[−][src]Trait alga::general::ComplexField

pub trait ComplexField: SubsetOf<Self> + SupersetOf<f64> + Field + Copy + Num + NumAssign + FromPrimitive + Neg<Output = Self> + MeetSemilattice + JoinSemilattice + Send + Sync + Any + 'static + Debug + 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 is_finite(&self) -> bool;

    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 try_sqrt(self) -> Option<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 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

Type of the coefficients of a complex number.

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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

Multiplies 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 is_finite(&self) -> bool

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 try_sqrt(self) -> Option<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

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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

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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> 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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