Trait simba::scalar::ComplexField [−][src]
pub trait ComplexField: SubsetOf<Self> + SupersetOf<f64> + Field<Element = Self, SimdBool = bool> + Neg<Output = Self> + Clone + Send + Sync + Any + 'static + Debug + Display {
type RealField: RealField;
Show 55 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 { ... }
}
Expand description
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
Required methods
Builds a pure-real complex number from the given value.
fn modulus_squared(self) -> Self::RealField
fn modulus_squared(self) -> Self::RealField
The squared modulus of this complex number.
The sum of the absolute value of this complex number’s real and imaginary part.
The absolute value of this complex number: self / self.signum()
.
This is equivalent to self.modulus()
.
Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
Provided methods
The polar form of this complex number: (modulus, arg)
The exponential form of this complex number: (modulus, e^{i arg})
Implementations on Foreign Types
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
.
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
.
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
.
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
.
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
.
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
.
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)) < ∞
.
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
.