# cics_explicit: Construct the explicit form of non-uniform clamped... In ICSsmoothing: Data Smoothing by Interpolating Cubic Splines

## Description

`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`.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```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`≥`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.

## Value

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 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```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 ```

ICSsmoothing documentation built on Jan. 16, 2021, 5:28 p.m.