Struct AdaptiveGrid1D 

pub struct AdaptiveGrid1D { /* private fields */ }

Adaptive grid generator using recursive bisection.

This generator recursively subdivides intervals in 1D, refining only where the underlying function exhibits high variance (error exceeds tolerance).

Algorithm:

1. Start with an interval [a, b]
2. Evaluate the function at a, midpoint m, and b
3. Compute the linear interpolation at m from endpoints
4. If |f(m) - interpolated(m)| > tolerance, bisect into [a, m] and [m, b] and recurse
5. Otherwise, mark the interval as sufficiently smooth

This guarantees adaptive refinement: dense grids form only near sharp features, while smooth regions remain coarse.

Implementations

impl AdaptiveGrid1D

pub fn new(start: f64, end: f64, tolerance: f64, max_depth: usize) -> Self

Create a new adaptive 1D grid generator.

Arguments

• start - Left boundary
• end - Right boundary
• tolerance - Error threshold for bisection
• max_depth - Maximum recursion depth (prevents pathological refinement)

pub fn generate<F>(&self, f: F) -> AdaptiveSegments

where F: Fn(f64) -> f64,

Generate an adaptive grid by evaluating f at points determined by tolerance.

Returns a strictly increasing list of grid points.