cov function

Variance, Covariance, and Correlation for Complex Data

Wrappers of stats::var , stats::cov , and stats::cor that are capable of handling complex input.

cov(
  x,
  y = NULL,
  na.rm = FALSE,
  method = "pearson",
  use = "everything",
  pseudo = FALSE,
  ...
)

cor(
  x,
  y = NULL,
  na.rm = FALSE,
  use = "everything",
  method = "pearson",
  pseudo = FALSE,
  ...
)

var(x, y = NULL, na.rm = FALSE, use = "everything", pseudo = FALSE, ...)

Arguments

• x: a numeric or complex vector, matrix, or dataframe.
• y: NULL (default) or a numeric vector, matrix, or dataframe with dimensions compatible with x.
• na.rm: logical. Should missing values be removed? Only considered when x is a vector.
• method: The method for calculating correlation coefficient. Only "pearson" is supported for complex variables, so this parameter is ignored.
• use: character string giving the desired method of computing covariances in the presence of missing values. Options are "everything" (default), "all.obs", "complete.obs", or "na.or.complete". See stats::cov for explanation of what each one does. Note that "pairwise.complete.obs" is not available for this complex method.
• pseudo: logical, if TRUE the pseudo variance, covariance, or correlation is calculated. i.e. no complex conjugation is performed.
• ...: Other parameters, ignored.

Returns

numeric or complex the sample variance, covariance, or correlation of the input data.

Details

For vector input, the sample variance is calculated as,

$sum(Conj( mean(x) - x ) * ( mean(x) - x )) / (length(x) - 1)$

And the sample covariance is calculated as,

$sum(Conj( mean(x) - x ) * ( mean(y) - y )) / (length(x) - 1)$

The Pearson correlation coefficient, which is the only kind available for complex data, is the covariance divided by the product of the standard deviations of all variables. If pseudo = TRUE, these same expressions, sans Conj(), are used to calculate the pseudo, AKA relational, versions of variance, covariance, or correlation.

Functions

• cor: Correlation coefficient of complex variables.
• var: S3 Variance or Pseudo Variance of Complex Variables, a synonym for cov .

Examples

set.seed(4242)
n <- 9
foo <- complex(real = rnorm(n), imaginary = rnorm(n))
var(foo)
bar <- complex(real = rnorm(n), imaginary = rnorm(n))
var(x = foo, y = bar)
foobar <- data.frame(foo, bar)
cov(foobar)
cor(foobar)