basis_sets {mosaicCalc}

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.