Struct num::complex::Complex
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pub struct Complex<T> {
pub re: T,
pub im: T,
}A complex number in Cartesian form.
Fields
re | Real portion of the complex number |
im | Imaginary portion of the complex number |
Methods
impl<T> Complex<T> where T: Clone + Num
fn new(re: T, im: T) -> Complex<T>
Create a new Complex
fn i() -> Complex<T>
Returns imaginary unit
fn norm_sqr(&self) -> T
Returns the square of the norm (since T doesn't necessarily
have a sqrt function), i.e. re^2 + im^2.
fn scale(&self, t: T) -> Complex<T>
Multiplies self by the scalar t.
fn unscale(&self, t: T) -> Complex<T>
Divides self by the scalar t.
impl<T> Complex<T> where T: Neg<Output=T> + Clone + Num
fn conj(&self) -> Complex<T>
Returns the complex conjugate. i.e. re - i im
fn inv(&self) -> Complex<T>
Returns 1/self
impl<T> Complex<T> where T: Clone + Float
fn norm(&self) -> T
Calculate |self|
fn arg(&self) -> T
Calculate the principal Arg of self.
fn to_polar(&self) -> (T, T)
Convert to polar form (r, theta), such that self = r * exp(i * theta)
fn from_polar(r: &T, theta: &T) -> Complex<T>
Convert a polar representation into a complex number.
fn exp(&self) -> Complex<T>
Computes e^(self), where e is the base of the natural logarithm.
fn ln(&self) -> Complex<T>
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) -> Complex<T>
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 sin(&self) -> Complex<T>
Computes the sine of self.
fn cos(&self) -> Complex<T>
Computes the cosine of self.
fn tan(&self) -> Complex<T>
Computes the tangent of self.
fn asin(&self) -> Complex<T>
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) -> Complex<T>
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) -> Complex<T>
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) -> Complex<T>
Computes the hyperbolic sine of self.
fn cosh(&self) -> Complex<T>
Computes the hyperbolic cosine of self.
fn tanh(&self) -> Complex<T>
Computes the hyperbolic tangent of self.
fn asinh(&self) -> Complex<T>
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) -> Complex<T>
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) -> Complex<T>
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.
fn is_nan(self) -> bool
Checks if the given complex number is NaN
fn is_infinite(self) -> bool
Checks if the given complex number is infinite
fn is_finite(self) -> bool
Checks if the given complex number is finite
fn is_normal(self) -> bool
Checks if the given complex number is normal