cics_unif_explicit {ICSsmoothing}

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.\gamma.

gamma

\gamma= vector of spline coefficients - function values and exterior-node derivatives that takes part in the explicit form S=B.\gamma.

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