Trait ComplexField

pub trait ComplexField:
    SubsetOf<Self>
    + SupersetOf<f32>
    + SupersetOf<f64>
    + FromPrimitive
    + Field<Element = Self, SimdBool = bool>
    + Neg<Output = Self>
    + 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: Self::RealField) -> Self

fn real(self) -> Self::RealField

fn imaginary(self) -> Self::RealField

fn norm1(self) -> Self::RealField

fn modulus(self) -> Self::RealField

fn modulus_squared(self) -> Self::RealField

fn argument(self) -> Self::RealField

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

fn recip(self) -> Self

fn conjugate(self) -> Self

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 abs(self) -> Self

fn signum(self) -> Self

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

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

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

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

fn sqrt(self) -> Self

fn try_sqrt(self) -> Option<Self>

fn exp(self) -> Self

fn exp2(self) -> Self

fn exp_m1(self) -> Self

fn ln_1p(self) -> Self

fn ln(self) -> Self

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

fn log2(self) -> Self

fn log10(self) -> Self

fn cbrt(self) -> Self

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

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn sin_cos(self) -> (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 is_finite(&self) -> bool

impl ComplexField for f64

type RealField = f64

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

fn real(self) -> Self::RealField

fn imaginary(self) -> Self::RealField

fn norm1(self) -> Self::RealField

fn modulus(self) -> Self::RealField

fn modulus_squared(self) -> Self::RealField

fn argument(self) -> Self::RealField

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

fn recip(self) -> Self

fn conjugate(self) -> Self

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 abs(self) -> Self

fn signum(self) -> Self

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

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

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

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

fn sqrt(self) -> Self

fn try_sqrt(self) -> Option<Self>

fn exp(self) -> Self

fn exp2(self) -> Self

fn exp_m1(self) -> Self

fn ln_1p(self) -> Self

fn ln(self) -> Self

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

fn log2(self) -> Self

fn log10(self) -> Self

fn cbrt(self) -> Self

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

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn sin_cos(self) -> (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 is_finite(&self) -> bool

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

fn exp(self) -> Self

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

fn ln(self) -> Self

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.

fn sqrt(self) -> Self

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.

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

Raises self to a floating point power.

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

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

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

Raises self to a complex power.

fn sin(self) -> Self

Computes the sine of self.

fn cos(self) -> Self

Computes the cosine of self.

fn tan(self) -> Self

Computes the tangent of self.

fn asin(self) -> Self

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.

fn acos(self) -> Self

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.

fn atan(self) -> Self

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.

fn sinh(self) -> Self

Computes the hyperbolic sine of self.

fn cosh(self) -> Self

Computes the hyperbolic cosine of self.

fn tanh(self) -> Self

Computes the hyperbolic tangent of self.

fn asinh(self) -> Self

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.

fn acosh(self) -> Self

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)) < ∞.

fn atanh(self) -> Self

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

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

fn real(self) -> Self::RealField

fn imaginary(self) -> Self::RealField

fn argument(self) -> Self::RealField

fn modulus(self) -> Self::RealField

fn modulus_squared(self) -> Self::RealField

fn norm1(self) -> Self::RealField

fn recip(self) -> Self

fn conjugate(self) -> Self

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 exp2(self) -> Self

fn exp_m1(self) -> Self

fn ln_1p(self) -> Self

fn log2(self) -> Self

fn log10(self) -> Self

fn cbrt(self) -> Self

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

fn is_finite(&self) -> bool

fn try_sqrt(self) -> Option<Self>

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

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

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

Implementors