Trait ComplexField

pub trait ComplexField:
    SubsetOf<Self>
    + SupersetOf<f32>
    + SupersetOf<f64>
    + FromPrimitive
    + Field<Element = Self, SimdBool = bool, Output = Self>
    + Neg
    + Clone
    + Send
    + Sync
    + Any
    + 'static
    + Debug
    + Display {
    type RealField: RealField;

    // Required methods
    fn from_real(re: Self::RealField) -> Self;
    fn real(self) -> Self::RealField;
    fn imaginary(self) -> Self::RealField;
    fn modulus(self) -> Self::RealField;
    fn modulus_squared(self) -> Self::RealField;
    fn argument(self) -> Self::RealField;
    fn norm1(self) -> Self::RealField;
    fn scale(self, factor: Self::RealField) -> Self;
    fn unscale(self, factor: Self::RealField) -> Self;
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn mul_add(self, a: Self, b: Self) -> Self;
    fn abs(self) -> Self::RealField;
    fn hypot(self, other: Self) -> Self::RealField;
    fn recip(self) -> Self;
    fn conjugate(self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn sin_cos(self) -> (Self, Self);
    fn tan(self) -> Self;
    fn asin(self) -> Self;
    fn acos(self) -> Self;
    fn atan(self) -> Self;
    fn sinh(self) -> Self;
    fn cosh(self) -> Self;
    fn tanh(self) -> Self;
    fn asinh(self) -> Self;
    fn acosh(self) -> Self;
    fn atanh(self) -> Self;
    fn log(self, base: Self::RealField) -> Self;
    fn log2(self) -> Self;
    fn log10(self) -> Self;
    fn ln(self) -> Self;
    fn ln_1p(self) -> Self;
    fn sqrt(self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn exp_m1(self) -> Self;
    fn powi(self, n: i32) -> Self;
    fn powf(self, n: Self::RealField) -> Self;
    fn powc(self, n: Self) -> Self;
    fn cbrt(self) -> Self;
    fn is_finite(&self) -> bool;
    fn try_sqrt(self) -> Option<Self>;

    // Provided methods
    fn to_polar(self) -> (Self::RealField, Self::RealField) { ... }
    fn to_exp(self) -> (Self::RealField, Self) { ... }
    fn signum(self) -> Self { ... }
    fn sinh_cosh(self) -> (Self, Self) { ... }
    fn sinc(self) -> Self { ... }
    fn sinhc(self) -> Self { ... }
    fn cosc(self) -> Self { ... }
    fn coshc(self) -> Self { ... }
}

Trait shared by all complex fields and its subfields (like real numbers).

Complex numbers are equipped with functions that are commonly used on complex numbers and reals. The results of those functions only have to be approximately equal to the actual theoretical values.

Required Associated Types

type RealField: RealField

Required Methods

fn from_real(re: Self::RealField) -> Self

Builds a pure-real complex number from the given value.

fn real(self) -> Self::RealField

The real part of this complex number.

fn imaginary(self) -> Self::RealField

The imaginary part of this complex number.

fn modulus(self) -> Self::RealField

The modulus of this complex number.

fn modulus_squared(self) -> Self::RealField

The squared modulus of this complex number.

fn argument(self) -> Self::RealField

The argument of this complex number.

fn norm1(self) -> Self::RealField

The sum of the absolute value of this complex number’s real and imaginary part.

fn scale(self, factor: Self::RealField) -> Self

Multiplies this complex number by factor.

fn unscale(self, factor: Self::RealField) -> Self

Divides this complex number by factor.

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn mul_add(self, a: Self, b: Self) -> Self

fn abs(self) -> Self::RealField

The absolute value of this complex number: self / self.signum().

This is equivalent to self.modulus().

fn hypot(self, other: Self) -> Self::RealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

fn recip(self) -> Self

fn conjugate(self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn sin_cos(self) -> (Self, Self)

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn asinh(self) -> Self

fn acosh(self) -> Self

fn atanh(self) -> Self

fn log(self, base: Self::RealField) -> Self

fn log2(self) -> Self

fn log10(self) -> Self

fn ln(self) -> Self

fn ln_1p(self) -> Self

fn sqrt(self) -> Self

fn exp(self) -> Self

fn exp2(self) -> Self

fn exp_m1(self) -> Self

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

fn powf(self, n: Self::RealField) -> Self

fn powc(self, n: Self) -> Self

fn cbrt(self) -> Self

fn is_finite(&self) -> bool

fn try_sqrt(self) -> Option<Self>

Provided Methods

fn to_polar(self) -> (Self::RealField, Self::RealField)

The polar form of this complex number: (modulus, arg)

fn to_exp(self) -> (Self::RealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})

fn signum(self) -> Self

The exponential part of this complex number: self / self.modulus()

fn sinh_cosh(self) -> (Self, Self)

fn sinc(self) -> Self

Cardinal sine

fn sinhc(self) -> Self

fn cosc(self) -> Self

Cardinal cos

fn coshc(self) -> Self

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl ComplexField for f32

type RealField = f32

fn from_real(re: <f32 as ComplexField>::RealField) -> f32

fn real(self) -> <f32 as ComplexField>::RealField

fn imaginary(self) -> <f32 as ComplexField>::RealField

fn norm1(self) -> <f32 as ComplexField>::RealField

fn modulus(self) -> <f32 as ComplexField>::RealField

fn modulus_squared(self) -> <f32 as ComplexField>::RealField

fn argument(self) -> <f32 as ComplexField>::RealField

fn to_exp(self) -> (f32, f32)

fn recip(self) -> f32

fn conjugate(self) -> f32

fn scale(self, factor: <f32 as ComplexField>::RealField) -> f32

fn unscale(self, factor: <f32 as ComplexField>::RealField) -> f32

fn floor(self) -> f32

fn ceil(self) -> f32

fn round(self) -> f32

fn trunc(self) -> f32

fn fract(self) -> f32

fn abs(self) -> f32

fn signum(self) -> f32

fn mul_add(self, a: f32, b: f32) -> f32

fn powi(self, n: i32) -> f32

fn powf(self, n: f32) -> f32

fn powc(self, n: f32) -> f32

fn sqrt(self) -> f32

fn try_sqrt(self) -> Option<f32>

fn exp(self) -> f32

fn exp2(self) -> f32

fn exp_m1(self) -> f32

fn ln_1p(self) -> f32

fn ln(self) -> f32

fn log(self, base: f32) -> f32

fn log2(self) -> f32

fn log10(self) -> f32

fn cbrt(self) -> f32

fn hypot(self, other: f32) -> <f32 as ComplexField>::RealField

fn sin(self) -> f32

fn cos(self) -> f32

fn tan(self) -> f32

fn asin(self) -> f32

fn acos(self) -> f32

fn atan(self) -> f32

fn sin_cos(self) -> (f32, f32)

fn sinh(self) -> f32

fn cosh(self) -> f32

fn tanh(self) -> f32

fn asinh(self) -> f32

fn acosh(self) -> f32

fn atanh(self) -> f32

fn is_finite(&self) -> bool

impl ComplexField for f64

type RealField = f64

fn from_real(re: <f64 as ComplexField>::RealField) -> f64

fn real(self) -> <f64 as ComplexField>::RealField

fn imaginary(self) -> <f64 as ComplexField>::RealField

fn norm1(self) -> <f64 as ComplexField>::RealField

fn modulus(self) -> <f64 as ComplexField>::RealField

fn modulus_squared(self) -> <f64 as ComplexField>::RealField

fn argument(self) -> <f64 as ComplexField>::RealField

fn to_exp(self) -> (f64, f64)

fn recip(self) -> f64

fn conjugate(self) -> f64

fn scale(self, factor: <f64 as ComplexField>::RealField) -> f64

fn unscale(self, factor: <f64 as ComplexField>::RealField) -> f64

fn floor(self) -> f64

fn ceil(self) -> f64

fn round(self) -> f64

fn trunc(self) -> f64

fn fract(self) -> f64

fn abs(self) -> f64

fn signum(self) -> f64

fn mul_add(self, a: f64, b: f64) -> f64

fn powi(self, n: i32) -> f64

fn powf(self, n: f64) -> f64

fn powc(self, n: f64) -> f64

fn sqrt(self) -> f64

fn try_sqrt(self) -> Option<f64>

fn exp(self) -> f64

fn exp2(self) -> f64

fn exp_m1(self) -> f64

fn ln_1p(self) -> f64

fn ln(self) -> f64

fn log(self, base: f64) -> f64

fn log2(self) -> f64

fn log10(self) -> f64

fn cbrt(self) -> f64

fn hypot(self, other: f64) -> <f64 as ComplexField>::RealField

fn sin(self) -> f64

fn cos(self) -> f64

fn tan(self) -> f64

fn asin(self) -> f64

fn acos(self) -> f64

fn atan(self) -> f64

fn sin_cos(self) -> (f64, f64)

fn sinh(self) -> f64

fn cosh(self) -> f64

fn tanh(self) -> f64

fn asinh(self) -> f64

fn acosh(self) -> f64

fn atanh(self) -> f64

fn is_finite(&self) -> bool

Implementors

impl<N> ComplexField for Complex<N>

where N: RealField + PartialOrd,

type RealField = N