basis_sets: Basis sets for for function approximation
In dtkaplan/mosaicUSAFA: Functions, data, and tutorials for the Math 141Z course

Description Usage Arguments Details Value

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

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)

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

`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
`fperiod`	number giving the fundamental period length for the Fourier basis

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.

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.