inprod.cent: Centered inner product matrix for a basis or pair of bases

In ctmva: Continuous-Time Multivariate Analysis

Centered inner product matrix for a basis or pair of bases

Description

Several methods of continous-time multivariate analysis require a matrix of inner products of pairs of centered functions from a basis, such as a B-spline basis, or pairs consisting of one function from each of two bases. This function computes such matrices via 7-point Newton-Cotes integration, which is exact for cubic B-splines. For a Fourier basis with the inner product taken over the entire range, a simple closed form is used instead of integration.

Usage

inprod.cent(basis1, basis2 = basis1, rng = NULL)

Arguments

basis1	basis object from the fda package.
basis2	an optional second basis
rng	time range. By default, the entire range spanned by the basis, or the intersection of the ranges of the two bases.

Value

Matrix of inner products of each pair of centered basis functions.

Author(s)

Biplab Paul <[e-mail]> and Philip Tzvi Reiss <[e-mail]>

See Also

create.bspline.basis from package fda, for the most commonly used basis object type.

Examples

require(fda)
bbasis6 <- create.bspline.basis(nbasis=6)
inprod.cent(bbasis6)
fbasis7 <- create.fourier.basis(nbasis=7)
inprod.cent(fbasis7)

ctmva documentation built on July 26, 2023, 5:18 p.m.