Struct idsp::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

Implementations

impl<T> Complex<T>

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

Create a new Complex

impl<T> Complex<T>

where T: Clone + Num,

pub fn i() -> Complex<T>

Returns the imaginary unit.

See also Complex::I.

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.

pub fn powu(&self, exp: u32) -> Complex<T>

Raises self to an unsigned integer power.

impl<T> Complex<T>

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

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

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

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

Returns 1/self

pub fn powi(&self, exp: i32) -> Complex<T>

Raises self to a signed integer power.

impl<T> Complex<T>

where T: Clone + Signed,

pub fn l1_norm(&self) -> T

Returns the L1 norm |re| + |im| – the Manhattan distance from the origin.

impl<T> Complex<T>

where T: FloatCore,

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

impl<T> Complex<T>

where T: ConstZero,

pub const ZERO: Complex<T> = _

A constant Complex 0.

impl<T> Complex<T>

where T: ConstOne + ConstZero,

pub const ONE: Complex<T> = _

A constant Complex 1.

pub const I: Complex<T> = _

A constant Complex i, the imaginary unit.

Trait Implementations

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>, ) -> <&'a Complex<T> as Add<&'b Complex<T>>>::Output

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> as Add<&'a Complex<T>>>::Output

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) -> <&'b Complex<T> as Add<&'a T>>::Output

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> as Add<&'a T>>::Output

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>) -> <&'a Complex<T> as Add<Complex<T>>>::Output

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) -> <&'a Complex<T> as Add<T>>::Output

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> as Add<T>>::Output

Performs the + operation.

impl<T> Add 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> as Add>::Output

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<'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<T> for Complex<T>

where T: Clone + NumAssign,

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T> AddAssign for Complex<T>

where T: Clone + NumAssign,

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

Performs the += operation.

impl<T, U> AsPrimitive<U> for Complex<T>

where T: AsPrimitive<U>, U: 'static + Copy,

fn as_(self) -> U

Convert a value to another, using the as operator.

impl<T> Binary for Complex<T>

where T: Binary + Num + PartialOrd + Clone,

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 ComplexExt<i32, u32> for Complex<i32>

fn from_angle(angle: i32) -> Self

Return a Complex on the unit circle given an angle.

Example:

use idsp::{Complex, ComplexExt};
Complex::<i32>::from_angle(0);
Complex::<i32>::from_angle(1 << 30); // pi/2
Complex::<i32>::from_angle(-1 << 30); // -pi/2

fn abs_sqr(&self) -> u32

Return the absolute square (the squared magnitude).

Note: Normalization is 1 << 32, i.e. U0.32.

Note(panic): This will panic for Complex(i32::MIN, i32::MIN)

Example:

use idsp::{Complex, ComplexExt};
assert_eq!(Complex::new(i32::MIN, 0).abs_sqr(), 1 << 31);
assert_eq!(Complex::new(i32::MAX, i32::MAX).abs_sqr(), u32::MAX - 3);

fn log2(&self) -> i32

log2(power) re full scale approximation

TODO: scale up, interpolate

Panic: This will panic for Complex(i32::MIN, i32::MIN)

Example:

use idsp::{Complex, ComplexExt};
assert_eq!(Complex::new(i32::MAX, i32::MAX).log2(), -1);
assert_eq!(Complex::new(i32::MAX, 0).log2(), -2);
assert_eq!(Complex::new(1, 0).log2(), -63);
assert_eq!(Complex::new(0, 0).log2(), -64);

fn arg(&self) -> i32

Return the angle.

Note: Normalization is 1 << 31 == pi.

Example:

use idsp::{Complex, ComplexExt};
assert_eq!(Complex::new(0, 0).arg(), 0);

fn saturating_add(&self, other: Self) -> Self

Staturating addition

fn saturating_sub(&self, other: Self) -> Self

Saturating subtraction

impl<T> ConstOne for Complex<T>

where T: Clone + Num + ConstOne + ConstZero,

const ONE: Complex<T> = Self::ONE

The multiplicative identity element of Self, 1.

impl<T> ConstZero for Complex<T>

where T: Clone + Num + ConstZero,

const ZERO: Complex<T> = Self::ZERO

The additive identity element of Self, 0.

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> Default for Complex<T>

where T: Default,

fn default() -> Complex<T>

Returns the “default value” for a type.

impl<'de, T> Deserialize<'de> for Complex<T>

where T: Deserialize<'de>,

fn deserialize<D>( deserializer: D, ) -> Result<Complex<T>, <D as Deserializer<'de>>::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T> Display for Complex<T>

where T: Display + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.

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>, ) -> <&'a Complex<T> as Div<&'b Complex<T>>>::Output

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> as Div<&'a Complex<T>>>::Output

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) -> <&'b Complex<T> as Div<&'a T>>::Output

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> as Div<&'a T>>::Output

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>) -> <&'a Complex<T> as Div<Complex<T>>>::Output

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) -> <&'a Complex<T> as Div<T>>::Output

Performs the / operation.

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> as Div<T>>::Output

Performs the / operation.

impl<T> Div 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> as Div>::Output

Performs the / operation.

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<T> for Complex<T>

where T: Clone + NumAssign,

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<T> DivAssign for Complex<T>

where T: Clone + NumAssign,

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

Performs the /= operation.

impl<'a, T> From<&'a T> for Complex<T>

where T: Clone + Num,

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

Converts to this type from the input type.

impl<T> From<T> for Complex<T>

where T: Clone + Num,

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

Converts to this type from the input type.

impl<T> FromPrimitive for Complex<T>

where T: FromPrimitive + Num,

fn from_usize(n: usize) -> Option<Complex<T>>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(n: isize) -> Option<Complex<T>>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(n: u8) -> Option<Complex<T>>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(n: u16) -> Option<Complex<T>>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(n: u32) -> Option<Complex<T>>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(n: u64) -> Option<Complex<T>>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i8(n: i8) -> Option<Complex<T>>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(n: i16) -> Option<Complex<T>>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(n: i32) -> Option<Complex<T>>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i64(n: i64) -> Option<Complex<T>>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Complex<T>>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Complex<T>>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(n: f32) -> Option<Complex<T>>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f64(n: f64) -> Option<Complex<T>>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl<T> FromStr for Complex<T>

where T: FromStr + Num + Clone,

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

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

The associated error which can be returned from parsing.

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, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<'a, T> Inv for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> <&'a Complex<T> as Inv>::Output

Returns the multiplicative inverse of self.

impl<T> Inv for Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> <Complex<T> as Inv>::Output

Returns the multiplicative inverse of self.

impl<T> LowerExp for Complex<T>

where T: LowerExp + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.

impl<T> LowerHex for Complex<T>

where T: LowerHex + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.

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>, ) -> <&'a Complex<T> as Mul<&'b Complex<T>>>::Output

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> as Mul<&'a Complex<T>>>::Output

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) -> <&'b Complex<T> as Mul<&'a T>>::Output

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> as Mul<&'a T>>::Output

Performs the * operation.

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>) -> <&'a Complex<T> as Mul<Complex<T>>>::Output

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) -> <&'a Complex<T> as Mul<T>>::Output

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> as Mul<T>>::Output

Performs the * operation.

impl<T> Mul 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> as Mul>::Output

Performs the * operation.

impl<'a, 'b, T> MulAdd<&'b Complex<T>> for &'a Complex<T>

where T: Clone + Num + MulAdd<Output = T>,

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation (self * a) + b

impl<T> MulAdd for Complex<T>

where T: Clone + Num + MulAdd<Output = T>,

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation (self * a) + b

impl<'a, 'b, T> MulAddAssign<&'a Complex<T>, &'b Complex<T>> for Complex<T>

where T: Clone + NumAssign + MulAddAssign,

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

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T> MulAddAssign for Complex<T>

where T: Clone + NumAssign + MulAddAssign,

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

Performs the fused multiply-add assignment operation *self = (*self * a) + b

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<'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<T> for Complex<T>

where T: Clone + NumAssign,

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<T> MulAssign for Complex<T>

where T: Clone + NumAssign,

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

Performs the *= operation.

impl MulScaled<Complex<i32>> for Complex<i32>

fn mul_scaled(self, other: Self) -> Self

Scaled multiplication for fixed point

impl MulScaled<i16> for Complex<i32>

fn mul_scaled(self, other: i16) -> Self

Scaled multiplication for fixed point

impl MulScaled<i32> for Complex<i32>

fn mul_scaled(self, other: i32) -> Self

Scaled multiplication for fixed point

impl<'a, T> Neg for &'a Complex<T>

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

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> <&'a Complex<T> as Neg>::Output

Performs the unary - operation.

impl<T> Neg for Complex<T>

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

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> <Complex<T> as Neg>::Output

Performs the unary - operation.

impl<T> Num for Complex<T>

where T: Num + Clone,

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

radix must be <= 18; larger radix would include i and j as digits, which cannot be supported.

The conversion returns an error if 18 <= radix <= 36; it panics if radix > 36.

The elements of T are parsed using Num::from_str_radix too, and errors (or panics) from that are reflected here as well.

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

impl<T> NumCast for Complex<T>

where T: NumCast + Num,

fn from<U>(n: U) -> Option<Complex<T>>

where U: ToPrimitive,

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned.

impl<T> Octal for Complex<T>

where T: Octal + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.

impl<T> One for Complex<T>

where T: Clone + Num,

fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

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

impl<T> PartialEq for Complex<T>

where T: PartialEq,

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

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, 'b, T> Pow<&'b i128> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i128) -> <&'a Complex<T> as Pow<&'b i128>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i16> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i16) -> <&'a Complex<T> as Pow<&'b i16>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i32> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i32) -> <&'a Complex<T> as Pow<&'b i32>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i64> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i64) -> <&'a Complex<T> as Pow<&'b i64>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i8> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i8) -> <&'a Complex<T> as Pow<&'b i8>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b isize> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &isize) -> <&'a Complex<T> as Pow<&'b isize>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u128> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u128) -> <&'a Complex<T> as Pow<&'b u128>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u16> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u16) -> <&'a Complex<T> as Pow<&'b u16>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u32> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u32) -> <&'a Complex<T> as Pow<&'b u32>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u64> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u64) -> <&'a Complex<T> as Pow<&'b u64>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u8> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u8) -> <&'a Complex<T> as Pow<&'b u8>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b usize> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &usize) -> <&'a Complex<T> as Pow<&'b usize>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<i128> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i128) -> <&'a Complex<T> as Pow<i128>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<i16> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i16) -> <&'a Complex<T> as Pow<i16>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<i32> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i32) -> <&'a Complex<T> as Pow<i32>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<i64> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i64) -> <&'a Complex<T> as Pow<i64>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<i8> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i8) -> <&'a Complex<T> as Pow<i8>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<isize> for &'a Complex<T>

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

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: isize) -> <&'a Complex<T> as Pow<isize>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<u128> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u128) -> <&'a Complex<T> as Pow<u128>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<u16> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u16) -> <&'a Complex<T> as Pow<u16>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<u32> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u32) -> <&'a Complex<T> as Pow<u32>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<u64> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u64) -> <&'a Complex<T> as Pow<u64>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<u8> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u8) -> <&'a Complex<T> as Pow<u8>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<usize> for &'a Complex<T>

where T: Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: usize) -> <&'a Complex<T> as Pow<usize>>::Output

Returns self to the power rhs.

impl<'a, T> Product<&'a Complex<T>> for Complex<T>

where T: 'a + Num + Clone,

fn product<I>(iter: I) -> Complex<T>

where I: Iterator<Item = &'a Complex<T>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T> Product for Complex<T>

where T: Num + Clone,

fn product<I>(iter: I) -> Complex<T>

where I: Iterator<Item = Complex<T>>,

Takes an iterator and generates Self from the elements by multiplying the items.

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>, ) -> <&'a Complex<T> as Rem<&'b Complex<T>>>::Output

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> as Rem<&'a Complex<T>>>::Output

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) -> <&'b Complex<T> as Rem<&'a T>>::Output

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> as Rem<&'a T>>::Output

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>) -> <&'a Complex<T> as Rem<Complex<T>>>::Output

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) -> <&'a Complex<T> as Rem<T>>::Output

Performs the % operation.

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> as Rem<T>>::Output

Performs the % operation.

impl<T> Rem 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> as Rem>::Output

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> 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 for Complex<T>

where T: Clone + NumAssign,

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

Performs the %= operation.

impl<T> Serialize for Complex<T>

where T: Serialize,

fn serialize<S>( &self, serializer: S, ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

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>, ) -> <&'a Complex<T> as Sub<&'b Complex<T>>>::Output

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> as Sub<&'a Complex<T>>>::Output

Performs the - operation.

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) -> <&'b Complex<T> as Sub<&'a T>>::Output

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> as Sub<&'a T>>::Output

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>) -> <&'a Complex<T> as Sub<Complex<T>>>::Output

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) -> <&'a Complex<T> as Sub<T>>::Output

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> as Sub<T>>::Output

Performs the - operation.

impl<T> Sub 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> as Sub>::Output

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<'a, T> SubAssign<&'a T> for Complex<T>

where T: Clone + NumAssign,

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

where T: Clone + NumAssign,

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

Performs the -= operation.

impl<'a, T> Sum<&'a Complex<T>> for Complex<T>

where T: 'a + Num + Clone,

fn sum<I>(iter: I) -> Complex<T>

where I: Iterator<Item = &'a Complex<T>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T> Sum for Complex<T>

where T: Num + Clone,

fn sum<I>(iter: I) -> Complex<T>

where I: Iterator<Item = Complex<T>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T> ToPrimitive for Complex<T>

where T: ToPrimitive + Num,

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

impl<T> UpperExp for Complex<T>

where T: UpperExp + Num + PartialOrd + 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 + 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.

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> Copy for Complex<T>

where T: Copy,

impl<T> Eq for Complex<T>

where T: Eq,

impl<T> StructuralPartialEq for Complex<T>