Struct num::Complex

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

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§

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impl<T> Complex<T>

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

Create a new Complex

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

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pub fn i() -> Complex<T>

Returns imaginary unit

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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.

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

Multiplies self by the scalar t.

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

Divides self by the scalar t.

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

Raises self to an unsigned integer power.

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

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

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

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

Returns 1/self

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

Raises self to a signed integer power.

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

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pub fn l1_norm(&self) -> T

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

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

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pub fn norm(self) -> T

Calculate |self|

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pub fn arg(self) -> T

Calculate the principal Arg of self.

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

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

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

Convert a polar representation into a complex number.

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

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

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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.

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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.

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pub fn cbrt(self) -> Complex<T>

Computes the principal value of the cube root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/3 ≤ arg(cbrt(z)) ≤ π/3.

Note that this does not match the usual result for the cube root of negative real numbers. For example, the real cube root of -8 is -2, but the principal complex cube root of -8 is 1 + i√3.

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

Raises self to a floating point power.

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

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

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

Raises self to a complex power.

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

Raises a floating point number to the complex power self.

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

Computes the sine of self.

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

Computes the cosine of self.

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

Computes the tangent of self.

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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.

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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.

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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.

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

Computes the hyperbolic sine of self.

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

Computes the hyperbolic cosine of self.

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

Computes the hyperbolic tangent of self.

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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.

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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)) < ∞.

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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.

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pub fn finv(self) -> Complex<T>

Returns 1/self using floating-point operations.

This may be more accurate than the generic self.inv() in cases where self.norm_sqr() would overflow to ∞ or underflow to 0.

§Examples
use num_complex::Complex64;
let c = Complex64::new(1e300, 1e300);

// The generic `inv()` will overflow.
assert!(!c.inv().is_normal());

// But we can do better for `Float` types.
let inv = c.finv();
assert!(inv.is_normal());
println!("{:e}", inv);

let expected = Complex64::new(5e-301, -5e-301);
assert!((inv - expected).norm() < 1e-315);
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pub fn fdiv(self, other: Complex<T>) -> Complex<T>

Returns self/other using floating-point operations.

This may be more accurate than the generic Div implementation in cases where other.norm_sqr() would overflow to ∞ or underflow to 0.

§Examples
use num_complex::Complex64;
let a = Complex64::new(2.0, 3.0);
let b = Complex64::new(1e300, 1e300);

// Generic division will overflow.
assert!(!(a / b).is_normal());

// But we can do better for `Float` types.
let quotient = a.fdiv(b);
assert!(quotient.is_normal());
println!("{:e}", quotient);

let expected = Complex64::new(2.5e-300, 5e-301);
assert!((quotient - expected).norm() < 1e-315);
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impl<T> Complex<T>
where T: FloatCore,

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pub fn is_nan(self) -> bool

Checks if the given complex number is NaN

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pub fn is_infinite(self) -> bool

Checks if the given complex number is infinite

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pub fn is_finite(self) -> bool

Checks if the given complex number is finite

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pub fn is_normal(self) -> bool

Checks if the given complex number is normal

Trait Implementations§

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

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add( self, other: &Complex<T> ) -> <&'a Complex<T> as Add<&'b Complex<T>>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: &Complex<T>) -> <Complex<T> as Add<&'a Complex<T>>>::Output

Performs the + operation. Read more
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impl<'a, 'b, T> Add<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: &T) -> <&'b Complex<T> as Add<&'a T>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: &T) -> <Complex<T> as Add<&'a T>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: Complex<T>) -> <&'a Complex<T> as Add<Complex<T>>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: T) -> <&'a Complex<T> as Add<T>>::Output

Performs the + operation. Read more
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impl<T> Add<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: T) -> <Complex<T> as Add<T>>::Output

Performs the + operation. Read more
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impl<T> Add for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: Complex<T>) -> <Complex<T> as Add>::Output

Performs the + operation. Read more
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impl<'a, T> AddAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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

Performs the += operation. Read more
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impl<'a, T> AddAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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

Performs the += operation. Read more
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impl<T> AddAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn add_assign(&mut self, other: T)

Performs the += operation. Read more
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impl<T> AddAssign for Complex<T>
where T: Clone + NumAssign,

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

Performs the += operation. Read more
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impl<T, U> AsPrimitive<U> for Complex<T>
where T: AsPrimitive<U>, U: 'static + Copy,

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fn as_(self) -> U

Convert a value to another, using the as operator.
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impl<T> Binary for Complex<T>
where T: Binary + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.
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impl<T> Clone for Complex<T>
where T: Clone,

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

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<T> Debug for Complex<T>
where T: Debug,

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

Formats the value using the given formatter. Read more
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impl<T> Default for Complex<T>
where T: Default,

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fn default() -> Complex<T>

Returns the “default value” for a type. Read more
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impl<T> Display for Complex<T>
where T: Display + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<T, Re, Im> Distribution<Complex<T>> for ComplexDistribution<Re, Im>
where T: Num + Clone, Re: Distribution<T>, Im: Distribution<T>,

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fn sample<R>(&self, rng: &mut R) -> Complex<T>
where R: Rng + ?Sized,

Generate a random value of T, using rng as the source of randomness.
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fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>
where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness. Read more
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fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>
where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F Read more
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impl<'a, 'b, T> Div<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div( self, other: &Complex<T> ) -> <&'a Complex<T> as Div<&'b Complex<T>>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: &Complex<T>) -> <Complex<T> as Div<&'a Complex<T>>>::Output

Performs the / operation. Read more
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impl<'a, 'b, T> Div<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: &T) -> <&'b Complex<T> as Div<&'a T>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: &T) -> <Complex<T> as Div<&'a T>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: Complex<T>) -> <&'a Complex<T> as Div<Complex<T>>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: T) -> <&'a Complex<T> as Div<T>>::Output

Performs the / operation. Read more
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impl<T> Div<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: T) -> <Complex<T> as Div<T>>::Output

Performs the / operation. Read more
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impl<T> Div for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: Complex<T>) -> <Complex<T> as Div>::Output

Performs the / operation. Read more
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impl<'a, T> DivAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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

Performs the /= operation. Read more
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impl<'a, T> DivAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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

Performs the /= operation. Read more
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impl<T> DivAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn div_assign(&mut self, other: T)

Performs the /= operation. Read more
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impl<T> DivAssign for Complex<T>
where T: Clone + NumAssign,

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

Performs the /= operation. Read more
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impl<'a, T> From<&'a T> for Complex<T>
where T: Clone + Num,

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

Converts to this type from the input type.
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impl<T> From<T> for Complex<T>
where T: Clone + Num,

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

Converts to this type from the input type.
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impl<T> FromPrimitive for Complex<T>
where T: FromPrimitive + Num,

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

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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

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

The associated error which can be returned from parsing.
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impl<T> Hash for Complex<T>
where T: Hash,

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

Feeds this value into the given Hasher. Read more
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fn hash_slice<H>(data: &[Self], state: &mut H)
where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl<'a, T> Inv for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn inv(self) -> <&'a Complex<T> as Inv>::Output

Returns the multiplicative inverse of self. Read more
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impl<T> Inv for Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn inv(self) -> <Complex<T> as Inv>::Output

Returns the multiplicative inverse of self. Read more
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impl<T> LowerExp for Complex<T>
where T: LowerExp + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.
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impl<T> LowerHex for Complex<T>
where T: LowerHex + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.
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impl<'a, 'b, T> Mul<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul( self, other: &Complex<T> ) -> <&'a Complex<T> as Mul<&'b Complex<T>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: &Complex<T>) -> <Complex<T> as Mul<&'a Complex<T>>>::Output

Performs the * operation. Read more
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impl<'a, 'b, T> Mul<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: &T) -> <&'b Complex<T> as Mul<&'a T>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: &T) -> <Complex<T> as Mul<&'a T>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: Complex<T>) -> <&'a Complex<T> as Mul<Complex<T>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: T) -> <&'a Complex<T> as Mul<T>>::Output

Performs the * operation. Read more
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impl<T> Mul<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: T) -> <Complex<T> as Mul<T>>::Output

Performs the * operation. Read more
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impl<T> Mul for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: Complex<T>) -> <Complex<T> as Mul>::Output

Performs the * operation. Read more
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impl<'a, 'b, T> MulAdd<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num + MulAdd<Output = T>,

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type Output = Complex<T>

The resulting type after applying the fused multiply-add.
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fn mul_add(self, other: &Complex<T>, add: &Complex<T>) -> Complex<T>

Performs the fused multiply-add operation.
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impl<T> MulAdd for Complex<T>
where T: Clone + Num + MulAdd<Output = T>,

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type Output = Complex<T>

The resulting type after applying the fused multiply-add.
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fn mul_add(self, other: Complex<T>, add: Complex<T>) -> Complex<T>

Performs the fused multiply-add operation.
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impl<'a, 'b, T> MulAddAssign<&'a Complex<T>, &'b Complex<T>> for Complex<T>

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

Performs the fused multiply-add operation.
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impl<T> MulAddAssign for Complex<T>

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

Performs the fused multiply-add operation.
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impl<'a, T> MulAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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

Performs the *= operation. Read more
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impl<'a, T> MulAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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

Performs the *= operation. Read more
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impl<T> MulAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn mul_assign(&mut self, other: T)

Performs the *= operation. Read more
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impl<T> MulAssign for Complex<T>
where T: Clone + NumAssign,

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

Performs the *= operation. Read more
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impl<'a, T> Neg for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn neg(self) -> <&'a Complex<T> as Neg>::Output

Performs the unary - operation. Read more
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impl<T> Neg for Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn neg(self) -> <Complex<T> as Neg>::Output

Performs the unary - operation. Read more
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impl<T> Num for Complex<T>
where T: Num + Clone,

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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

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

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

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

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

Formats the value using the given formatter.
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impl<T> One for Complex<T>
where T: Clone + Num,

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fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1. Read more
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fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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impl<T> PartialEq for Complex<T>
where T: PartialEq,

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

This method tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<'a, 'b, T> Pow<&'b Complex<T>> for &'a Complex<T>
where T: Float,

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type Output = Complex<T>

The result after applying the operator.
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fn pow( self, _: &'b Complex<T> ) -> <&'a Complex<T> as Pow<&'b Complex<T>>>::Output

Returns self to the power rhs. Read more
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impl<'b, T> Pow<&'b Complex<T>> for Complex<T>
where T: Float,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, _: &'b Complex<T>) -> <Complex<T> as Pow<&'b Complex<T>>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b f32> for &'a Complex<T>
where T: Float, f32: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, _: &f32) -> <&'a Complex<T> as Pow<&'b f32>>::Output

Returns self to the power rhs. Read more
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impl<'b, T> Pow<&'b f32> for Complex<T>
where T: Float, f32: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, _: &f32) -> <Complex<T> as Pow<&'b f32>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b f64> for &'a Complex<T>
where T: Float, f64: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, _: &f64) -> <&'a Complex<T> as Pow<&'b f64>>::Output

Returns self to the power rhs. Read more
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impl<'b, T> Pow<&'b f64> for Complex<T>
where T: Float, f64: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, _: &f64) -> <Complex<T> as Pow<&'b f64>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i128> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i128) -> <&'a Complex<T> as Pow<&'b i128>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i16> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i16) -> <&'a Complex<T> as Pow<&'b i16>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i32> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i32) -> <&'a Complex<T> as Pow<&'b i32>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i64> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i64) -> <&'a Complex<T> as Pow<&'b i64>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i8> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i8) -> <&'a Complex<T> as Pow<&'b i8>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b isize> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &isize) -> <&'a Complex<T> as Pow<&'b isize>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u128> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u128) -> <&'a Complex<T> as Pow<&'b u128>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u16> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u16) -> <&'a Complex<T> as Pow<&'b u16>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u32> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u32) -> <&'a Complex<T> as Pow<&'b u32>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u64> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u64) -> <&'a Complex<T> as Pow<&'b u64>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u8> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u8) -> <&'a Complex<T> as Pow<&'b u8>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b usize> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &usize) -> <&'a Complex<T> as Pow<&'b usize>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<Complex<T>> for &'a Complex<T>
where T: Float,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: Complex<T>) -> <&'a Complex<T> as Pow<Complex<T>>>::Output

Returns self to the power rhs. Read more
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impl<T> Pow<Complex<T>> for Complex<T>
where T: Float,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: Complex<T>) -> <Complex<T> as Pow<Complex<T>>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<f32> for &'a Complex<T>
where T: Float, f32: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: f32) -> <&'a Complex<T> as Pow<f32>>::Output

Returns self to the power rhs. Read more
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impl<T> Pow<f32> for Complex<T>
where T: Float, f32: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: f32) -> <Complex<T> as Pow<f32>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<f64> for &'a Complex<T>
where T: Float, f64: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: f64) -> <&'a Complex<T> as Pow<f64>>::Output

Returns self to the power rhs. Read more
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impl<T> Pow<f64> for Complex<T>
where T: Float, f64: Into<T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: f64) -> <Complex<T> as Pow<f64>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i128> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i128) -> <&'a Complex<T> as Pow<i128>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i16> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i16) -> <&'a Complex<T> as Pow<i16>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i32> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i32) -> <&'a Complex<T> as Pow<i32>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i64> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i64) -> <&'a Complex<T> as Pow<i64>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i8> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i8) -> <&'a Complex<T> as Pow<i8>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<isize> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: isize) -> <&'a Complex<T> as Pow<isize>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u128> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u128) -> <&'a Complex<T> as Pow<u128>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u16> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u16) -> <&'a Complex<T> as Pow<u16>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u32> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u32) -> <&'a Complex<T> as Pow<u32>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u64> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u64) -> <&'a Complex<T> as Pow<u64>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u8> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u8) -> <&'a Complex<T> as Pow<u8>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<usize> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: usize) -> <&'a Complex<T> as Pow<usize>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Product<&'a Complex<T>> for Complex<T>
where T: 'a + Num + Clone,

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fn product<I>(iter: I) -> Complex<T>
where I: Iterator<Item = &'a Complex<T>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.
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impl<T> Product for Complex<T>
where T: Num + Clone,

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fn product<I>(iter: I) -> Complex<T>
where I: Iterator<Item = Complex<T>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.
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impl<'a, 'b, T> Rem<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem( self, other: &Complex<T> ) -> <&'a Complex<T> as Rem<&'b Complex<T>>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: &Complex<T>) -> <Complex<T> as Rem<&'a Complex<T>>>::Output

Performs the % operation. Read more
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impl<'a, 'b, T> Rem<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: &T) -> <&'b Complex<T> as Rem<&'a T>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: &T) -> <Complex<T> as Rem<&'a T>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: Complex<T>) -> <&'a Complex<T> as Rem<Complex<T>>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: T) -> <&'a Complex<T> as Rem<T>>::Output

Performs the % operation. Read more
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impl<T> Rem<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: T) -> <Complex<T> as Rem<T>>::Output

Performs the % operation. Read more
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impl<T> Rem for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, modulus: Complex<T>) -> <Complex<T> as Rem>::Output

Performs the % operation. Read more
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impl<'a, T> RemAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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

Performs the %= operation. Read more
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impl<'a, T> RemAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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

Performs the %= operation. Read more
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impl<T> RemAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn rem_assign(&mut self, other: T)

Performs the %= operation. Read more
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impl<T> RemAssign for Complex<T>
where T: Clone + NumAssign,

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

Performs the %= operation. Read more
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impl<'a, 'b, T> Sub<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub( self, other: &Complex<T> ) -> <&'a Complex<T> as Sub<&'b Complex<T>>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: &Complex<T>) -> <Complex<T> as Sub<&'a Complex<T>>>::Output

Performs the - operation. Read more
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impl<'a, 'b, T> Sub<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: &T) -> <&'b Complex<T> as Sub<&'a T>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: &T) -> <Complex<T> as Sub<&'a T>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: Complex<T>) -> <&'a Complex<T> as Sub<Complex<T>>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: T) -> <&'a Complex<T> as Sub<T>>::Output

Performs the - operation. Read more
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impl<T> Sub<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: T) -> <Complex<T> as Sub<T>>::Output

Performs the - operation. Read more
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impl<T> Sub for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: Complex<T>) -> <Complex<T> as Sub>::Output

Performs the - operation. Read more
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impl<'a, T> SubAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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

Performs the -= operation. Read more
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impl<'a, T> SubAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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

Performs the -= operation. Read more
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impl<T> SubAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn sub_assign(&mut self, other: T)

Performs the -= operation. Read more
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impl<T> SubAssign for Complex<T>
where T: Clone + NumAssign,

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

Performs the -= operation. Read more
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impl<'a, T> Sum<&'a Complex<T>> for Complex<T>
where T: 'a + Num + Clone,

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fn sum<I>(iter: I) -> Complex<T>
where I: Iterator<Item = &'a Complex<T>>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.
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impl<T> Sum for Complex<T>
where T: Num + Clone,

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fn sum<I>(iter: I) -> Complex<T>
where I: Iterator<Item = Complex<T>>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.
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impl<T> ToPrimitive for Complex<T>
where T: ToPrimitive + Num,

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

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

Formats the value using the given formatter.
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impl<T> UpperHex for Complex<T>
where T: UpperHex + Num + PartialOrd + Clone,

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

Formats the value using the given formatter.
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impl<T> Zero for Complex<T>
where T: Clone + Num,

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fn zero() -> Complex<T>

Returns the additive identity element of Self, 0. Read more
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fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.
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fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.
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impl<T> Copy for Complex<T>
where T: Copy,

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

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impl<T> StructuralPartialEq for Complex<T>

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

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

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

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

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

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T> NumAssign for T
where T: Num + NumAssignOps,

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impl<T, Rhs> NumAssignOps<Rhs> for T
where T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>,

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impl<T> NumAssignRef for T
where T: NumAssign + for<'r> NumAssignOps<&'r T>,

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impl<T, Rhs, Output> NumOps<Rhs, Output> for T
where T: Sub<Rhs, Output = Output> + Mul<Rhs, Output = Output> + Div<Rhs, Output = Output> + Add<Rhs, Output = Output> + Rem<Rhs, Output = Output>,

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impl<T> NumRef for T
where T: Num + for<'r> NumOps<&'r T>,

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impl<T, Base> RefNum<Base> for T
where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base>,