Struct num_complex::Complex

pub struct Complex<T> {
    pub re: T,
    pub im: T,
}

A complex number in Cartesian form.

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Methods

impl<T: Clone + Num> Complex<T>

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: Clone + Num + Neg<Output=T>> Complex<T>

fn conj(&self) -> Complex<T>

Returns the complex conjugate. i.e. re - i im

fn inv(&self) -> Complex<T>

Returns 1/self

impl<T: Clone + Float> Complex<T>

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

Trait Implementations

impl<T: Encodable> Encodable for Complex<T>

fn encode<__ST: Encoder>(&self, __arg_0: &mut __ST) -> Result<(), __ST::Error>

impl<T: Decodable> Decodable for Complex<T>

fn decode<__DT: Decoder>(__arg_0: &mut __DT) -> Result<Complex<T>, __DT::Error>

impl<T: PartialEq> PartialEq for Complex<T>

fn eq(&self, __arg_0: &Complex<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, __arg_0: &Complex<T>) -> bool

This method tests for !=.

impl<T: Copy> Copy for Complex<T>

impl<T: Clone> Clone for Complex<T>

fn clone(&self) -> Complex<T>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Hash> Hash for Complex<T>

fn hash<__HT: Hasher>(&self, __arg_0: &mut __HT)

Feeds this value into the state given, updating the hasher as necessary.

fn hash_slice<H>(data: &[Self], state: &mut H) where H: Hasher

Feeds a slice of this type into the state provided.

impl<T: Debug> Debug for Complex<T>

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<T: Clone + Num> From<T> for Complex<T>

fn from(re: T) -> Complex<T>

Performs the conversion.

impl<'a, T: Clone + Num> From<&'a T> for Complex<T>

fn from(re: &T) -> Complex<T>

Performs the conversion.

impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: &Complex<T>) -> Complex<T>

The method for the + operator

impl<'a, T: Clone + Num> Add<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: Complex<T>) -> Complex<T>

The method for the + operator

impl<'a, T: Clone + Num> Add<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: &Complex<T>) -> Complex<T>

The method for the + operator

impl<T: Clone + Num> Add<Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: Complex<T>) -> Complex<T>

The method for the + operator

impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: &Complex<T>) -> Complex<T>

The method for the - operator

impl<'a, T: Clone + Num> Sub<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: Complex<T>) -> Complex<T>

The method for the - operator

impl<'a, T: Clone + Num> Sub<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: &Complex<T>) -> Complex<T>

The method for the - operator

impl<T: Clone + Num> Sub<Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: Complex<T>) -> Complex<T>

The method for the - operator

impl<'a, 'b, T: Clone + Num> Mul<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: &Complex<T>) -> Complex<T>

The method for the * operator

impl<'a, T: Clone + Num> Mul<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: Complex<T>) -> Complex<T>

The method for the * operator

impl<'a, T: Clone + Num> Mul<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: &Complex<T>) -> Complex<T>

The method for the * operator

impl<T: Clone + Num> Mul<Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: Complex<T>) -> Complex<T>

The method for the * operator

impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: &Complex<T>) -> Complex<T>

The method for the / operator

impl<'a, T: Clone + Num> Div<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: Complex<T>) -> Complex<T>

The method for the / operator

impl<'a, T: Clone + Num> Div<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: &Complex<T>) -> Complex<T>

The method for the / operator

impl<T: Clone + Num> Div<Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: Complex<T>) -> Complex<T>

The method for the / operator

impl<T: Clone + Num + Neg<Output=T>> Neg for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn neg(self) -> Complex<T>

The method for the unary - operator

impl<'a, T: Clone + Num + Neg<Output=T>> Neg for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn neg(self) -> Complex<T>

The method for the unary - operator

impl<'a, T: Clone + Num> Add<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: &T) -> Complex<T>

The method for the + operator

impl<'a, T: Clone + Num> Add<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: T) -> Complex<T>

The method for the + operator

impl<'a, 'b, T: Clone + Num> Add<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: &T) -> Complex<T>

The method for the + operator

impl<'a, T: Clone + Num> Sub<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: &T) -> Complex<T>

The method for the - operator

impl<'a, T: Clone + Num> Sub<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: T) -> Complex<T>

The method for the - operator

impl<'a, 'b, T: Clone + Num> Sub<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: &T) -> Complex<T>

The method for the - operator

impl<'a, T: Clone + Num> Mul<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: &T) -> Complex<T>

The method for the * operator

impl<'a, T: Clone + Num> Mul<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: T) -> Complex<T>

The method for the * operator

impl<'a, 'b, T: Clone + Num> Mul<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: &T) -> Complex<T>

The method for the * operator

impl<'a, T: Clone + Num> Div<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: &T) -> Complex<T>

The method for the / operator

impl<'a, T: Clone + Num> Div<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: T) -> Complex<T>

The method for the / operator

impl<'a, 'b, T: Clone + Num> Div<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: &T) -> Complex<T>

The method for the / operator

impl<T: Clone + Num> Add<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator

fn add(self, other: T) -> Complex<T>

The method for the + operator

impl<T: Clone + Num> Sub<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator

fn sub(self, other: T) -> Complex<T>

The method for the - operator

impl<T: Clone + Num> Mul<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator

fn mul(self, other: T) -> Complex<T>

The method for the * operator

impl<T: Clone + Num> Div<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator

fn div(self, other: T) -> Complex<T>

The method for the / operator

impl<T: Clone + Num> Zero for Complex<T>

fn zero() -> Complex<T>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

impl<T: Clone + Num> One for Complex<T>

fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1.

impl<T> Display for Complex<T> where T: Display + Num + PartialOrd + Clone

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.