Struct bacon_sci::polynomial::Polynomial

pub struct Polynomial<N: ComplexField + FromPrimitive + Copy> where
    <N as ComplexField>::RealField: FromPrimitive + Copy,  { /* fields omitted */ }

Polynomial on a ComplexField.

Implementations

impl<N: ComplexField + FromPrimitive + Copy> Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

pub fn new() -> Self

Returns the zero polynomial on a given field

pub fn with_tolerance(
    tolerance: <N as ComplexField>::RealField
) -> Result<Self, String>

pub fn with_capacity(capacity: usize) -> Self

Returns the zero polynomial on a given field with preallocated memory

pub fn from_slice(data: &[N]) -> Self

Create a polynomial from a slice, with the first element of the slice being the highest power

pub fn set_tolerance(
    &mut self,
    tolerance: <N as ComplexField>::RealField
) -> Result<(), String>

pub fn get_tolerance(&self) -> <N as ComplexField>::RealField

pub fn order(&self) -> usize

Get the order of the polynomial

pub fn get_coefficients(&self) -> Vec<N>

Returns the coefficients in the correct order to recreate the polynomial with Polynomial::from_slice(data: &[N]);

pub fn get_coefficient(&self, ind: usize) -> N

Get the coefficient of a power

pub fn make_complex(
    &self
) -> Polynomial<Complex<<N as ComplexField>::RealField>>

Make a polynomial complex

pub fn evaluate(&self, x: N) -> N

Evaluate a polynomial at a value

pub fn evaluate_derivative(&self, x: N) -> (N, N)

Evaluate a polynomial and its derivative at a value

pub fn set_coefficient(&mut self, power: u32, coefficient: N)

Set a coefficient of a power in the polynomial

pub fn purge_coefficient(&mut self, power: usize)

Remove the coefficient of a power in the polynomial

pub fn purge_leading(&mut self)

Remove all leading 0 coefficients

pub fn derivative(&self) -> Self

Get the derivative of the polynomial

pub fn antiderivative(&self, constant: N) -> Self

Get the antiderivative of the polynomial with specified constant

pub fn integrate(&self, lower: N, upper: N) -> N

Integrate this polynomial between to starting points

pub fn divide(&self, divisor: &Polynomial<N>) -> Result<(Self, Self), String>

Divide this polynomial by another, getting a quotient and remainder, using tol to check for 0

pub fn roots(
    &self,
    tol: <N as ComplexField>::RealField,
    n_max: usize
) -> Result<VecDeque<Complex<<N as ComplexField>::RealField>>, String>

Get the n (possibly including repeats) of the polynomial given n using Laguerre’s method

pub fn dft(&self, size: usize) -> Vec<Complex<<N as ComplexField>::RealField>>

Get the polynomial in point form evaluated at roots of unity at k points where k is the smallest power of 2 greater than or equal to size

pub fn idft(
    vec: &[Complex<<N as ComplexField>::RealField>],
    tol: <N as ComplexField>::RealField
) -> Self

Trait Implementations

impl<N: ComplexField + FromPrimitive + Copy> Add<&'_ Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: &Polynomial<N>) -> Polynomial<N>

Performs the + operation.

impl<N: ComplexField + FromPrimitive + Copy> Add<&'_ Polynomial<N>> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: &Polynomial<N>) -> Polynomial<N>

Performs the + operation.

impl<N: ComplexField + FromPrimitive + Copy> Add<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: N) -> Polynomial<N>

Performs the + operation.

impl<N: ComplexField + FromPrimitive + Copy> Add<N> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: N) -> Polynomial<N>

Performs the + operation.

impl<N: ComplexField + FromPrimitive + Copy> Add<Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: Polynomial<N>) -> Polynomial<N>

Performs the + operation.

impl<N: ComplexField + FromPrimitive + Copy> Add<Polynomial<N>> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: Polynomial<N>) -> Polynomial<N>

Performs the + operation.

impl<N: ComplexField + FromPrimitive + Copy> AddAssign<&'_ Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn add_assign(&mut self, rhs: &Polynomial<N>)

Performs the += operation.

impl<N: ComplexField + FromPrimitive + Copy> AddAssign<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn add_assign(&mut self, rhs: N)

Performs the += operation.

impl<N: ComplexField + FromPrimitive + Copy> AddAssign<Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn add_assign(&mut self, rhs: Polynomial<N>)

Performs the += operation.

impl<N: Clone + ComplexField + FromPrimitive + Copy> Clone for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn clone(&self) -> Polynomial<N>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug + ComplexField + FromPrimitive + Copy> Debug for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

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

Formats the value using the given formatter.

impl<N: ComplexField + FromPrimitive + Copy> Default for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn default() -> Self

Returns the “default value” for a type.

impl<N: ComplexField + FromPrimitive + Copy> Div<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the / operator.

fn div(self, rhs: N) -> Polynomial<N>

Performs the / operation.

impl<N: ComplexField + FromPrimitive + Copy> Div<N> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the / operator.

fn div(self, rhs: N) -> Polynomial<N>

Performs the / operation.

impl<N: ComplexField + FromPrimitive + Copy> DivAssign<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn div_assign(&mut self, rhs: N)

Performs the /= operation.

impl<N: ComplexField + FromPrimitive + Copy> From<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn from(n: N) -> Polynomial<N>

Performs the conversion.

impl<N: RealField + FromPrimitive + Copy> From<Polynomial<N>> for Polynomial<Complex<N>>

fn from(poly: Polynomial<N>) -> Polynomial<Complex<N>>

Performs the conversion.

impl<N: ComplexField + FromPrimitive + Copy> FromIterator<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn from_iter<I: IntoIterator<Item = N>>(iter: I) -> Polynomial<N>

Creates a value from an iterator.

impl<N: ComplexField + FromPrimitive + Copy> Mul<&'_ Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &Polynomial<N>) -> Polynomial<N>

Performs the * operation.

impl<N: ComplexField + FromPrimitive + Copy> Mul<&'_ Polynomial<N>> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &Polynomial<N>) -> Polynomial<N>

Performs the * operation.

impl<N: ComplexField + FromPrimitive + Copy> Mul<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: N) -> Polynomial<N>

Performs the * operation.

impl<N: ComplexField + FromPrimitive + Copy> Mul<N> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: N) -> Polynomial<N>

Performs the * operation.

impl<N: ComplexField + FromPrimitive + Copy> Mul<Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Polynomial<N>) -> Polynomial<N>

Performs the * operation.

impl<N: ComplexField + FromPrimitive + Copy> Mul<Polynomial<N>> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Polynomial<N>) -> Polynomial<N>

Performs the * operation.

impl<N: ComplexField + FromPrimitive + Copy> MulAssign<&'_ Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn mul_assign(&mut self, rhs: &Polynomial<N>)

Performs the *= operation.

impl<N: ComplexField + FromPrimitive + Copy> MulAssign<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn mul_assign(&mut self, rhs: N)

Performs the *= operation.

impl<N: ComplexField + FromPrimitive + Copy> MulAssign<Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn mul_assign(&mut self, rhs: Polynomial<N>)

Performs the *= operation.

impl<N: ComplexField + FromPrimitive + Copy> Neg for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn neg(self) -> Polynomial<N>

Performs the unary - operation.

impl<N: ComplexField + FromPrimitive + Copy> Neg for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn neg(self) -> Polynomial<N>

Performs the unary - operation.

impl<N: ComplexField + FromPrimitive + Copy> Sub<&'_ Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: &Polynomial<N>) -> Polynomial<N>

Performs the - operation.

impl<N: ComplexField + FromPrimitive + Copy> Sub<&'_ Polynomial<N>> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: &Polynomial<N>) -> Polynomial<N>

Performs the - operation.

impl<N: ComplexField + FromPrimitive + Copy> Sub<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: N) -> Polynomial<N>

Performs the - operation.

impl<N: ComplexField + FromPrimitive + Copy> Sub<N> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: N) -> Polynomial<N>

Performs the - operation.

impl<N: ComplexField + FromPrimitive + Copy> Sub<Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Polynomial<N>) -> Polynomial<N>

Performs the - operation.

impl<N: ComplexField + FromPrimitive + Copy> Sub<Polynomial<N>> for &Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

type Output = Polynomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Polynomial<N>) -> Polynomial<N>

Performs the - operation.

impl<N: ComplexField + FromPrimitive + Copy> SubAssign<&'_ Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn sub_assign(&mut self, rhs: &Polynomial<N>)

Performs the -= operation.

impl<N: ComplexField + FromPrimitive + Copy> SubAssign<N> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn sub_assign(&mut self, rhs: N)

Performs the -= operation.

impl<N: ComplexField + FromPrimitive + Copy> SubAssign<Polynomial<N>> for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn sub_assign(&mut self, rhs: Polynomial<N>)

Performs the -= operation.

impl<N: ComplexField + FromPrimitive + Copy> Zero for Polynomial<N> where
    <N as ComplexField>::RealField: FromPrimitive + Copy, 

fn zero() -> Polynomial<N>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.