cics_explicit function

Construct the explicit form of non-uniform clamped interpolating cubic spline (NcICS).

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

cics_explicit(
  uu,
  yy,
  d,
  clrs = c("blue", "red"),
  xlab = NULL,
  ylab = NULL,
  title = NULL
)

Arguments

• uu: a vector of arbitrary nodes (ordered ascendingly), with magnitude n+2, n$\ge$1.
• 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 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.

Returns

a list with components - spline_coeffs: matrix, whose i-th row contains coefficients of non-uniform ICS's i-th component.

• spline_polynomials: list of NcICS'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

• 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

cics_explicit(
 uu = c(1, 2.2, 3, 3.8, 7),
 CERN$y[1:5],
 d=c(0,-2),
 xlab="X axis",
 ylab="Y axis"
)

uu <- c(0, 1, 4, 6);
yy <- c(4, 5, 2, 1.8);
sp <- cics_explicit(uu, yy, c(1,0))
sp$spline_polynomials
### <~~>
### Spline components' coefficients
explicit_spline(sp$B, sp$gamma)
sp$spline_coeffs == .Last.value