Struct Polynomial 

pub struct Polynomial {
    pub coefs: ColVec,
    pub deg: usize,
}

Use Polynomial to implement RealValuedFunction when the coefficients of a polynomial is given.

• There is no performance difference between Polynomial::ats_incr() and Polynomial::ats().
• The coefs is the coefficients of a polynomial. For example, coefs=[a2, a1, a0] means the quadratic polynomial a2 x^2 + a1 x + a0.
• Polynomial::deriv() gives the derivative of the polynomial.
• Polynomial::from_interp() interpolates data and return a polynomial. Do not use it for 7-or-more-degree polynomials. It is numerically unstable. Use BarycentricPolynomial whenever possible.

Examples

use ndarray::prelude::*;
use te1d::prelude::*;
use te1d::func::Polynomial;
 
// create a new polynomial
let f = Polynomial::new(&array![1.5, -1.2, 0.5, 0.7]);
let result = f.ats(&array![-1.0, -0.5, 0.0, 0.3, 0.9]);
let sol = array![-2.5, -0.0375, 0.7, 0.7825, 1.2715];
assert!(all_close(&result, &sol, 1e-05, 1e-08));
assert!(is_close(f.at(0.75), 1.0328125, 1e-05, 1e-08));
assert_eq!(&result, &f.ats_incr(&array![-1.0, -0.5, 0.0, 0.3, 0.9]));
 
// find the derivative
let deriv = f.deriv();
assert_eq!(&deriv, &Polynomial::new(&array![4.5, -2.4, 0.5]));
 
// polynomial interpolation
let xs: ColVec = array![0.0, 0.5, 2.5, 3.0];
let fs: ColVec = array![1.0, 0.0, 2.0, 3.0];
let f = Polynomial::from_interp(&xs, &fs).unwrap();
assert!(all_close(&f.ats(&xs), &fs, 1e-05, 1e-08));
assert_eq!(f.deg, 3);

Fields

coefs: ColVec

The coefficients of the polynomial.

deg: usize

The degree of the polynomial.

Implementations

impl Polynomial

pub fn new(coefs: &ColVec) -> Self

Construct a new polynomial by giving its coefficients.

pub fn deriv(&self) -> Self

Compute the derivative of the polynomial.

pub fn from_interp(xs: &ColVec, fs: &ColVec) -> Result<Self, LinalgError>

Perform the polynomial interpolation.

Trait Implementations

impl Clone for Polynomial

fn clone(&self) -> Polynomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Polynomial

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

Formats the value using the given formatter.

impl PartialEq for Polynomial

fn eq(&self, other: &Polynomial) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl RealValuedFunction for Polynomial

fn at(&self, x: f64) -> f64

Evaluate the function value at a given point x.

fn ats_incr(&self, incr_xs: &ColVec) -> ColVec

Evaluate the function values at the given increasing points incr_xs.

fn ats(&self, xs: &ColVec) -> ColVec

Evaluate the function values at the given points xs.

impl StructuralPartialEq for Polynomial