Struct Complex 

pub struct Complex<T: RealField> {
    pub re: T,
    pub im: T,
}

Represents a complex number with real and imaginary parts.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, satisfying the equation i^2 = -1.

The Complex struct is generic over a type T that implements RealField, allowing it to work with different floating-point precisions (e.g., f32 or f64).

Fields

• re: The real part of the complex number.
• im: The imaginary part of the complex number.

Examples

use deep_causality_num::Complex;

let c1 = Complex::new(1.0, 2.0); // Represents 1.0 + 2.0i
let c2 = Complex { re: 3.0, im: -1.0 }; // Represents 3.0 - 1.0i

assert_eq!(c1.re, 1.0);
assert_eq!(c2.im, -1.0);

Fields

re: T

im: T

Implementations

impl<T: RealField> Complex<T>

pub fn norm(&self) -> T

Computes the norm (magnitude or absolute value) of the complex number.

pub fn arg(&self) -> T

Computes the argument (phase angle) of the complex number in radians.

pub fn powi(&self, n: i32) -> Self

Raises to an integer power.

pub fn powf(&self, n: T) -> Self

Raises a to a real (scalar) power.

pub fn powc(&self, n: Self) -> Self

Raises to a complex power.

pub fn sqrt(self) -> Self

Computes the principal square root of a complex number.

pub fn exp(self) -> Self

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

pub fn ln(self) -> Self

Computes the natural logarithm of a complex number.

pub fn sin(self) -> Self

Computes the sine of a complex number.

pub fn cos(self) -> Self

Computes the cosine of a complex number.

pub fn tan(self) -> Self

Computes the tangent of a complex number.

pub fn sinh(self) -> Self

Computes the hyperbolic sine of a complex number.

pub fn cosh(self) -> Self

Computes the hyperbolic cosine of a complex number.

pub fn tanh(self) -> Self

Computes the hyperbolic tangent of a complex number.

impl<T: RealField> Complex<T>

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

Creates a new complex number from its real and imaginary parts.

pub fn from_real(re: T) -> Self

Creates a new complex number from a real number.

impl<T: RealField> Complex<T>

pub fn re(&self) -> T

Returns the real part of the complex number.

pub fn im(&self) -> T

Returns the imaginary part of the complex number.

Trait Implementations

impl<T: RealField> Add<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, rhs: T) -> Self

Performs the + operation.

impl<T: RealField> Add for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl<T: RealField> AddAssign<T> for Complex<T>

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<T: RealField> AddAssign for Complex<T>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

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

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

fn as_(self) -> U

Convert a value to another, using the as operator.

impl<T: Clone + RealField> Clone for Complex<T>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: RealField> ComplexField<T> for Complex<T>

fn real(&self) -> T

Returns the real part of the complex number.

fn imag(&self) -> T

Returns the imaginary part of the complex number.

fn conjugate(&self) -> Self

Returns the complex conjugate.

fn norm_sqr(&self) -> T

Returns the squared modulus (norm squared).

fn norm(&self) -> T

Returns the modulus (absolute value).

fn arg(&self) -> T

Returns the argument (phase angle) in radians.

fn from_re_im(re: T, im: T) -> Self

Constructs a complex number from real and imaginary parts.

fn from_polar(r: T, theta: T) -> Self

Constructs a complex number from polar form.

fn i() -> Self

Returns the imaginary unit i.

fn is_real(&self) -> bool

Returns true if the imaginary part is zero.

fn is_imaginary(&self) -> bool

Returns true if the real part is zero.

impl<T> ConstOne for Complex<T>

where T: RealField + ConstOne + ConstZero,

const ONE: Self

The multiplicative identity element of Self, 1.

impl<T> ConstZero for Complex<T>

where T: RealField + ConstZero,

const ZERO: Self

The additive identity element of Self, 0.

impl<T: Debug + RealField> Debug for Complex<T>

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

Formats the value using the given formatter.

impl<T: Default + RealField> Default for Complex<T>

fn default() -> Complex<T>

Returns the “default value” for a type.

impl<T: RealField + Display> Display for Complex<T>

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

Formats the value using the given formatter.

impl<T: RealField> Div<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Self

Performs the / operation.

impl<T: RealField> Div for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self

Performs the / operation.

impl<T: RealField> DivAssign<T> for Complex<T>

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<T: RealField> DivAssign for Complex<T>

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<T: RealField> DivisionAlgebra<T> for Complex<T>

fn conjugate(&self) -> Self

Computes the conjugate of an element.

fn norm_sqr(&self) -> T

Computes the squared norm of an element.

fn inverse(&self) -> Self

Computes the multiplicative inverse of an element.

impl<T: RealField + FromPrimitive> FromPrimitive for Complex<T>

fn from_isize(n: isize) -> Option<Self>

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_i8(n: i8) -> Option<Self>

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<Self>

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<Self>

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<Self>

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_i128(n: i128) -> Option<Self>

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_usize(n: usize) -> Option<Self>

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_u8(n: u8) -> Option<Self>

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<Self>

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<Self>

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<Self>

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_u128(n: u128) -> Option<Self>

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_f32(n: f32) -> Option<Self>

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<Self>

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: RealField> Mul<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self

Performs the * operation.

impl<T: RealField> Mul for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl<T: RealField> MulAssign<T> for Complex<T>

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T: RealField> MulAssign for Complex<T>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<T: RealField> Neg for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<T: RealField + NumCast> NumCast for Complex<T>

fn from<N: ToPrimitive>(n: N) -> Option<Self>

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> One for Complex<T>

where T: RealField,

fn one() -> Self

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: RealField + Ord> Ord for Complex<T>

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T: PartialEq + RealField> PartialEq for Complex<T>

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

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

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

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

impl<T: RealField> PartialOrd for Complex<T>

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T: RealField> Product for Complex<T>

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

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

impl<T: RealField> Rotation<T> for Complex<T>

fn rotate_x(&self, _angle: T) -> Self

Rotation around the X-axis. Quaternions: Axis i. Quantum: Pauli X.

fn rotate_y(&self, _angle: T) -> Self

Rotation around the Y-axis. Quaternions: Axis j. Quantum: Pauli Y.

fn rotate_z(&self, angle: T) -> Self

Rotation around the Z-axis (Phase). Quaternions: Axis k. Quantum: Pauli Z.

fn global_phase(&self, angle: T) -> Self

Global Phase Shift. $P(\phi) = e^{i\phi}$.

impl<T: RealField> Sub<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, rhs: T) -> Self

Performs the - operation.

impl<T: RealField> Sub for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl<T: RealField> SubAssign<T> for Complex<T>

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl<T: RealField> SubAssign for Complex<T>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<T: RealField> Sum for Complex<T>

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

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

impl<T: RealField + ToPrimitive> ToPrimitive for Complex<T>

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_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_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_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_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_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_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> Zero for Complex<T>

where T: RealField,

fn zero() -> Self

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: RealField> AbelianGroup for Complex<T>

impl<T: RealField> Associative for Complex<T>

impl<T: RealField> Commutative for Complex<T>

impl<T: Copy + RealField> Copy for Complex<T>

impl<T: RealField> Distributive for Complex<T>

impl<T: RealField> Eq for Complex<T>

impl<T: RealField> StructuralPartialEq for Complex<T>