Trait nalgebra::ComplexField

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

    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.

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

Implementations on Foreign Types

impl ComplexField for f64

type RealField = f64

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

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

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

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

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

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

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

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

pub fn recip(self) -> f64

pub fn conjugate(self) -> f64

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

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

pub fn floor(self) -> f64

pub fn ceil(self) -> f64

pub fn round(self) -> f64

pub fn trunc(self) -> f64

pub fn fract(self) -> f64

pub fn abs(self) -> f64

pub fn signum(self) -> f64

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

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

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

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

pub fn sqrt(self) -> f64

pub fn try_sqrt(self) -> Option<f64>

pub fn exp(self) -> f64

pub fn exp2(self) -> f64

pub fn exp_m1(self) -> f64

pub fn ln_1p(self) -> f64

pub fn ln(self) -> f64

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

pub fn log2(self) -> f64

pub fn log10(self) -> f64

pub fn cbrt(self) -> f64

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

pub fn sin(self) -> f64

pub fn cos(self) -> f64

pub fn tan(self) -> f64

pub fn asin(self) -> f64

pub fn acos(self) -> f64

pub fn atan(self) -> f64

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

pub fn sinh(self) -> f64

pub fn cosh(self) -> f64

pub fn tanh(self) -> f64

pub fn asinh(self) -> f64

pub fn acosh(self) -> f64

pub fn atanh(self) -> f64

pub fn is_finite(&self) -> bool

impl ComplexField for f32

type RealField = f32

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

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

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

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

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

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

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

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

pub fn recip(self) -> f32

pub fn conjugate(self) -> f32

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

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

pub fn floor(self) -> f32

pub fn ceil(self) -> f32

pub fn round(self) -> f32

pub fn trunc(self) -> f32

pub fn fract(self) -> f32

pub fn abs(self) -> f32

pub fn signum(self) -> f32

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

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

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

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

pub fn sqrt(self) -> f32

pub fn try_sqrt(self) -> Option<f32>

pub fn exp(self) -> f32

pub fn exp2(self) -> f32

pub fn exp_m1(self) -> f32

pub fn ln_1p(self) -> f32

pub fn ln(self) -> f32

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

pub fn log2(self) -> f32

pub fn log10(self) -> f32

pub fn cbrt(self) -> f32

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

pub fn sin(self) -> f32

pub fn cos(self) -> f32

pub fn tan(self) -> f32

pub fn asin(self) -> f32

pub fn acos(self) -> f32

pub fn atan(self) -> f32

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

pub fn sinh(self) -> f32

pub fn cosh(self) -> f32

pub fn tanh(self) -> f32

pub fn asinh(self) -> f32

pub fn acosh(self) -> f32

pub fn atanh(self) -> f32

pub fn is_finite(&self) -> bool

Implementors

impl<N> ComplexField for Complex<N> where
    N: RealField + PartialOrd<N>, 

pub fn exp(self) -> Complex<N>

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

pub fn ln(self) -> Complex<N>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

• (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

pub fn sqrt(self) -> Complex<N>

Computes the principal value of the square root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

pub fn powf(self, exp: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Raises self to a floating point power.

pub fn log(self, base: N) -> Complex<N>

Returns the logarithm of self with respect to an arbitrary base.

pub fn powc(self, exp: Complex<N>) -> Complex<N>

Raises self to a complex power.

pub fn sin(self) -> Complex<N>

Computes the sine of self.

pub fn cos(self) -> Complex<N>

Computes the cosine of self.

pub fn tan(self) -> Complex<N>

Computes the tangent of self.

pub fn asin(self) -> Complex<N>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

pub fn acos(self) -> Complex<N>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

pub fn atan(self) -> Complex<N>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

• (-∞i, -i], continuous from the left.
• [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

pub fn sinh(self) -> Complex<N>

Computes the hyperbolic sine of self.

pub fn cosh(self) -> Complex<N>

Computes the hyperbolic cosine of self.

pub fn tanh(self) -> Complex<N>

Computes the hyperbolic tangent of self.

pub fn asinh(self) -> Complex<N>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

• (-∞i, -i), continuous from the left.
• (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

pub fn acosh(self) -> Complex<N>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

• (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

pub fn atanh(self) -> Complex<N>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

• (-∞, -1], continuous from above.
• [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

type RealField = N

pub fn from_real(re: <Complex<N> as ComplexField>::RealField) -> Complex<N>

pub fn real(self) -> <Complex<N> as ComplexField>::RealField

pub fn imaginary(self) -> <Complex<N> as ComplexField>::RealField

pub fn argument(self) -> <Complex<N> as ComplexField>::RealField

pub fn modulus(self) -> <Complex<N> as ComplexField>::RealField

pub fn modulus_squared(self) -> <Complex<N> as ComplexField>::RealField

pub fn norm1(self) -> <Complex<N> as ComplexField>::RealField

pub fn recip(self) -> Complex<N>

pub fn conjugate(self) -> Complex<N>

pub fn scale(
    self,
    factor: <Complex<N> as ComplexField>::RealField
) -> Complex<N>

pub fn unscale(
    self,
    factor: <Complex<N> as ComplexField>::RealField
) -> Complex<N>

pub fn floor(self) -> Complex<N>

pub fn ceil(self) -> Complex<N>

pub fn round(self) -> Complex<N>

pub fn trunc(self) -> Complex<N>

pub fn fract(self) -> Complex<N>

pub fn mul_add(self, a: Complex<N>, b: Complex<N>) -> Complex<N>

pub fn abs(self) -> <Complex<N> as ComplexField>::RealField

pub fn exp2(self) -> Complex<N>

pub fn exp_m1(self) -> Complex<N>

pub fn ln_1p(self) -> Complex<N>

pub fn log2(self) -> Complex<N>

pub fn log10(self) -> Complex<N>

pub fn cbrt(self) -> Complex<N>

pub fn powi(self, n: i32) -> Complex<N>

pub fn is_finite(&self) -> bool

pub fn try_sqrt(self) -> Option<Complex<N>>

pub fn hypot(self, b: Complex<N>) -> <Complex<N> as ComplexField>::RealField

pub fn sin_cos(self) -> (Complex<N>, Complex<N>)

pub fn sinh_cosh(self) -> (Complex<N>, Complex<N>)