Crate semiflow

Expand description

§semiflow

Status: beta (0.15.0-beta). The API is stabilising toward 1.0; minor versions may still make breaking changes. Bug reports and feedback are welcome.

SemiFlow solves evolution equations ∂ₜu = Lu (heat, diffusion, Schrödinger, graph and manifold PDEs, …) by Chernoff approximation of operator semigroups: no matrix exponentials, no linear solves, a flat memory footprint. The core is a no_std + alloc Rust library with 3 runtime dependencies (num-traits, libm, num-complex); the same engines are available from Python, JavaScript/WebAssembly and C.

The method evaluates e^{tL}f by iterating an explicit step operator S(τ): (S(t/n))ⁿ f → e^{tL} f as n → ∞. Each step is an explicit stencil over a Vec-backed grid with reused scratch buffers, so steady-state evolution does not allocate.

Mathematical foundation: Theorem 6 of I. D. Remizov (2025), Vladikavkaz Math. J. 27(4), 124–135 (doi:10.46698/a3908-1212-5385-q).

Honest performance note. The primary measured advantage is memory frugality: a flat ~3 MB working set across the 1D/2D/3D families versus 50–418 MB for heavy frameworks. Wall-clock speed is not a general strength — for matched-accuracy PDE solving SemiFlow is slower than adaptive ODE solvers and spectral methods, and parallelism pays off only on large 3D grids. Two measured niches: tail-latency-sensitive pricing (Diffusion4thChernoff ≈ 41 ns p99.9 per tick) and L1-resident low-rank carriers (TtChernoff, ReverseChernoff). Treat memory and latency as measured properties of the concrete grid types, not guarantees of the traits. The 2026-10 overhaul (docs/perf/overhaul-v0_15.md) made the grid engines 2.6–39× faster bit-for-bit, the stiff Chebyshev graph action O(√(λt)) instead of O(λt) (559× on issue #16), ETDRK4 2.1× and the general Taylor action 2.1× faster; Richardson extrapolation (richardson=) raises any engine’s order by levels − 1. Head-to-head comparisons quoted in the user guide predate it.

§Install

[dependencies]
semiflow = "0.15.0-beta"

MSRV: Rust 1.81. The default build is #![no_std] + alloc with AVX2/NEON kernels (feature simd, scalar lanes elsewhere); std is needed only for parallel. See below.

§Quickstart

Solve ∂ₜu = ½·∂ₓₓu from u₀(x) = e^{-x²} to t = 1 and compare with the closed-form solution u(1,x) = 3^{-1/2}·e^{-x²/3}:

use semiflow::{ChernoffSemigroup, DiffusionChernoff, Grid1D, GridFn1D, State};

let grid = Grid1D::new(-10.0, 10.0, 1000).expect("valid grid");
let u0 = GridFn1D::from_fn(grid, |x| (-x * x).exp());

// L = a(x)·∂²ₓ with a ≡ ½ (a' = a'' = 0), bound ‖a‖ = ½.
let diffusion = DiffusionChernoff::new(|_| 0.5_f64, |_| 0.0, |_| 0.0, 0.5, grid);
let semigroup = ChernoffSemigroup::new(diffusion, 100).expect("n >= 1");
let u1 = semigroup.evolve(1.0, &u0).expect("evolve");

let exact = GridFn1D::from_fn(grid, |x| (-x * x / 3.0).exp() / 3.0_f64.sqrt());
let mut err = u1.clone();
err.axpy(-1.0, &exact);
assert!(err.norm_sup() < 1e-5, "sup-norm error {}", err.norm_sup());

More: Quickstart, User Guide and the runnable examples (cargo run -p semiflow --example heat_2d_demo).

§`no_std`

[dependencies]
semiflow = "0.15.0-beta"   # no_std + alloc, SIMD kernels

The crate is #![no_std] by default and needs only alloc; the std feature is needed only for parallel. What that means in practice:

Your binary provides a #[global_allocator] and a #[panic_handler], as for any no_std + alloc program (a std program already has both).
The target needs pointer-sized atomics (the engines share coefficient closures through alloc::sync::Arc): Cortex-M3/M4/M7/M33, RISC-V with the a extension, x86_64-unknown-none and similar work; thumbv6m does not.
SemiflowError implements Debug, Display and core::error::Error (the same trait as std::error::Error) in every build.
f32/f64 transcendentals come from the pure-Rust libm in every build, and the SIMD kernels use the same lane arithmetic with or without intrinsics, so std, no_std, simd and non-simd builds give bit-identical results on every CPU.
simd works without std (the intrinsics come from core::arch); parallel requires std.

This is verified on every pull request, not just type-checked:

CI job	What it proves
`no-std`	the default and the featureless build for the host, `thumbv7em-none-eabihf`, `thumbv7m-none-eabi`, `riscv32imac-unknown-none-elf`, and at MSRV 1.81
`no-std-test`	the full `semiflow` test suite passes in the default (`no_std`) configuration
`no-std-libm`	`semiflow-nostd-check` — closed-form oracle checks plus per-scenario output digests: the default `no_std` build (the job fails if anything enables `num-traits/std`), the `std` build and its AVX2 lanes must all produce the committed bits
`no-std-libm-neon`	the same digests from the `std` build on aarch64 (NEON lanes)
`no-std-qemu`	the same checks and digests as a bare-metal `#![no_main]` binary on Cortex-M3 (soft float) and Cortex-M4F (hard float) under QEMU — see `nostd-qemu`

§Feature flags

Feature	Default	Effect
`simd`	yes	AVX2 (x86_64) / NEON (aarch64) kernels via `core::arch`, scalar lanes elsewhere. Works in `no_std`. Results are bit-identical to a non-`simd` build.
`std`	no	Links `std`. Needed only by `parallel`; math is `libm` either way, so results do not change. Without it the crate is `no_std + alloc` (the default).
`parallel`	no	Multi-threaded `apply` for 1D kernels and 2D/3D compositions via `std::thread::scope`; bit-identical across thread counts. Implies `std`; not for `wasm32`.
`linear-interp`	no	Enables `InterpKind::Linear` grid sampling (otherwise it returns `SemiflowError::Unsupported`).
`s3-poc`	no	Experimental S³ evolvers with a proven-boundary API (ADR-0169).
`slow-tests`	no	Internal: enables the long convergence gates. Not needed by users.
`diff-scipy`	no	Internal: SciPy differential test (needs Python). Not needed by users.
`tracking-alloc`	no	Internal: allocation counting in the `latency_tail` example. Not needed by users.

§Engine catalogue

§1D Chernoff functions

Type	Order	Description
`DiffusionChernoff`	2	5-point formula for `a(x)∂²_x`
`Diffusion4thChernoff`	4	4th-order spatial diffusion
`Diffusion6thChernoff`	6	6th-order spatial diffusion
`Diffusion4thZeta4Chernoff`	4	ζ⁴ Richardson
`Diffusion6thZeta6Chernoff`	6	ζ⁶ nested-Richardson
`Diffusion8thZeta8Chernoff`	8	ζ⁸ Chebyshev M=64
`DiffusionExpmvChernoff<F>`	—	Al-Mohy–Higham expmv action
`TruncatedExpDiffusionChernoff`	2	Truncated-exponential diffusion
`TruncatedExp4thDiffusionChernoff`	4	Truncated-exponential 4th-order
`DriftReactionChernoff`	exact	Characteristic-flow formula for `b(x)∂_x + c(x)`
`DriftReactionZeta4Chernoff`	4	ζ⁴ WITH drift via Richardson
`ShiftChernoff1D`	2	Formula (6) of Theorem 6, Remizov 2025

§Compositions

Type	Description
`StrangSplit<D, R>`	Strang 2nd-order splitting: `D(τ/2) ∘ R(τ) ∘ D(τ/2)`
`AxisLift<C>`	Lift a 1D `ChernoffFunction` to a 2D grid row or column

§2D tensor-product

Type	Description
`Strang2D<X, Y>`	Palindromic Strang: `Sx(τ/2) ∘ Sy(τ) ∘ Sx(τ/2)`, global order 2
`NonSeparable2DChernoff`	Non-separable isotropic 2D operator
`NonSeparable2DAnisotropicChernoff`	Non-separable anisotropic 2D operator

§3D tensor-product

Type	Description
`AxisLift3D<C>`	Lift a 1D `ChernoffFunction` to a 3D grid along `Axis::X/Y/Z`
`Strang3D<X, Y, Z>`	3D palindromic Strang

§Adaptive

Type	Description
`AdaptivePI<C>`	PI step-size controller wrapping any `ChernoffFunction`

§Boundary conditions

Type	Description
`BoundaryPolicy::Dirichlet { value }`	Fixed-value stencil BC
`BoundaryPolicy::Neumann`	Clamp-to-boundary stencil BC
`BoundaryPolicy::Robin { alpha, beta }`	Robin stencil BC
`BoundaryPolicy::OddReflect`	Odd-image stencil BC (used by `DirichletHeat2ndChernoff`)
`KillingChernoff<C, R, F>`	Operator-level Dirichlet via Feynman-Kac killing
`Killing2ndChernoff<C, K, F>`	Order-2 soft-killing `e^{-τκ/2}·C(τ)·e^{-τκ/2}`
`ReflectedHeatChernoff<C, R, F>`	Neumann via Walsh 1986 image method
`DirichletHeat2ndChernoff<C, R, F>`	Order-2 absorbing wall via odd-image method (math §21.9)
`ObstacleChernoff<C, O, F>`	Projective-splitting obstacle / variational-inequality evolver

§Resolvent and nonautonomous

Type	Description
`LaplaceChernoffResolvent<C, F>`	`(λI − A)⁻¹ g` via Gauss-Laguerre 32-pt quadrature — unique to Remizov
`HowlandLift<C, F>`	Nonautonomous Howland lift on `L²([0,T], X)`
`HdrSnapshot<F>`	NIST nearest-rank percentile library (`no_std + alloc`)

§Riemannian manifold

Type	Description
`ManifoldChernoff<M, F>`	Curvature-corrected Gaussian on `T_xM`; order 1 (base) or 2 (with R/12)
`Torus<F, D>`	Flat torus backend
`Sphere2<F>`	Round 2-sphere backend
`Hyperbolic2<F>`	Poincaré disk backend (also the SABR volatility manifold)
`FubiniStudyCp1`	Kähler CP¹ / Fubini-Study backend

§High-dimensional and sparse-grid

Type	Description
`AnisotropicShiftChernoffND<F, D>`	d-D Gaussian shift via Gauss-Hermite tensor quadrature
`AnisotropicShiftZeta2ND`	Order-2 ζ²-correction variant
`AnisotropicShiftAdaptiveQ`	Adaptive per-point GH quadrature (41% fewer nodes/axis)
`SmolyakGridND<F, const D>`	Smolyak sparse-grid backend for D ≥ 5

§Matrix-valued operators

Type	Description
`MatrixDiffusionChernoff<F, M>`	Coupled M-component 1D diffusion; Padé[13/13] expm
`MatrixDiffusionChernoff2D<F, M>`	Palindromic Strang 2D for M-component diffusion
`MatrixDiffusionChernoff3D<F, M>`	Same for 3D
`MatrixDiffusionChernoffComplex<F, M>`	Complex-valued Padé[13/13] coupled diffusion

§Quantum graphs

Type	Description
`QuantumGraphHeatChernoff<F>`	Heat on quantum graphs with Kirchhoff vertex condition
`QuantumSchrödingerChernoff<C>`	Complex Schrödinger on quantum graphs

§Reverse-mode AD

Type	Description
`ReverseChernoff<F>`	Reverse-mode AD over `(F_θ(τ))ⁿ u₀` via binomial checkpointing
`CheckpointSchedule`	`O(√n)` default schedule (Griewank-Walther)
`RegionMap`	DoF-aligned region partition enabling K>1 per-region parameter sensitivity

Scope: constant-a DiffusionChernoff<F> only. Multi-parameter (K>1) sensitivity via ReverseChernoff::with_region_map. Variable-coefficient kernels are deferred.

§Tensor-train carrier

Type	Description
`TtChernoff<F>`	TT-Chernoff evolver; storage `O(d·n·r²)`
`TtState<F>`	Tensor-train state `u(i₁,…,i_d) = G₁[i₁]·…·G_d[i_d]`
`VarCoefTt<F>`	Variable-coefficient TT carrier for separable diagonal `a_j(x_j)`

Scope: linear diagonal-A Gaussian class (TtChernoff); separable diagonal variable coefficients (VarCoefTt). Non-separable variable coefficients and off-diagonal A are research-track. VarCoefTt::new returns SemiflowError::VarCoefOutOfClass when inputs fall outside the separable diagonal class.

§Gridless / particle-ensemble

Type	Description
`GridlessChernoff<F, const D>`	Particle-ensemble Chernoff; implements `ChernoffFunction<F>`
`MeasureState<F, D>`	Particle-ensemble state; exposes `first_moment`, `variance`, `variance_per_axis` diagnostics (math §38.12)
`ParticleReduction`	Particle cap policy: `WeightedVoronoi { cap }` or `GaussianBackground`

§Schrödinger, graph and quantum-graph operators

Type	Description
`SchrödingerChernoffComplex` / `SchrodingerChernoff`	Schrödinger equation on a native complex (or real-pair) carrier
`GraphHeatChernoff`	Heat semigroup of a graph Laplacian
`GraphKrylovChernoff`, `graph_expmv_frechet`	Depth-independent `e^{−tL}·v` (Chebyshev / Lanczos) and its all-parameter Fréchet gradient (graded-mesh Duhamel quadrature: quadrature error independent of `λ_max·t`; f64 conditioning floor ≈ (r+n)·u·ρ̄t; `ImplicitEuler` path keeps its O(Δt) bias)
`QuantumGraphHeatChernoff` / `QuantumSchrödingerChernoff`	Metric graphs with Kirchhoff vertex conditions

§Conservative, stiff and semilinear problems

Type	Description
`ConservativeDiffusionChernoff`, `assemble_conservative_csr_1d`, `assemble_conservative_csr_nd`	Divergence-form `∂ₓ(k(x)∂ₓu)` with harmonic-mean faces (sharp material interfaces, optional contact resistance)
`MultilayerStack`, `multilayer_evolve`, `MassWeightedConservativeChernoff`	Stiff multilayer conduction in one depth-flat Krylov action
`SymmetricOperator`, `MassKOperator`, `EntrySensitivity`, `mass_lumped_evolve`	Externally assembled symmetric PSD sparse operators (FEM), the `(M, K)` problem without forming `M⁻¹K`, entry-wise gradients
`general_operator::GeneralOperator`	Possibly non-symmetric CSR operators via Taylor `expmv` or adaptive Arnoldi (`expmv_krylov`)
`SpdResolvent`, `SpdSolver`	`(λM + A)⁻¹b`: exact O(N) tridiagonal `LDLᵀ`, PCG with IC(0) or Jacobi; factor once, solve many (steady states, implicit steps)
`RationalKrylov`, `RationalKrylovChernoff`, `rational_krylov_expmv`	Shift-and-invert Krylov `e^{−tM⁻¹A}v` for very stiff SPD operators: solve count independent of `λ_max t`
`phi_action`, `phi_action_batched`, `phi_combination`, `Etdrk4`, `Nonlinearity`	Semilinear `∂ₜu = Lu + N(u)` by exponential time differencing (order 4)
`phi_combination_krylov`, `PhiSolver`, `KrylovPhiOptions`	Adaptive Arnoldi φ-actions for non-symmetric generators (`Etdrk4::with_phi_solver`): 33× fewer generator applications than Taylor at `τ‖G‖ = 4·10³`
`ReactionDiffusion`, `Species`, `ReactionSolver`, `RosenbrockOptions`	Multi-species `∂ₜu = D Δu + f(t, x, u)` by Strang splitting on any grid engine; stiff kinetics by adaptive L-stable Rosenbrock (ROS2)
`CrossDiffusion`	Constant `K×K` cross-diffusion matrix `D` by exact modal splitting (`D = PΛP⁻¹` verified; complex, negative or defective `D` rejected), with `ReactionDiffusion::with_cross_diffusion`
`SubordinatedChernoff`	Bochner–Phillips subordination of any engine
`HypoellipticChernoff`	Kolmogorov, Heisenberg and Engel (step-2/3 Carnot) operators

§Executor

ChernoffSemigroup<C, S> — wraps a ChernoffFunction and a step count; call .evolve(t, &f) to compute (S(t/n))ⁿ f.

§Examples

Example	Description
`heat_2d_demo.rs`	2D tensor heat equation (Gaussian oracle, convergence table)
`strang_advdiff_demo.rs`	Strang splitting for 1D advection-diffusion
`cev_european_call.rs`	CEV European option pricing vs Schroder (1989) closed form
`boundary_demo.rs`	Boundary policy showcase (Dirichlet, Neumann, periodic)
`latency_tail.rs`	HFT-style p99.9 latency benchmark
`resolvent_perf.rs`	`LaplaceChernoffResolvent` L-gate bench harness
`heston_pricer.rs`	Heston ρ→0 pricer via palindromic Strang
`sabr_pricer.rs`	SABR-on-H² via `ManifoldChernoff<Hyperbolic2>`
`graph_par_speedup.rs`	Parallel graph-heat speedup (`--features parallel`)
`rough_heston_pricer.rs`	Oracle-validated risk-neutral rough-Heston pricer (`--rate`/`--price`); honest scope: solver of a 4-factor Markov approximation, not validated vs true rough-Heston

cargo run -p semiflow --example heat_2d_demo

§Bindings

Language	Package	Notes
Rust	`semiflow` (docs.rs)	The full engine catalogue; `no_std + alloc`
Python	`semiflow-pde`	90 classes and the functions `version()`, `heisenberg_heat_kernel()`, `sample_gridfn2d()`, `edge_weight_grad()`, `edge_weight_grad_batched()`, `graph_expmv_frechet()`, `symmetric_op_expmv_frechet()`, `assemble_conservative_csr_1d()`, `mass_lumped_evolve()`, `phi_action()`, `phi_action_batched()`, `phi_combination()`, `shift1d_coeff_grad()`, `richardson_weights()`; NumPy in/out; complete `.pyi` stubs; see the PyPI page
JavaScript / WASM	`@semiflow/wasm`	Lite build on npm; the heavy-grid engines need a `--features full` build; see the npm page
C / C++	`semiflow-ffi`	`extern "C"` ABI with `catch_unwind` on every entry point; header `semiflow.h`

The bindings mirror the user-facing engines, not the internal composition types (AxisLift, StrangSplit, … are Rust-side building blocks). Variable coefficients cross the language boundary as pre-sampled arrays (evaluated in Rust, no call back into the host language during evolve); some classes also accept a host-language callback (e.g. Heat1D.with_a_function in Python, Heat1D.withAFunction in JS, smf_state_new_with_closure in C). The Bindings guide has side-by-side examples.

§Documentation

If you want to…	Read
Get started	Quickstart · User Guide · Install
Use a binding	Bindings guide (C / Python / WASM)
Browse the Rust API	docs.rs/semiflow
See worked examples	`crates/semiflow/examples`
Understand accuracy and stability policy	Precision policy · API stability
Read design decisions	Architecture Decision Records
Follow changes	CHANGELOG · GitHub Releases

§Accuracy and design

Every numerical claim is gated in CI against a closed-form or high-order reference oracle (convergence-order and sup-norm tests). Design principles: no_std + alloc core; 3 runtime dependencies; SIMD hot paths isolated to src/simd/ (AVX2 on x86_64, NEON on aarch64, scalar fallback elsewhere); bit-reproducible parallelism across thread counts; no unsafe in the math kernels. Builds with and without simd agree to rounding but not always bit for bit, so golden files are tied to one configuration.

§How to cite

If you use SemiFlow in academic work, cite both the software and the theorem.

@software{volkov2026semiflow,
  author  = {Volkov, Ilia},
  title   = {{SemiFlow}: {Chernoff} Approximation of Operator Semigroups},
  year    = {2026},
  version = {0.15.0-beta},
  doi     = {10.5281/zenodo.20837851},
  url     = {https://doi.org/10.5281/zenodo.20837851}
}

@article{Remizov2025,
  author  = {I. D. Remizov},
  title   = {Chernoff Approximations of the Solution of Linear ODE with Variable Coefficients},
  journal = {Vladikavkaz Math. J.},
  volume  = {27},
  number  = {4},
  pages   = {124--135},
  year    = {2025},
  doi     = {10.46698/a3908-1212-5385-q}
}

The concept DOI 10.5281/zenodo.20837851 always resolves to the latest version; CITATION.cff has the full entry (GitHub’s “Cite this repository” reads it).

§License

Dual-licensed under MIT or Apache-2.0, at your option.

§Author, contributing, security

SemiFlow is created and maintained by Ilia Volkov. See CONTRIBUTING.md and CODE_OF_CONDUCT.md. Report vulnerabilities privately as described in SECURITY.md — not in public issues.

Re-exports§

pub use crate::adaptive::AdaptiveOutcome;
pub use crate::adaptive::AdaptivePI;
pub use crate::adjoint::AdjointApply;
pub use crate::adjoint::AdjointChernoff;
pub use crate::adjoint_fp::AdjointFokkerPlanckChernoff;
pub use crate::adjoint_fp::Adjointable;
pub use crate::adjoint_fp::MeasureState;
pub use crate::approximation::assert_in_subspace;
pub use crate::approximation::ApproximationSubspace;
pub use crate::approximation::LadderRung;
pub use crate::axis::Axis;
pub use crate::axis::AxisLift;
pub use crate::carnot_complex::ComplexTripleJump;
pub use crate::carnot_complex::CplxGridFn5;
pub use crate::carnot_complex::GAMMA_STAR;
pub use crate::carnot_stepk::Filiform5X1;
pub use crate::carnot_stepk::Filiform5X2;
pub use crate::chernoff::ApplyChernoffExt;
pub use crate::chernoff::ChernoffFunction;
pub use crate::chernoff::ChernoffSemigroup;
pub use crate::chernoff::Evolver;
pub use crate::chernoff::Growth;
pub use crate::complex::SemiflowComplex;
pub use crate::conservative::steady_state_dirichlet_1d;
pub use crate::conservative::ConservativeDiffusionChernoff;
pub use crate::conservative_assemble::assemble_conservative_csr_1d;
pub use crate::conservative_assemble::assemble_conservative_csr_nd;
pub use crate::controller::ClassicalPI;
pub use crate::controller::H211bFilter;
pub use crate::controller::StepController;
pub use crate::cross_diffusion::CrossDiffusion;
pub use crate::diffusion::DiffusionChernoff;
pub use crate::diffusion4::Diffusion4thChernoff;
pub use crate::diffusion4_zeta4::Diffusion4thZeta4Chernoff;
pub use crate::diffusion6::Diffusion6thChernoff;
pub use crate::diffusion6_zeta6::Diffusion6thZeta6Chernoff;
pub use crate::diffusion8_zeta8::Diffusion8thZeta8Chernoff;
pub use crate::drift_reaction::DriftReactionChernoff;
pub use crate::drift_reaction_zeta4::DriftReactionZeta4Chernoff;
pub use crate::dual::Dual;
pub use crate::entry_sensitivity::EntrySensitivity;
pub use crate::error::SemiflowError;
pub use crate::etdrk4::Etdrk4;
pub use crate::expmv::DiffusionExpmvChernoff;
pub use crate::float::SemiflowFloat;
pub use crate::generator_action::CsrGenerator;
pub use crate::generator_action::DivFormGenerator;
pub use crate::generator_action::GeneratorAction;
pub use crate::generator_action::NegLaplacianGenerator;
pub use crate::graph::Graph;
pub use crate::graph::Laplacian;
pub use crate::graph::LaplacianKind;
pub use crate::graph_adjoint_presampled::fill_abscissa_times;
pub use crate::graph_adjoint_presampled::PreSampledLaplacianSeq;
pub use crate::graph_adjoint_presampled::PreSampledMagnusAdj;
pub use crate::graph_adjoint_presampled::PreSampledVarCoefAdj;
pub use crate::graph_frechet::graph_expmv_frechet;
pub use crate::graph_frechet_mesh::graph_expmv_frechet_plan;
pub use crate::graph_frechet_mesh::FrechetPlan;
pub use crate::graph_heat::GraphHeatChernoff;
pub use crate::graph_heat4::GraphHeat4thChernoff;
pub use crate::graph_heat6::GraphHeat6thChernoff;
pub use crate::graph_krylov::dense_graph_expmv_ref;
pub use crate::graph_krylov::graph_expmv_krylov;
pub use crate::graph_krylov::graph_expmv_matvec_count;
pub use crate::graph_krylov::GraphKrylovChernoff;
pub use crate::graph_krylov::KrylovPath;
pub use crate::graph_krylov::MAX_DENSE_N;
pub use crate::graph_sensitivity::adjoint_state_gradient;
pub use crate::graph_sensitivity::apply_edge_weight_deriv;
pub use crate::graph_sensitivity::magnus_step_jvp_into;
pub use crate::graph_sensitivity::EdgeWeightSensitivity;
pub use crate::graph_sensitivity::GeneratorSensitivity;
pub use crate::graph_sensitivity::NodeTimescaleSensitivity;
pub use crate::graph_signal::CsrRowIter;
pub use crate::graph_signal::GraphSignal;
pub use crate::graph_traj::GraphTraj;
pub use crate::graph_traj::SegmentWeightFn;
pub use crate::graph_traj::MAX_GRAPH_TRAJ_SEGMENTS;
pub use crate::graph_var_coef::VarCoefGraphHeatChernoff;
pub use crate::grid::BoundaryPolicy;
pub use crate::grid::Grid1D;
pub use crate::grid::InterpKind;
pub use crate::grid::OobPolicy;
pub use crate::grid2d::Grid2D;
pub use crate::grid3d::Grid3D;
pub use crate::grid_fn::GridFn1D;
pub use crate::grid_fn2d::GridFn2D;
pub use crate::grid_fn3d::GridFn3D;
pub use crate::grid_nd::GridFnND;
pub use crate::grid_nd::GridND;
pub use crate::gridless::GridlessChernoff;
pub use crate::gridless::ParticleReduction;
pub use crate::hdr::HdrSnapshot;
pub use crate::heisenberg_kernel::heisenberg_heat_kernel;
pub use crate::hormander::HeisenbergGroup;
pub use crate::hormander::HeisenbergX;
pub use crate::hormander::HeisenbergY;
pub use crate::hormander::HypoellipticChernoff;
pub use crate::hormander::KolmogorovDiffusionX1;
pub use crate::hormander::KolmogorovDriftX0;
pub use crate::hormander::KolmogorovPhaseSpace;
pub use crate::hormander::VectorField;
pub use crate::hormander_engel::EngelX1;
pub use crate::hormander_engel::EngelX2;
pub use crate::howland::HowlandLift;
pub use crate::howland::HowlandState;
pub use crate::howland::TimedChernoffFunction;
pub use crate::killed_dirichlet::KilledDirichletChernoff;
pub use crate::killing::BallRegion;
pub use crate::killing::BoxRegion;
pub use crate::killing::KillingChernoff;
pub use crate::killing::KillingRegion;
pub use crate::killing_order2::DirichletHeat2ndChernoff;
pub use crate::killing_soft::ClosureKillingRate;
pub use crate::killing_soft::Killing2ndChernoff;
pub use crate::killing_soft::KillingRate;
pub use crate::magnus6_graph::MagnusGraphHeat6thChernoff;
pub use crate::magnus_graph::LaplacianAtTime;
pub use crate::magnus_graph::MagnusGraphHeatChernoff;
pub use crate::manifold::BoundedGeometryManifold;
pub use crate::manifold::Hyperbolic2;
pub use crate::manifold::Sphere2;
pub use crate::manifold::Torus;
pub use crate::manifold_chernoff::ManifoldChernoff;
pub use crate::manifold_kahler::FubiniStudyCp1;
pub use crate::mass_operator::dense_massk_expmv_ref;
pub use crate::mass_operator::mass_lumped_evolve;
pub use crate::mass_operator::MassKOperator;
pub use crate::mass_operator::TriangularFactor;
pub use crate::matrix_2d3d::MatrixDiffusionChernoff2D;
pub use crate::matrix_2d3d::MatrixDiffusionChernoff3D;
pub use crate::matrix_2d3d::MatrixGridFn2D;
pub use crate::matrix_2d3d::MatrixGridFn3D;
pub use crate::matrix_system::MatrixDiffusionChernoff;
pub use crate::matrix_system::MatrixGridFn1D;
pub use crate::matrix_system_complex::MatrixDiffusionChernoffComplex;
pub use crate::matrix_system_complex::MatrixGridFnComplex1D;
pub use crate::multilayer::multilayer_evolve;
pub use crate::multilayer::Layer;
pub use crate::multilayer::MassWeightedConservativeChernoff;
pub use crate::multilayer::MultilayerStack;
pub use crate::nonlinearity::AllenCahn;
pub use crate::nonlinearity::Nonlinearity;
pub use crate::nonlinearity::NonlinearityDiff;
pub use crate::nonseparable2d::NonSeparable2DChernoff;
pub use crate::nonseparable2d_aniso::NonSeparable2DAnisotropicChernoff;
pub use crate::nonseparable_mixed::NonSeparableMixedChernoff;
pub use crate::obstacle::ClosureObstacle;
pub use crate::obstacle::ConstantObstacle;
pub use crate::obstacle::Obstacle;
pub use crate::obstacle::ObstacleChernoff;
pub use crate::obstacle_nd::ObstacleChernoffND;
pub use crate::phi_action::dense_phi_aug_ref;
pub use crate::phi_action::phi_action;
pub use crate::phi_action::phi_action_batched;
pub use crate::phi_action::phi_combination;
pub use crate::phi_action::phi_cost_probe;
pub use crate::phi_action::PHI_MAX;
pub use crate::phi_krylov::expmv_krylov;
pub use crate::phi_krylov::phi_combination_krylov;
pub use crate::phi_krylov::KrylovPhiOptions;
pub use crate::phi_krylov::KrylovPhiReport;
pub use crate::phi_krylov::PhiSolver;
pub use crate::phi_shift::phi_sweep_probe;
pub use crate::point_eval::sample_gridfn2d;
pub use crate::point_eval::PointEval;
pub use crate::quantum_graph::KirchhoffVertex;
pub use crate::quantum_graph::QuantumGraph;
pub use crate::quantum_graph::QuantumGraphHeatChernoff;
pub use crate::quantum_graph::QuantumGraphSignal;
pub use crate::quantum_schrodinger::QuantumGraphComplexSignal;
pub use crate::quantum_schrodinger::QuantumSchrödingerChernoff;
pub use crate::rational_krylov::rational_krylov_expmv;
pub use crate::rational_krylov::RationalKrylov;
pub use crate::rational_krylov::RationalKrylovChernoff;
pub use crate::rational_krylov::RationalOptions;
pub use crate::rational_krylov::RationalReport;
pub use crate::reaction::AllenCahnReaction;
pub use crate::reaction::Brusselator;
pub use crate::reaction::FisherKpp;
pub use crate::reaction::FitzHughNagumo;
pub use crate::reaction::FnReaction;
pub use crate::reaction::GrayScott;
pub use crate::reaction::Kinetics;
pub use crate::reaction::LinearReaction;
pub use crate::reaction::Nagumo;
pub use crate::reaction_diffusion::NodalField;
pub use crate::reaction_diffusion::ReactionDiffusion;
pub use crate::reaction_diffusion::Species;
pub use crate::reaction_diffusion::SpeciesEngine;
pub use crate::reaction_stiff::ReactionSolver;
pub use crate::reaction_stiff::RosenbrockOptions;
pub use crate::reflection::HalfSpaceRegion;
pub use crate::reflection::ReflectedHeatChernoff;
pub use crate::reflection::ReflectingRegion;
pub use crate::resolvent::LaplaceChernoffResolvent;
pub use crate::resolvent::LaplaceChernoffResolventResidual;
pub use crate::resolvent::LaplaceQuadrature;
pub use crate::resolvent::Sampleable;
pub use crate::resolvent_complex::EvalComplex;
pub use crate::resolvent_jump::ResolventJumpChernoff;
pub use crate::resolvent_jump_nd::ResolventJumpChernoff2D;
pub use crate::resolvent_jump_nd::ResolventJumpChernoff3D;
pub use crate::reverse_ad::forward_with_checkpoints;
pub use crate::reverse_ad::recompute_segment;
pub use crate::reverse_ad::step_jacobian_col;
pub use crate::reverse_ad::CheckpointSchedule;
pub use crate::reverse_ad::ReverseChernoff;
pub use crate::reverse_ad::TransposeApply;
pub use crate::reverse_region::RegionMap;
pub use crate::richardson::extrapolate_into;
pub use crate::richardson::richardson_weights;
pub use crate::richardson::StepIntegrator;
pub use crate::richardson::MAX_RICHARDSON_LEVELS;
pub use crate::robin::HalfSpaceRobin;
pub use crate::robin::RobinHeatChernoff;
pub use crate::robin::RobinRegion;
pub use crate::schrodinger::SchrodingerChernoff;
pub use crate::schrodinger::SchrodingerState;
pub use crate::schrodinger_complex::SchrödingerChernoffComplex;
pub use crate::schrodinger_complex_state::GridFnComplex1D;
pub use crate::scratch::ScratchPool;
pub use crate::scratch::ScratchVec;
pub use crate::shift1d::ShiftChernoff1D;
pub use crate::shift_nd::AnisotropicShiftChernoffND;
pub use crate::shift_nd::GaussHermiteTensor;
pub use crate::shift_nd::SquareMatrix;
pub use crate::shift_nd_adaptive::AnisotropicShiftAdaptiveQ;
pub use crate::shift_nd_zeta2::AnisotropicShiftZeta2ND;
pub use crate::smolyak::SmolyakGridND;
pub use crate::spd_resolvent::Precond;
pub use crate::spd_resolvent::ResolventMethod;
pub use crate::spd_resolvent::SolveReport;
pub use crate::spd_resolvent::SpdResolvent;
pub use crate::spd_resolvent::SpdSolver;
pub use crate::state::Discrete;
pub use crate::state::HilbertState;
pub use crate::state::State;
pub use crate::strang::StrangSplit;
pub use crate::strang2d::Strang2D;
pub use crate::strang3d::Strang3D;
pub use crate::strang3d_axislift::AxisLift3D;
pub use crate::strang_graph::StrangSplitGraph;
pub use crate::subordinated::GammaSubordinator;
pub use crate::subordinated::InverseGaussianSubordinator;
pub use crate::subordinated::LevySubordinator;
pub use crate::subordinated::StableSubordinator;
pub use crate::subordinated::SubordinatedChernoff;
pub use crate::symmetric_operator::dense_csr_expmv_ref;
pub use crate::symmetric_operator::SymmetricLinearOp;
pub use crate::symmetric_operator::SymmetricOperator;
pub use crate::truncated_exp::TruncatedExpDiffusionChernoff;
pub use crate::truncated_exp4::TruncatedExp4WithCache;
pub use crate::truncated_exp4::TruncatedExp4thDiffusionChernoff;
pub use crate::tt_chernoff::TtChernoff;
pub use crate::tt_chernoff::TtState;
pub use crate::tt_coupled::CoupledTtChernoff;
pub use crate::tt_coupled::CouplingTopology;
pub use crate::tt_varcoef::VarCoefTt;
pub use crate::varcoef_magnus_graph::compute_rho_bar;
pub use crate::varcoef_magnus_graph::VarCoefMagnusGraphHeatChernoff;
pub use crate::varcoef_magnus_graph::WeightAtTime;
pub use crate::wentzell::DynamicWentzellChernoff;
pub use crate::wentzell::HalfSpaceWentzell;
pub use crate::wentzell::WentzellRegion;
pub use crate::tt_dense_coupling_api::S3DenseCouplingEvolver;s3-poc
pub use crate::tt_drift_spectral_api::S3DriftSpectralEvolver;s3-poc
pub use crate::tt_nonlinear_spectral::Reaction;s3-poc
pub use crate::tt_nonlinear_spectral_api::S3BurgersColeHopf;s3-poc
pub use crate::tt_nonlinear_spectral_api::S3ReactionDiffusion;s3-poc
pub use crate::tt_nonsep_varcoef::CoefRole;s3-poc
pub use crate::tt_nonsep_varcoef::CpCoef;s3-poc
pub use crate::tt_nonsep_varcoef::CpTerm;s3-poc
pub use crate::tt_nonsep_varcoef_api::S3NonSepVarCoefEvolver;s3-poc
pub use crate::tt_varcoef_spectral::AxisCoef;s3-poc
pub use crate::tt_varcoef_spectral::S3VarCoefEvolver;s3-poc

Modules§

adaptive: AdaptivePI — generic adaptive PI integrator (Wave 4, ADR-0044).
adjoint: Adjoint (backward) semigroup wrapper for any ChernoffFunction<F> whose state implements HilbertState<F>.
adjoint_fp: Adjoint Fokker-Planck Chernoff on M(ℝ^D), weak-* topology (ADR-0107 AMD1, §38).
approximation: ApproximationSubspace<const K, F> — opt-in marker super-trait (v3.0 B1, ADR-0073). LadderRung<const K, F> — sealed super-trait for ζ-ladder rungs (v5.0 A.6, ADR-0100).
axis: Axis discriminator and AxisLift per-axis adapter.
boundary: Boundary policies, hit records, and index/value dispatch helpers.
carnot_complex: Complex-time order-4 Carnot Chernoff via the complex triple-jump (ADR-0136 Amendment 2 STRONG-GO, math.md §28.bis.8, v8.0.0 F4).
carnot_stepk: Step-4 filiform Carnot group Chernoff approximation (ADR-0136 Amendment 1, math.md §28.bis.7, v8.0.0 F4 order-2 real baseline).
chernoff: Core Chernoff abstraction: ChernoffFunction trait and Evolver executor.
complex: v4.0 B6 — SemiflowComplex trait (ADR-0079, math.md §30.2).
conservative: ConservativeDiffusionChernoff — order-2 conservative (FV divergence-form) variable-coefficient diffusion (ADR-0187 D2, §56).
conservative_assemble: Harmonic-mean face assembler → SymmetricOperator<F> (ADR-0187 D1, §56.1–56.2).
controller: Step-size controllers for crate::AdaptivePI (Wave 4, ADR-0044).
cross_diffusion: Cross-diffusion with a constant matrix: ∂ₜu = DΔu + f(t, x, u) (ADR-0213, math §70).
diffusion: DiffusionChernoff — ζ-A Chernoff for A_self = ∂_x(a(x)·∂_x) (v0.3.0, ADR-0008).
diffusion4: Diffusion4thChernoff — ζ⁴ Chernoff for A_self = ∂_x(a(x)·∂_x) (v0.6.0, ADR-0013).
diffusion6: Diffusion6thChernoff — ζ⁶ Chernoff for A_self = ∂_x(a(x)·∂_x) (v0.7.0, ADR-0015).
diffusion4_zeta4: Diffusion4thZeta4Chernoff — order-4-temporal ζ⁴ kernel (ADR-0086 Path β resolution).
diffusion6_zeta6: Diffusion6thZeta6Chernoff — order-6-temporal ζ⁶ kernel (ADR-0088 Wave I, ADR-0086 Path β-ladder rung K=3).
diffusion8_zeta8: Diffusion8thZeta8Chernoff — order-8-temporal ζ⁸ kernel (ADR-0088 Wave II, ADR-0090).
drift_reaction: DriftReactionChernoff — RK2 characteristic-flow Chernoff for B = b(x)∂_x + c(x) (v0.2.2, ADR-0006 Amendment 5, math.md §9.3).
drift_reaction_zeta4: DriftReactionZeta4Chernoff — order-4-temporal ζ⁴ sibling for L = a(x)∂ₓₓ + b(x)∂ₓ + c(x) (ADR-0131, math.md §27.7-bis, v7.0.0).
dual: Dual<F> — forward-mode dual-number scalar field for automatic differentiation.
entry_sensitivity: Fréchet sensitivity w.r.t. individual CSR entries of a symmetric operator (ADR-0186, §55.5).
error: Error taxonomy for semiflow.
etdrk4: ETDRK4 exponential time-differencing driver (ADR-0189 §D2).
expmv: DiffusionExpmvChernoff — tolerance-driven e^{τA}·v via Al-Mohy & Higham (2011) expmv action kernel (ADR-0121, math.md §45).
float: Sealed scalar-float trait used throughout semiflow.
general_operator: GeneralOperator — externally-assembled possibly non-symmetric CSR operator, and its scaled-truncated-Taylor action (ADR-0195, Issue #24).
generator_action: GeneratorAction<F> — minimal adapter trait over linear PDE generators (ADR-0189 §58.1).
graph: Frozen sparse weighted graph (Graph<F>) and graph Laplacian (Laplacian<F>) in hand-rolled CSR layout (ADR-0048, §1/§3).
graph_adjoint_presampled: Pre-sampled time-grid path for graph state-adjoint (ADR-0180).
graph_batched: Batched multi-channel evolve for graph heat kernels (ADR-0184, Issue #10). [C, N] channel-major layout; 0-ULP vs serial (D5); hoisted GL₄/GL₆/VC samples.
graph_frechet: graph_expmv_frechet — VJP gradient via the exact Duhamel integral (ADR-0185, ADR-0203).
graph_heat: Graph heat Chernoff kernels: order-1 (leading) and order-2 (ζ-A Taylor).
graph_heat4: Order-4 graph heat Chernoff via Padé[0,4] operator Taylor truncation.
graph_heat6: Order-6 graph heat Chernoff via operator-Taylor truncation.
graph_krylov: Depth-independent graph-semigroup action e^{-tL_G}·v via Krylov methods.
graph_sensitivity: Adjoint-state parameter-sensitivity for graph / Magnus kernels (Issue #1, ADR-0115).
graph_signal: GraphSignal<F> — dense Vec<F>-backed function on a graph’s node set.
graph_traj: Piecewise-smooth graph trajectory data structure.
graph_var_coef: Variable-coefficient graph heat Chernoff with ζ-A τ²-correction.
grid: Uniform 1-D grid and sub-grid interpolation.
grid2d: Grid2D — rectangular tensor-product geometry for the 2D extension.
grid3d: Grid3D — cuboid tensor-product geometry for the 3D extension.
grid_batched: Batched multi-channel evolve for 1-D grid kernels (ADR-0194, Issue #19).
grid_fn: GridFn1D — a function sampled on a Grid1D, implementing State.
grid_fn2d: GridFn2D — a function sampled on a Grid2D, implementing State.
grid_fn3d: GridFn3D — a function sampled on a Grid3D, implementing State.
grid_nd: GridND and GridFnND — d-dimensional tensor-product grid (v4.0 Wave C).
gridless: Gridless particle-ensemble Chernoff evolver — GridlessChernoff (v9.0.0, ADR-0155).
hdr: HDR percentile snapshot for L-gate latency harness.
heisenberg_kernel: Heisenberg group H₁ heat kernel oracle via Gaveau-Hulanicki integral form.
hormander: v3.1 A3 — Hörmander hypoelliptic Chernoff approximation (math.md §28, ADR-0077).
hormander_engel: Engel step-3 filiform Carnot group Chernoff approximation (ADR-0095, math.md §28.bis).
howland: B2 — Howland Nonautonomous Lift (math.md §23, ADR-0070).
killed_dirichlet: Order-2 hard absorbing wall via the killed Dirichlet generator Cayley map.
killing: Operator-level Dirichlet via Feynman–Kac killing (Butko 2018).
killing_order2: §21.9 — Order-2 hard-wall Dirichlet via the ODD (antisymmetric) image method (ADR-0176).
killing_soft: Killing2ndChernoff<C, K, F> — order-2 soft killing via symmetric Strang split.
magnus6_graph: Sixth-order Magnus expansion for time-dependent graph heat: ∂_t u = −L_G(t) u on a fixed-topology weighted graph.
magnus_graph: Fourth-order Magnus expansion for time-dependent graph heat: ∂_t u = −L_G(t) u on a fixed-topology weighted graph.
magnus_graph_adjoint: Graph state-adjoint for the truncated Magnus K=4 map (Issue #2, ADR-0115).
manifold: A4 — Riemannian Manifold Chernoff (math.md §24, ADR-0071).
manifold_chernoff: ManifoldChernoff<M, F> — Riemannian Chernoff wrapper (math.md §24, ADR-0071).
manifold_hyperbolic: Hyperbolic2<F> — Poincaré disk backend for BoundedGeometryManifold.
manifold_kahler: B5 (ADR-0129) — CP¹ Fubini-Study Kähler manifold backend (math.md §24.7-bis).
mass_operator: Generalized (M, K) entry point for lumped and consistent mass matrices (ADR-0186, §55.3–§55.4).
matrix_2d3d: MatrixDiffusionChernoff2D/3D — per-axis palindromic Strang for M-component coupled diffusion on 2D/3D tensor-product grids (ADR-0124).
matrix_system: v4.x Wave 2 — MatrixDiffusionChernoff<F, M> with palindromic Strang splitting.
matrix_system_complex: Complex matrix-valued Chernoff kernel (ADR-0128, §33.8 Para 3).
multilayer: Multilayer thermal stack for stiff multi-material conduction (§57, issue #14).
nonlinearity: Nonlinearity<F> and NonlinearityDiff<F> traits + concrete impls (ADR-0189 §D3).
nonseparable2d: NonSeparable2DChernoff — thin compatibility shim (v2.2 Wave C, ADR-0058).
nonseparable2d_aniso: NonSeparable2DAnisotropicChernoff — thin compatibility shim (v2.2 Wave C, ADR-0058).
nonseparable_mixed: NonSeparableMixedChernoff<X, Y, F, S> — generic non-separable 2D Chernoff operator.
nonseparable_mixed_closure: Closure-backed coupling implementations for NonSeparableMixedChernoff.
obstacle: Projective-splitting obstacle evolver / variational inequalities (math §44).
obstacle_gamma: Inactive-set Γ = V″ primitive for ObstacleChernoff (math §44.5.bis).
obstacle_nd: D≥2 projective-splitting obstacle evolver (math §44.5.ter).
phi_action: φ-function actions via the augmented-matrix construction (ADR-0189 §58.2).
phi_krylov: Adaptive Krylov (Arnoldi) φ-combination for any generator (ADR-0211, math §68).
point_eval: v4.0 A6 — PointEval<F> first-class API (ADR-0080, math.md §31).
quantum_graph: v3.1 B7 — Quantum graphs, Kirchhoff vertex condition (math §29, ADR-0078).
quantum_schrodinger: v7.0.0 #16 — Schrödinger on quantum graphs via complex Kirchhoff (ADR-0130, math §30.5-bis).
rational_krylov: Rational (shift-and-invert) Krylov action e^{−t·M⁻¹A}·v for SPD sparse operators (ADR-0206, math §66).
reaction: Pointwise reaction terms ∂ₜu = f(t, x, u) for ReactionDiffusion (ADR-0208).
reaction_diffusion: Semilinear reaction–diffusion systems on any Chernoff engine (ADR-0208).
reaction_stiff: Stiff kinetics: adaptive two-stage Rosenbrock (ROS2) reaction flow (ADR-0212, math §69).
reflection: B4 — Neumann via image method (math.md §25, ADR-0072).
reflection_regions: Additive ReflectingRegion<F> impls for BoxRegion<F, D> and BallRegion<F, D>.
resolvent: A1 — Laplace-Chernoff Resolvent (math.md §22, ADR-0069).
resolvent_complex: Complex-λ Laplace-Chernoff resolvent (math.md §22.9, ADR-0127).
resolvent_jump: F2 — Resolvent time-jump amortization (math.md §47, ADR-0134).
resolvent_jump_nd: F2 — 2D/3D parabolic LHP backends (math.md §47.8, ADR-0148, v8.2.0).
reverse_ad: ReverseChernoff — genuine reverse-mode AD over (F(τ))ⁿ via binomial checkpointing (math §51, ADR-0156 Amendment 2; v9.1.0 Shift B GENUINE).
reverse_region: DoF-aligned region partition for K>1 reverse-AD (§51.10, ADR-0177). RegionMap — DoF-aligned region partition for K>1 reverse-AD (math §51.10, ADR-0177; issue #1).
richardson: Richardson extrapolation in the step count (ADR-0207).
robin: A.3 Robin BC partial-additive port (math.md §3.5.tris, ADR-0098).
schrodinger: Schrödinger Chernoff i ψ_t = (−Δ + V(x)) ψ via palindromic Strang splitting.
schrodinger_complex: v4.0 B6 — Schrödinger Option B native-complex implementation (ADR-0079, math.md §30.3).
scratch: Grow-only scratch-buffer pool for allocation-free Chernoff hot loops (Wave 1, ADR-0041).
shift1d: ShiftChernoff1D — Chernoff function for L = a(x)∂² + b(x)∂ + c(x).
shift1d_vjp: Gradients w.r.t. ShiftChernoff1D’s coefficient fields (ADR-0197, Issue #25).
shift_nd: v4.0 A2 — AnisotropicShiftChernoffND<F, const D: usize> flagship (ADR-0081, math.md §32).
shift_nd_adaptive: ADR-0122 — adaptive per-point Gauss-Hermite quadrature q for AnisotropicShiftChernoffND (math.md §32.8).
shift_nd_zeta2: ADR-0112 AMENDMENT 2 — order-2 ζ² correction for AnisotropicShiftChernoffND.
smolyak: ADR-0123 — SmolyakGridND<F, const D: usize> sparse-grid quadrature backend.
spd_resolvent: SPD resolvent / steady solve x = (λ·M + A)⁻¹ b (ADR-0202 D1, math §62.1–§62.2).
state: State, HilbertState, and Discrete traits — 3-layer vector interface for Chernoff iteration (Wave 3, ADR-0043, v2.0 MAJOR).
strang: StrangSplit — Strang operator-splitting composer.
strang2d: Strang2D — palindromic Strang composition for 2D tensor-product generators.
strang2d_pencil: Strang2DPencil — palindromic Strang with per-pencil 1-D kernels (ADR-0196, Issue #21).
strang3d: Strang3D palindromic composition for 3D tensor-product generators.
strang3d_axislift: AxisLift3D — per-axis adapter lifting a 1D ChernoffFunction to 3D.
strang_graph: Palindromic Strang split for commuting graph Chernoff kernels.
subordinated: A.5 — SubordinatedChernoff via Butko 2018 (math.md §37, ADR-0103).
symmetric_operator: Generic symmetric positive-semidefinite operator entry point (ADR-0186, §55).
truncated_exp: TruncatedExpDiffusionChernoff — truncated-exp K=4 Chernoff for A_self = ∂_x(a(x)·∂_x) (v0.4.0, ADR-0011).
truncated_exp4: TruncatedExp4thDiffusionChernoff — truncated-exp K=4 + 4th-order stencil (v0.6.0, ADR-0013).
truncated_exp4_cached: Wave B2 cache types for TruncatedExp4thDiffusionChernoff (v0.13.0, ADR-0034 Amendment 1).
tt_chernoff: TT-Chernoff evolver — tensor-train Chernoff semigroup (math §50, §52.2 Amd 1).
tt_core: TT-core data structures and SVD rounding kernel (no_std+alloc, no new deps).
tt_coupled: CoupledTtChernoff — genuine cross-axis TT evolver (v9.1.0 Shift C, §52.9).
tt_dense_couplings3-poc: S³ POC — Dense / non-adjacent (all-pairs) coupling curse-escape.
tt_dense_coupling_apis3-poc: Public wrapper type for tt_dense_coupling (ADR-0169, v9.2.0).
tt_drift_spectrals3-poc: S³ POC — Complex-spectral drift pair factor (DriftSpectralPairFactor).
tt_drift_spectral_apis3-poc: Public wrapper type for tt_drift_spectral (ADR-0169, v9.2.0).
tt_nonlinear_spectrals3-poc: S³ nonlinear POC — Cole-Hopf Burgers (Seam A) + Strang-split RD (Seam B).
tt_nonlinear_spectral_apis3-poc: Public wrapper types for tt_nonlinear_spectral (ADR-0169, v9.2.0).
tt_nonsep_varcoefs3-poc: S³ POC — Non-separable variable-coefficient evolver (NonSepVarCoefSpectral).
tt_nonsep_varcoef_apis3-poc: Public wrapper type for tt_nonsep_varcoef (ADR-0169, v9.2.0).
tt_varcoef: VarCoefTt — additive-separable variable-coefficient evolver on crate::tt_chernoff::TtState.
tt_varcoef_spectrals3-poc: S³ POC — Variable-coefficient additive-split evolver (VarCoefSplitSpectral).
varcoef_magnus_graph: Variable-coefficient × time-dependent Magnus K=4 on graphs (ADR-0063).
wentzell: C-9 — Dynamic Wentzell/Robin BC via implicit Cayley boundary step (math.md §49, ADR-0151).

Macros§

impl_state_for_gridfn: Generate State<F> and HilbertState<F> impls for a grid-fn type.

Structs§

FrechetPlan: Pure cost/accuracy plan of one graph_expmv_frechet channel.
GridFnComplex1D: Native complex grid function: ψ(x_i) ∈ C for each node i.

Functions§

graph_expmv_frechet_plan: Predict node count, chain length, max degree, rounding weight and SpMV bound (§63.8). Pure.
phi_sweep_probe: (s, m) the φ-actions actually use for op and tau — shift-aware, unlike crate::phi_action::phi_cost_probe, which takes only a norm. Each φ sweep costs s·m generator applications. (0, 0) for an invalid τ or bound.

Crate semiflow

Crate semiflow Copy item path

§semiflow

§Install

§Quickstart

§no_std

§Feature flags

§Engine catalogue

§1D Chernoff functions

§Compositions

§2D tensor-product

§3D tensor-product

§Adaptive

§Boundary conditions

§Resolvent and nonautonomous

§Riemannian manifold

§High-dimensional and sparse-grid

§Matrix-valued operators

§Quantum graphs

§Reverse-mode AD

§Tensor-train carrier

§Gridless / particle-ensemble

§Schrödinger, graph and quantum-graph operators

§Conservative, stiff and semilinear problems

§Executor

§Examples

§Bindings

§Documentation

§Accuracy and design

§How to cite

§License

§Author, contributing, security

Re-exports§

Modules§

Macros§

Structs§

Functions§

Crate semiflow

§`no_std`