Struct num::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 cis(phase: T) -> Complex<T>

Create a new Complex with a given phase: exp(i * phase). See cis (mathematics).

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: Float + FloatConst, 

pub fn exp2(self) -> Complex<T>

Computes 2^(self).

pub fn log2(self) -> Complex<T>

Computes the principal value of log base 2 of self.

pub fn log10(self) -> Complex<T>

Computes the principal value of log base 10 of self.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

fn add_assign(&mut self, other: T)

Performs the += operation.

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

fn as_(self) -> U

Convert a value to another, using the as operator.

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

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

Formats the value using the given formatter.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T> ComplexFloat for Complex<T> where
    T: Float + FloatConst, 

type Real = T

The type used to represent the real coefficients of this complex number.

fn re(self) -> <Complex<T> as ComplexFloat>::Real

Returns the real part of the number.

fn im(self) -> <Complex<T> as ComplexFloat>::Real

Returns the imaginary part of the number.

fn abs(self) -> <Complex<T> as ComplexFloat>::Real

Returns the absolute value of the number. See also Complex::norm

fn recip(self) -> Complex<T>

Take the reciprocal (inverse) of a number, 1/x. See also Complex::finv.

fn l1_norm(&self) -> <Complex<T> as ComplexFloat>::Real

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

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

fn arg(self) -> <Complex<T> as ComplexFloat>::Real

Computes the argument of the number.

fn powc(
    self,
    exp: Complex<<Complex<T> as ComplexFloat>::Real>
) -> Complex<<Complex<T> as ComplexFloat>::Real>

Raises self to a complex power.

fn exp2(self) -> Complex<T>

Returns 2^(self).

fn log(self, base: <Complex<T> as ComplexFloat>::Real) -> Complex<T>

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

fn log2(self) -> Complex<T>

Returns the base 2 logarithm of the number.

fn log10(self) -> Complex<T>

Returns the base 10 logarithm of the number.

fn powf(self, f: <Complex<T> as ComplexFloat>::Real) -> Complex<T>

Raises self to a real power.

fn sqrt(self) -> Complex<T>

Take the square root of a number.

fn cbrt(self) -> Complex<T>

Take the cubic root of a number.

fn exp(self) -> Complex<T>

Returns e^(self), (the exponential function).

fn expf(self, base: <Complex<T> as ComplexFloat>::Real) -> Complex<T>

Returns base^(self).

fn ln(self) -> Complex<T>

Returns the natural logarithm of the number.

fn sin(self) -> Complex<T>

Computes the sine of a number (in radians).

fn cos(self) -> Complex<T>

Computes the cosine of a number (in radians).

fn tan(self) -> Complex<T>

Computes the tangent of a number (in radians).

fn asin(self) -> Complex<T>

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

fn acos(self) -> Complex<T>

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

fn atan(self) -> Complex<T>

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn sinh(self) -> Complex<T>

Hyperbolic sine function.

fn cosh(self) -> Complex<T>

Hyperbolic cosine function.

fn tanh(self) -> Complex<T>

Hyperbolic tangent function.

fn asinh(self) -> Complex<T>

Inverse hyperbolic sine function.

fn acosh(self) -> Complex<T>

Inverse hyperbolic cosine function.

fn atanh(self) -> Complex<T>

Inverse hyperbolic tangent function.

fn powi(self, n: i32) -> Complex<T>

Raises self to a signed integer power.

fn conj(self) -> Complex<T>

Computes the complex conjugate of the number.

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

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

Formats the value using the given formatter.

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

fn default() -> Complex<T>

Returns the “default value” for a type.

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

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

Formats the value using the given formatter.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

fn div_assign(&mut self, other: T)

Performs the /= operation.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The associated error which can be returned from parsing.

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

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

Feeds this value into the given Hasher.

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

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.

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.

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, 

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, 

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.

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.

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.

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.

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

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'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.

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.

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>, 

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>, 

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, 

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn mul_assign(&mut self, other: T)

Performs the *= operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the unary - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the unary - operation.

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

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

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

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

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

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

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

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

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

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

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

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

Formats the value using the given formatter.

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

fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

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

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

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

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

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

This method tests for !=.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

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

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

fn pow(self, &f32) -> <&'a 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.

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.

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.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i16> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i32> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i64> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b i8> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u128> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u16> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u32> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u64> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, 'b, T> Pow<&'b u8> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

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.

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

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

fn pow(self, exp: f32) -> <&'a 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.

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.

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.

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

Returns self to the power rhs.

impl<'a, T> Pow<i16> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<i32> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<i64> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<i8> for &'a Complex<T> where
    T: Clone + Num + Neg<Output = T>, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<u128> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<u16> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<u32> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<u64> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

impl<'a, T> Pow<u8> for &'a Complex<T> where
    T: Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

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

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, 

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

fn rem_assign(&mut self, other: T)

Performs the %= operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

fn sub_assign(&mut self, other: T)

Performs the -= operation.

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

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

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, 

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, 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Formats the value using the given formatter.

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

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

Formats the value using the given formatter.

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

fn zero() -> Complex<T>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

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

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

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

impl<T> StructuralEq for Complex<T>

impl<T> StructuralPartialEq for Complex<T>