Struct Dual 

pub struct Dual<const N: usize> {
    pub v: Scalar,
    pub d: [Scalar; N],
}

A value together with its gradient with respect to up to N seeded variables — as many as the residual it is computed for depends on.

Fields

v: Scalar

d: [Scalar; N]

Implementations

impl<const N: usize> Dual<N>

pub const fn cst(v: Scalar) -> Self

A constant, with no dependence on any variable.

pub fn var(v: Scalar, slot: usize) -> Self

The slot-th independent variable, with value v.

pub fn embed<const M: usize>(self, slot: usize, vars: usize) -> Dual<M>

The same value in a gradient of M variables: its own first vars the ones from slot on — and no dependence on any other (its own beyond vars it has none of).

pub fn chain(self, v: Scalar, df: Scalar) -> Self

f(self) for a scalar function with value v and derivative df = f'(self.v): d <- d * df by the chain rule.

Trait Implementations

impl<const N: usize> Clone for Dual<N>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize> Copy for Dual<N>

impl<const N: usize> Debug for Dual<N>

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

Formats the value using the given formatter.

impl<const N: usize> Default for Dual<N>

fn default() -> Self

Returns the “default value” for a type.

impl<const N: usize> Display for Dual<N>

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

Formats the value using the given formatter.

impl<const N: usize> Number for Dual<N>

fn acos(self) -> GeopResult<Self>

d acos(x) = -1 / sqrt(1 - x^2), which fails where it is infinite, at x = ±1.

fn is_sharp(self) -> bool

A single, exactly known point: a sharp value that does not vary with any variable. A value that is sharp but moves with a variable is no point — taking it for one drops the gradient.

fn union(self, other: Self) -> Self

The union of the values, with self‘s derivatives: the width a series’ remainder adds (see crate::primitives::Pose::exp).

const ZERO: Self

const ONE: Self

const TWO: Self

const PI: Self

fn from_i64(v: i64) -> Self

fn from_f64(v: f64) -> Self

fn from_scalar(s: Scalar) -> Self

The scalar s as a constant: depending on no variable.

fn from_ratio(num: i64, den: i64) -> GeopResult<Self>

fn to_f64(self) -> f64

The value’s midpoint, for rendering and debugging.

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

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

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

fn neg(self) -> Self

fn div(self, o: Self) -> GeopResult<Self>

Fails where the divisor could be zero.

fn abs(self) -> Self

fn sqrt(self) -> GeopResult<Self>

fn sin(self) -> Self

fn cos(self) -> Self

fn could_be_equal(self, other: Self) -> bool

fn definitely_not_equal(self, other: Self) -> bool

fn could_be_greater(self, other: Self) -> bool

fn definitely_greater(self, other: Self) -> bool

fn could_be_less(self, other: Self) -> bool

fn definitely_less(self, other: Self) -> bool

fn is_exactly(self, other: Self) -> bool

Whether its value is exactly other’s, as a set (see Scalar::is_exactly).

fn degrees_to_radians(self) -> GeopResult<Self>

The angle self, given in degrees, in radians.