Struct automatica::rational_function::Rf

pub struct Rf<T> { /* private fields */ }

Rational function

Implementations

impl<T: Clone + PartialEq> Rf<T>

Implementation of rational function methods

pub fn inv_mut(&mut self)

Compute the reciprocal of a rational function in place.

impl<T> Rf<T>where T: Clone + PartialEq + Zero,

pub fn new<R, S>(num: R, den: S) -> Selfwhere R: AsRef<[T]>, S: AsRef<[T]>,

Create a new rational function given its numerator and denominator

Arguments

• num - Rational function numerator
• den - Rational function denominator

Example

use automatica::Rf;
let rf = Rf::new([1., 2.], [-4., 6., -2.]);

pub fn num(&self) -> impl Polynomial<T>

Extract rational function numerator

Example

use automatica::{Polynomial, Rf};
let num = [1., 2.];
let rf = Rf::new(num.clone(), [-4., 6., -2.]);
assert_eq!(num, rf.num().as_slice());

pub fn den(&self) -> impl Polynomial<T>

Extract rational function denominator

Example

use automatica::{Polynomial, Rf};
let den = [-4., 6., -2.];
let rf = Rf::new([1., 2.], den.clone());
assert_eq!(den, rf.den().as_slice());

impl<T: Clone + PartialEq + Zero> Rf<T>

pub fn relative_degree(&self) -> i32

Calculate the relative degree between denominator and numerator.

Example

use automatica::{Inv, Rf};
let rf = Rf::new([1., 2.], [-4., 6., -2.]);
let expected = rf.relative_degree();
assert_eq!(expected, 1);
assert_eq!(rf.inv().relative_degree(), -1);

impl<T> Rf<T>where T: Abs + Add<Output = T> + Clone + Copy + Div<Output = T> + EigenConst + Epsilon + Hypot + Inv<Output = T> + Max + Mul<Output = T> + Neg<Output = T> + One + PartialOrd + Pow<T> + Sign + Sqrt + Sub<Output = T> + Zero,

pub fn real_poles(&self) -> Option<Vec<T>>

Calculate the poles of the rational function

pub fn complex_poles(&self) -> Vec<(T, T)>

Calculate the poles of the rational function

pub fn real_zeros(&self) -> Option<Vec<T>>

Calculate the zeros of the rational function

pub fn complex_zeros(&self) -> Vec<(T, T)>

Calculate the zeros of the rational function

impl<T> Rf<T>where T: Clone + Div<Output = T> + One + PartialEq + Zero,

pub fn normalize(&self) -> Self

Normalization of rational function. If the denominator is zero the same rational function is returned.

from:

       b_n*z^n + b_(n-1)*z^(n-1) + ... + b_1*z + b_0
G(z) = ---------------------------------------------
       a_n*z^n + a_(n-1)*z^(n-1) + ... + a_1*z + a_0

to:

       b'_n*z^n + b'_(n-1)*z^(n-1) + ... + b'_1*z + b'_0
G(z) = -------------------------------------------------
         z^n + a'_(n-1)*z^(n-1) + ... + a'_1*z + a'_0

Example

use automatica::Rf;
let rf = Rf::new([1., 2.], [-4., 6., -2.]);
let expected = Rf::new([-0.5, -1.], [2., -3., 1.]);
assert_eq!(expected, rf.normalize());

pub fn normalize_mut(&mut self)

In place normalization of rational function. If the denominator is zero no operation is done.

from:

       b_n*z^n + b_(n-1)*z^(n-1) + ... + b_1*z + b_0
G(z) = ---------------------------------------------
       a_n*z^n + a_(n-1)*z^(n-1) + ... + a_1*z + a_0

to:

       b'_n*z^n + b'_(n-1)*z^(n-1) + ... + b'_1*z + b'_0
G(z) = -------------------------------------------------
         z^n + a'_(n-1)*z^(n-1) + ... + a'_1*z + a'_0

Example

use automatica::Rf;
let mut rf = Rf::new([1., 2.], [-4., 6., -2.]);
rf.normalize_mut();
let expected = Rf::new([-0.5, -1.], [2., -3., 1.]);
assert_eq!(expected, rf);

impl<T> Rf<T>where T: Clone + PartialEq,

pub fn eval_by_val<N>(&self, s: N) -> Nwhere N: Add<T, Output = N> + Clone + Div<Output = N> + Mul<Output = N> + Zero,

Evaluate the rational function.

Arguments

• s - Value at which the rational function is evaluated.

Example

use automatica::{Complex as C, Rf};
let rf = Rf::new([1., 2., 3.], [-4., -3., 1.]);
assert_eq!(-8.5, rf.eval_by_val(3.));
assert_eq!(C::new(0.64, -0.98), rf.eval_by_val(C::new(0., 2.0)));

impl<T> Rf<T>where T: Clone + PartialEq,

pub fn eval<N>(&self, s: &N) -> Nwhere N: Add<T, Output = N> + Clone + Div<Output = N> + Mul<N, Output = N> + Zero,

Evaluate the rational function.

Arguments

• s - Value at which the rational function is evaluated.

Example

use automatica::{Complex as C, Rf};
let rf = Rf::new([1., 2., 3.], [-4., -3., 1.]);
assert_eq!(-8.5, rf.eval(&3.));
assert_eq!(C::new(0.64, -0.98), rf.eval(&C::new(0., 2.0)));

Trait Implementations

impl<T> Add<&Rf<T>> for &Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function addition

type Output = Rf<T>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<T> Add<&T> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + PartialEq + Zero,

Implementation of rational function addition

type Output = Rf<T>

The resulting type after applying the + operator.

fn add(self, rhs: &T) -> Self

Performs the + operation.

impl<T> Add<Rf<T>> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function addition

type Output = Rf<T>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl<T> Add<T> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + PartialEq + Zero,

Implementation of rational function addition

type Output = Rf<T>

The resulting type after applying the + operator.

fn add(self, rhs: T) -> Self

Performs the + operation.

impl<T: Clone> Clone for Rf<T>

fn clone(&self) -> Rf<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for Rf<T>

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

Formats the value using the given formatter.

impl<T> Display for Rf<T>where T: Clone + Display + One + PartialEq + PartialOrd + Zero,

Implementation of rational function printing

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

Formats the value using the given formatter.

impl<T> Div<&Rf<T>> for &Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function division

type Output = Rf<T>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self::Output

Performs the / operation.

impl<T> Div<Rf<T>> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function division

type Output = Rf<T>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self

Performs the / operation.

impl<T> Inv for &Rf<T>where T: Clone + PartialEq + Zero,

fn inv(self) -> Self::Output

Compute the reciprocal of a rational function.

type Output = Rf<T>

Result of multiplicative inversion

impl<T: Clone + PartialEq> Inv for Rf<T>

fn inv(self) -> Self::Output

Compute the reciprocal of a rational function.

type Output = Rf<T>

Result of multiplicative inversion

impl<T> Mul<&Rf<T>> for &Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function multiplication

type Output = Rf<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<T> Mul<&Rf<T>> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function multiplication

type Output = Rf<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Rf<T>) -> Self

Performs the * operation.

impl<T> Mul<Rf<T>> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + One + PartialEq + Zero,

Implementation of rational function multiplication

type Output = Rf<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl<T> Neg for &Rf<T>where T: Clone + Neg<Output = T> + PartialEq + Zero,

Implementation of rational function negation. Negative sign is transferred to the numerator.

type Output = Rf<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T> Neg for Rf<T>where T: Clone + Neg<Output = T> + PartialEq,

Implementation of rational function negation. Negative sign is transferred to the numerator.

type Output = Rf<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: PartialEq> PartialEq<Rf<T>> for Rf<T>

fn eq(&self, other: &Rf<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

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

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

impl<T> Sub<&Rf<T>> for &Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + Neg<Output = T> + PartialEq + Sub<Output = T> + Zero + One,

Implementation of rational function subtraction

type Output = Rf<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<T> Sub<Rf<T>> for Rf<T>where T: Add<Output = T> + Clone + Mul<Output = T> + Neg<Output = T> + One + PartialEq + Sub<Output = T> + Zero,

Implementation of rational function subtraction

type Output = Rf<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl<T> Zero for Rf<T>where T: Clone + One + PartialEq + Zero,

fn zero() -> Self

Additive identity

fn is_zero(&self) -> bool

Check if self is the additive identity

impl<T> Zero for Rf<T>where T: Clone + One + PartialEq + Zero,

fn zero() -> Self

Additive identity

fn is_zero(&self) -> bool

Check if self is the additive identity

impl<T> StructuralPartialEq for Rf<T>