Struct HilbertSpace 

pub struct HilbertSpace {
    pub dx: f64,
    pub n: usize,
}

A discrete Hilbert space over a uniform grid with spacing dx.

Provides inner product, norm, orthonormalization (Gram-Schmidt), and projection operations.

Fields

dx: f64

Grid spacing for integration approximation.

n: usize

Number of grid points.

Implementations

impl HilbertSpace

pub fn new(n: usize, dx: f64) -> Self

Create a new HilbertSpace with n grid points and spacing dx.

pub fn inner_product(&self, f: &[f64], g: &[f64]) -> f64

Compute the L² inner product ⟨f, g⟩.

pub fn norm(&self, f: &[f64]) -> f64

Compute the L² norm ‖f‖.

pub fn orthonormalize(&self, basis: &[Vec<f64>]) -> Vec<Vec<f64>>

Orthonormalize a set of vectors using the modified Gram-Schmidt process.

Returns the orthonormal set in the same order; linearly dependent vectors become zero.

pub fn project(&self, f: &[f64], basis: &[Vec<f64>]) -> Vec<f64>

Project f onto the subspace spanned by basis.

basis does not need to be orthonormal; a fresh Gram-Schmidt step is performed internally. Returns the projected vector (same length as f).

pub fn distance(&self, f: &[f64], g: &[f64]) -> f64

Compute the distance between two functions f and g.

pub fn are_orthogonal(&self, f: &[f64], g: &[f64], tol: f64) -> bool

Check if f and g are orthogonal (inner product < tol).

pub fn normalize(&self, f: &[f64]) -> Vec<f64>

Normalize f in-place to unit L² norm. Returns a normalized copy.

Trait Implementations

impl Clone for HilbertSpace

fn clone(&self) -> HilbertSpace

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for HilbertSpace

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

Formats the value using the given formatter.