Struct ComplexPolar 

#[repr(C)]
pub struct ComplexPolar<FT> {
    pub abs: FT,
    pub arg: FT,
}

A complex number in polar form.

Fields

abs: FT

arg: FT

Implementations

impl ComplexPolar<f32>

pub const I: Self

pub const NEG_ONE: Self

pub const NEG_I: Self

impl ComplexPolar<f64>

pub const I: Self

pub const NEG_ONE: Self

pub const NEG_I: Self

impl<FT> ComplexPolar<FT>

pub const fn new(abs: FT, arg: FT) -> Self

Creates a complex number.

impl<FT: Number> ComplexPolar<FT>

pub const ZERO: Self

pub const ONE: Self

pub fn conjugate(self) -> Self

Computes the conjugate.

pub fn re(self) -> FT

Computes the real component.

pub fn im(self) -> FT

Computes the imaginary component.

pub fn abs_sq(self) -> FT

Computes the squared absolute value.

pub fn recip(self) -> Self

Computes the reciprocal.

pub fn sqrt(self) -> Self

Computes the principal square root.

pub fn to_rectangular(self) -> Rectangular<FT>

Convert to rectangular form.

pub fn exp(self) -> Self

Computes e^self where e is the base of the natural logarithm.

pub fn exp2(self) -> Self

Computes 2^self.

pub fn expm1(self) -> Rectangular<FT>

Computes e^self - 1.

More numerically stable than self.exp().to_rectangular() - 1 when self ≈ 0.

pub fn ln(self) -> Rectangular<FT>

Computes the principal natural logarithm.

pub fn ln_1p(self) -> Rectangular<FT>

Computes the principal natural logarithm of 1 + self.

More numerically stable than (self + 1).ln() when self ≈ 0.

pub fn log2(self) -> Rectangular<FT>

Computes the principal logarithm in base 2.

pub fn log10(self) -> Rectangular<FT>

Computes the principal logarithm in base 10.

pub fn ln_branch(self, k: i32) -> Rectangular<FT>

Computes the k-th branch of the natural logarithm.

The principal value is k = 0. Each increment of k adds 2πi.

pub fn ln_1p_branch(self, k: i32) -> Rectangular<FT>

Computes the k-th branch of the natural logarithm of 1 + self.

The principal value is k = 0. Each increment of k adds 2πi.

pub fn log2_branch(self, k: i32) -> Rectangular<FT>

Computes the k-th branch of the base-2 logarithm.

pub fn log10_branch(self, k: i32) -> Rectangular<FT>

Computes the k-th branch of the base-10 logarithm.

pub fn sqrt_branch(self, k: i32) -> Self

Computes the k-th square root.

The principal value is k = 0. Only k = 0 and k = 1 give distinct values.

pub fn nth_root(self, n: i32, k: i32) -> Self

Computes the k-th value of the n-th root.

The n distinct values correspond to k = 0..n-1.

pub fn pow_rational(self, p: i32, q: i32, k: i32) -> Self

Raises self to the rational power p/q, selecting the k-th branch.

There are q distinct values corresponding to k = 0..q-1, provided p/q is in lowest terms. If p/q is not reduced, first reduce it to find the true number of distinct values.

pub fn powf(self, x: FT) -> Self

Raises self to a floating point power.

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

Raises self to an integer power.

pub fn normalize(self) -> Self

Normalizes the absolute value and the argument into the range [0, ∞) and (-π, +π] respectively.

pub fn is_finite(self) -> bool

Returns whether both the absolute value and argument are finite.

Trait Implementations

impl<FT: AbsDiffEq + Copy> AbsDiffEq for ComplexPolar<FT>

where <FT as AbsDiffEq>::Epsilon: Copy,

Available on crate feature approx only.

type Epsilon = <FT as AbsDiffEq>::Epsilon

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<FT: Clone> Clone for ComplexPolar<FT>

fn clone(&self) -> ComplexPolar<FT>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<FT: Copy> Copy for ComplexPolar<FT>

impl<FT: Debug> Debug for ComplexPolar<FT>

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

Formats the value using the given formatter.

impl<FT: Default> Default for ComplexPolar<FT>

fn default() -> ComplexPolar<FT>

Returns the “default value” for a type.

impl<FT: Number + Display> Display for ComplexPolar<FT>

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

Formats the value using the given formatter.

impl Distribution<ComplexPolar<f32>> for StandardUniform

Available on crate feature rand only.

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> ComplexPolar<f32>

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

fn sample_iter<R>(self, rng: R) -> Iter<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) -> Map<Self, F, T, S>

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

Map sampled values to type S

impl Distribution<ComplexPolar<f64>> for StandardUniform

Available on crate feature rand only.

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> ComplexPolar<f64>

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

fn sample_iter<R>(self, rng: R) -> Iter<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) -> Map<Self, F, T, S>

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

Map sampled values to type S

impl<FT: Number> Div for ComplexPolar<FT>

type Output = ComplexPolar<FT>

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<ComplexPolar<f32>> for f32

type Output = ComplexPolar<f32>

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<ComplexPolar<f64>> for f64

type Output = ComplexPolar<f64>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<FT: Number> Div<FT> for ComplexPolar<FT>

type Output = ComplexPolar<FT>

The resulting type after applying the / operator.

fn div(self, re: FT) -> Self

Performs the / operation.

impl<FT: Number> DivAssign for ComplexPolar<FT>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<FT: Number> DivAssign<FT> for ComplexPolar<FT>

fn div_assign(&mut self, re: FT)

Performs the /= operation.

impl<FT: Number> From<FT> for ComplexPolar<FT>

fn from(value: FT) -> Self

Converts to this type from the input type.

impl<FT: Number> Mul for ComplexPolar<FT>

type Output = ComplexPolar<FT>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<ComplexPolar<f32>> for f32

type Output = ComplexPolar<f32>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<ComplexPolar<f64>> for f64

type Output = ComplexPolar<f64>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<FT: Number> Mul<FT> for ComplexPolar<FT>

type Output = ComplexPolar<FT>

The resulting type after applying the * operator.

fn mul(self, re: FT) -> Self::Output

Performs the * operation.

impl<FT: Number> MulAssign for ComplexPolar<FT>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<FT: Number> MulAssign<FT> for ComplexPolar<FT>

fn mul_assign(&mut self, re: FT)

Performs the *= operation.

impl<FT: Number> Neg for ComplexPolar<FT>

type Output = ComplexPolar<FT>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<FT: PartialEq> PartialEq for ComplexPolar<FT>

fn eq(&self, other: &ComplexPolar<FT>) -> bool

Equality operator ==.

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

Inequality operator !=.

impl<FT: RelativeEq + Copy> RelativeEq for ComplexPolar<FT>

where <FT as AbsDiffEq>::Epsilon: Copy,

Available on crate feature approx only.

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

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

A test for equality that uses a relative comparison if the values are far apart.

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

The inverse of RelativeEq::relative_eq.

impl<FT: PartialEq> StructuralPartialEq for ComplexPolar<FT>

impl<FT: UlpsEq + Copy> UlpsEq for ComplexPolar<FT>

where <FT as AbsDiffEq>::Epsilon: Copy,

Available on crate feature approx only.

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.