Struct birli::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 imaginary unit

pub fn norm_sqr(&self) -> T

Returns the square of the norm (since T doesn’t necessarily have a sqrt function), i.e. re^2 + im^2.

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

Multiplies self by the scalar t.

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

Divides self by the scalar t.

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: Float, 

pub fn norm(self) -> T

Calculate |self|

pub fn arg(self) -> T

Calculate the principal Arg of self.

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

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

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

Convert a polar representation into a complex number.

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

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

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

Computes the principal value of natural logarithm of self.

This function has one branch cut:

• (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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

Computes the principal value of the square root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

pub fn 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.

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

Raises self to a floating point power.

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

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

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

Raises self to a complex power.

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

Raises a floating point number to the complex power self.

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

Computes the sine of self.

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

Computes the cosine of self.

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

Computes the tangent of self.

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

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

• (-∞i, -i], continuous from the left.
• [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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

Computes the hyperbolic sine of self.

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

Computes the hyperbolic cosine of self.

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

Computes the hyperbolic tangent of self.

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

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

• (-∞i, -i), continuous from the left.
• (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

• (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

• (-∞, -1], continuous from above.
• [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

pub fn 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);

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);

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

Trait Implementations

impl<T> AbsDiffEq<Complex<T>> for Complex<T> where
    T: AbsDiffEq<T>,
    <T as AbsDiffEq<T>>::Epsilon: Clone, 

type Epsilon = <T as AbsDiffEq<T>>::Epsilon

Used for specifying relative comparisons.

pub fn default_epsilon() -> <T as AbsDiffEq<T>>::Epsilon

The default tolerance to use when testing values that are close together.

pub fn abs_diff_eq(
    &self,
    other: &Complex<T>,
    epsilon: <T as AbsDiffEq<T>>::Epsilon
) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of [AbsDiffEq::abs_diff_eq].

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.

pub fn add(
    self,
    other: &Complex<T>
) -> <Complex<T> as Add<&'a Complex<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.

pub fn add(self, other: &T) -> <Complex<T> as Add<&'a 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.

pub fn add(self, other: &T) -> <&'b Complex<T> as Add<&'a T>>::Output

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

pub fn add(
    self,
    other: &Complex<T>
) -> <&'a Complex<T> as Add<&'b Complex<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.

pub fn add(
    self,
    other: Complex<T>
) -> <&'a Complex<T> as Add<Complex<T>>>::Output

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

pub 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.

pub fn add(self, other: T) -> <Complex<T> as Add<T>>::Output

Performs the + operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

pub fn as_(self) -> U

Convert a value to another, using the as operator.

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

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

Formats the value using the given formatter.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

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

pub fn default() -> Complex<T>

Returns the “default value” for a type.

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

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

Formats the value using the given formatter.

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.

pub 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.

pub 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.

pub fn div(self, other: &T) -> <Complex<T> as Div<&'a T>>::Output

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

pub fn div(
    self,
    other: &Complex<T>
) -> <&'a Complex<T> as Div<&'b Complex<T>>>::Output

Performs the / operation.

impl<F> Div<Complex<F>> for Jones<F> where
    F: Float, 

type Output = Jones<F>

The resulting type after applying the / operator.

pub fn div(self, rhs: Complex<F>) -> Jones<F>

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.

pub fn div(
    self,
    other: Complex<T>
) -> <&'a Complex<T> as Div<Complex<T>>>::Output

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

pub 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.

pub fn div(self, other: T) -> <Complex<T> as Div<T>>::Output

Performs the / operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<F> DivAssign<Complex<F>> for Jones<F> where
    F: Float + NumAssign, 

pub fn div_assign(&mut self, rhs: Complex<F>)

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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, 

pub 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, 

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns the multiplicative inverse of self.

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.

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

Returns the multiplicative inverse of self.

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

pub 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<T> + Clone, 

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

Formats the value using the given formatter.

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.

pub fn mul(
    self,
    other: &Complex<T>
) -> <Complex<T> as Mul<&'a Complex<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.

pub fn mul(self, other: &T) -> <Complex<T> as Mul<&'a 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.

pub fn mul(self, other: &T) -> <&'b Complex<T> as Mul<&'a T>>::Output

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

pub fn mul(
    self,
    other: &Complex<T>
) -> <&'a Complex<T> as Mul<&'b Complex<T>>>::Output

Performs the * operation.

impl<F> Mul<Complex<F>> for Jones<F> where
    F: Float, 

type Output = Jones<F>

The resulting type after applying the * operator.

pub fn mul(self, rhs: Complex<F>) -> Jones<F>

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.

pub fn mul(
    self,
    other: Complex<T>
) -> <&'a Complex<T> as Mul<Complex<T>>>::Output

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

pub 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.

pub fn mul(self, other: T) -> <Complex<T> as Mul<T>>::Output

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation.

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

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation.

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

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

Performs the fused multiply-add operation.

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

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

Performs the fused multiply-add operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<F> MulAssign<Complex<F>> for Jones<F> where
    F: Float + NumAssign, 

pub fn mul_assign(&mut self, rhs: Complex<F>)

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= 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.

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

Performs the unary - operation.

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.

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

Performs the unary - operation.

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

pub 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

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

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

pub 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<T> + Clone, 

pub 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, 

pub fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1.

pub fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

pub fn set_one(&mut self)

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

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

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

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

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

This method tests for !=.

impl<'b, T> Pow<&'b Complex<T>> for Complex<T> where
    T: Float, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b Complex<T>> for &'a Complex<T> where
    T: Float, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b f32> for &'a Complex<T> where
    T: Float,
    f32: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, &f32) -> <&'a Complex<T> as Pow<&'b f32>>::Output

Returns self to the power rhs.

impl<'b, T> Pow<&'b f32> for Complex<T> where
    T: Float,
    f32: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, &f32) -> <Complex<T> as Pow<&'b f32>>::Output

Returns self to the power rhs.

impl<'b, T> Pow<&'b f64> for Complex<T> where
    T: Float,
    f64: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, &f64) -> <Complex<T> as Pow<&'b f64>>::Output

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b f64> for &'a Complex<T> where
    T: Float,
    f64: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, &f64) -> <&'a Complex<T> as Pow<&'b f64>>::Output

Returns self to the power rhs.

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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, exp: Complex<T>) -> <Complex<T> as Pow<Complex<T>>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<Complex<T>> for &'a Complex<T> where
    T: Float, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<f32> for &'a Complex<T> where
    T: Float,
    f32: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, exp: f32) -> <&'a Complex<T> as Pow<f32>>::Output

Returns self to the power rhs.

impl<T> Pow<f32> for Complex<T> where
    T: Float,
    f32: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, exp: f32) -> <Complex<T> as Pow<f32>>::Output

Returns self to the power rhs.

impl<T> Pow<f64> for Complex<T> where
    T: Float,
    f64: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, exp: f64) -> <Complex<T> as Pow<f64>>::Output

Returns self to the power rhs.

impl<'a, T> Pow<f64> for &'a Complex<T> where
    T: Float,
    f64: Into<T>, 

type Output = Complex<T>

The result after applying the operator.

pub fn pow(self, exp: f64) -> <&'a Complex<T> as Pow<f64>>::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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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, 

pub 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.

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

pub 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.

impl<T> RelativeEq<Complex<T>> for Complex<T> where
    T: RelativeEq<T>,
    <T as AbsDiffEq<T>>::Epsilon: Clone, 

pub fn default_max_relative() -> <T as AbsDiffEq<T>>::Epsilon

The default relative tolerance for testing values that are far-apart.

pub fn relative_eq(
    &self,
    other: &Complex<T>,
    epsilon: <T as AbsDiffEq<T>>::Epsilon,
    max_relative: <T as AbsDiffEq<T>>::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of [RelativeEq::relative_eq].

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.

pub 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.

pub 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.

pub fn rem(self, other: &T) -> <Complex<T> as Rem<&'a T>>::Output

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

pub fn rem(
    self,
    other: &Complex<T>
) -> <&'a Complex<T> as Rem<&'b Complex<T>>>::Output

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

pub fn rem(self, modulus: Complex<T>) -> <Complex<T> as Rem<Complex<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.

pub fn rem(
    self,
    other: Complex<T>
) -> <&'a Complex<T> as Rem<Complex<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.

pub fn rem(self, other: T) -> <Complex<T> as Rem<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.

pub fn rem(self, other: T) -> <&'a Complex<T> as Rem<T>>::Output

Performs the % operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

pub 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.

pub 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.

pub fn sub(self, other: &T) -> <Complex<T> as Sub<&'a T>>::Output

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

pub fn sub(
    self,
    other: &Complex<T>
) -> <&'a Complex<T> as Sub<&'b Complex<T>>>::Output

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

pub fn sub(self, other: Complex<T>) -> <Complex<T> as Sub<Complex<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.

pub 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.

pub 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.

pub fn sub(self, other: T) -> <Complex<T> as Sub<T>>::Output

Performs the - operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

pub 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.

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

pub 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.

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

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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.

pub 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> UlpsEq<Complex<T>> for Complex<T> where
    T: UlpsEq<T>,
    <T as AbsDiffEq<T>>::Epsilon: Clone, 

pub fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

pub fn ulps_eq(
    &self,
    other: &Complex<T>,
    epsilon: <T as AbsDiffEq<T>>::Epsilon,
    max_ulps: u32
) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of [UlpsEq::ulps_eq].

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

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

Formats the value using the given formatter.

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

pub 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, 

pub fn zero() -> Complex<T>

Returns the additive identity element of Self, 0.

pub fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

pub 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> StructuralEq for Complex<T>

impl<T> StructuralPartialEq for Complex<T>