# cardinalBasis_ceschino: Cardinal Basis for cubic Ceschino interpolation In smint: Smooth Multivariate Interpolation for Gridded and Scattered Data

## Description

Cardinal Basis for cubic Ceschino interpolation.

## Usage

 `1` ```cardinalBasis_ceschino(x, xout, cubic = TRUE, deriv = 0) ```

## Arguments

 `x` Numeric vector of design points. `xout` Numeric vector giving new points. `cubic` Logical. Use cubic interpolation or basic linear? `deriv` Integer or logical. Compute the derivative?

## Details

This is a simple and raw interface to `alterp` Fortran subroutine.

## Value

A list with the following elements

 `x` Numeric vector of abscissas at which the basis is evaluated. This is a copy of `xout`. `CB` Matrix of the Cardinal Basis function values. `deriv, cubic` Copy of input. `method` Character description of the method involved in the CB determination.

## Note

This function does not allow extrapolation, so an error will result when `xout` contains element outside of the range of `x`.

## Author(s)

Alain Hebert for Fortran code.

Yves Deville for R interface.

`interp_ceschino` for the related interpolation function, `cardinalBasis_natSpline` and `cardinalBasis_lagrange` for other Cardinal Basis constructions.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```set.seed(123) n <- 16L; nout <- 300L x <- sort(runif(n)) ## let 'xout' contain n + nout points including nodes xout <- sort(c(x, runif(nout, min = x[1], max = x[n]))) y <- sin(2 * pi * x) res <- cardinalBasis_ceschino(x, xout = xout, deriv = 0) matplot(res\$x, res\$CB, type = "n", main = "Cardinal Basis") abline(v = x, h = 1.0, col = "gray") points(x = x, y = rep(0, n), pch = 21, col = "black", lwd = 2, bg = "white") matlines(res\$x, res\$CB, type = "l") ## interpolation error should be fairly small max(abs(sin(2 * pi * xout) - res\$CB \%*\% y)) ```