Struct Complex

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

Complex number.

Implementations

impl<T> Complex<T>

pub fn new(w: T, x: T) -> Self

pub fn from_vector(vec: Vector2<T>) -> Self

pub fn from_array(arr: [T; 2]) -> Self

pub fn from_tuple(tup: (T, T)) -> Self

pub fn from_num(nc: NumComplex<T>) -> Self

pub fn into_vector(self) -> Vector2<T>

pub fn into_array(self) -> [T; 2]

pub fn into_tuple(self) -> (T, T)

pub fn into_num(self) -> NumComplex<T>

impl<T: Copy> Complex<T>

pub fn re(&self) -> T

pub fn im(&self) -> T

impl<T> Complex<T>

pub fn re_ref(&self) -> &T

pub fn im_ref(&self) -> &T

pub fn re_mut(&mut self) -> &mut T

pub fn im_mut(&mut self) -> &mut T

impl<T> Complex<T>

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

pub fn into_matrix(self) -> Matrix2x2<T>

impl<T> Complex<T>

where T: Neg<Output = T>,

pub fn conj(self) -> Self

impl<T> Complex<T>

where T: Zero + One,

pub fn i() -> Self

impl<T> Complex<T>

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

pub fn norm_sqr(self) -> T

impl<T: Float> Complex<T>

pub fn norm(self) -> T

pub fn arg(self) -> T

pub fn to_polar(self) -> (T, T)

pub fn from_polar(r: T, theta: T) -> Self

impl<T> Complex<T>

where T: Float,

pub fn normalize(self) -> Self

impl<T> Complex<T>

where T: Neg<Output = T> + Num + Copy,

pub fn inv(self) -> Self

impl<T: Num + Copy> Complex<T>

pub fn powu(&self, exp: u32) -> Self

impl<T: Neg<Output = T> + Num + Copy> Complex<T>

pub fn powi(&self, exp: i32) -> Self

impl<T: Float> Complex<T>

pub fn exp(self) -> Self

pub fn ln(self) -> Self

pub fn sqrt(self) -> Self

pub fn cbrt(self) -> Self

pub fn powf(self, exp: T) -> Self

pub fn log(self, base: T) -> Self

pub fn powc(self, exp: Self) -> Self

pub fn expf(self, base: T) -> Self

pub fn sin(self) -> Self

pub fn cos(self) -> Self

pub fn tan(self) -> Self

pub fn asin(self) -> Self

pub fn acos(self) -> Self

pub fn atan(self) -> Self

pub fn sinh(self) -> Self

pub fn cosh(self) -> Self

pub fn tanh(self) -> Self

pub fn asinh(self) -> Self

pub fn acosh(self) -> Self

pub fn atanh(self) -> Self

pub fn finv(self) -> Self

pub fn fdiv(self, other: Self) -> Self

Trait Implementations

impl<T> AbsDiffEq for Complex<T>

where T: AbsDiffEq<Epsilon = T> + Copy,

type Epsilon = T

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<T> Add<Complex<T>> for Quaternion<T>

where T: Add<Output = T>,

type Output = Quaternion<T>

The resulting type after applying the + operator.

fn add(self, other: Complex<T>) -> Self

Performs the + operation.

impl Add<Complex<f32>> for f32

Workaround for reverse addition.

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: Complex<f32>) -> Self::Output

Performs the + operation.

impl Add<Complex<f64>> for f64

Workaround for reverse addition.

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: Complex<f64>) -> Self::Output

Performs the + operation.

impl Add<Quaternion<f32>> for Complex<f32>

Workaround for reverse addition.

type Output = Quaternion<f32>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<f32>) -> Self::Output

Performs the + operation.

impl Add<Quaternion<f64>> for Complex<f64>

Workaround for reverse addition.

type Output = Quaternion<f64>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<f64>) -> Self::Output

Performs the + operation.

impl<T> Add<T> for Complex<T>

where T: Add<Output = T>,

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> Add for Complex<T>

where T: Add<Output = T>,

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> AddAssign<Complex<T>> for Quaternion<T>

where T: AddAssign,

fn add_assign(&mut self, other: Complex<T>)

Performs the += operation.

impl<T> AddAssign<T> for Complex<T>

where T: AddAssign,

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T> AddAssign for Complex<T>

where T: AddAssign,

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<T: Clone> Clone for Complex<T>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T> Conj for Complex<T>

where T: Neg<Output = T>,

fn conj(self) -> Self

Perform complex conjugation.

impl<T: Debug> Debug for Complex<T>

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

Formats the value using the given formatter.

impl<T: Default> Default for Complex<T>

fn default() -> Complex<T>

Returns the “default value” for a type.

impl<T> Directional<Complex<T>> for Moebius<Complex<T>>

where Self: Transform<Complex<T>>, Complex<T>: Normalize,

fn apply_dir(&self, pos: Complex<T>, dir: Complex<T>) -> Complex<T>

Returns the result of the direction transformation at the specified position.

fn apply_normal(&self, pos: Complex<T>, normal: Complex<T>) -> Complex<T>

Returns the result of the normal transformation at the specified position.

impl<T: Display> Display for Complex<T>

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

Formats the value using the given formatter.

impl<T: Float> Distribution<Complex<T>> for NonZero

where NonZero: Distribution<Vector<T, 2>>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T> Distribution<Complex<T>> for Normal

where Normal: Distribution<Vector<T, 2>>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T: Float> Distribution<Complex<T>> for Unit

where Unit: Distribution<Vector<T, 2>>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T> Div<Complex<T>> for Quaternion<T>

where T: Neg<Output = T> + Num + Copy,

type Output = Quaternion<T>

The resulting type after applying the / operator.

fn div(self, other: Complex<T>) -> Self

Performs the / operation.

impl Div<Complex<f32>> for f32

Workaround for reverse division.

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: Complex<f32>) -> Self::Output

Performs the / operation.

impl Div<Complex<f64>> for f64

Workaround for reverse division.

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: Complex<f64>) -> Self::Output

Performs the / operation.

impl<T> Div<Quaternion<T>> for Complex<T>

where T: Neg<Output = T> + Num + Copy,

type Output = Quaternion<T>

The resulting type after applying the / operator.

fn div(self, other: Quaternion<T>) -> Self::Output

Performs the / operation.

impl<T> Div<T> for Complex<T>

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

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Self

Performs the / operation.

impl<T> Div for Complex<T>

where T: Neg<Output = T> + Num + Copy,

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> DivAssign<Complex<T>> for Quaternion<T>

where Self: Div<Complex<T>, Output = Self> + Copy,

fn div_assign(&mut self, other: Complex<T>)

Performs the /= operation.

impl<T> DivAssign<T> for Complex<T>

where Self: Div<T, Output = Self> + Copy,

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<T> DivAssign for Complex<T>

where Self: Div<Output = Self> + Copy,

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<T> Dot for Complex<T>

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

type Output = T

Dot product output type.

fn dot(self, other: Self) -> T

Perform dot product.

impl<T> From<[T; 2]> for Complex<T>

fn from(arr: [T; 2]) -> Self

Converts to this type from the input type.

impl<T> From<(T, T)> for Complex<T>

fn from(tup: (T, T)) -> Self

Converts to this type from the input type.

impl<T> From<Complex<T>> for [T; 2]

fn from(comp: Complex<T>) -> Self

Converts to this type from the input type.

impl<T> From<Complex<T>> for (T, T)

fn from(comp: Complex<T>) -> Self

Converts to this type from the input type.

impl<T> From<Complex<T>> for Complex<T>

fn from(nc: NumComplex<T>) -> Self

Converts to this type from the input type.

impl<T> From<Complex<T>> for Complex<T>

fn from(comp: Complex<T>) -> Self

Converts to this type from the input type.

impl<T> From<Complex<T>> for Rotation2<T>

fn from(comp: Complex<T>) -> Self

Converts to this type from the input type.

impl<T> From<Complex<T>> for Vector2<T>

fn from(comp: Complex<T>) -> Self

Converts to this type from the input type.

impl<T> From<Rotation2<T>> for Complex<T>

fn from(rot: Rotation2<T>) -> Self

Converts to this type from the input type.

impl<T> From<Vector<T, 2>> for Complex<T>

fn from(vec: Vector2<T>) -> Self

Converts to this type from the input type.

impl<T> Inv for Complex<T>

where T: Float,

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Self

Returns the multiplicative inverse of self.

impl<T> Mul<Complex<T>> for Quaternion<T>

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

type Output = Quaternion<T>

The resulting type after applying the * operator.

fn mul(self, other: Complex<T>) -> Self

Performs the * operation.

impl Mul<Complex<f32>> for f32

Workaround for reverse multiplication.

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f32>) -> Self::Output

Performs the * operation.

impl Mul<Complex<f64>> for f64

Workaround for reverse multiplication.

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f64>) -> Self::Output

Performs the * operation.

impl<T> Mul<Quaternion<T>> for Complex<T>

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

type Output = Quaternion<T>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<T>) -> Self::Output

Performs the * operation.

impl<T> Mul<T> for Complex<T>

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

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self

Performs the * operation.

impl<T> Mul for Complex<T>

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> MulAssign<Complex<T>> for Quaternion<T>

where Self: Mul<Complex<T>, Output = Self> + Copy,

fn mul_assign(&mut self, other: Complex<T>)

Performs the *= operation.

impl<T> MulAssign<T> for Complex<T>

where Self: Mul<T, Output = Self> + Copy,

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<T> MulAssign for Complex<T>

where Self: Mul<Output = Self> + Copy,

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<T> Neg for Complex<T>

where T: Neg<Output = T>,

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<T> NormL1 for Complex<T>

where Vector2<T>: NormL1<Output = T>,

type Output = T

Type of the norm.

fn norm_l1(self) -> T

Norm of the element.

impl<T: Float> NormL2 for Complex<T>

type Output = T

Type of the norm.

fn norm_l2(self) -> T

Norm of the element.

fn norm_l2_sqr(self) -> T

Square norm of the element.

impl<T> Normalize for Complex<T>

where T: Float,

fn normalize(self) -> Self

Normalize object.

impl<T: Neg<Output = T> + Num + Copy> Num for Complex<T>

type FromStrRadixErr = ParseComplexError<<T as Num>::FromStrRadixErr>

fn from_str_radix(s: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl<T> One for Complex<T>

where T: Zero + One + Sub<Output = T> + Copy,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<T: PartialEq> PartialEq for Complex<T>

fn eq(&self, other: &Complex<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> Product for Complex<T>

where Self: One + Mul,

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

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

impl<T: Neg<Output = T> + Num + Copy> Rem for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T> Sub<Complex<T>> for Quaternion<T>

where T: Sub<Output = T>,

type Output = Quaternion<T>

The resulting type after applying the - operator.

fn sub(self, other: Complex<T>) -> Self

Performs the - operation.

impl Sub<Complex<f32>> for f32

Workaround for reverse subtraction.

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f32>) -> Self::Output

Performs the - operation.

impl Sub<Complex<f64>> for f64

Workaround for reverse subtraction.

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f64>) -> Self::Output

Performs the - operation.

impl Sub<Quaternion<f32>> for Complex<f32>

Workaround for reverse subtraction.

type Output = Quaternion<f32>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<f32>) -> Self::Output

Performs the - operation.

impl Sub<Quaternion<f64>> for Complex<f64>

Workaround for reverse subtraction.

type Output = Quaternion<f64>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<f64>) -> Self::Output

Performs the - operation.

impl<T> Sub<T> for Complex<T>

where T: Sub<Output = T>,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Self

Performs the - operation.

impl<T> Sub for Complex<T>

where T: Sub<Output = T>,

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> SubAssign<Complex<T>> for Quaternion<T>

where T: SubAssign,

fn sub_assign(&mut self, other: Complex<T>)

Performs the -= operation.

impl<T> SubAssign<T> for Complex<T>

where T: SubAssign,

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<T> SubAssign for Complex<T>

where T: SubAssign,

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<T> Sum for Complex<T>

where Self: Zero + Add,

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> Transform<Complex<T>> for Moebius<Complex<T>>

where T: Neg<Output = T> + Num + Copy,

fn identity() -> Self

Identity transformation.

fn inv(self) -> Self

Inverse transformation.

fn apply(&self, pos: Complex<T>) -> Complex<T>

Perform the transformation itself.

fn deriv(&self, pos: Complex<T>, dir: Complex<T>) -> Complex<T>

Find transformation directional derivative at specified point.

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

Chain two transformations into a new one.

impl<T> Zero for Complex<T>

where T: Zero,

fn zero() -> Self

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.

impl<T: Copy> Copy for Complex<T>

impl<T> StructuralPartialEq for Complex<T>