Struct HardySpaceAtom 

pub struct HardySpaceAtom {
    pub lo: usize,
    pub hi: usize,
    pub values: Vec<f64>,
}

A discrete H¹ atom checker over a finite signal.

An H¹-atom supported on an interval I = [lo, hi] satisfies:

1. supp(a) ⊆ I
2. ‖a‖_{L∞} ≤ 1/|I|
3. ∫ a = 0 (zero-mean / cancellation condition)

Fields

lo: usize

Support interval [lo, hi] (index range).

hi: usize

Support interval hi (inclusive).

values: Vec<f64>

Values of the atom (length = full signal length; zero outside support).

Implementations

impl HardySpaceAtom

pub fn new(lo: usize, hi: usize, values: Vec<f64>) -> Self

Create a new H¹ atom with the given support and values.

pub fn support_length(&self) -> usize

Length of the support interval.

pub fn has_compact_support(&self) -> bool

Check that all values outside [lo, hi] are zero.

pub fn satisfies_linfty_bound(&self) -> bool

Check the L∞ bound: ‖a‖_{L∞} ≤ 1/|I|.

pub fn has_zero_mean(&self) -> bool

Check the cancellation condition: ∫ a = 0.

pub fn is_valid_atom(&self) -> bool

Verify all three H¹ atom conditions.

pub fn canonical(signal_len: usize, lo: usize, hi: usize) -> Self

Construct a canonical atom supported on [lo, hi] with +1/|I| on first half, -1/|I| on second half (or ±1/|I| for |I|=1 → zero atom).

Trait Implementations

impl Clone for HardySpaceAtom

fn clone(&self) -> HardySpaceAtom

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for HardySpaceAtom

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

Formats the value using the given formatter.