Struct num::complex::Complex

#[repr(C)]
pub struct Complex<T> {
    pub re: T,
    pub im: T,
}

A complex number in Cartesian form.

Representation and Foreign Function Interface Compatibility

Complex<T> is memory layout compatible with an array [T; 2].

Note that Complex<F> where F is a floating point type is only memory layout compatible with C's complex types, not necessarily calling convention compatible. This means that for FFI you can only pass Complex<F> behind a pointer, not as a value.

Examples

Example of extern function declaration.

use num_complex::Complex;
use std::os::raw::c_int;

extern "C" {
    fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,
              x: *const Complex<f64>, incx: *const c_int,
              y: *mut Complex<f64>, incy: *const c_int);
}

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Methods

impl<T> Complex<T> where
    T: Clone + Num, 

pub fn new(re: T, im: T) -> Complex<T>

Create a new Complex

pub fn i() -> Complex<T>

Returns imaginary unit

pub 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.

pub fn scale(&self, t: T) -> Complex<T>

Multiplies self by the scalar t.

pub fn unscale(&self, t: T) -> Complex<T>

Divides self by the scalar t.

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

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

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

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

Returns 1/self

impl<T> Complex<T> where
    T: Clone + Float, 

pub fn norm(&self) -> T

Calculate |self|

pub fn arg(&self) -> T

Calculate the principal Arg of self.

pub fn to_polar(&self) -> (T, T)

Convert to polar form (r, theta), such that self = r * exp(i * theta)

pub fn from_polar(r: &T, theta: &T) -> Complex<T>

Convert a polar representation into a complex number.

pub fn exp(&self) -> Complex<T>

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

pub 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.

pub 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.

pub fn powf(&self, exp: T) -> Complex<T>

Raises self to a floating point power.

pub fn log(&self, base: T) -> Complex<T>

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

pub fn powc(&self, exp: Complex<T>) -> Complex<T>

Raises self to a complex power.

pub fn expf(&self, base: T) -> Complex<T>

Raises a floating point number to the complex power self.

pub fn sin(&self) -> Complex<T>

Computes the sine of self.

pub fn cos(&self) -> Complex<T>

Computes the cosine of self.

pub fn tan(&self) -> Complex<T>

Computes the tangent of self.

pub 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.

pub 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.

pub 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.

pub fn sinh(&self) -> Complex<T>

Computes the hyperbolic sine of self.

pub fn cosh(&self) -> Complex<T>

Computes the hyperbolic cosine of self.

pub fn tanh(&self) -> Complex<T>

Computes the hyperbolic tangent of self.

pub 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.

pub 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)) < ∞.

pub 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.

pub fn is_nan(self) -> bool

Checks if the given complex number is NaN

pub fn is_infinite(self) -> bool

Checks if the given complex number is infinite

pub fn is_finite(self) -> bool

Checks if the given complex number is finite

pub fn is_normal(self) -> bool

Checks if the given complex number is normal

Trait Implementations

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

fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<T> SubAssign<Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn sub_assign(&mut self, other: Complex<T>)

Performs the -= operation.

impl<T> SubAssign<T> for Complex<T> where
    T: Clone + NumAssign, 

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<'a, T> SubAssign<&'a T> for Complex<T> where
    T: Clone + NumAssign, 

fn sub_assign(&mut self, other: &T)

Performs the -= operation.

impl<'a, T> SubAssign<&'a Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn sub_assign(&mut self, other: &Complex<T>)

Performs the -= operation.

impl<T> Eq for Complex<T> where
    T: Eq, 

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

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

Formats the value using the given formatter.

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

fn encode<__S>(&self, s: &mut __S) -> Result<(), <__S as Encoder>::Error> where
    __S: Encoder, 

Serialize a value using an Encoder.

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

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

Formats the value using the given formatter.

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

fn zero() -> Complex<T>

Returns the additive identity element of Self, 0. # Purity

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

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

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

Formats the value using the given formatter.

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

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

Formats the value using the given formatter.

impl<T> Rem<T> for Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T> Rem<Complex<T>> for Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, modulus: Complex<T>) -> Complex<T>

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<'a, T> RemAssign<&'a T> for Complex<T> where
    T: Clone + NumAssign, 

fn rem_assign(&mut self, other: &T)

Performs the %= operation.

impl<T> RemAssign<T> for Complex<T> where
    T: Clone + NumAssign, 

fn rem_assign(&mut self, other: T)

Performs the %= operation.

impl<T> RemAssign<Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn rem_assign(&mut self, other: Complex<T>)

Performs the %= operation.

impl<'a, T> RemAssign<&'a Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn rem_assign(&mut self, other: &Complex<T>)

Performs the %= operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

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

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

This method tests for !=.

impl<T> Debug for Complex<T> where
    T: Debug, 

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

Formats the value using the given formatter.

impl<T> Clone for Complex<T> where
    T: Clone, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Formats the value using the given formatter.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T> AddAssign<&'a Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn add_assign(&mut self, other: &Complex<T>)

Performs the += operation.

impl<T> AddAssign<T> for Complex<T> where
    T: Clone + NumAssign, 

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<'a, T> AddAssign<&'a T> for Complex<T> where
    T: Clone + NumAssign, 

fn add_assign(&mut self, other: &T)

Performs the += operation.

impl<T> AddAssign<Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn add_assign(&mut self, other: Complex<T>)

Performs the += operation.

impl<T> Hash for Complex<T> where
    T: Hash, 

fn hash<__H>(&self, state: &mut __H) where
    __H: Hasher, 

Feeds this value into the given [Hasher].

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

Feeds a slice of this type into the given [Hasher].

impl<T> Default for Complex<T> where
    T: Default, 

fn default() -> Complex<T>

Returns the "default value" for a type.

impl<T> Num for Complex<T> where
    T: Clone + Num, 

type FromStrRadixErr = ParseComplexError<<T as Num>::FromStrRadixErr>

fn from_str_radix(
    s: &str,
    radix: u32
) -> Result<Complex<T>, <Complex<T> as Num>::FromStrRadixErr>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

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

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Complex<T>

Performs the unary - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Complex<T>

Performs the unary - operation.

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

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

Performs the conversion.

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

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

Performs the conversion.

impl<'a, T> DivAssign<&'a Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn div_assign(&mut self, other: &Complex<T>)

Performs the /= operation.

impl<'a, T> DivAssign<&'a T> for Complex<T> where
    T: Clone + NumAssign, 

fn div_assign(&mut self, other: &T)

Performs the /= operation.

impl<T> DivAssign<Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn div_assign(&mut self, other: Complex<T>)

Performs the /= operation.

impl<T> DivAssign<T> for Complex<T> where
    T: Clone + NumAssign, 

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<'a, T> MulAssign<&'a T> for Complex<T> where
    T: Clone + NumAssign, 

fn mul_assign(&mut self, other: &T)

Performs the *= operation.

impl<T> MulAssign<Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn mul_assign(&mut self, other: Complex<T>)

Performs the *= operation.

impl<'a, T> MulAssign<&'a Complex<T>> for Complex<T> where
    T: Clone + NumAssign, 

fn mul_assign(&mut self, other: &Complex<T>)

Performs the *= operation.

impl<T> MulAssign<T> for Complex<T> where
    T: Clone + NumAssign, 

fn mul_assign(&mut self, other: T)

Performs the *= operation.

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

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

Formats the value using the given formatter.

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

fn decode<__D>(d: &mut __D) -> Result<Complex<T>, <__D as Decoder>::Error> where
    __D: Decoder, 

Deserialize a value using a Decoder.

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

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

Formats the value using the given formatter.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> FromStr for Complex<T> where
    T: FromStr + Num + Clone, 

type Err = ParseComplexError<<T as FromStr>::Err>

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Complex<T>, <Complex<T> as FromStr>::Err>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

impl<T> Copy for Complex<T> where
    T: Copy,