Title:	S3 Classes and Methods for Tidy Functional Data
Version:	0.3.4
Description:	Defines S3 vector data types for vectors of functional data (grid-based, spline-based or functional principal components-based) with all arithmetic and summary methods, derivation, integration and smoothing, plotting, data import and export, and data wrangling, such as re-evaluating, subsetting, sub-assigning, zooming into sub-domains, or extracting functional features like minima/maxima and their locations. The implementation allows including such vectors in data frames for joint analysis of functional and scalar variables.
License:	AGPL (≥ 3)
URL:	https://tidyfun.github.io/tf/, https://github.com/tidyfun/tf/
BugReports:	https://github.com/tidyfun/tf/issues
Depends:	R (≥ 4.1)
Imports:	checkmate, methods, mgcv, mvtnorm, pracma, purrr, rlang, stats, vctrs (≥ 0.2.4), zoo
Suggests:	covr, dplyr, knitr, refund, testthat (≥ 3.0.0)
Encoding:	UTF-8
RoxygenNote:	7.3.1
Collate:	'approx.R' 'bibentries.R' 'brackets.R' 'calculus.R' 'convert-construct-utils.R' 'convert.R' 'depth.R' 'evaluate.R' 'fwise.R' 'globals.R' 'graphics.R' 'interpolate.R' 'ops.R' 'math.R' 'methods.R' 'print-format.R' 'rebase.R' 'rng.R' 'smooth.R' 'soft-impute-svd.R' 'summarize.R' 'tf-package.R' 'tfb-fpc.R' 'tfb-spline.R' 'tfb-class.R' 'tfd-class.R' 'tf-s4.R' 'tfb-fpc-utils.R' 'tfb-spline-utils.R' 'utils.R' 'vctrs-cast.R' 'vctrs-ptype2.R' 'where.R' 'zoom.R'
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2024-05-22 09:51:25 UTC; fabians
Author:	Fabian Scheipl [aut, cre], Jeff Goldsmith [aut], Julia Wrobel [ctb], Maximilian Muecke [ctb], Sebastian Fischer [ctb], Trevor Hastie [ctb] (softImpute author), Rahul Mazumder [ctb] (softImpute author), Chen Meng [ctb] (mogsa author)
Maintainer:	Fabian Scheipl <fabian.scheipl@googlemail.com>
Repository:	CRAN
Date/Publication:	2024-05-22 10:30:03 UTC

tf: S3 Classes and Methods for Tidy Functional Data

Description

tf is a light-weight package with few dependencies that provides the class definitions and methods infrastructure for tidyfun – tf gives you:

• new S3 data types for representing (vectors of) functional data: tfd() & tfb()

• arithmetic operators for such data (Ops.tf()),

• simple descriptive statistics: e.g. mean.tf(), median.tf()

• base graphics functions for such data: plot.tf()

• functions to do smoothing (tf_smooth.tfd()), differentiation tf_derive.tfd()) and integration (tf_derive.tfd())

The goal of the add-on package tidyfun is to make data wrangling and exploratory analysis for functional data in R quick and easy, using tidyverse syntax and standards.

Please also install tidyfun for the full functionality to access the full documentation including a number of vignettes and case studies, or visit the tidyfun website.

Author(s)

Maintainer: Fabian Scheipl fabian.scheipl@googlemail.com (ORCID)

Authors:

• Jeff Goldsmith

Other contributors:

• Julia Wrobel (ORCID) [contributor]

• Maximilian Muecke (ORCID) [contributor]

• Sebastian Fischer (ORCID) [contributor]

• Trevor Hastie (softImpute author) [contributor]

• Rahul Mazumder (softImpute author) [contributor]

• Chen Meng (mogsa author) [contributor]

See Also

Useful links:

• https://tidyfun.github.io/tf/

• https://github.com/tidyfun/tf/

• Report bugs at https://github.com/tidyfun/tf/issues

Math, Summary and Ops Methods for tf

Description

These methods and operators mostly work arg-value-wise on tf objects, see ?groupGeneric for implementation details.

Usage

## S3 method for class 'tf'
Ops(e1, e2)

## S3 method for class 'tfd'
e1 == e2

## S3 method for class 'tfd'
e1 != e2

## S3 method for class 'tfb'
e1 == e2

## S3 method for class 'tfb'
e1 != e2

## S3 method for class 'tfd'
Ops(e1, e2)

## S3 method for class 'tfb'
Ops(e1, e2)

## S3 method for class 'tfd'
Math(x, ...)

## S3 method for class 'tfb'
Math(x, ...)

## S3 method for class 'tf'
Summary(...)

## S3 method for class 'tfd'
cummax(...)

## S3 method for class 'tfd'
cummin(...)

## S3 method for class 'tfd'
cumsum(...)

## S3 method for class 'tfd'
cumprod(...)

## S3 method for class 'tfb'
cummax(...)

## S3 method for class 'tfb'
cummin(...)

## S3 method for class 'tfb'
cumsum(...)

## S3 method for class 'tfb'
cumprod(...)

Arguments

Details

See examples below. Equality checks of functional objects are even more iffy than usual for computer math and not very reliable. Note that max and min are not guaranteed to be maximal/minimal over the entire domain, only on the evaluation grid used for computation. With the exception of addition and multiplication, operations on tfb-objects first evaluate the data on their arg, perform computations on these evaluations and then convert back to an tfb- object, so a loss of precision should be expected – especially so for small spline bases and/or very wiggly data.

Value

a tf- or logical vector with the computed result

See Also

tf_fwise() for scalar summaries of each function in a tf-vector

Examples

set.seed(1859)
f <- tf_rgp(4)
2 * f == f + f
sum(f) == f[1] + f[2] + f[3] + f[4]
log(exp(f)) == f
plot(f, points = FALSE)
lines(range(f), col = 2, lty = 2)

f2 <- tf_rgp(5) |> exp() |> tfb(k = 25)
layout(t(1:3))
plot(f2, col = gray.colors(5))
plot(cummin(f2), col = gray.colors(5))
plot(cumsum(f2), col = gray.colors(5))

# ?tf_integrate for integrals, ?tf_fwise for scalar summaries of each function

Convert functional data back to tabular data formats

Description

Various converters to turn tfb- or tfd-vectors into data.frames or matrices, or even an actual R function.

Usage

## S3 method for class 'tf'
as.data.frame(x, row.names = NULL, optional = FALSE, unnest = FALSE, ...)

## S3 method for class 'tf'
as.matrix(x, arg, interpolate = FALSE, ...)

## S3 method for class 'tf'
as.function(x, ...)

Arguments

Value

for as.data.frame.tf: if unnest is FALSE (default), a one-column data.frame with a tf-column containing x. if unnest is TRUE, a 3-column data frame with columns id for the (unique) names of x or a numeric identifier, arg and value, with each row containing one function evaluation at the original arg-values.

for as.matrix.tf: a matrix with one row per function and one column per arg.

for as.function.tf: an R function with argument arg that evaluates x on arg and returns the list of function values

Turns any object into a list

Description

See above.

Usage

ensure_list(x)

Arguments

Value

x turned into a list.

See Also

Other tidyfun developer tools: prep_plotting_arg(), unique_id()

Eigenfunctions via weighted, regularized SVD

Description

Compute (truncated) orthonormal eigenfunctions and scores for (partially missing) data on a common (potentially non-equidistant) grid.

Usage

fpc_wsvd(data, arg, pve = 0.995)

## S3 method for class 'matrix'
fpc_wsvd(data, arg, pve = 0.995)

## S3 method for class 'data.frame'
fpc_wsvd(data, arg, pve = 0.995)

Arguments

Details

Performs a weighted SVD with trapezoidal quadrature weights s.t. returned vectors represent (evaluations of) orthonormal eigenfunctions \phi_j(t), not eigenvectors \phi_j = (\phi_j(t_1), \dots, \phi_j(t_n)), specifically:
\int_T \phi_j(t)^2 dt \approx \sum_i \Delta_i \phi_j(t_i)^2 = 1 given quadrature weights \Delta_i, not \phi_j'\phi_j = \sum_i \phi_j(t_i)^2 = 1;
\int_T \phi_j(t) \phi_k(t) dt = 0 not \phi_j'\phi_k = \sum_i \phi_j(t_i)\phi_k(t_i) = 0, c.f. mogsa::wsvd().
For incomplete data, this uses an adaptation of softImpute::softImpute(), see references. Note that will not work well for data on a common grid if more than a few percent of data points are missing, and it breaks down completely for truly irregular data with no/few common timepoints, even if observed very densely. For such data, either re-evaluate on a common grid first or use more advanced FPCA approaches like refund::fpca_sc(), see last example for tfb_fpc()

Value

a list with entries

• mu estimated mean function (numeric vector)

• efunctions estimated FPCs (numeric matrix, columns represent FPCs)

• scores estimated FPC scores (one row per observed curve)

• npc how many FPCs were returned for the given pve (integer)

• scoring_function a function that returns FPC scores for new data and given eigenfunctions, see tf:::.fpc_wsvd_scores for an example.

Author(s)

Trevor Hastie, Rahul Mazumder, Cheng Meng, Fabian Scheipl

References

code adapted from / inspired by mogsa::wsvd() by Cheng Meng and softImpute::softImpute() by Trevor Hastie and Rahul Mazumder.
Meng C (2023). mogsa: Multiple omics data integrative clustering and gene set analysis. https://bioconductor.org/packages/mogsa.
Mazumder, Rahul, Hastie, Trevor, Tibshirani, Robert (2010). “Spectral regularization algorithms for learning large incomplete matrices.” The Journal of Machine Learning Research, 11, 2287-2322.
Hastie T, Mazumder R (2021). softImpute: Matrix Completion via Iterative Soft-Thresholded SVD. R package version 1.4-1, https://CRAN.R-project.org/package=softImpute.

See Also

Other tfb-class: tfb, tfb_fpc(), tfb_spline()

Other tfb_fpc-class: tfb_fpc()

Summarize each tf in a vector

Description

These functions extract (user-specified) function-wise summary statistics from each entry in a tf-vector. To summarize a vector of functions at each argument value, see ?tfsummaries. Note that 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

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

Value

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

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))

See Also

Other tidyfun summary functions: tfsummaries

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)
plot(x_std, col = 1:3)
# Custom functions:
# 80%tiles of each function's values:
tf_fwise(x, ~ quantile(.x$value, .8)) |> unlist()
# minimal value of each function for t >.5
tf_fwise(x, ~ min(.x$value[.x$arg > .5])) |> unlist()

tf_crosscor(x, -x)
tf_crosscov(x, x) == tf_fvar(x)

Find out if values are inside given bounds

Description

in_range and its infix-equivalent ⁠%inr%⁠ return TRUE for all values in the numeric vector f that are within the range of values in r.

Usage

in_range(f, r)

f %inr% r

Arguments

Value

a logical vector of the same length as f

See Also

Other tidyfun utility functions: tf_arg(), tf_zoom()

base plots for tfs

Description

Some base functions for displaying functional data in spaghetti- (i.e., line plots) and lasagna- (i.e., heat map) flavors.

Usage

## S3 method for class 'tf'
plot(
  x,
  y,
  n_grid = 50,
  points = is_irreg(x),
  type = c("spaghetti", "lasagna"),
  alpha = min(1, max(0.05, 2/length(x))),
  ...
)

## S3 method for class 'tf'
lines(x, arg, n_grid = 50, alpha = min(1, max(0.05, 2/length(x))), ...)

## S3 method for class 'tf'
points(
  x,
  arg,
  n_grid = NA,
  alpha = min(1, max(0.05, 2/length(x))),
  interpolate = FALSE,
  ...
)

Arguments

Details

If no second argument y is given, evaluation points (arg) for the functions are given by the union of the tf's arg and an equidistant grid over its domain with n_grid points. If you want to only see the original data for tfd-objects without inter-/extrapolation, use n_grid < 1 or n_grid = NA.

Value

the plotted tf-object, invisibly.

References

Swihart, J B, Caffo, Brian, James, D B, Strand, Matthew, Schwartz, S B, Punjabi, M N (2010). “Lasagna plots: a saucy alternative to spaghetti plots.” Epidemiology (Cambridge, Mass.), 21(5), 621–625.

Preprocess evaluation grid for plotting

Description

(internal function exported for re-use in upstream packages)

Usage

prep_plotting_arg(f, n_grid)

Arguments

Value

a semi-regular grid rounded down to appropriate resolution

See Also

Other tidyfun developer tools: ensure_list(), unique_id()

Pretty printing and formatting for functional data

Description

Print/format tf-objects.

Usage

## S3 method for class 'tf'
print(x, n = 5, ...)

## S3 method for class 'tfd_reg'
print(x, n = 5, ...)

## S3 method for class 'tfd_irreg'
print(x, n = 5, ...)

## S3 method for class 'tfb'
print(x, n = 5, ...)

## S3 method for class 'tf'
format(
  x,
  digits = 2,
  nsmall = 0,
  width = options()$width,
  n = 5,
  prefix = TRUE,
  ...
)

Arguments

Value

prints out x and returns it invisibly

Inter- and extrapolation functions for tfd-objects

Description

These are the currently available evaluator-functions for tfd-objects, which control how the entries are inter-/extrapolated to previously unseen arg-values. They all are merely wrappers around zoo::na.fill(), zoo::na.approx(), etc... Note that these are not meant to be called directly – they are internal functions used by tf_evaluate.tfd() to do its thing.

The list:

• tf_approx_linear for linear interpolation without extrapolation (i.e., zoo::na.approx() with na.rm = FALSE) – this is the default,

• tf_approx_spline for cubic spline interpolation, (i.e., zoo::na.spline() with na.rm = FALSE),

• tf_approx_none in order to not inter-/extrapolate ever (i.e., zoo::na.fill() with fill = NA)

• tf_approx_fill_extend for linear interpolation and constant extrapolation (i.e., zoo::na.fill() with fill = "extend")

• tf_approx_locf for "last observation carried forward" (i.e., zoo::na.locf() with na.rm = FALSE and

• tf_approx_nocb for "next observation carried backward" (i.e., zoo::na.locf() with ⁠na.rm = FALSE, fromLast = TRUE⁠).

For implementing your own, see source code of tf:::zoo_wrapper.

Usage

tf_approx_linear(x, arg, evaluations)

tf_approx_spline(x, arg, evaluations)

tf_approx_none(x, arg, evaluations)

tf_approx_fill_extend(x, arg, evaluations)

tf_approx_locf(x, arg, evaluations)

tf_approx_nocb(x, arg, evaluations)

Arguments

Value

a vector of values of the function defined by the given (x_i, f(x_i))=⁠(arg, evaluations)⁠-tuples at new argument values x.

See Also

tfd

Other tidyfun inter/extrapolation functions: tf_evaluate(), tf_interpolate()

Other tidyfun inter/extrapolation functions: tf_evaluate(), tf_interpolate()

Other tidyfun inter/extrapolation functions: tf_evaluate(), tf_interpolate()

Other tidyfun inter/extrapolation functions: tf_evaluate(), tf_interpolate()

Other tidyfun inter/extrapolation functions: tf_evaluate(), tf_interpolate()

Other tidyfun inter/extrapolation functions: tf_evaluate(), tf_interpolate()

Utility functions for tf-objects

Description

A bunch of methods & utilities that do what they say: get or set the respective attributes of a tf-object.

Usage

tf_arg(f)

tf_evaluations(f)

tf_count(f)

tf_domain(f)

tf_domain(x) <- value

tf_evaluator(f)

tf_evaluator(x) <- value

tf_basis(f, as_tfd = FALSE)

tf_arg(x) <- value

## S3 replacement method for class 'tfd_irreg'
tf_arg(x) <- value

## S3 replacement method for class 'tfd_reg'
tf_arg(x) <- value

## S3 replacement method for class 'tfb'
tf_arg(x) <- value

## S3 method for class 'tfb'
coef(object, ...)

## S3 method for class 'tf'
rev(x)

## S3 method for class 'tf'
is.na(x)

## S3 method for class 'tfd_irreg'
is.na(x)

is_tf(x)

is_tfd(x)

is_reg(x)

is_tfd_reg(x)

is_irreg(x)

is_tfd_irreg(x)

is_tfb(x)

is_tfb_spline(x)

is_tfb_fpc(x)

Arguments

Value

either the respective attribute or, for setters (assignment functions), the input object with modified properties.

See Also

Other tidyfun utility functions: in_range(), tf_zoom()

Functional Data Depth

Description

Data depths for functional data. Currently implemented: Modified Band-2 Depth, see reference.

Usage

tf_depth(x, arg, depth = "MBD", na.rm = TRUE, ...)

## S3 method for class 'matrix'
tf_depth(x, arg, depth = "MBD", na.rm = TRUE, ...)

## S3 method for class 'tf'
tf_depth(x, arg, depth = "MBD", na.rm = TRUE, ...)

Arguments

Value

vector of tf_depth values

References

Sun, Ying, Genton, G M, Nychka, W D (2012). “Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked?” Stat, 1(1), 68–74.

López-Pintado, Sara, Romo, Juan (2009). “On the concept of depth for functional data.” Journal of the American statistical Association, 104(486), 718–734.

Differentiating functional data: approximating derivative functions

Description

Derivatives of tf-objects use finite differences of the evaluations for tfd and finite differences of the basis functions for tfb.

Usage

tf_derive(f, arg, order = 1, ...)

## S3 method for class 'matrix'
tf_derive(f, arg, order = 1, ...)

## S3 method for class 'tfd'
tf_derive(f, arg, order = 1, ...)

## S3 method for class 'tfb_spline'
tf_derive(f, arg, order = 1, ...)

## S3 method for class 'tfb_fpc'
tf_derive(f, arg, order = 1, ...)

Arguments

Details

The derivatives of tfd objects use centered finite differences, e.g. for first derivatives f'((t_i + t_{i+1})/2) \approx \frac{f(t_i) + f(t_{i+1})}{t_{i+1} - t_i}, so the domains of differentiated tfd will shrink (slightly) at both ends. Unless the tfd has a rather fine and regular grid, representing the data in a suitable basis representation with tfb() and then computing the derivatives or integrals of those is usually preferable.

Note that, for some spline bases like "cr" or "tp" which always begin/end linearly, computing second derivatives will produce artefacts at the outer limits of the functions' domain due to these boundary constraints. Basis "bs" does not have this problem for sufficiently high orders, but tends to yield slightly less stable fits.

Value

a tf (with slightly different arg or basis for the derivatives, see Details)

Methods (by class)

• tf_derive(matrix): row-wise finite differences

• tf_derive(tfd): derivatives by finite differencing.

• tf_derive(tfb_spline): derivatives by finite differencing.

• tf_derive(tfb_fpc): derivatives by finite differencing.

See Also

Other tidyfun calculus functions: tf_integrate()

Evaluate tf-vectors for given argument values

Description

Also used internally by the [-operator for tf data (see ?tfbrackets) to evaluate object, see examples.

Usage

tf_evaluate(object, arg, ...)

## Default S3 method:
tf_evaluate(object, arg, ...)

## S3 method for class 'tfd'
tf_evaluate(object, arg, evaluator = tf_evaluator(object), ...)

## S3 method for class 'tfb'
tf_evaluate(object, arg, ...)

Arguments

Value

A list of numeric vectors containing the function evaluations on arg.

See Also

Other tidyfun inter/extrapolation functions: tf_approx_linear(), tf_interpolate()

Examples

f <- tf_rgp(3, arg = seq(0, 1, length.out = 11))
tf_evaluate(f) |> str()
tf_evaluate(f, arg = 0.5) |> str()
# equivalent, as matrix:
f[, 0.5]
new_grid <- seq(0, 1, length.out = 6)
tf_evaluate(f, arg = new_grid) |> str()
# equivalent, as matrix:
f[, new_grid]

Integrals and anti-derivatives of functional data

Description

Integrals of tf-objects are computed by simple quadrature (trapezoid rule). By default the scalar definite integral \int^{upper}_{lower}f(s)ds is returned (option definite = TRUE), alternatively for definite = FALSE the anti-derivative on ⁠[lower, upper]⁠, e.g. a tfd or tfb object representing F(t) \approx \int^{t}_{lower}f(s)ds, for t \in⁠[lower, upper]⁠, is returned.

Usage

tf_integrate(f, arg, lower, upper, ...)

## Default S3 method:
tf_integrate(f, arg, lower, upper, ...)

## S3 method for class 'tfd'
tf_integrate(
  f,
  arg,
  lower = tf_domain(f)[1],
  upper = tf_domain(f)[2],
  definite = TRUE,
  ...
)

## S3 method for class 'tfb'
tf_integrate(
  f,
  arg,
  lower = tf_domain(f)[1],
  upper = tf_domain(f)[2],
  definite = TRUE,
  ...
)

Arguments

Value

For definite = TRUE, the definite integrals of the functions in f. For definite = FALSE and tf-inputs, a tf object containing their anti-derivatives

See Also

Other tidyfun calculus functions: tf_derive()

Re-evaluate tf-objects on a new grid of argument values.

Description

Change the internal representation of a tf-object so that it uses a different grid of argument values (arg). Useful for

• thinning out dense grids to make data smaller

• filling out sparse grids to make derivatives/integrals and locating extrema or zero crossings more accurate (... if the interpolation works well ...)

• making irregular functional data into (more) regular data.

For tfd-objects, this is just syntactic sugar for tfd(object, arg = arg). To inter/extrapolate more reliably and avoid NAs, call tf_interpolate with evaluator = tf_approx_fill_extend.
For tfb-objects, this re-evaluates basis functions on the new grid which can speed up subsequent computations if they all use that grid. NB: To reliably impute very irregular data on a regular, common grid, you'll be better off doing FPCA-based imputation or other model-based approaches in most cases.

Usage

tf_interpolate(object, arg, ...)

## S3 method for class 'tfb'
tf_interpolate(object, arg, ...)

## S3 method for class 'tfd'
tf_interpolate(object, arg, ...)

Arguments

Value

a tfd or tfb object on the new grid given by arg

See Also

tf_rebase(), which is more general.

Other tidyfun inter/extrapolation functions: tf_approx_linear(), tf_evaluate()

Examples

# thinning out a densely observed tfd
dense <- tf_rgp(10, arg = seq(0, 1, length.out = 1001))
less_dense <- tf_interpolate(dense, arg = seq(0, 1, length.out = 101))
dense
less_dense
# filling out sparse data (use a suitable evaluator-function!)
sparse <- tf_rgp(10, arg = seq(0, 5, length.out = 11))
plot(sparse, points = TRUE)
# change evaluator for better interpolation
tfd(sparse, evaluator = tf_approx_spline) |>
  tf_interpolate(arg = seq(0, 5, length.out = 201)) |>
  lines(col = 2, lty = 2)

set.seed(1860)
sparse_irregular <- tf_rgp(5) |>
  tf_sparsify(0.5) |>
  tf_jiggle()
tf_interpolate(sparse_irregular, arg = seq(0, 1, length.out = 51))

Make a tf (more) irregular

Description

Randomly create some irregular functional data from regular ones. jiggle it by randomly moving around its arg-values. Only for tfd. sparsify it by setting (100*dropout)% of its values to NA.

Usage

tf_jiggle(f, amount = 0.4, ...)

tf_sparsify(f, dropout = 0.5, ...)

Arguments

Value

an (irregular) tfd object

See Also

Other tidyfun RNG functions: tf_rgp()

Other tidyfun RNG functions: tf_rgp()

Change (basis) representation of a tf-object

Description

Apply the representation of one tf-object to another; i.e. re-express it in the other's basis, on its grid, etc.
Useful for making different functional data objects compatible so they can be combined, compared or computed with.

Usage

tf_rebase(object, basis_from, arg = tf_arg(basis_from), ...)

## S3 method for class 'tfd'
tf_rebase(object, basis_from, arg = tf_arg(basis_from), ...)

## S3 method for class 'tfb'
tf_rebase(object, basis_from, arg = tf_arg(basis_from), ...)

Arguments

Details

This uses double dispatch (S3) internally, so the methods defined below are themselves generics for methods tf_rebase.tfd.tfd, tf_rebase.tfd.tfb_spline, tf_rebase.tfd.tfb_fpc, tf_rebase.tfb.tfd, tf_rebase.tfb.tfb that dispatch on object_from.

Value

a tf-vector containing the data of object in the same representation as basis_from (potentially modified by the arguments given in ...).

Methods (by class)

• tf_rebase(tfd): re-express a tfd-vector in the same representation as some other tf-vector

• tf_rebase(tfb): re-express a tfb-vector in the same representation as some other tf-vector.

Gaussian Process random generator

Description

Generates n realizations of a zero-mean Gaussian process. The function also accepts user-defined covariance functions (without "nugget" effect, see cov), The implemented defaults with scale parameter \phi, order o and nugget effect variance \sigma^2 are:

• squared exponential covariance Cov(x(t), x(t')) = \exp(-(t-t')^2)/\phi) + \sigma^2 \delta_{t}(t').

• Wiener process covariance Cov(x(t), x(t')) = \min(t',t)/\phi + \sigma^2 \delta_{t}(t'),

• Matèrn process covariance Cov(x(t), x(t')) = \tfrac{2^{1-o}}{\Gamma(o)} (\tfrac{\sqrt{2o}|t-t'|}{\phi})^o \text{Bessel}_o(\tfrac{\sqrt{2o}|t-t'|}{s}) + \sigma^2 \delta_{t}(t')

Usage

tf_rgp(
  n,
  arg = 51L,
  cov = c("squareexp", "wiener", "matern"),
  scale = diff(range(arg))/10,
  nugget = scale/200,
  order = 1.5
)

Arguments

Value

an tfd-vector of length n

See Also

Other tidyfun RNG functions: tf_jiggle()

Simple smoothing of tf objects

Description

Apply running means or medians, lowess or Savitzky-Golay filtering to smooth functional data. This does nothing for tfb-objects, which should be smoothed by using a smaller basis / stronger penalty.

Usage

tf_smooth(x, ...)

## S3 method for class 'tfb'
tf_smooth(x, verbose = TRUE, ...)

## S3 method for class 'tfd'
tf_smooth(
  x,
  method = c("lowess", "rollmean", "rollmedian", "savgol"),
  verbose = TRUE,
  ...
)

Arguments

Details

tf_smooth.tfd overrides/automatically sets some defaults of the used methods:

• lowess uses a span parameter of f = 0.15 (instead of 0.75) by default.

• rollmean/median use a window size of k = $<$number of grid points$>$/20 (i.e., the nearest odd integer to that) and sets fill= "extend" (i.e., constant extrapolation to replace missing values at the extremes of the domain) by default. Use fill= NA for zoo's default behavior of shortening the smoothed series.

• savgol uses a window size of k = $<$number of grid points$>$/10 (i.e., the nearest odd integer to that).

Value

a smoothed version of the input. For some methods/options, the smoothed functions may be shorter than the original ones (at both ends).

Examples

library(zoo)
library(pracma)
f <- tf_sparsify(tf_jiggle(tf_rgp(4, 201, nugget = 0.05)))
f_lowess <- tf_smooth(f, "lowess")
# these methods ignore the distances between arg-values:
f_mean <- tf_smooth(f, "rollmean")
f_median <- tf_smooth(f, "rollmean", k = 31)
f_sg <- tf_smooth(f, "savgol", fl = 31)
layout(t(1:4))
plot(f, points = FALSE, main = "original")
plot(f_lowess,
  points = FALSE, col = "blue", main = "lowess (default,\n span 0.9 in red)"
)
lines(tf_smooth(f, "lowess", f = 0.9), col = "red", alpha = 0.2)
plot(f_mean,
  points = FALSE, col = "blue", main = "rolling means &\n medians (red)"
)
lines(f_median, col = "red", alpha = 0.2) # note constant extrapolation at both ends!
plot(f, points = FALSE, main = "orginal and\n savgol (red)")
lines(f_sg, col = "red")

Find out where functional data fulfills certain conditions.

Description

tf_where allows to define a logical expression about the function values and returns the argument values for which that condition is true.
tf_anywhere is syntactic sugar for tf_where with return = "any" to get a logical flag for each function if the condition is TRUE anywhere, see below.

Usage

tf_where(f, cond, return = c("all", "first", "last", "range", "any"), arg)

tf_anywhere(f, cond, arg)

Arguments

Details

Entries in f that do not fulfill cond anywhere yield numeric(0).
cond is evaluated as a base::subset()-statement on a data.frame containing a single entry in f with columns arg and value, so most of the usual dplyr tricks are available as well, see examples.
Any condition evaluates to NA on NA-entries in f.

Value

depends on return:

• return = "any", i.e, anywhere: a logical vector of the same length as f.

• return = "all": a list of vectors of the same length as f, with empty vectors for the functions that never fulfill the condition.

• return = "range": a data frame with columns "begin" and "end".

• else, a numeric vector of the same length as f with NA for entries of f that nowhere fulfill the condition.

Examples

lin <- 1:4 * tfd(seq(-1, 1, length.out = 11), seq(-1, 1, length.out = 11))
tf_where(lin, value %inr% c(-1, 0.5))
tf_where(lin, value %inr% c(-1, 0.5), "range")
a <- 1
tf_where(lin, value > a, "first")
tf_where(lin, value < a, "last")
tf_where(lin, value > 2, "any")
tf_anywhere(lin, value > 2)

set.seed(4353)
f <- tf_rgp(5, 11)
plot(f, pch = as.character(1:5), points = TRUE)
tf_where(f, value == max(value))
# where is the function increasing/decreasing?
tf_where(f, value > dplyr::lag(value, 1, value[1]))
tf_where(f, value < dplyr::lead(value, 1, tail(value, 1)))
# where are the (interior) extreme points (sign changes of `diff(value)`)?
tf_where(
  f,
  sign(c(diff(value)[1], diff(value))) !=
    sign(c(diff(value), tail(diff(value), 1)))
)
# where in its second half is the function positive?
tf_where(f, arg > 0.5 & value > 0)
# does the function ever exceed?
tf_anywhere(f, value > 1)

Functions to zoom in/out on functions

Description

These are used to redefine or restrict the domain of tf objects.

Usage

tf_zoom(f, begin, end, ...)

## S3 method for class 'tfd'
tf_zoom(f, begin = tf_domain(f)[1], end = tf_domain(f)[2], ...)

## S3 method for class 'tfb'
tf_zoom(f, begin = tf_domain(f)[1], end = tf_domain(f)[2], ...)

## S3 method for class 'tfb_fpc'
tf_zoom(f, begin = tf_domain(f)[1], end = tf_domain(f)[2], ...)

Arguments

Value

an object like f on a new domain (potentially). Note that regular functional data and functions in basis representation will be turned into irregular tfd-objects iff begin or end are not scalar.

See Also

Other tidyfun utility functions: in_range(), tf_arg()

Examples

x <- tf_rgp(10)
plot(x)
tf_zoom(x, 0.5, 0.9)
tf_zoom(x, 0.5, 0.9) |> lines(col = "red")
tf_zoom(x, seq(0, 0.5, length.out = 10), seq(0.5, 1, length.out = 10)) |>
  lines(col = "blue", lty = 3)

Constructors for functional data in basis representation

Description

Various constructors for tfb-vectors from different kinds of inputs.

Usage

tfb(data = data.frame(), basis = c("spline", "fpc", "wavelet"), ...)

tfb_wavelet(data, ...)

as.tfb(data, basis = c("spline", "fpc"), ...)

Arguments

Details

tfb is a wrapper for functions that set up spline-, principal component- or wavelet-based representations of functional data. For all three, the input data x_i(t) are represented as weighted sums of a set of common basis functions B_k(t); k = 1,\dots, K identical for all observations and weight or coefficient vectors b_i = (b_{i1}, \dots, b_{iK}) estimated for each observation: x_i(t) \approx \sum_k B_k(t) b_{ik}. Depending on the value of basis, the basis functions B(t) will either be spline functions or the first few estimated eigenfunctions of the covariance operator of the x(t) (fpc) or wavelets (wavelet).

See tfb_spline() for more details on spline basis representation (the default). See tfb_fpc() for using an functional principal component representation with an orthonormal basis estimated from the data instead.

Value

a tfb-object (or a data.frame/matrix for the conversion functions, obviously.)

See Also

Other tfb-class: fpc_wsvd(), tfb_fpc(), tfb_spline()

Other tfb-class: fpc_wsvd(), tfb_fpc(), tfb_spline()

Functional data in FPC-basis representation

Description

These functions perform a (functional) principal component analysis (FPCA) of the input data and return an tfb_fpc tf-object that uses the empirical eigenfunctions as basis functions for representing the data. The default ("method = fpc_wsvd") uses a (truncated) weighted SVD for complete data on a common grid and a nuclear-norm regularized (truncated) weighted SVD for partially missing data on a common grid, see fpc_wsvd(). The latter is likely to break down for high PVE and/or high amounts of missingness.

Usage

tfb_fpc(data, ...)

## S3 method for class 'data.frame'
tfb_fpc(
  data,
  id = 1,
  arg = 2,
  value = 3,
  domain = NULL,
  method = fpc_wsvd,
  ...
)

## S3 method for class 'matrix'
tfb_fpc(data, arg = NULL, domain = NULL, method = fpc_wsvd, ...)

## S3 method for class 'numeric'
tfb_fpc(data, arg = NULL, domain = NULL, method = fpc_wsvd, ...)

## S3 method for class 'tf'
tfb_fpc(data, arg = NULL, method = fpc_wsvd, ...)

## Default S3 method:
tfb_fpc(data, arg = NULL, domain = NULL, method = fpc_wsvd, ...)

Arguments

Details

For the FPC basis, any factorization method that accepts a data.frame with columns id, arg, value containing the functional data and returns a list with eigenfunctions and FPC scores structured like the return object of fpc_wsvd() can be used for the 'method“ argument, see example below. Note that the mean function, with a fixed "score" of 1 for all functions, is used as the first basis function for all FPC bases.

Value

an object of class tfb_fpc, inheriting from tfb. The basis used by tfb_fpc is a tfd-vector containing the estimated mean and eigenfunctions.

Methods (by class)

• tfb_fpc(default): convert tfb: default method, returning prototype when data is NULL

See Also

fpc_wsvd() for FPCA options.

Other tfb-class: fpc_wsvd(), tfb, tfb_spline()

Other tfb_fpc-class: fpc_wsvd()

Examples

set.seed(13121)
x <- tf_rgp(25, nugget = .02)
x_pc <- tfb_fpc(x, pve = .9)
x_pc
plot(x, lwd = 3)
lines(x_pc, col = 2, lty = 2)
x_pc_full <- tfb_fpc(x, pve = .995)
x_pc_full
lines(x_pc_full, col = 3, lty = 2)
# partially missing data on common grid:
x_mis <- x |> tf_sparsify(dropout = .05)
x_pc_mis <- tfb_fpc(x_mis, pve = .9)
x_pc_mis
plot(x_mis, lwd = 3)
lines(x_pc_mis, col = 4, lty = 2)
# extract FPC basis --
# first "eigenvector" in black is (always) the mean function
x_pc |> tf_basis(as_tfd = TRUE) |> plot(col = 1:5)

# Apply FPCA for sparse, irregular data using refund::fpca.sc:
set.seed(99290)
# create small, sparse, irregular data:
x_irreg <- x[1:8] |>
  tf_jiggle() |> tf_sparsify(dropout = 0.3)
plot(x_irreg)
x_df <- x_irreg |>
  as.data.frame(unnest = TRUE)
# wrap refund::fpca_sc for use as FPCA method in tfb_fpc --
# 1. define scoring function (simple weighted LS fit)
fpca_scores <- function(data_matrix, efunctions, mean, weights) {
  w_mat <- matrix(weights, ncol = length(weights), nrow = nrow(data_matrix),
                  byrow = TRUE)
  w_mat[is.na(data_matrix)] <- 0
  data_matrix[is.na(data_matrix)] <- 0
  data_wc <- t((t(data_matrix) - mean) * sqrt(t(w_mat)))
  t(qr.coef(qr(efunctions), t(data_wc) / sqrt(weights)))
}
# 2. define wrapper for fpca_sc:
fpca_sc_wrapper <- function(data, arg, pve = 0.995, ...) {
  data_mat <- tfd(data) |> as.matrix(interpolate = TRUE)
  fpca <- refund::fpca.sc(
    Y = data_mat, argvals = attr(data_mat, "arg"), pve = pve, ...
  )
  c(fpca[c("mu", "efunctions", "scores", "npc")],
    scoring_function = fpca_scores)
}
x_pc <- tfb_fpc(x_df, method = fpca_sc_wrapper)
lines(x_pc, col = 2, lty = 2)

Spline-based representation of functional data

Description

Represent curves as a weighted sum of spline basis functions.

Usage

tfb_spline(data, ...)

## S3 method for class 'data.frame'
tfb_spline(
  data,
  id = 1,
  arg = 2,
  value = 3,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

## S3 method for class 'matrix'
tfb_spline(
  data,
  arg = NULL,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

## S3 method for class 'numeric'
tfb_spline(
  data,
  arg = NULL,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

## S3 method for class 'list'
tfb_spline(
  data,
  arg = NULL,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

## S3 method for class 'tfd'
tfb_spline(
  data,
  arg = NULL,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

## S3 method for class 'tfb'
tfb_spline(
  data,
  arg = NULL,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

## Default S3 method:
tfb_spline(
  data,
  arg = NULL,
  domain = NULL,
  penalized = TRUE,
  global = FALSE,
  verbose = TRUE,
  ...
)

Arguments

Details

The basis to be used is set up via a call to mgcv::s() and all the spline bases discussed in mgcv::smooth.terms() are available, in principle. Depending on the value of the penalized- and global-flags, the coefficient vectors for each observation are then estimated via fitting a GAM (separately for each observation, if !global) via mgcv::magic() (least square error, the default) or mgcv::gam() (if a family argument was supplied) or unpenalized least squares / maximum likelihood.

After the "smoothed" representation is computed, the amount of smoothing that was performed is reported in terms of the "percentage of variability preserved", which is the variance (or the explained deviance, in the general case if family was specified) of the smoothed function values divided by the variance of the original values (the null deviance, in the general case). Reporting can be switched off with verbose = FALSE.

The ... arguments supplies arguments to both the spline basis (via mgcv::s()) and the estimation (via mgcv::magic() or mgcv::gam()), the most important arguments are:

• k: how many basis functions should the spline basis use, default is 25.

• bs: which type of spline basis should be used, the default is cubic regression splines (bs = "cr")

• family argument: use this if minimizing squared errors is not a reasonable criterion for the representation accuracy (see mgcv::family.mgcv() for what's available) and/or if function values are restricted to be e.g. positive (family = Gamma()/tw()/...), in [0,1] (family = betar()), etc.

• sp: numeric value for the smoothness penalty weight, for manually setting the amount of smoothing for all curves, see mgcv::s(). This (drastically) reduces computation time. Defaults to -1, i.e., automatic optimization of sp using mgcv::magic() (LS fits) or mgcv::gam() (GLM), source code in R/tfb-spline-utils.R.

If global == TRUE, this uses a small subset of curves (10⁠%⁠ of curves, at least 5, at most 100; non-random sample using every j-th curve in the data) on which smoothing parameters per curve are estimated and then takes the mean of the log smoothing parameter of those as sp for all curves. This is much faster than optimizing for each curve on large data sets. For very sparse or noisy curves, estimating a common smoothing parameter based on the data for all curves simultaneously is likely to yield better results, this is not what's implemented here.

Value

a tfb-object

Methods (by class)

• tfb_spline(data.frame): convert data frames

• tfb_spline(matrix): convert matrices

• tfb_spline(numeric): convert matrices

• tfb_spline(list): convert lists

• tfb_spline(tfd): convert tfd (raw functional data)

• tfb_spline(tfb): convert tfb: modify basis representation, smoothing.

• tfb_spline(default): convert tfb: default method, returning prototype when data is missing

See Also

mgcv::smooth.terms() for spline basis options.

Other tfb-class: fpc_wsvd(), tfb, tfb_fpc()

Accessing, evaluating, subsetting and subassigning tf vectors

Description

These functions access, subset, replace and evaluate tf objects. For more information on creating tf objects and converting them to/from list, data.frame or matrix, see tfd() and tfb(). See Details.

Usage

## S3 method for class 'tf'
x[i, j, interpolate = TRUE, matrix = TRUE]

## S3 replacement method for class 'tf'
x[i] <- value

Arguments

Details

Note that these break certain (terrible) R conventions for vector-like objects:

• no argument recycling,

• no indexing with NA,

• no indexing with names not present in x,

• no indexing with integers ⁠> length(x)⁠

All of the above will trigger errors.

Value

If j is missing, a subset of the functions in x as given by i.
If j is given and matrix == TRUE, a numeric matrix of function evaluations in which each row represents one function and each column represents one argval as given in argument j, with an attribute arg=j and row- and column-names derived from x[i] and j.
If j is given and matrix == FALSE, a list of tbl_dfs with columns arg = j and value = evaluations at j for each observation in i.

Examples

x <- 1:3 * tfd(data = 0:10, arg = 0:10)
plot(x)
# this operator's 2nd argument is quite overloaded -- you can:
# 1. simply extract elements from the vector if no second arg is given:
x[1]
x[c(TRUE, FALSE, FALSE)]
x[-(2:3)]
# 2. use the second argument and optional additional arguments to
#    extract specific function evaluations in a number of formats:
x[1:2, c(4.5, 9)] # returns a matrix of function evaluations
x[1:2, c(4.5, 9), interpolate = FALSE] # NA for arg-values not in the original data
x[-3, seq(1, 9, by = 2), matrix = FALSE] # list of data.frames for each function
# in order to evaluate a set of observed functions on a new grid and
# save them as a functional data vector again, use `tfd` or `tfb` instead:
tfd(x, arg = seq(0, 10, by = 0.01))

Constructors for vectors of "raw" functional data

Description

Various constructor methods for tfd-objects.

tfd.matrix accepts a numeric matrix with one function per row (!). If arg is not provided, it tries to guess arg from the column names and falls back on 1:ncol(data) if that fails.

tfd.data.frame uses the first 3 columns of data for function information by default: (id, arg, value)

tfd.list accepts a list of vectors of identical lengths containing evaluations or a list of 2-column matrices/data.frames with arg in the first and evaluations in the second column

tfd.default returns class prototype when argument to tfd() is NULL or not a recognised class

Usage

tfd(data, ...)

## S3 method for class 'matrix'
tfd(data, arg = NULL, domain = NULL, evaluator = tf_approx_linear, ...)

## S3 method for class 'numeric'
tfd(data, arg = NULL, domain = NULL, evaluator = tf_approx_linear, ...)

## S3 method for class 'data.frame'
tfd(
  data,
  id = 1,
  arg = 2,
  value = 3,
  domain = NULL,
  evaluator = tf_approx_linear,
  ...
)

## S3 method for class 'list'
tfd(data, arg = NULL, domain = NULL, evaluator = tf_approx_linear, ...)

## S3 method for class 'tf'
tfd(data, arg = NULL, domain = NULL, evaluator = NULL, ...)

## Default S3 method:
tfd(data, arg = NULL, domain = NULL, evaluator = tf_approx_linear, ...)

as.tfd(data, ...)

as.tfd_irreg(data, ...)

Arguments

Details

evaluator: must be the (quoted or bare) name of a function with signature ⁠function(x, arg, evaluations)⁠ that returns the functions' (approximated/interpolated) values at locations x based on the function evaluations available at locations arg.
Available evaluator-functions:

• tf_approx_linear for linear interpolation without extrapolation (i.e., zoo::na.approx() with na.rm = FALSE) – this is the default,

• tf_approx_spline for cubic spline interpolation, (i.e., zoo::na.spline() with na.rm = FALSE),

• tf_approx_fill_extend for linear interpolation and constant extrapolation (i.e., zoo::na.fill() with fill = "extend")

• tf_approx_locf for "last observation carried forward" (i.e., zoo::na.locf() with na.rm = FALSE and

• tf_approx_nocb for "next observation carried backward" (i.e., zoo::na.locf() with ⁠na.rm = FALSE, fromLast = TRUE⁠). See tf:::zoo_wrapper and tf:::tf_approx_linear, which is simply zoo_wrapper(zoo::na.tf_approx, na.rm = FALSE), for examples of implementations of this.

Value

an tfd-object (or a data.frame/matrix for the conversion functions, obviously.)

Examples

# turn irregular to regular tfd by evaluating on a common grid:

f <- c(
  tf_rgp(1, arg = seq(0, 1, length.out = 11)),
  tf_rgp(1, arg = seq(0, 1, length.out = 21))
)
tfd(f, arg = seq(0, 1, length.out = 21))

set.seed(1213)
f <- tf_rgp(3, arg = seq(0, 1, length.out = 51)) |> tf_sparsify(0.9)
# does not yield regular data because linear extrapolation yields NAs
#   outside observed range:
tfd(f, arg = seq(0, 1, length.out = 101))
# this "works" (but may not yield sensible values..!!) for
#   e.g. constant extrapolation:
tfd(f, evaluator = tf_approx_fill_extend, arg = seq(0, 1, length.out = 101))
plot(f, col = 2)
tfd(f,
  arg = seq(0, 1, length.out = 151), evaluator = tf_approx_fill_extend
) |> lines()

Functions that summarize tf objects across argument values

Description

These will return a tf object containing the respective functional statistic. See tf_fwise() for scalar summaries (e.g. tf_fmean for means, tf_fmax for max. values) of each entry in a tf-vector.

Usage

## S3 method for class 'tf'
mean(x, ...)

## S3 method for class 'tf'
median(x, na.rm = FALSE, depth = c("MBD", "pointwise"), ...)

sd(x, na.rm = FALSE)

## Default S3 method:
sd(x, na.rm = FALSE)

## S3 method for class 'tf'
sd(x, na.rm = FALSE)

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

## Default S3 method:
var(x, y = NULL, na.rm = FALSE, use)

## S3 method for class 'tf'
var(x, y = NULL, na.rm = FALSE, use)

## S3 method for class 'tf'
summary(object, ...)

Arguments

Value

a tf object with the computed result.
summary.tf returns a tf-vector with the mean function, the variance function, the functional median, and the functional range (i.e., pointwise min/max) of the central half of the functions, as defined by tf_depth().

See Also

tf_fwise()

Other tidyfun summary functions: functionwise

Make syntactically valid unique names

Description

See above.

Usage

unique_id(x)

Arguments

Value

x turned into a list.

See Also

Other tidyfun developer tools: ensure_list(), prep_plotting_arg()

vctrs methods for tf objects

Description

These functions are the extensions that allow tf vectors to work with vctrs.

Usage

## S3 method for class 'tfd_reg'
vec_cast(x, to, ...)

## S3 method for class 'tfd_irreg'
vec_cast(x, to, ...)

## S3 method for class 'tfd_reg'
vec_cast.tfd_reg(x, to, ...)

## S3 method for class 'tfd_irreg'
vec_cast.tfd_reg(x, to, ...)

## S3 method for class 'tfb_spline'
vec_cast.tfd_reg(x, to, ...)

## S3 method for class 'tfb_fpc'
vec_cast.tfd_reg(x, to, ...)

## S3 method for class 'tfd_reg'
vec_cast.tfd_irreg(x, to, ...)

## S3 method for class 'tfd_irreg'
vec_cast.tfd_irreg(x, to, ...)

## S3 method for class 'tfb_spline'
vec_cast.tfd_irreg(x, to, ...)

## S3 method for class 'tfb_fpc'
vec_cast.tfd_irreg(x, to, ...)

## S3 method for class 'tfb_spline'
vec_cast(x, to, ...)

## S3 method for class 'tfb_fpc'
vec_cast(x, to, ...)

## S3 method for class 'tfb_spline'
vec_cast.tfb_spline(x, to, ...)

## S3 method for class 'tfb_fpc'
vec_cast.tfb_spline(x, to, ...)

## S3 method for class 'tfb_spline'
vec_cast.tfb_fpc(x, to, ...)

## S3 method for class 'tfb_fpc'
vec_cast.tfb_fpc(x, to, ...)

## S3 method for class 'tfd_reg'
vec_cast.tfb_spline(x, to, ...)

## S3 method for class 'tfd_irreg'
vec_cast.tfb_spline(x, to, ...)

## S3 method for class 'tfd_reg'
vec_cast.tfb_fpc(x, to, ...)

## S3 method for class 'tfd_irreg'
vec_cast.tfb_fpc(x, to, ...)

## S3 method for class 'tfd_reg'
vec_ptype2(x, y, ...)

## S3 method for class 'tfd_reg'
vec_ptype2.tfd_reg(x, y, ...)

## S3 method for class 'tfd_irreg'
vec_ptype2.tfd_reg(x, y, ...)

## S3 method for class 'tfb_spline'
vec_ptype2.tfd_reg(x, y, ...)

## S3 method for class 'tfb_fpc'
vec_ptype2.tfd_reg(x, y, ...)

## S3 method for class 'tfd_irreg'
vec_ptype2(x, y, ...)

## S3 method for class 'tfd_reg'
vec_ptype2.tfd_irreg(x, y, ...)

## S3 method for class 'tfd_irreg'
vec_ptype2.tfd_irreg(x, y, ...)

## S3 method for class 'tfb_spline'
vec_ptype2.tfd_irreg(x, y, ...)

## S3 method for class 'tfb_fpc'
vec_ptype2.tfd_irreg(x, y, ...)

## S3 method for class 'tfb_spline'
vec_ptype2(x, y, ...)

## S3 method for class 'tfb_spline'
vec_ptype2.tfb_spline(x, y, ...)

## S3 method for class 'tfb_fpc'
vec_ptype2.tfb_spline(x, y, ...)

## S3 method for class 'tfd_reg'
vec_ptype2.tfb_spline(x, y, ...)

## S3 method for class 'tfd_irreg'
vec_ptype2.tfb_spline(x, y, ...)

## S3 method for class 'tfb_fpc'
vec_ptype2(x, y, ...)

## S3 method for class 'tfb_spline'
vec_ptype2.tfb_fpc(x, y, ...)

## S3 method for class 'tfb_fpc'
vec_ptype2.tfb_fpc(x, y, ...)

## S3 method for class 'tfd_reg'
vec_ptype2.tfb_fpc(x, y, ...)

## S3 method for class 'tfd_irreg'
vec_ptype2.tfb_fpc(x, y, ...)

Arguments

Details

Notes on vec_cast: Use tf_rebase() to change the representations of tf-vectors, these methods are only for internal use – automatic/implicit casting of tf objects is tricky because it's hard to determine automatically whether such an operation would lose precision (different bases with different expressivity? different argument grids?), and it's not generally clear which instances of which tf-subclasses should be considered the "richer" objects. Rules for casting:

• If the casted object's domain would not contain the entire original domain, no casting is possible (would lose data).

• Every cast that evaluates (basis) functions on different arg values is a lossy cast, since it might lose precision (vctrs::maybe_lossy_cast).

• As long as the casted object's domain contains the entire original domain:

  • every tfd_reg, tfd_irreg or tfb can always be cast into an equivalent tfd_irreg (which may also change its evaluator and domain).

  • every tfd_reg can always be cast to tfd_reg (which may change its evaluator and domain)

  • every tfb can be cast losslessly to tfd (regular or irregular, note it's lossless only on the original arg-grid)

• Any cast of a tfd into tfb is potentially lossy (because we don't know how expressive the chosen basis is)

• Only tfb with identical bases and domains can be cast into one another losslessly

Value

for vec_cast: the casted tf-vector, for vec_ptype2: the common prototype

See Also

vctrs::vec_cast(), vctrs::vec_ptype2()