Summarize each tf in a vector (function-wise)

These functions extract (user-specified) function-wise summary statistics from every entry in a tf-vector. To summarize a vector of functions at each argument value, see ?tfsummaries. Note that most of these will tend to yield lots of NAs for irregular tfd unless you set a tf_evaluator()-function that does inter- and extrapolation for them beforehand.

Usage

tf_fwise(x, .f, arg = tf_arg(x), ...)

tf_fmax(x, arg = tf_arg(x), na.rm = FALSE)

tf_fmin(x, arg = tf_arg(x), na.rm = FALSE)

tf_fmedian(x, arg = tf_arg(x), na.rm = FALSE)

tf_frange(x, arg = tf_arg(x), na.rm = FALSE, finite = FALSE)

tf_fmean(x, arg = tf_arg(x))

tf_fvar(x, arg = tf_arg(x))

tf_fsd(x, arg = tf_arg(x))

tf_crosscov(x, y, arg = tf_arg(x))

tf_crosscor(x, y, arg = tf_arg(x))

Arguments

x: a tf object.
.f: a function or formula that is applied to each entry of x, see purrr::as_mapper() and details.
arg: defaults to standard argument values of x.
...: additional arguments for purrr::as_mapper().
na.rm: a logical (TRUE or FALSE) indicating whether missing values should be removed.
finite: logical, indicating if all non-finite elements should be omitted.
y: a tf object.

Value

a list (or vector) of the same length as x with the respective summaries.

Details

tf_fwise turns x into a list of data.frames with columns arg and values internally, so the function/formula in .f gets a data.frame .x with these columns, see examples below or source code for tf_fmin(), tf_fmax(), etc.

Functions

tf_fwise(): User-specified function-wise summary statistics
tf_fmax(): maximal value of each function
tf_fmin(): minimal value of each function
tf_fmedian(): median value of each function
tf_frange(): range of values of each function
tf_fmean(): mean of each function: \(\tfrac{1}{|T|}\int_T x_i(t) dt\)
tf_fvar(): variance of each function: \(\tfrac{1}{|T|}\int_T (x_i(t) - \bar x(t))^2 dt\)
tf_fsd(): standard deviation of each function: \(\sqrt{\tfrac{1}{|T|}\int_T (x_i(t) - \bar x(t))^2 dt}\)
tf_crosscov(): cross-covariances between two functional vectors: \(\tfrac{1}{|T|}\int_T (x_i(t) - \bar x(t)) (y_i(t)-\bar y(t)) dt\)
tf_crosscor(): cross-correlation between two functional vectors: tf_crosscov(x, y) / (tf_fsd(x) * tf_fsd(y))

Examples

x <- tf_rgp(3)
layout(t(1:3))
plot(x, col = 1:3)
#  each function's values to [0,1]:
x_clamp <- (x - tf_fmin(x)) / (tf_fmax(x) - tf_fmin(x))
plot(x_clamp, col = 1:3)
# standardize each function to have mean / integral 0 and sd 1:
x_std <- (x - tf_fmean(x)) / tf_fsd(x)
tf_fvar(x_std) == c(1, 1, 1)
#> [1]  TRUE FALSE FALSE
plot(x_std, col = 1:3)

# Custom functions:
# 80%tiles of each function's values:
tf_fwise(x, \(.x) quantile(.x$value, 0.8)) |> unlist()
#>       1.80%       2.80%       3.80% 
#>  0.54956138 -0.06731273  1.15582713 
# minimal value of each function for t > 0.5
tf_fwise(x, \(.x) min(.x$value[.x$arg > 0.5])) |> unlist()
#>           1           2           3 
#> -0.04494065 -2.82525685 -0.17442921 

tf_crosscor(x, -x)
#> [1] -1 -1 -1
tf_crosscov(x, x) == tf_fvar(x)
#> [1] TRUE TRUE TRUE

Summarize each `tf` in a vector (function-wise)