Find roots

CHANGELOG.md

@@ -5,7 +5,23 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.1.0/),
 and this project follows [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
-## [Unreleased]
+## [0.4.0] - 2026-06-07
+
+### Added
+
+- `fit_dyn_from_fn` and `fit_coeffs_dyn` for dynamic Chebyshev fitting on normalized `[-1, 1]`.
+- `ChebySeriesDyn<f64>::roots`, `roots_with`, and `tail_norm` for root finding on the unit interval via Durand–Kerner iteration with Chebyshev-node fallback for tangency roots.
+- `ChebySeriesDyn<f64>::shifted_constant` and `shift_constant_in_place` for level-set root searches without refitting.
+- `ChebySeriesDynOn<f64, X>::roots` and `roots_with` for domain-mapped roots.
+- `RootOptions` with `validated` and `effective` tolerance sanitization.
+- Comprehensive root-finding tests and benchmarks.
+
+### Changed
+
+- Shared fixed-size and dynamic coefficient fitting through a single `accumulate_coeffs` helper.
+- Root finding converts Chebyshev coefficients to power basis, applies Durand–Kerner, verifies residuals against `RootOptions::zero_tol`, and falls back to node scanning when needed.
+- Constant and identically-zero series return an empty root list.
+- `fit_dyn_from_fn(0, …)` now produces a single-coefficient constant fit.
 
 ## [0.3.0] - 2026-05-18
 
@@ -28,21 +44,6 @@ and this project follows [Semantic Versioning](https://semver.org/spec/v2.0.0.ht
   `quadrature`, `spectral`, `serde`, `binary`, `fast-dct`, and `full`.
 - The README, examples, benchmarks, and CI configuration were rewritten to
   match the new crate architecture and release posture.
-
-### Added
-
-- `#![forbid(unsafe_code)]` at the crate root.
-- Core abstractions:
-  `Domain<X>`, `ChebyError`, `ChebySeries<T, N>`, `ChebySeriesDyn<T>`,
-  `ChebySeriesOn<T, X, N>`, `ChebyScalar`, `ChebyTime`,
-  `DifferentiateWith<X>`, and `IntegrateWith<X>`.
-- Chebyshev basis functions in `core::basis`:
-  `t(n, x)` and `u(n, x)`.
-- First-class node families in `core::nodes`:
-  `Roots`, `Extrema`, `Lobatto`, `Gauss`, and `GaussLobatto`.
-- Stable Clenshaw evaluation in `core::eval`:
-  `evaluate`, `evaluate_both`, and the compatibility `evaluate_derivative`.
-- Approximation APIs in `approx`:
   coefficient fitting, function fitting on normalized and typed domains,
   barycentric interpolation, adaptive fitting with `FitReport`, coefficient-tail
   error estimates, and a Remez-style minimax interface.

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "cheby"
-version = "0.3.0"
+version = "0.4.0"
 edition = "2021"
 authors = ["VPRamon <vallespuigramon@gmail.com>"]
 description = "Unit-safe Chebyshev approximation and spectral numerics for Rust."

README.md

@@ -136,6 +136,40 @@ and segments apply the chain rule and use `qtty` multiplication/division so:
 - velocity over time integrates to position,
 - angular rate over time integrates to angle.
 
+## Root finding
+
+With the `alloc` feature, dynamic series support real root finding on the
+normalized interval `[-1, 1]`:
+
+```rust
+use cheby::{fit_dyn_from_fn, RootOptions};
+
+let series = fit_dyn_from_fn(12, |tau| tau * tau - 0.25).unwrap();
+let roots = series.roots(); // normalized tau in [-1, 1]
+
+let opts = RootOptions {
+    zero_tol: 1e-10,
+    ..RootOptions::default()
+};
+let refined = series.roots_with(opts);
+```
+
+The solver converts the Chebyshev expansion to a monic power polynomial and finds
+roots with a **Durand–Kerner** iteration, then verifies residuals on `[-1, 1]`.
+When the primary pass misses roots (tangency, repeated roots), a fallback
+Chebyshev-node scan uses Brent refinement and minimum search. Constant or
+identically-zero series return an empty root list.
+
+[`RootOptions`] controls bracket width (`unit_tol`), residual tolerance
+(`zero_tol`), and deduplication (`dedupe_eps`). Root finding is intended for
+moderate polynomial degrees and can be less stable than Clenshaw evaluation at
+high degree.
+
+Map normalized roots to a physical domain with [`ChebySeriesDynOn::roots`],
+or shift the constant term without refitting via
+[`ChebySeriesDyn::shifted_constant`] when searching multiple level sets of the
+same fitted signal.
+
 ## Quadrature
 
 `quadrature` contains Chebyshev-related rules only: Clenshaw-Curtis style