Trait ComplexField 

pub trait ComplexField:
    NumAssign
    + Clone
    + Copy
    + Send
    + Sync
    + Debug
    + Zero
    + One
    + Neg<Output = Self>
    + 'static {
    type Real: Float + NumAssign + FromPrimitive + ToPrimitive + Send + Sync + Debug + 'static;

    // Required methods
    fn conj(&self) -> Self;
    fn norm_sqr(&self) -> Self::Real;
    fn from_real(r: Self::Real) -> Self;
    fn from_re_im(re: Self::Real, im: Self::Real) -> Self;
    fn re(&self) -> Self::Real;
    fn im(&self) -> Self::Real;
    fn inv(&self) -> Self;
    fn sqrt(&self) -> Self;

    // Provided methods
    fn norm(&self) -> Self::Real { ... }
    fn is_zero_approx(&self, tol: Self::Real) -> bool { ... }
    fn vec_dot(x: &Array1<Self>, y: &Array1<Self>) -> Self { ... }
    fn vec_norm_sqr(x: &Array1<Self>) -> Self::Real { ... }
    fn vec_axpy(alpha: Self, x: &Array1<Self>, y: &mut Array1<Self>) { ... }
    fn vec_scale(x: &mut Array1<Self>, alpha: Self) { ... }
}

Trait for scalar types that can be used in linear algebra operations.

This trait abstracts over real and complex number types, providing a unified interface for operations like conjugation, norm computation, and conversion from real values.

Required Associated Types

type Real: Float + NumAssign + FromPrimitive + ToPrimitive + Send + Sync + Debug + 'static

The real number type underlying this field

Required Methods

fn conj(&self) -> Self

Complex conjugate

fn norm_sqr(&self) -> Self::Real

Squared magnitude |z|²

fn from_real(r: Self::Real) -> Self

Create from a real value

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

Create from real and imaginary parts

fn re(&self) -> Self::Real

Real part

fn im(&self) -> Self::Real

Imaginary part

fn inv(&self) -> Self

Multiplicative inverse (1/z)

fn sqrt(&self) -> Self

Square root

Provided Methods

fn norm(&self) -> Self::Real

Magnitude |z|

fn is_zero_approx(&self, tol: Self::Real) -> bool

Check if this is approximately zero

fn vec_dot(x: &Array1<Self>, y: &Array1<Self>) -> Self

Inner product: Σ conj(x_i) * y_i

fn vec_norm_sqr(x: &Array1<Self>) -> Self::Real

Squared vector norm: Σ |x_i|²

fn vec_axpy(alpha: Self, x: &Array1<Self>, y: &mut Array1<Self>)

AXPY: y += α * x

fn vec_scale(x: &mut Array1<Self>, alpha: Self)

In-place scale: x *= α

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl ComplexField for f32

type Real = f32

fn conj(&self) -> Self

fn norm_sqr(&self) -> f32

fn from_real(r: f32) -> Self

fn from_re_im(re: f32, _im: f32) -> Self

fn re(&self) -> f32

fn im(&self) -> f32

fn inv(&self) -> Self

fn sqrt(&self) -> Self

fn vec_dot(x: &Array1<Self>, y: &Array1<Self>) -> Self

fn vec_norm_sqr(x: &Array1<Self>) -> Self

fn vec_axpy(alpha: Self, x: &Array1<Self>, y: &mut Array1<Self>)

fn vec_scale(x: &mut Array1<Self>, alpha: Self)

impl ComplexField for f64

type Real = f64

fn conj(&self) -> Self

fn norm_sqr(&self) -> f64

fn from_real(r: f64) -> Self

fn from_re_im(re: f64, _im: f64) -> Self

fn re(&self) -> f64

fn im(&self) -> f64

fn inv(&self) -> Self

fn sqrt(&self) -> Self

fn vec_dot(x: &Array1<Self>, y: &Array1<Self>) -> Self

fn vec_norm_sqr(x: &Array1<Self>) -> Self

fn vec_axpy(alpha: Self, x: &Array1<Self>, y: &mut Array1<Self>)

fn vec_scale(x: &mut Array1<Self>, alpha: Self)

impl ComplexField for Complex32

type Real = f32

fn conj(&self) -> Self

fn norm_sqr(&self) -> f32

fn from_real(r: f32) -> Self

fn from_re_im(re: f32, im: f32) -> Self

fn re(&self) -> f32

fn im(&self) -> f32

fn inv(&self) -> Self

fn sqrt(&self) -> Self

impl ComplexField for Complex64

type Real = f64

fn conj(&self) -> Self

fn norm_sqr(&self) -> f64

fn from_real(r: f64) -> Self

fn from_re_im(re: f64, im: f64) -> Self

fn re(&self) -> f64

fn im(&self) -> f64

fn inv(&self) -> Self

fn sqrt(&self) -> Self

Implementors