Struct DualNumber

pub struct DualNumber<T>(pub T, pub T);

Tuple Fields

0: T

1: T

Implementations

impl<T> DualNumber<T>

pub fn transpose(self) -> Self

impl<T> DualNumber<T>

where T: Zero + One,

pub fn epsilon() -> Self

impl<T> DualNumber<T>

where T: Neg<Output = T>,

pub fn conjugate(self) -> Self

impl<T> DualNumber<T>

where T: Add<Output = T> + Mul<Output = T>,

pub fn eval(self, eps: T) -> T

impl<T> DualNumber<T>

where T: Div<Output = T> + Neg<Output = T>,

pub fn root(self) -> T

Trait Implementations

impl<T> Add<&DualNumber<T>> for &DualNumber<T>

where T: Clone + Add<Output = T>,

type Output = <DualNumber<T> as Add>::Output

The resulting type after applying the + operator.

fn add( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Add<DualNumber<T>>>::Output

Performs the + operation.

impl<T> Add<&DualNumber<T>> for DualNumber<T>

where T: Clone + Add<Output = T>,

type Output = <DualNumber<T> as Add>::Output

The resulting type after applying the + operator.

fn add( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Add<DualNumber<T>>>::Output

Performs the + operation.

impl<T> Add<&T> for &DualNumber<T>

where T: Clone + Add<Output = T>,

type Output = <DualNumber<T> as Add<T>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &T) -> <DualNumber<T> as Add<T>>::Output

Performs the + operation.

impl<T> Add<&T> for DualNumber<T>

where T: Clone + Add<Output = T>,

type Output = <DualNumber<T> as Add<T>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: &T) -> <DualNumber<T> as Add<T>>::Output

Performs the + operation.

impl<T> Add<DualNumber<T>> for &DualNumber<T>

where T: Clone + Add<Output = T>,

type Output = <DualNumber<T> as Add>::Output

The resulting type after applying the + operator.

fn add( self, rhs: DualNumber<T>, ) -> <DualNumber<T> as Add<DualNumber<T>>>::Output

Performs the + operation.

impl<T> Add<T> for &DualNumber<T>

where T: Clone + Add<Output = T>,

type Output = <DualNumber<T> as Add<T>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: T) -> <DualNumber<T> as Add<T>>::Output

Performs the + operation.

impl<T> Add<T> for DualNumber<T>

where T: Add<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> Add for DualNumber<T>

where T: Add<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> AddAssign<&DualNumber<T>> for DualNumber<T>

where T: Clone + Add<Output = T>,

fn add_assign(&mut self, rhs: &DualNumber<T>)

Performs the += operation.

impl<T> AddAssign<&T> for DualNumber<T>

where T: Clone + Add<Output = T>,

fn add_assign(&mut self, rhs: &T)

Performs the += operation.

impl<T> AddAssign<T> for DualNumber<T>

where T: Clone + Add<Output = T>,

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<T> AddAssign for DualNumber<T>

where T: Clone + Add<Output = T>,

fn add_assign(&mut self, rhs: DualNumber<T>)

Performs the += operation.

impl<T: Clone> Clone for DualNumber<T>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for DualNumber<T>

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

Formats the value using the given formatter.

impl<T: Default> Default for DualNumber<T>

fn default() -> DualNumber<T>

Returns the “default value” for a type.

impl<T> Div<&DualNumber<T>> for &DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + One,

type Output = <DualNumber<T> as Div>::Output

The resulting type after applying the / operator.

fn div( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Div<DualNumber<T>>>::Output

Performs the / operation.

impl<T> Div<&DualNumber<T>> for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + One,

type Output = <DualNumber<T> as Div>::Output

The resulting type after applying the / operator.

fn div( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Div<DualNumber<T>>>::Output

Performs the / operation.

impl<T> Div<&T> for &DualNumber<T>

where T: Clone + Div<Output = T> + One,

type Output = <DualNumber<T> as Div<T>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: &T) -> <DualNumber<T> as Div<T>>::Output

Performs the / operation.

impl<T> Div<&T> for DualNumber<T>

where T: Clone + Div<Output = T> + One,

type Output = <DualNumber<T> as Div<T>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: &T) -> <DualNumber<T> as Div<T>>::Output

Performs the / operation.

impl<T> Div<DualNumber<T>> for &DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + One,

type Output = <DualNumber<T> as Div>::Output

The resulting type after applying the / operator.

fn div( self, rhs: DualNumber<T>, ) -> <DualNumber<T> as Div<DualNumber<T>>>::Output

Performs the / operation.

impl<T> Div<T> for &DualNumber<T>

where T: Clone + Div<Output = T> + One,

type Output = <DualNumber<T> as Div<T>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: T) -> <DualNumber<T> as Div<T>>::Output

Performs the / operation.

impl<T> Div<T> for DualNumber<T>

where T: Clone + One + Div<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div for DualNumber<T>

where T: Clone + One + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> DivAssign<&DualNumber<T>> for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + One,

fn div_assign(&mut self, rhs: &DualNumber<T>)

Performs the /= operation.

impl<T> DivAssign<&T> for DualNumber<T>

where T: Clone + Div<Output = T> + One,

fn div_assign(&mut self, rhs: &T)

Performs the /= operation.

impl<T> DivAssign<T> for DualNumber<T>

where T: Clone + Div<Output = T> + One,

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<T> DivAssign for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + One,

fn div_assign(&mut self, rhs: DualNumber<T>)

Performs the /= operation.

impl<T: Hash> Hash for DualNumber<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T> Mul<&DualNumber<T>> for &DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,

type Output = <DualNumber<T> as Mul>::Output

The resulting type after applying the * operator.

fn mul( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Mul<DualNumber<T>>>::Output

Performs the * operation.

impl<T> Mul<&DualNumber<T>> for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,

type Output = <DualNumber<T> as Mul>::Output

The resulting type after applying the * operator.

fn mul( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Mul<DualNumber<T>>>::Output

Performs the * operation.

impl<T> Mul<&T> for &DualNumber<T>

where T: Clone + Mul<Output = T>,

type Output = <DualNumber<T> as Mul<T>>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: &T) -> <DualNumber<T> as Mul<T>>::Output

Performs the * operation.

impl<T> Mul<&T> for DualNumber<T>

where T: Clone + Mul<Output = T>,

type Output = <DualNumber<T> as Mul<T>>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: &T) -> <DualNumber<T> as Mul<T>>::Output

Performs the * operation.

impl<T> Mul<DualNumber<T>> for &DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,

type Output = <DualNumber<T> as Mul>::Output

The resulting type after applying the * operator.

fn mul( self, rhs: DualNumber<T>, ) -> <DualNumber<T> as Mul<DualNumber<T>>>::Output

Performs the * operation.

impl<T> Mul<T> for &DualNumber<T>

where T: Clone + Mul<Output = T>,

type Output = <DualNumber<T> as Mul<T>>::Output

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> <DualNumber<T> as Mul<T>>::Output

Performs the * operation.

impl<T> Mul<T> for DualNumber<T>

where T: Clone + Mul<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> MulAssign<&DualNumber<T>> for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,

fn mul_assign(&mut self, rhs: &DualNumber<T>)

Performs the *= operation.

impl<T> MulAssign<&T> for DualNumber<T>

where T: Clone + Mul<Output = T>,

fn mul_assign(&mut self, rhs: &T)

Performs the *= operation.

impl<T> MulAssign<T> for DualNumber<T>

where T: Clone + Mul<Output = T>,

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T> MulAssign for DualNumber<T>

where T: Clone + Add<Output = T> + Sub<Output = T> + Mul<Output = T>,

fn mul_assign(&mut self, rhs: DualNumber<T>)

Performs the *= operation.

impl<T> Neg for &DualNumber<T>

where T: Clone + Neg<Output = T>,

type Output = <DualNumber<T> as Neg>::Output

The resulting type after applying the - operator.

fn neg(self) -> <DualNumber<T> as Neg>::Output

Performs the unary - operation.

impl<T> Neg for DualNumber<T>

where T: Neg<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T> One for DualNumber<T>

where T: Zero + One,

fn one() -> Self

fn is_one(&self) -> bool

where Self: PartialEq,

fn set_one(&mut self)

impl<T: Ord> Ord for DualNumber<T>

fn cmp(&self, other: &DualNumber<T>) -> Ordering

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T: PartialEq> PartialEq for DualNumber<T>

fn eq(&self, other: &DualNumber<T>) -> 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<T: PartialOrd> PartialOrd for DualNumber<T>

fn partial_cmp(&self, other: &DualNumber<T>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<'a, T> Product<&'a DualNumber<T>> for DualNumber<T>

where T: Clone + One + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + 'a,

fn product<I: Iterator<Item = &'a DualNumber<T>>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T> Product for DualNumber<T>

where T: One + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Clone,

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T> Sub<&DualNumber<T>> for &DualNumber<T>

where T: Clone + Sub<Output = T>,

type Output = <DualNumber<T> as Sub>::Output

The resulting type after applying the - operator.

fn sub( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Sub<DualNumber<T>>>::Output

Performs the - operation.

impl<T> Sub<&DualNumber<T>> for DualNumber<T>

where T: Clone + Sub<Output = T>,

type Output = <DualNumber<T> as Sub>::Output

The resulting type after applying the - operator.

fn sub( self, rhs: &DualNumber<T>, ) -> <DualNumber<T> as Sub<DualNumber<T>>>::Output

Performs the - operation.

impl<T> Sub<&T> for &DualNumber<T>

where T: Clone + Sub<Output = T>,

type Output = <DualNumber<T> as Sub<T>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: &T) -> <DualNumber<T> as Sub<T>>::Output

Performs the - operation.

impl<T> Sub<&T> for DualNumber<T>

where T: Clone + Sub<Output = T>,

type Output = <DualNumber<T> as Sub<T>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: &T) -> <DualNumber<T> as Sub<T>>::Output

Performs the - operation.

impl<T> Sub<DualNumber<T>> for &DualNumber<T>

where T: Clone + Sub<Output = T>,

type Output = <DualNumber<T> as Sub>::Output

The resulting type after applying the - operator.

fn sub( self, rhs: DualNumber<T>, ) -> <DualNumber<T> as Sub<DualNumber<T>>>::Output

Performs the - operation.

impl<T> Sub<T> for &DualNumber<T>

where T: Clone + Sub<Output = T>,

type Output = <DualNumber<T> as Sub<T>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: T) -> <DualNumber<T> as Sub<T>>::Output

Performs the - operation.

impl<T> Sub<T> for DualNumber<T>

where T: Sub<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> Sub for DualNumber<T>

where T: Sub<Output = T>,

type Output = DualNumber<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> SubAssign<&DualNumber<T>> for DualNumber<T>

where T: Clone + Sub<Output = T>,

fn sub_assign(&mut self, rhs: &DualNumber<T>)

Performs the -= operation.

impl<T> SubAssign<&T> for DualNumber<T>

where T: Clone + Sub<Output = T>,

fn sub_assign(&mut self, rhs: &T)

Performs the -= operation.

impl<T> SubAssign<T> for DualNumber<T>

where T: Clone + Sub<Output = T>,

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl<T> SubAssign for DualNumber<T>

where T: Clone + Sub<Output = T>,

fn sub_assign(&mut self, rhs: DualNumber<T>)

Performs the -= operation.

impl<'a, T> Sum<&'a DualNumber<T>> for DualNumber<T>

where T: Clone + Zero + Add<Output = T> + 'a,

fn sum<I: Iterator<Item = &'a DualNumber<T>>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T> Sum for DualNumber<T>

where T: Zero + Add<Output = T>,

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T> Zero for DualNumber<T>

where T: Zero,

fn zero() -> Self

fn is_zero(&self) -> bool

where Self: PartialEq,

fn set_zero(&mut self)

impl<T: Copy> Copy for DualNumber<T>

impl<T: Eq> Eq for DualNumber<T>

impl<T> StructuralPartialEq for DualNumber<T>