# cardinalBasis_lagrange: Cardinal Basis for Lagrange (broken line) interpolation In smint: Smooth Multivariate Interpolation for Gridded and Scattered Data

## Description

Cardinal Basis for Lagrange interpolation.

## Usage

 `1` ```cardinalBasis_lagrange(x, xout) ```

## Arguments

 `x` Numeric vector of design points. `xout` Numeric vector giving new points.

## Details

This is a simple and raw interface to `alterp` Fortran subroutine. It is a wrapper for `cardinalBasis_ceschino` function with `cubic = FALSE` and `deriv = 0L`.

## 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.

## Note

This function does not allow extrapolation, so an error will result when `xout` contains element outside of the range of `x`. The function used here is a spline of degree 1 (order 2).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```set.seed(123) n <- 16; nout <- 300 x <- sort(runif(n)) ##' ## let 'xout' contain n + nout points including nodes xout <- sort(c(x, runif(nout, min = x[1], max = x[n]))) res <- cardinalBasis_lagrange(x, xout = xout) 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") ## Lebesgue's function is constant = 1.0: check it L <- apply(res\$CB, 1, function(x) sum(abs(x))) range(L) ```

smint documentation built on April 14, 2017, 1:49 p.m.