basis_sets: Basis sets for for function approximation
In mosaicCalc: R-Language Based Calculus Operations for Teaching

basis_sets

R Documentation

Basis sets for for function approximation

Description

These functions generate the mathematical functions for three different basis sets: Fourier (sines), Legendre (orthogonal polynomials), and Splines (low-order smooth approximation)

Usage

legendre_set(df = 3, left = -1, right = 1)

legendre_M(x, df, left = -1, right = 1)

ns_set(df = 3, left = -1, right = 1)

fourier_M(x, n, fperiod = NULL)

ns_M(x, df = NULL, knots = NULL, intercept = FALSE, Boundary.knots = range(x))

fourier_set(df, left = -1, right = 1)

Arguments

`df`	number of basis functions to construct
`left`	number giving left-hand boundary of the interval
`right`	number giving right-hand boundary of the interval
`x`	inputs at which to evaluate the functions (in the `⁠_M⁠` functions)
`n`	number of fourier components to generate
`fperiod`	number giving the fundamental period length for the Fourier basis
`knots`	breakpoints that define the spline. The default is no knots; together with the natural boundary conditions this results in a basis for linear regression on `x`. Typical values are the mean or median for one knot, quantiles for more knots. See also `Boundary.knots`.
`intercept`	if `TRUE`, an intercept is included in the basis; default is `FALSE`.
`Boundary.knots`	boundary points at which to impose the natural boundary conditions and anchor the B-spline basis (default the range of the data). If both `knots` and `Boundary.knots` are supplied, the basis parameters do not depend on `x`. Data can extend beyond `Boundary.knots`

Details

For each basis, there are two different forms for the generating functions. Names ending in ⁠_set⁠ create a set of functions with arguments x and n, where integer n provides an index into the set. The same names with a ⁠_M⁠ suffix produce a model matrix corresponding to a specified set of x values. These are useful with lm() and similar model-building functions in the same way that poly() and ns() are useful. (ns_M() is just an alias for splines::ns().) Like poly() and ns(), the ⁠_M⁠ suffix functions do NOT include an intercept column.

Value

The ⁠_M⁠ functions return a model matrix. The ⁠_set⁠ functions return a function with arguments x and n. The integer n specifies which function to use, while x is the set of values at which to evaluate that function.