Struct Poly

pub struct Poly { /* private fields */ }

A polynomial of dynamic degree.

It would be nice to have polynomials of type-level degree, but that’s a bit awkward without const generic expressions (e.g. to express the type of the derivative). It could be done with typenum and generic_array…

Implementations

impl Poly

pub fn new(coeffs: impl IntoIterator<Item = f64>) -> Self

Constructs a new polynomial from coefficients.

The first coefficient provided will be the constant term, the second will be the linear term, and so on.

pub fn deriv(&self) -> Poly

Returns the polynomial that’s the derivative of this polynomial.

pub fn eval(&self, x: f64) -> f64

Evaluates this polynomial at a point.

pub fn degree(&self) -> usize

The degree of this polynomial.

This function only looks at the presence of coefficients, not their value. If you construct a polynomial with three coefficients, this method will say that it has degree 2 even if all of those coefficients are zero.

A polynomial with no coefficients will give zero as its degree, as will a polynomial with one coefficient.

pub fn to_cubic(&self) -> Option<Cubic>

If this polynomial has degree 3 or less, converts it to a cubic.

pub fn roots_in(&self, lower: f64, upper: f64, x_error: f64) -> Vec<f64>

Finds all the roots in an interval, using Yuksel’s algorithm.

This is a numerical, iterative method. It first constructs critical points to find bracketing intervals (intervals [x0, x1] where self.eval(x0) and self.eval(x1) have different signs). Then it uses a kind of modified Newton method to find a root on each bracketing interval. It has a few limitations:

• if there is only a small interval where the polynomial changes sign, it can miss roots. For example, when two roots are very close together it can miss them both.
• run time is quadratic in the degree. However, it is often very fast in practice for polynomials of low degree, especially if the interval [lower, upper] contains few roots.

Trait Implementations

impl Clone for Poly

fn clone(&self) -> Poly

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Poly

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Mul<&Poly> for Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: &Poly) -> Poly

Performs the * operation.

impl<'a> Mul for &'a Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: &Poly) -> Poly

Performs the * operation.