# Glossary of Common Terms¶

This glossary contains concepts and API elements specific to the functional
data analysis setting or for the package `scikit-fda`

. If the term you
are looking is not listed here, it may be a more generally applicable term
listed in the scikit-learn Glossary of Common Terms and API Elements.

## General Concepts¶

- codomain¶
The set of allowed output values of a function. Note that the set of actual output values, called the image, can be a strict subset of the codomain.

- curve¶
- trajectory¶
A functional data object whose domain and codomain are both the set of real numbers (\(\mathbb{R}\)). Thus, its

`dim_domain`

and`dim_codomain`

attributes shall both be 1.- domain¶
The set of possible input values of a function.

- domain range¶
The valid range where a function can be evaluated. It is a Python sequence that contains, for each dimension of the domain, a tuple with the minimum and maximum values for that dimension. Usually used in plotting functions and as the domain of integration for this function.

- FDA¶
- Functional Data Analysis¶
The branch of statistics that deals with curves, surfaces or other objects varying over a a continuum (functional data objects).

- functional data¶
A collection of functional data objects. Represented by a

`FData`

object.- functional data object¶
- functional data objects¶
- functional object¶
- functional objects¶
An object of study of Functional Data Analysis. It is a function between \(\mathbb{R}^p\) and \(\mathbb{R}^q\). Usually represented by a

`FData`

object of length 1, but in some cases regular Python callables are also accepted.- functional observation¶
- functional observations¶
An observed functional data object, represented as a

`FData`

object of length 1.- image¶
The set of actual ouput values that a function takes. It must be a (non necessarily strict) subset of the codomain.

- multivariate functional data¶
Often used for functional data where each functional data object is a vector-valued function.

- multivariate object¶
- multivariate objects¶
An object of study of multivariate statistics. It is a vector of possibly related variables, represented as a 1d array.

- operator¶
- operators¶
Function whose domain is a set of functions.

- vector-valued function¶
A functional data object that outputs vectors, that is, its codomain has dimension greater than 1.