# interpol.matrix: Interpolation matrix In far: Modelization for Functional AutoRegressive Processes

## Description

Calculate the matrix giving the linear interpolation of regularly spaced points.

## Usage

 `1` ```interpol.matrix(n = 12, m = 24, tol = sqrt(.Machine\$double.eps)) ```

## Arguments

 `n` Number (integer) of points in output space `m` Number (integer) of points in the input function (or space) `tol` A relative tolerance to detect zero singular values.

## Details

The general principle is, considering a function for which we know values at `m` equally spaced points (for instance 1/`m`, 2/`m`, ..., 1), to compute the matrix giving the linear approximation of `n` equally spaced points (for instance 1/`n`, 2/`n`, ..., 1).

The function works whether `n` or `m` is the largest.

The function is vectorized, so `m` and `n` can be vectors of integers. In this case, they have to be of the same size and the resulting matrix is block diagonal.

## Value

A `n`x`m` matrix if they are integer, else a `sum(n)`x`sum(m)` matrix.

## Author(s)

J. Damon

`theoretical.coef`, `simul.far` or `simul.farx`.
 ```1 2 3 4``` ``` mat1 <- interpol.matrix(12,24) mat2 <- interpol.matrix(c(3,5),c(12,12)) print(mat1 %*% base.simul.far(24,5)) print(mat2 %*% base.simul.far(24,5)) ```