R: Polynomial in One or Two Variables

polynom {spatstat} | R Documentation

## Polynomial in One or Two Variables

### Description

This function is used to represent a polynomial term in a model formula. It computes the homogeneous terms in the polynomial of degree `n` in one variable `x` or two variables `x,y`.

### Usage

      polynom(x, ...)

### Arguments

`x` | A numerical vector.
`...` | Either a single integer `n` specifying the degree of the polynomial, or two arguments `y,n` giving another vector of data `y` and the degree of the polynomial.

### Details

This function is typically used inside a model formula in order to specify the most general possible polynomial of order `n` involving one numerical variable `x` or two numerical variables `x,y`.

It is equivalent to `poly(, raw=TRUE)`.

If only one numerical vector argument `x` is given, the function computes the vectors `x^k` for `k = 1, 2, ..., n`. These vectors are combined into a matrix with `n` columns.

If two numerical vector arguments `x,y` are given, the function computes the vectors `x^k * y^m` for `k >= 0` and `m >= 0` satisfying `0 < k + m <= n`. These vectors are combined into a matrix with one column for each homogeneous term.

### Value

A numeric matrix, with rows corresponding to the entries of `x`, and columns corresponding to the terms in the polynomial.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`poly`, `harmonic`

### Examples

       x <- 1:4
       y <- 10 * (0:3)
       polynom(x, 3)
       polynom(x, y, 3)

[Package spatstat version 1.63-3 Index]