases 
daybasis3 <- create.fourier.basis(c(0, 365))
daybasis5 <- create.fourier.basis(c(0, 365), 5)
tempfd3 <- with(CanadianWeather, smooth.basis(day.5, 
       daybasis3, fdnames=list("Day", "Station", "Deg C"))$fd )
precfd5 <- with(CanadianWeather, smooth.basis(day.5, 
       daybasis5, fdnames=list("Day", "Station", "Deg C"))$fd )

# Compare with structure described above under 'value':
str(tempPrecVar3.5 <- var.fd(tempfd3, precfd5))

## The following produces contour and perspective plots

# Evaluate at a 53 by 53 grid for plotting

daybasis65 <- create.fourier.basis(rangeval=c(0, 365), nbasis=65)

daytempfd <- with(CanadianWeather, smooth.basis(day.5, 
       daybasis65, fdnames=list("Day", "Station", "Deg C"))$fd )
str(tempvarbifd <- var.fd(daytempfd))

str(tempvarmat  <- eval.bifd(weeks,weeks,tempvarbifd))
# dim(tempvarmat)= c(53, 53)

par(mfrow=c(1,2), pty="s")
#contour(tempvarmat, xlab="Days", ylab="Days")
contour(weeks, weeks, tempvarmat, 
        xlab="Daily Average Temperature",
        ylab="Daily Average Temperature",
        main=paste("Variance function across locations\n",
          "for Canadian Anual Temperature Cycle"),
        cex.main=0.8, axes=FALSE)
axisIntervals(1, atTick1=seq(0, 365, length=5), atTick2=NA, 
            atLabels=seq(1/8, 1, 1/4)*365,
            labels=paste("Q", 1:4) )
axisIntervals(2, atTick1=seq(0, 365, length=5), atTick2=NA, 
            atLabels=seq(1/8, 1, 1/4)*365,
            labels=paste("Q", 1:4) )
persp(weeks, weeks, tempvarmat,
      xlab="Days", ylab="Days", zlab="Covariance")
mtext("Temperature Covariance", line=-4, outer=TRUE)

fda documentation built on May 29, 2024, 11:26 a.m.