basis_sets: 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)

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.

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.