Trait simba::scalar::ComplexField[−][src]

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

Show 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>;

    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[src]

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Required methods

fn from_real(re: Self::RealField) -> Self[src]

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

fn real(self) -> Self::RealField[src]

The real part of this complex number.

fn imaginary(self) -> Self::RealField[src]

The imaginary part of this complex number.

fn modulus(self) -> Self::RealField[src]

The modulus of this complex number.

fn modulus_squared(self) -> Self::RealField[src]

The squared modulus of this complex number.

fn argument(self) -> Self::RealField[src]

The argument of this complex number.

fn norm1(self) -> Self::RealField[src]

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

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

Multiplies this complex number by factor.

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

Divides this complex number by factor.

fn floor(self) -> Self[src]

fn ceil(self) -> Self[src]

fn round(self) -> Self[src]

fn trunc(self) -> Self[src]

fn fract(self) -> Self[src]

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

fn abs(self) -> Self::RealField[src]

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

This is equivalent to self.modulus().

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

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

fn recip(self) -> Self[src]

fn conjugate(self) -> Self[src]

fn sin(self) -> Self[src]

fn cos(self) -> Self[src]

fn sin_cos(self) -> (Self, Self)[src]

fn tan(self) -> Self[src]

fn asin(self) -> Self[src]

fn acos(self) -> Self[src]

fn atan(self) -> Self[src]

fn sinh(self) -> Self[src]

fn cosh(self) -> Self[src]

fn tanh(self) -> Self[src]

fn asinh(self) -> Self[src]

fn acosh(self) -> Self[src]

fn atanh(self) -> Self[src]

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

fn log2(self) -> Self[src]

fn log10(self) -> Self[src]

fn ln(self) -> Self[src]

fn ln_1p(self) -> Self[src]

fn sqrt(self) -> Self[src]

fn exp(self) -> Self[src]

fn exp2(self) -> Self[src]

fn exp_m1(self) -> Self[src]

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

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

fn powc(self, n: Self) -> Self[src]

fn cbrt(self) -> Self[src]

fn is_finite(&self) -> bool[src]

fn try_sqrt(self) -> Option<Self>[src]

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Provided methods

fn to_polar(self) -> (Self::RealField, Self::RealField)[src]

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

fn to_exp(self) -> (Self::RealField, Self)[src]

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

fn signum(self) -> Self[src]

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

fn sinh_cosh(self) -> (Self, Self)[src]

fn sinc(self) -> Self[src]

Cardinal sine

fn sinhc(self) -> Self[src]

fn cosc(self) -> Self[src]

Cardinal cos

fn coshc(self) -> Self[src]

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Implementations on Foreign Types

impl ComplexField for f32[src]

type RealField = f32

impl ComplexField for f64[src]

type RealField = f64

impl<N: RealField + PartialOrd> ComplexField for Complex<N>[src]

type RealField = N

fn exp(self) -> Self[src]

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

fn ln(self) -> Self[src]

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[src]

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[src]

Raises self to a floating point power.

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

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

fn powc(self, exp: Self) -> Self[src]

Raises self to a complex power.

fn sin(self) -> Self[src]

Computes the sine of self.

fn cos(self) -> Self[src]

Computes the cosine of self.

fn tan(self) -> Self[src]

Computes the tangent of self.

fn asin(self) -> Self[src]

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[src]

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[src]

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[src]

Computes the hyperbolic sine of self.

fn cosh(self) -> Self[src]

Computes the hyperbolic cosine of self.

fn tanh(self) -> Self[src]

Computes the hyperbolic tangent of self.

fn asinh(self) -> Self[src]

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[src]

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[src]

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.

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Implementors

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