cics_unif_explicit: Construct the explicit form of uniform clamped interpolating...

In ICSsmoothing: Data Smoothing by Interpolating Cubic Splines

Construct the explicit form of uniform clamped interpolating cubic spline (UcICS).

Description

cics_unif_explicit constructs the explicit form of uniform clamped interpolating cubic spline (via Hermite cubic spline) for nodes uu, function values yy and exterior-node derivatives d.

Usage

cics_unif_explicit(
  uumin,
  uumax,
  yy,
  d,
  clrs = c("blue", "red"),
  xlab = NULL,
  ylab = NULL,
  title = NULL
)

Arguments

uumin	a starting node.
uumax	an ending node.
yy	a vector of function values pertaining to nodes in uu.
d	a vector of two values of derivative, in the first and the last node of uu.
clrs	a vector (optional parameter) of colours that are used alternately to plot the graph of spline's components.
xlab	a title (optional parameter) for the x axis.
ylab	a title (optional parameter) for the y axis.
title	a title (optional parameter) for the plot.

Value

A list of spline components

spline_coeffs	matrix, whose i-th row contains coefficients of uniform ICS's i-th component.
spline_polynomials	list of UcICS's components string representations.
B	4-element array of (n+1)x(n+4) matrices, whereas element in i-th row and j-th column of l-th matrix contains coefficient by x^{l-1} of cubic polynomial that is in i-th row and j-th column of matrix B from spline's explicit form S=B.γ.
gamma	γ= vector of spline coefficients - function values and exterior-node derivatives that takes part in the explicit form S=B.γ.
aux_BF	A basis function of the spline
aux_tridiag_inverse	An inverse of the tridiagonal matrix used for spline derivatives construction

Examples

yy <- c(4, 5, 2, 1.8);
sp <- cics_unif_explicit(0, 6, yy, c(2, 0.9))
sp$spline_polynomials
### <~~>
### Spline components' coefficients
explicit_spline(sp$B, sp$gamma)
sp$spline_coeffs == .Last.value

ICSsmoothing documentation built on Jan. 9, 2023, 1:23 a.m.