Struct nalgebra::Complex

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

A complex number in Cartesian form.

Representation and Foreign Function Interface Compatibility

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

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

Examples

Example of extern function declaration.

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

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

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Methods

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

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

Create a new Complex

pub fn i() -> Complex<T>

Returns imaginary unit

pub fn norm_sqr(&self) -> T

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

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

Multiplies self by the scalar t.

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

Divides self by the scalar t.

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

Raises self to an unsigned integer power.

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

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

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

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

Returns 1/self

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: Clone + Float, 

pub fn norm(&self) -> T

Calculate |self|

pub fn arg(&self) -> T

Calculate the principal Arg of self.

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

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

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

Convert a polar representation into a complex number.

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

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

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

Computes the principal value of natural logarithm of self.

This function has one branch cut:

• (-∞, 0], continuous from above.

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

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

Computes the principal value of the square root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

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

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

type Output = Complex<T>

The resulting type after applying the % operator.

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

Performs the % operation.

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

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

Formats the value using the given formatter.

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

fn div_assign(&mut self, other: T)

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<T> DivAssign<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> Serialize for Complex<T> where
    T: Serialize, 

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

Serialize this value into the given Serde serializer.

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

fn mul_add_assign(&mut self, other: Complex<T>, add: 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 + MulAddAssign<T, T> + NumAssign, 

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

Performs the fused multiply-add operation.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<'a, 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<'de, T> Deserialize<'de> for Complex<T> where
    T: Deserialize<'de> + Num + Clone, 

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

Deserialize this value from the given Serde deserializer.

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

fn zero() -> Complex<T>

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

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<'a, T> SubAssign<&'a 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> 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> Default for Complex<T> where
    T: Default, 

fn default() -> Complex<T>

Returns the "default value" for a type.

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> Eq for Complex<T> where
    T: Eq, 

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

fn hash<__HT>(&self, state: &mut __HT) where
    __HT: 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<'a, T> Inv for &'a Complex<T> where
    T: Neg<Output = T> + Clone + Num, 

type Output = Complex<T>

The result after applying the operator.

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

Returns the multiplicative inverse of self.

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

type Output = Complex<T>

The result after applying the operator.

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

Returns the multiplicative inverse of self.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Complex<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

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

Performs the %= operation.

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

fn rem_assign(&mut self, other: T)

Performs the %= operation.

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

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

The associated error which can be returned from parsing.

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

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

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

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

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

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

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

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, 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<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<'a, 'b, T> Pow<&'b i128> for &'a Complex<T> where
    T: Neg<Output = T> + Clone + Num, 

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

type Output = Complex<T>

The result after applying the operator.

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

Returns self to the power rhs.

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

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

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

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

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

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<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<'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, T> Pow<i128> for &'a Complex<T> where
    T: Neg<Output = T> + Clone + Num, 

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

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

Formats the value using the given formatter.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the unary - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the unary - operation.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Complex<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div<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<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.

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

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

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

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

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

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: Clone + Num, 

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

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

Formats the value using the given formatter.

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

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

Converts the value of self to a usize.

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

Converts the value of self to an isize.

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

Converts the value of self to an u8.

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

Converts the value of self to an u16.

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

Converts the value of self to an u32.

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

Converts the value of self to an u64.

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

Converts the value of self to an i8.

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

Converts the value of self to an i16.

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

Converts the value of self to an i32.

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

Converts the value of self to an i64.

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

Converts the value of self to an u128.

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

Converts the value of self to an i128.

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

Converts the value of self to an f32.

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

Converts the value of self to an f64.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Complex<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

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

type Output = Complex<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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 + MulAdd<T, T, Output = T> + Num, 

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

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, 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<N> NormedSpace for Complex<N> where
    N: RealField, 

type RealField = N

The result of the norm (not necessarily the same same as the field used by this vector space).

type ComplexField = N

The field of this space must be this complex number.

fn norm_squared(&self) -> <Complex<N> as NormedSpace>::RealField

The squared norm of this vector.

fn norm(&self) -> <Complex<N> as NormedSpace>::RealField

The norm of this vector.

fn normalize(&self) -> Complex<N>

Returns a normalized version of this vector.

fn normalize_mut(&mut self) -> <Complex<N> as NormedSpace>::RealField

Normalizes this vector in-place and returns its norm.

fn try_normalize(
    &self,
    eps: <Complex<N> as NormedSpace>::RealField
) -> Option<Complex<N>>

Returns a normalized version of this vector unless its norm as smaller or equal to eps.

fn try_normalize_mut(
    &mut self,
    eps: <Complex<N> as NormedSpace>::RealField
) -> Option<<Complex<N> as NormedSpace>::RealField>

Normalizes this vector in-place or does nothing if its norm is smaller or equal to eps.

impl<N> Module for Complex<N> where
    N: RingCommutative + NumAssign, 

type Ring = N

The underlying scalar field.

impl<N> AbstractMonoid<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq, 

Checks whether operating with the identity element is a no-op for the given argument.

impl<N> AbstractMonoid<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq, 

Checks whether operating with the identity element is a no-op for the given argument.

impl<N> ComplexField for Complex<N> where
    N: RealField, 

type RealField = N

Type of the coefficients of a complex number.

fn from_real(re: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Builds a pure-real complex number from the given value.

fn real(self) -> <Complex<N> as ComplexField>::RealField

The real part of this complex number.

fn imaginary(self) -> <Complex<N> as ComplexField>::RealField

The imaginary part of this complex number.

fn argument(self) -> <Complex<N> as ComplexField>::RealField

The argument of this complex number.

fn modulus(self) -> <Complex<N> as ComplexField>::RealField

The modulus of this complex number.

fn modulus_squared(self) -> <Complex<N> as ComplexField>::RealField

The squared modulus of this complex number.

fn norm1(self) -> <Complex<N> as ComplexField>::RealField

The sum of the absolute value of this complex number's real and imaginary part.

fn recip(self) -> Complex<N>

fn conjugate(self) -> Complex<N>

fn scale(self, factor: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Multiplies this complex number by factor.

fn unscale(self, factor: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Multiplies this complex number by factor.

fn floor(self) -> Complex<N>

fn ceil(self) -> Complex<N>

fn round(self) -> Complex<N>

fn trunc(self) -> Complex<N>

fn fract(self) -> Complex<N>

fn mul_add(self, a: Complex<N>, b: Complex<N>) -> Complex<N>

fn abs(self) -> <Complex<N> as ComplexField>::RealField

The absolute value of this complex number: self / self.signum().

fn exp2(self) -> Complex<N>

fn exp_m1(self) -> Complex<N>

fn ln_1p(self) -> Complex<N>

fn log2(self) -> Complex<N>

fn log10(self) -> Complex<N>

fn cbrt(self) -> Complex<N>

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

fn is_finite(&self) -> bool

fn exp(self) -> Complex<N>

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

fn ln(self) -> Complex<N>

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.

fn sqrt(self) -> Complex<N>

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.

fn try_sqrt(self) -> Option<Complex<N>>

fn hypot(self, b: Complex<N>) -> <Complex<N> as ComplexField>::RealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

fn powf(self, exp: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Raises self to a floating point power.

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

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

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

Raises self to a complex power.

fn sin(self) -> Complex<N>

Computes the sine of self.

fn cos(self) -> Complex<N>

Computes the cosine of self.

fn sin_cos(self) -> (Complex<N>, Complex<N>)

fn tan(self) -> Complex<N>

Computes the tangent of self.

fn asin(self) -> Complex<N>

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.

fn acos(self) -> Complex<N>

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.

fn atan(self) -> Complex<N>

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.

fn sinh(self) -> Complex<N>

Computes the hyperbolic sine of self.

fn cosh(self) -> Complex<N>

Computes the hyperbolic cosine of self.

fn sinh_cosh(self) -> (Complex<N>, Complex<N>)

fn tanh(self) -> Complex<N>

Computes the hyperbolic tangent of self.

fn asinh(self) -> Complex<N>

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.

fn acosh(self) -> Complex<N>

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)) < ∞.

fn atanh(self) -> Complex<N>

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.

fn to_polar(self) -> (Self::RealField, Self::RealField)

The polar form of this complex number: (modulus, arg)

fn to_exp(self) -> (Self::RealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})

fn signum(self) -> Self

The exponential part of this complex number: self / self.modulus()

fn sinc(self) -> Self

Cardinal sine

fn sinhc(self) -> Self

fn cosc(self) -> Self

Cardinal cos

fn coshc(self) -> Self

impl<N> TwoSidedInverse<Multiplicative> for Complex<N> where
    N: ClosedNeg + Clone + Num, 

fn two_sided_inverse(&self) -> Complex<N>

Returns the two_sided_inverse of self, relative to the operator O.

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<N> TwoSidedInverse<Additive> for Complex<N> where
    N: TwoSidedInverse<Additive>, 

fn two_sided_inverse(&self) -> Complex<N>

Returns the two_sided_inverse of self, relative to the operator O.

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<N> AbstractMagma<Multiplicative> for Complex<N> where
    N: Clone + Num, 

fn operate(&self, lhs: &Complex<N>) -> Complex<N>

Performs an operation.

fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N> AbstractMagma<Additive> for Complex<N> where
    N: AbstractMagma<Additive>, 

fn operate(&self, lhs: &Complex<N>) -> Complex<N>

Performs an operation.

fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N> MeetSemilattice for Complex<N> where
    N: MeetSemilattice, 

fn meet(&self, other: &Complex<N>) -> Complex<N>

Returns the meet (aka. infimum) of two values.

impl<N> AbstractGroupAbelian<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications.

fn prop_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the operator is commutative for the given argument tuple.

impl<N> AbstractGroupAbelian<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications.

fn prop_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the operator is commutative for the given argument tuple.

impl<N1, N2> SubsetOf<Complex<N2>> for Complex<N1> where
    N2: SupersetOf<N1>, 

fn to_superset(&self) -> Complex<N2>

The inclusion map: converts self to the equivalent element of its superset.

unsafe fn from_superset_unchecked(element: &Complex<N2>) -> Complex<N1>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn is_in_subset(c: &Complex<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N> AbstractField<Additive, Multiplicative> for Complex<N> where
    N: ClosedNeg + AbstractField<Additive, Multiplicative> + Clone + Num, 

impl<N> Identity<Additive> for Complex<N> where
    N: Identity<Additive>, 

fn identity() -> Complex<N>

The identity element.

fn id(O) -> Self

Specific identity.

impl<N> Identity<Multiplicative> for Complex<N> where
    N: Clone + Num, 

fn identity() -> Complex<N>

The identity element.

fn id(O) -> Self

Specific identity.

impl<N> AbstractLoop<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

impl<N> AbstractLoop<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

impl<N> JoinSemilattice for Complex<N> where
    N: JoinSemilattice, 

fn join(&self, other: &Complex<N>) -> Complex<N>

Returns the join (aka. supremum) of two values.

impl<N> VectorSpace for Complex<N> where
    N: Field + NumAssign, 

type Field = N

The underlying scalar field.

impl<N> AbstractRingCommutative<Additive, Multiplicative> for Complex<N> where
    N: ClosedNeg + AbstractRingCommutative<Additive, Multiplicative> + Clone + Num, 

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the multiplication operator is commutative for the given argument tuple. Approximate equality is used for verifications.

fn prop_mul_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the multiplication operator is commutative for the given argument tuple.

impl<N> AbstractSemigroup<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.

impl<N> AbstractSemigroup<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.

impl<N> AbstractRing<Additive, Multiplicative> for Complex<N> where
    N: ClosedNeg + AbstractRing<Additive, Multiplicative> + Clone + Num, 

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the multiplication and addition operators are distributive for the given argument tuple. Approximate equality is used for verifications.

fn prop_mul_and_add_are_distributive(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if the multiplication and addition operators are distributive for the given argument tuple.

impl<N> AbstractGroup<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

impl<N> AbstractGroup<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

impl<N> AbstractModule<Additive, Additive, Multiplicative> for Complex<N> where
    N: ClosedNeg + AbstractRingCommutative<Additive, Multiplicative> + Num, 

type AbstractRing = N

The underlying scalar field.

fn multiply_by(&self, r: N) -> Complex<N>

Multiplies an element of the ring with an element of the module.

impl<N> AbstractQuasigroup<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.

impl<N> AbstractQuasigroup<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.