# Module map
**Generated file — do not edit.** Produced by
[`tools/gen_module_map.py`](../tools/gen_module_map.py) from the source
tree; CI fails if it is out of date. Regenerate with:
```bash
python3 tools/gen_module_map.py
```
Every figure below is parsed from the sources. Summaries are the first
sentence of each module's `//!` documentation. Public-item counts exclude
anything inside `#[cfg(test)]`, and tell a method from a free function by
the enclosing `impl` block rather than by indentation -- an indented
`pub fn` inside an inline `pub mod` is a free function, and there are 175
of those.
The count is syntactic, so an item generated by a macro is counted once
where the macro defines it rather than once per expansion. That affects
two places: `units::quantity`, whose `unit_ctor!` generates about thirty
constructors from one template, and `spatial::kdtree`, whose macro
generates two tree types from one.
**295 modules** across **71 public top-level modules**, **266,122 lines** in **296 files** (the modules plus the crate root `src/lib.rs`), **4,124 public functions** and **2,241 public methods**, **431 public types**.
`verification` is compiled and tested but declared `mod` rather than `pub mod`, so it is not part of the public API and is excluded from the module count above.
## Tree
A directory's figure is its own `mod.rs` plus everything beneath it.
```
src/ lines
├── lib.rs 159 (crate root)
├── acoustics.rs 576
├── astrophysics/ 6,122
│ ├── collisions.rs 318
│ ├── coords.rs 1,051
│ ├── gravitational_waves.rs 233
│ ├── habitable_zone.rs 127
│ ├── kepler.rs 913
│ ├── lagrange.rs 195
│ ├── lambert.rs 553
│ ├── magnetosphere.rs 405
│ ├── maneuvers.rs 618
│ ├── nbody.rs 403
│ ├── orbital_elements.rs 660
│ ├── tidal.rs 209
│ └── time_systems.rs 399
├── atmosphere.rs 409
├── audio/ 10,716
│ ├── analysis.rs 1,950
│ ├── effects.rs 1,669
│ ├── envelope.rs 604
│ ├── oscillators.rs 939
│ ├── physical.rs 1,331
│ ├── spatial.rs 1,132
│ ├── synthesis.rs 1,260
│ ├── tuning.rs 517
│ ├── vocoder.rs 862
│ └── wav.rs 370
├── biophysics/ 11,396
│ ├── epidemiology.rs 1,924
│ ├── neuro.rs 2,519
│ ├── phylo.rs 1,979
│ ├── population.rs 2,356
│ └── seq_align.rs 2,150
├── cfd/ 16,732
│ ├── advection.rs 869
│ ├── boundary_layer.rs 579
│ ├── grid.rs 685
│ ├── lbm.rs 1,142
│ ├── level_set.rs 2,066
│ ├── multiphase.rs 778
│ ├── porous.rs 695
│ ├── potential_flow.rs 1,523
│ ├── riemann.rs 1,564
│ ├── shallow_water.rs 938
│ ├── sph.rs 1,154
│ ├── stable_fluids.rs 1,776
│ ├── turbulence.rs 1,537
│ └── vortex.rs 1,304
├── chemistry.rs 334
├── classical.rs 786
├── codes/ 8,243
│ ├── block.rs 1,579
│ ├── checksum.rs 880
│ ├── compression.rs 1,420
│ ├── convolutional.rs 1,335
│ ├── crypto_math.rs 1,501
│ └── reed_solomon.rs 1,519
├── color_science.rs 788
├── continuum_mechanics.rs 508
├── control_systems/ 744
│ └── kalman.rs 291
├── core/ 984
│ ├── compensated.rs 117
│ ├── dual.rs 410
│ └── interval.rs 451
├── curves.rs 500
├── discrete/ 9,047
│ ├── combinatorics.rs 2,827
│ ├── disjoint_set.rs 352
│ ├── number_theory.rs 2,345
│ ├── partitions.rs 784
│ ├── primes.rs 1,238
│ └── sequences.rs 1,491
├── dsp/ 3,928
│ ├── fir.rs 996
│ ├── iir.rs 1,666
│ ├── phase.rs 270
│ ├── resample.rs 513
│ └── windows.rs 446
├── electromagnetism.rs 822
├── electronics.rs 445
├── error.rs 103
├── exact/ 9,249
│ ├── bigfloat.rs 2,000
│ ├── bigint.rs 1,463
│ ├── contfrac.rs 524
│ ├── polynomial.rs 2,286
│ ├── rational.rs 1,079
│ └── symbolic.rs 1,882
├── fem/ 4,725
│ ├── fdtd.rs 1,154
│ ├── fem1d.rs 952
│ ├── fem2d.rs 1,901
│ └── spectral_pde.rs 693
├── fields.rs 211
├── finance/ 5,119
│ ├── options.rs 2,090
│ ├── portfolio.rs 865
│ ├── rates.rs 1,388
│ └── risk.rs 751
├── fluid_instabilities.rs 451
├── fluids.rs 709
├── fractals/ 9,454
│ ├── attractors.rs 1,104
│ ├── automata.rs 2,881
│ ├── escape_time.rs 1,044
│ ├── ifs.rs 924
│ ├── lsystem.rs 1,056
│ └── noise.rs 1,803
├── general_relativity.rs 427
├── geometry/ 1,522
│ ├── delaunay.rs 262
│ ├── geodesy.rs 342
│ ├── hull.rs 310
│ └── mesh.rs 155
├── geophysics.rs 483
├── graph/ 13,493
│ ├── coloring.rs 1,649
│ ├── core.rs 2,862
│ ├── flow.rs 1,519
│ ├── layout.rs 1,935
│ ├── matching.rs 1,399
│ ├── paths.rs 2,133
│ └── spectral.rs 1,984
├── gravitation.rs 236
├── information_theory.rs 367
├── learn/ 4,213
│ ├── cluster.rs 1,295
│ ├── gp.rs 839
│ ├── nn.rs 1,163
│ └── tree.rs 900
├── linalg/ 3,295
│ ├── cholesky.rs 147
│ ├── eigen.rs 492
│ ├── lu.rs 223
│ ├── matrix.rs 344
│ ├── qr.rs 205
│ ├── sparse.rs 360
│ ├── svd.rs 321
│ └── tridiagonal.rs 233
├── magnetohydrodynamics.rs 359
├── manifold/ 20,431
│ ├── clifford.rs 2,830
│ ├── dec.rs 1,618
│ ├── embedding.rs 1,624
│ ├── geodesic.rs 1,422
│ ├── hyperbolic.rs 1,710
│ ├── lie.rs 3,225
│ ├── metric.rs 1,382
│ ├── polytope4.rs 2,142
│ ├── spacetime.rs 1,556
│ ├── spherical.rs 1,671
│ └── vecn.rs 1,146
├── materials/ 3,548
│ ├── common.rs 349
│ ├── elements.rs 2,632
│ ├── fluids.rs 308
│ └── gases.rs 242
├── math.rs 621
├── mesh/ 6,516
│ ├── analyze.rs 1,201
│ ├── generate.rs 881
│ ├── isosurface.rs 1,052
│ ├── parameterize.rs 652
│ ├── subdivide.rs 616
│ └── surfaces.rs 1,043
├── monte_carlo/ 982
│ └── quasi.rs 282
├── neutronics.rs 409
├── nonlinear.rs 432
├── nuclear.rs 303
├── numerical/ 2,563
│ ├── bvp.rs 201
│ ├── integrate.rs 270
│ ├── interpolate.rs 648
│ ├── ode/ 740
│ │ ├── adaptive.rs 309
│ │ ├── explicit.rs 63
│ │ ├── implicit.rs 232
│ │ └── symplectic.rs 125
│ └── roots.rs 280
├── optics.rs 348
├── optimization/ 15,189
│ ├── convex.rs 2,410
│ ├── game_theory.rs 3,326
│ ├── integer.rs 2,694
│ ├── least_squares.rs 371
│ ├── lp.rs 2,600
│ ├── metaheuristics.rs 1,577
│ └── network.rs 1,383
├── particle_physics.rs 402
├── patterns/ 12,404
│ ├── aperiodic.rs 1,807
│ ├── knots.rs 831
│ ├── packing.rs 1,130
│ ├── phyllotaxis.rs 490
│ ├── polygon_ops.rs 2,022
│ ├── polyhedra.rs 2,032
│ ├── sampling.rs 1,220
│ ├── space_filling.rs 755
│ ├── symmetry.rs 996
│ └── tilings.rs 1,107
├── photonics.rs 485
├── plasma.rs 297
├── propulsion.rs 361
├── quantum/ 11,941
│ ├── algorithms.rs 1,707
│ ├── circuit.rs 2,460
│ ├── schrodinger.rs 2,607
│ ├── solid_state.rs 1,685
│ ├── spin.rs 1,703
│ └── wavefunction.rs 1,368
├── quaternion.rs 562
├── radiation.rs 335
├── relativity.rs 302
├── resonance/ 4,275
│ ├── cavity.rs 931
│ ├── coupled.rs 828
│ ├── nonlinear.rs 704
│ ├── oscillator.rs 636
│ └── structural.rs 1,134
├── rf.rs 440
├── signal_processing.rs 708
├── sim/ 4,927
│ ├── cloth_sim.rs 970
│ ├── em_sim.rs 638
│ ├── fluid_sim.rs 1,161
│ ├── heat_sim.rs 774
│ ├── rigid_body.rs 681
│ └── wave_sim.rs 682
├── solid_mechanics.rs 380
├── spatial/ 7,020
│ ├── bvh.rs 513
│ ├── contain.rs 527
│ ├── distance.rs 495
│ ├── frame.rs 215
│ ├── intersect.rs 908
│ ├── kdtree.rs 510
│ ├── mat4.rs 504
│ ├── octree.rs 342
│ ├── primitives.rs 1,128
│ ├── projective.rs 447
│ ├── quadtree.rs 359
│ ├── sdf.rs 731
│ └── transform2d.rs 308
├── special/ 1,955
│ ├── bessel.rs 528
│ ├── beta.rs 145
│ ├── elliptic.rs 333
│ ├── erf.rs 335
│ ├── expint.rs 126
│ ├── gamma.rs 219
│ └── legendre.rs 243
├── statistical_mechanics/ 9,687
│ ├── ising.rs 2,004
│ ├── kinetics.rs 2,806
│ ├── lattice_models.rs 1,199
│ └── md.rs 3,237
├── statistics/ 2,125
│ ├── descriptive.rs 114
│ ├── distributions.rs 1,013
│ ├── fourier.rs 56
│ ├── inference.rs 415
│ └── resampling.rs 239
├── stochastic/ 15,707
│ ├── extreme.rs 1,852
│ ├── hmm.rs 1,451
│ ├── markov.rs 1,952
│ ├── point_process.rs 1,373
│ ├── queueing.rs 1,933
│ ├── rmt.rs 1,217
│ ├── sde.rs 1,939
│ └── timeseries.rs 3,979
├── thermodynamics.rs 808
├── transforms/ 6,353
│ ├── dct.rs 489
│ ├── fft.rs 962
│ ├── hilbert.rs 570
│ ├── laplace.rs 435
│ ├── radon.rs 619
│ ├── spectral.rs 808
│ ├── stft.rs 695
│ ├── wavelet.rs 1,022
│ └── wavelet_tables.rs 699
├── trigonometry.rs 493
├── units/ 2,785
│ ├── dimensional.rs 974
│ └── quantity.rs 998
├── vector_calculus.rs 1,195
├── verification/ 394 (private)
│ ├── core.rs 27
│ ├── linalg.rs 27
│ ├── physics.rs 236
│ └── spatial.rs 41
└── waves.rs 784
```
## By area
### Numeric foundations
| **`core`** | 984 | 34 | 2 | Pure numeric building blocks: compensated summation, forward-mode automatic differentiation, and interval arithmetic. |
| **`math`** | 621 | 23 | 2 | Vectors and the crate's table of physical constants. |
| **`linalg`** | 3,295 | 74 | 8 | Dense and sparse linear algebra. |
| **`numerical`** | 2,563 | 43 | 4 | Numerical methods: quadrature, root finding, ODE solvers, and interpolation. |
| **`special`** | 1,955 | 34 | 0 | Special functions: error function family, gamma family, and beta functions. |
| **`error`** | 103 | 0 | 2 | Error types shared by the numerical solvers. |
### Exact and symbolic
| **`exact`** | 9,249 | 242 | 8 | Exact arithmetic: arbitrary-precision integers, exact rationals, arbitrary-precision binary floating point, polynomials, and continued fractions. |
| **`discrete`** | 9,047 | 181 | 1 | Discrete mathematics: primes and factorization, elementary and analytic number theory, counting and enumeration, integer partitions, integer… |
| **`graph`** | 13,493 | 182 | 3 | Graphs: representation and structure, shortest paths, network flow, matchings, spectral graph theory, colouring, and drawing. |
| **`codes`** | 8,243 | 225 | 16 | Error detection, error correction, compression, and the arithmetic cryptography is built on. |
### Classical mechanics
| **`classical`** | 786 | 54 | 0 | Newtonian mechanics: kinematics, dynamics, and the harmonic oscillator. |
| **`gravitation`** | 236 | 14 | 0 | Newtonian gravity and two-body orbits. |
| **`solid_mechanics`** | 380 | 23 | 0 | Strength of materials: stress, strain, elastic constants and beams. |
| **`continuum_mechanics`** | 508 | 19 | 0 | Stress and strain as tensors, and the yield criteria built on them. |
| **`resonance`** | 4,275 | 144 | 7 | Resonance and vibration: single and coupled oscillators, acoustic and electromagnetic cavities, nonlinear resonance, and structural dynamics. |
| **`geophysics`** | 483 | 22 | 0 | The solid Earth: gravity, seismology, and heat. |
### Thermal and statistical
| **`thermodynamics`** | 808 | 52 | 0 | Thermodynamics: gases, heat transfer, cycles and phase change. |
| **`statistical_mechanics`** | 9,687 | 161 | 9 | Statistical mechanics: the elementary relations here, with lattice models and Monte Carlo in submodules. |
| **`radiation`** | 335 | 14 | 0 | Thermal radiation and radiative transfer. |
### Electromagnetism
| **`electromagnetism`** | 822 | 60 | 0 | Classical electromagnetism, from Coulomb's law to radiating dipoles. |
| **`electronics`** | 445 | 17 | 0 | Semiconductor device physics. |
| **`rf`** | 440 | 28 | 0 | Radio-frequency engineering: links, lines and noise. |
| **`photonics`** | 485 | 26 | 0 | Laser beams, optical fibre, and interferometry. |
| **`plasma`** | 297 | 16 | 0 | Plasma parameters: the characteristic lengths, frequencies and speeds. |
| **`magnetohydrodynamics`** | 359 | 19 | 0 | Magnetohydrodynamics: a conducting fluid and the field frozen into it. |
### Waves and signals
| **`waves`** | 784 | 48 | 0 | Wave propagation: mechanical, acoustic and seismic. |
| **`optics`** | 348 | 20 | 0 | Geometric and wave optics. |
| **`acoustics`** | 576 | 31 | 0 | Room acoustics, psychoacoustic scales, and musical pitch. |
| **`transforms`** | 6,353 | 120 | 8 | Discrete transforms: FFT (any length), DCT/DST, STFT, wavelets, Hilbert, Laplace inversion, Radon, and spectral estimation. |
| **`dsp`** | 3,928 | 94 | 7 | Digital signal processing: window functions, FIR/IIR filter design, resampling, and phase utilities. |
| **`signal_processing`** | 708 | 16 | 0 | Time-domain signal operations and test waveforms. |
| **`audio`** | 10,716 | 350 | 49 | Audio synthesis, analysis, effects, and I/O. |
### Fluids
| **`fluids`** | 709 | 45 | 0 | Fluid statics and single-phase flow. |
| **`cfd`** | 16,732 | 477 | 50 | Computational fluid dynamics: staggered grids, advection schemes, and (in later modules) incompressible solvers, shallow water, SPH, LBM, level… |
| **`fluid_instabilities`** | 451 | 19 | 0 | When a fluid configuration stops being stable, and how fast it comes apart. |
| **`propulsion`** | 361 | 15 | 0 | Rocket propulsion and impulsive orbital transfers. |
### Modern physics
| **`relativity`** | 302 | 18 | 0 | Special relativity. |
| **`general_relativity`** | 427 | 23 | 0 | General relativity: black holes and cosmology. |
| **`quantum`** | 11,941 | 267 | 8 | Quantum mechanics: the elementary relations here, with the wavefunction machinery and the Schrodinger solvers in submodules. |
| **`particle_physics`** | 402 | 20 | 0 | Relativistic kinematics and scattering for particle collisions. |
| **`nuclear`** | 303 | 20 | 0 | Radioactive decay, nuclear binding, and dosimetry. |
| **`neutronics`** | 409 | 22 | 0 | Reactor physics: criticality, neutron diffusion, and shielding. |
### Space
| **`astrophysics`** | 6,122 | 111 | 9 | Astrodynamics and astrophysics. |
### PDE solvers
| **`fem`** | 4,725 | 52 | 6 | Finite elements, finite-difference time domain, and spectral methods. |
| **`sim`** | 4,927 | 101 | 15 | Time-stepping simulation engines. |
| **`fields`** | 211 | 10 | 2 | Uniform-grid scalar fields. |
| **`vector_calculus`** | 1,195 | 14 | 0 | Vector calculus operators and field theory for physics grids. |
### Chemistry and life
| **`chemistry`** | 334 | 18 | 0 | Reaction kinetics, chemical thermodynamics and electrochemistry. |
| **`biophysics`** | 11,396 | 177 | 7 | Biophysics: the elementary membrane, transport and mechanics relations here, with the population-scale models in submodules. |
### Probability and data
| **`statistics`** | 2,125 | 52 | 14 | Statistics: descriptive measures, probability distributions, and Fourier utilities. |
| **`stochastic`** | 15,707 | 253 | 19 | Stochastic processes: Markov chains, Markov chain Monte Carlo, and hidden state models. |
| **`monte_carlo`** | 982 | 28 | 3 | Monte Carlo methods and the random number generator behind them. |
| **`information_theory`** | 367 | 16 | 0 | Shannon information: entropy, divergence, and channel capacity. |
| **`learn`** | 4,213 | 55 | 13 | Learning algorithms, written to be read rather than to be fast. |
### Decisions
| **`optimization`** | 15,189 | 177 | 19 | Optimization: continuous, combinatorial, and strategic. |
| **`finance`** | 5,119 | 60 | 6 | Quantitative finance: derivative pricing, interest rates, portfolio construction and risk measurement. |
### Geometry
| **`geometry`** | 1,522 | 49 | 3 | Areas, volumes and surface areas of the standard shapes. |
| **`curves`** | 500 | 25 | 0 | Plane curves: conics, Bézier curves, and parametric families. |
| **`trigonometry`** | 493 | 33 | 0 | Triangle solving, trigonometric identities, and hyperbolic functions. |
| **`quaternion`** | 562 | 18 | 1 | Unit quaternions for 3-D rotation. |
| **`manifold`** | 20,431 | 720 | 33 | Manifolds and higher-dimensional geometry: generic n-dimensional vectors and tensors, metric-driven curvature, and (in later modules) geodesics,… |
| **`spatial`** | 7,020 | 254 | 25 | Spatial data structures, transforms, geometric primitives, and queries. |
| **`mesh`** | 6,516 | 136 | 10 | Indexed triangle meshes: construction, mass properties, cleanup, spatial queries, and OBJ/STL interchange. |
### Patterns and chaos
| **`fractals`** | 9,454 | 288 | 38 | Fractals: escape-time sets, attractors, automata and noise. |
| **`patterns`** | 12,404 | 239 | 12 | Geometric patterns: polygon algorithms, sampling distributions, phyllotaxis, tilings, symmetry groups, packings, space-filling curves, polyhedra,… |
| **`nonlinear`** | 432 | 13 | 0 | Chaos in low-dimensional systems. |
### Reference and utility
| **`units`** | 2,785 | 85 | 3 | Unit conversions, dimensional analysis and the CODATA constants. |
| **`materials`** | 3,548 | 11 | 6 | Reference property tables. |
| **`color_science`** | 788 | 14 | 0 | Colour: the standard spaces, the transforms between them, and perceptual measures. |
| **`control_systems`** | 744 | 27 | 3 | Linear control: system response, stability margins and PID tuning. |
| **`atmosphere`** | 409 | 17 | 0 | The standard atmosphere, humidity, and near-surface wind. |
| **`verification`** | 394 | 0 | 0 | Kani proof harnesses. |
## Every module
| `acoustics.rs` | `acoustics` | 576 | 31 | 0 | 0 | Room acoustics, psychoacoustic scales, and musical pitch. |
| `astrophysics/mod.rs` | `astrophysics` | 38 | 0 | 0 | 0 | Astrodynamics and astrophysics. |
| `astrophysics/collisions.rs` | `astrophysics::collisions` | 318 | 8 | 0 | 3 | Impacts, mergers, and collision probability. |
| `astrophysics/coords.rs` | `astrophysics::coords` | 1,051 | 11 | 0 | 2 | Astronomical coordinates, low-precision ephemerides and TLE parsing. |
| `astrophysics/gravitational_waves.rs` | `astrophysics::gravitational_waves` | 233 | 8 | 0 | 0 | Gravitational radiation from a compact binary. |
| `astrophysics/habitable_zone.rs` | `astrophysics::habitable_zone` | 127 | 6 | 0 | 0 | Habitable zone boundaries and tidal locking. |
| `astrophysics/kepler.rs` | `astrophysics::kepler` | 913 | 9 | 0 | 0 | Kepler's equation, anomaly conversions and two-body propagation. |
| `astrophysics/lagrange.rs` | `astrophysics::lagrange` | 195 | 4 | 0 | 0 | The five Lagrange points of the circular restricted three-body problem. |
| `astrophysics/lambert.rs` | `astrophysics::lambert` | 553 | 4 | 0 | 0 | Lambert's problem: the orbit connecting two positions in a given time. |
| `astrophysics/magnetosphere.rs` | `astrophysics::magnetosphere` | 405 | 6 | 0 | 1 | Planetary dipole fields and the magnetopause. |
| `astrophysics/maneuvers.rs` | `astrophysics::maneuvers` | 618 | 8 | 0 | 0 | Orbital manoeuvres: combined burns, patched conics, gravity assists and the perturbation that dominates low orbits. |
| `astrophysics/nbody.rs` | `astrophysics::nbody` | 403 | 8 | 7 | 2 | Direct N-body gravitational simulation. |
| `astrophysics/orbital_elements.rs` | `astrophysics::orbital_elements` | 660 | 15 | 5 | 1 | Keplerian elements: conversion, propagation, and the anomalies. |
| `astrophysics/tidal.rs` | `astrophysics::tidal` | 209 | 7 | 0 | 0 | Tidal forces and the Roche limit. |
| `astrophysics/time_systems.rs` | `astrophysics::time_systems` | 399 | 5 | 0 | 0 | Astronomical time: Julian dates and sidereal time. |
| `atmosphere.rs` | `atmosphere` | 409 | 17 | 0 | 0 | The standard atmosphere, humidity, and near-surface wind. |
| `audio/mod.rs` | `audio` | 82 | 0 | 0 | 0 | Audio synthesis, analysis, effects, and I/O. |
| `audio/analysis.rs` | `audio::analysis` | 1,950 | 60 | 0 | 2 | Audio analysis: pitch detection (YIN, autocorrelation, cepstral, HPS, McLeod), onset/tempo/beat tracking, MFCCs, LPC and formants, LSPs, spectral… |
| `audio/effects.rs` | `audio::effects` | 1,669 | 21 | 52 | 20 | Audio effects: delays, reverbs (Schroeder, Freeverb, FDN), convolution, modulation effects, dynamics, distortion, EQ, imaging, loudness (ITU-R… |
| `audio/envelope.rs` | `audio::envelope` | 604 | 9 | 18 | 5 | Envelopes, LFOs, followers, fades, and glides. |
| `audio/oscillators.rs` | `audio::oscillators` | 939 | 16 | 15 | 5 | Audio-rate oscillators and test signals: PolyBLEP anti-aliased classics, additive resynthesis, mipmapped wavetables, colored noise, chirps, and… |
| `audio/physical.rs` | `audio::physical` | 1,331 | 12 | 34 | 8 | Physical modeling synthesis: digital waveguides (plucked/struck/bowed strings, clarinet and flute bores), modal synthesis (bars, membranes,… |
| `audio/spatial.rs` | `audio::spatial` | 1,132 | 28 | 0 | 0 | Spatial audio: panning laws, VBAP, ambisonics, simple binaural cues, Doppler, distance/air attenuation, geometric room acoustics (image source and… |
| `audio/synthesis.rs` | `audio::synthesis` | 1,260 | 29 | 7 | 4 | Sound synthesis: additive, FM (DX7-style operator routing), Karplus-Strong, subtractive, granular, formant, waveshaping, drums, and note/sequence… |
| `audio/tuning.rs` | `audio::tuning` | 517 | 25 | 0 | 2 | Musical tuning: temperaments, interval math, Scala parsing, consonance models, stretch tuning, and pitch-class utilities. |
| `audio/vocoder.rs` | `audio::vocoder` | 862 | 8 | 8 | 2 | Phase vocoder and related voice/spectral processors: time stretching, pitch shifting, robotization, channel and LPC vocoders, WSOLA, PSOLA,… |
| `audio/wav.rs` | `audio::wav` | 370 | 8 | 0 | 1 | WAV (RIFF) reading and writing: PCM 8/16/24/32-bit, IEEE float 32/64-bit, and WAVE_FORMAT_EXTENSIBLE containers. |
| `biophysics/mod.rs` | `biophysics` | 468 | 19 | 0 | 0 | Biophysics: the elementary membrane, transport and mechanics relations here, with the population-scale models in submodules. |
| `biophysics/epidemiology.rs` | `biophysics::epidemiology` | 1,924 | 22 | 1 | 1 | Compartment models of epidemics, their stochastic counterparts, and the quantities estimated from case data. |
| `biophysics/neuro.rs` | `biophysics::neuro` | 2,519 | 35 | 2 | 1 | Computational neuroscience: single neurons, spike trains, synapses and the small networks built from them. |
| `biophysics/phylo.rs` | `biophysics::phylo` | 1,979 | 9 | 19 | 2 | Phylogenetics: trees, the distance and character methods that build them, and the statistics read off them. |
| `biophysics/population.rs` | `biophysics::population` | 2,356 | 36 | 0 | 1 | Population dynamics and population genetics: growth laws, interacting species, age-structured projection, discrete maps, and the drift, selection… |
| `biophysics/seq_align.rs` | `biophysics::seq_align` | 2,150 | 30 | 4 | 2 | Sequence alignment and the elementary sequence analysis around it. |
| `cfd/mod.rs` | `cfd` | 122 | 0 | 0 | 0 | Computational fluid dynamics: staggered grids, advection schemes, and (in later modules) incompressible solvers, shallow water, SPH, LBM, level… |
| `cfd/advection.rs` | `cfd::advection` | 869 | 17 | 0 | 2 | Advection schemes: classic 1D finite-volume methods (upwind, Lax-Wendroff, MUSCL with slope limiters, WENO5), 2D semi-Lagrangian transport with… |
| `cfd/boundary_layer.rs` | `cfd::boundary_layer` | 579 | 31 | 0 | 0 | Boundary layers: Blasius and Falkner-Skan similarity solutions (shooting), Thwaites and Head integral methods, turbulent wall laws, transition and… |
| `cfd/grid.rs` | `cfd::grid` | 685 | 0 | 30 | 4 | Staggered (MAC) grids and cell-centered scalar fields for incompressible flow solvers. |
| `cfd/lbm.rs` | `cfd::lbm` | 1,142 | 8 | 22 | 4 | Lattice Boltzmann method: D2Q9 with BGK/TRT/MRT/cumulant-style collisions, bounce-back solids, Zou-He open boundaries, Guo forcing, D3Q19 and… |
| `cfd/level_set.rs` | `cfd::level_set` | 2,066 | 12 | 34 | 6 | Interface capturing: level sets (upwind/WENO advection, Sussman reinitialization, fast marching, marching squares/tetrahedra), volume of fluid… |
| `cfd/multiphase.rs` | `cfd::multiphase` | 778 | 35 | 1 | 2 | Multiphase flow correlations: mixture properties, drift-flux and void fraction models, two-phase pressure drop, flow-pattern maps, bubble and… |
| `cfd/porous.rs` | `cfd::porous` | 695 | 24 | 8 | 1 | Porous-media flow: Darcy's law and extensions, unsaturated flow (Richards equation with Van Genuchten retention), well hydraulics, solute… |
| `cfd/potential_flow.rs` | `cfd::potential_flow` | 1,523 | 27 | 19 | 5 | Incompressible potential flow: elementary singularities, complex potentials, Joukowski and Karman-Trefftz airfoils, NACA sections, the Hess-Smith… |
| `cfd/riemann.rs` | `cfd::riemann` | 1,564 | 26 | 16 | 6 | 1D/2D compressible Euler equations: exact and approximate Riemann solvers (HLL, HLLC, Roe with entropy fix, Rusanov, AUSM+), MUSCL finite-volume… |
| `cfd/shallow_water.rs` | `cfd::shallow_water` | 938 | 14 | 12 | 1 | Shallow water equations: well-balanced HLL finite volumes with hydrostatic reconstruction and wet/dry handling (1D and 2D), the Stoker dam-break… |
| `cfd/sph.rs` | `cfd::sph` | 1,154 | 9 | 23 | 7 | Smoothed-particle hydrodynamics: standard kernel family, spatial hashing, weakly compressible (WCSPH) and predictive-corrective solvers with… |
| `cfd/stable_fluids.rs` | `cfd::stable_fluids` | 1,776 | 8 | 19 | 3 | Stable-fluids incompressible solver on a MAC grid: MacCormack advection, implicit viscosity, buoyancy, vorticity confinement, and a pressure… |
| `cfd/turbulence.rs` | `cfd::turbulence` | 1,537 | 34 | 12 | 5 | Turbulence modelling and statistics. |
| `cfd/vortex.rs` | `cfd::vortex` | 1,304 | 17 | 19 | 4 | Vortex methods: regularized Biot-Savart particle methods in 2D and 3D, classical vortex solutions (Lamb-Oseen, Rankine, Burgers, Hill), point… |
| `chemistry.rs` | `chemistry` | 334 | 18 | 0 | 0 | Reaction kinetics, chemical thermodynamics and electrochemistry. |
| `classical.rs` | `classical` | 786 | 54 | 0 | 0 | Newtonian mechanics: kinematics, dynamics, and the harmonic oscillator. |
| `codes/mod.rs` | `codes` | 9 | 0 | 0 | 0 | Error detection, error correction, compression, and the arithmetic cryptography is built on. |
| `codes/block.rs` | `codes::block` | 1,579 | 11 | 35 | 2 | Binary linear block codes. |
| `codes/checksum.rs` | `codes::checksum` | 880 | 21 | 0 | 0 | Checksums and check digits: cheap ways to notice that data changed. |
| `codes/compression.rs` | `codes::compression` | 1,420 | 28 | 7 | 3 | Lossless compression, and the string machinery it is built on. |
| `codes/convolutional.rs` | `codes::convolutional` | 1,335 | 17 | 27 | 3 | Convolutional and turbo codes, and the channels they run over. |
| `codes/crypto_math.rs` | `codes::crypto_math` | 1,501 | 24 | 14 | 2 | The arithmetic underneath public-key cryptography, for study rather than for use. |
| `codes/reed_solomon.rs` | `codes::reed_solomon` | 1,519 | 4 | 37 | 6 | Reed-Solomon and BCH codes over finite fields. |
| `color_science.rs` | `color_science` | 788 | 14 | 0 | 0 | Colour: the standard spaces, the transforms between them, and perceptual measures. |
| `continuum_mechanics.rs` | `continuum_mechanics` | 508 | 19 | 0 | 0 | Stress and strain as tensors, and the yield criteria built on them. |
| `control_systems/mod.rs` | `control_systems` | 453 | 18 | 3 | 1 | Linear control: system response, stability margins and PID tuning. |
| `control_systems/kalman.rs` | `control_systems::kalman` | 291 | 0 | 6 | 2 | Kalman filtering. |
| `core/mod.rs` | `core` | 6 | 0 | 0 | 0 | Pure numeric building blocks: compensated summation, forward-mode automatic differentiation, and interval arithmetic. |
| `core/compensated.rs` | `core::compensated` | 117 | 3 | 0 | 0 | Compensated (error-free-transformation) summation. |
| `core/dual.rs` | `core::dual` | 410 | 3 | 15 | 1 | Forward-mode automatic differentiation with dual numbers. |
| `core/interval.rs` | `core::interval` | 451 | 1 | 12 | 1 | Rigorous interval arithmetic with outward rounding. |
| `curves.rs` | `curves` | 500 | 25 | 0 | 0 | Plane curves: conics, Bézier curves, and parametric families. |
| `discrete/mod.rs` | `discrete` | 10 | 0 | 0 | 0 | Discrete mathematics: primes and factorization, elementary and analytic number theory, counting and enumeration, integer partitions, integer… |
| `discrete/combinatorics.rs` | `discrete::combinatorics` | 2,827 | 59 | 0 | 0 | Counting, enumeration, and the permutation group. |
| `discrete/disjoint_set.rs` | `discrete::disjoint_set` | 352 | 0 | 10 | 1 | Union-find over `0..n` with path compression and union by size. |
| `discrete/number_theory.rs` | `discrete::number_theory` | 2,345 | 49 | 0 | 0 | Elementary and analytic number theory. |
| `discrete/partitions.rs` | `discrete::partitions` | 784 | 15 | 0 | 0 | Integer partitions, Young diagrams, and the RSK correspondence. |
| `discrete/primes.rs` | `discrete::primes` | 1,238 | 26 | 0 | 0 | Primes: sieves, primality testing, factorization, and prime counting. |
| `discrete/sequences.rs` | `discrete::sequences` | 1,491 | 22 | 0 | 0 | Integer sequences, linear recurrences, and generating functions. |
| `dsp/mod.rs` | `dsp` | 37 | 0 | 0 | 0 | Digital signal processing: window functions, FIR/IIR filter design, resampling, and phase utilities. |
| `dsp/fir.rs` | `dsp::fir` | 996 | 18 | 3 | 1 | FIR filter design and application. |
| `dsp/iir.rs` | `dsp::iir` | 1,666 | 22 | 26 | 4 | Infinite impulse response filters: RBJ biquads, second-order-section cascades, and classical designs (Butterworth, Chebyshev I/II, elliptic,… |
| `dsp/phase.rs` | `dsp::phase` | 270 | 8 | 0 | 0 | Phase utilities: unwrapping (1D and Itoh 2D), phase-locked loops, interpolated zero crossings, and phase measurement against a reference tone. |
| `dsp/resample.rs` | `dsp::resample` | 513 | 10 | 0 | 0 | Sample-rate conversion: integer up/down sampling, polyphase rational resampling, windowed-sinc/linear/cubic interpolation, CIC decimation, and… |
| `dsp/windows.rs` | `dsp::windows` | 446 | 7 | 0 | 2 | Window functions for spectral analysis and FIR design. |
| `electromagnetism.rs` | `electromagnetism` | 822 | 60 | 0 | 0 | Classical electromagnetism, from Coulomb's law to radiating dipoles. |
| `electronics.rs` | `electronics` | 445 | 17 | 0 | 0 | Semiconductor device physics. |
| `error.rs` | `error` | 103 | 0 | 0 | 2 | Error types shared by the numerical solvers. |
| `exact/mod.rs` | `exact` | 15 | 0 | 0 | 0 | Exact arithmetic: arbitrary-precision integers, exact rationals, arbitrary-precision binary floating point, polynomials, and continued fractions. |
| `exact/bigfloat.rs` | `exact::bigfloat` | 2,000 | 5 | 39 | 1 | Arbitrary-precision binary floating point. |
| `exact/bigint.rs` | `exact::bigint` | 1,463 | 0 | 41 | 1 | Arbitrary-precision signed integers. |
| `exact/contfrac.rs` | `exact::contfrac` | 524 | 10 | 0 | 0 | Continued fractions: expansions, convergents, the periodic expansion of a square root, Pell's equation, generalized continued fractions by the… |
| `exact/polynomial.rs` | `exact::polynomial` | 2,286 | 5 | 76 | 2 | Dense univariate polynomials with `f64` coefficients ([`Poly`]) and with exact rational coefficients ([`PolyQ`]). |
| `exact/rational.rs` | `exact::rational` | 1,079 | 8 | 26 | 1 | Exact rational arithmetic over [`BigInt`]. |
| `exact/symbolic.rs` | `exact::symbolic` | 1,882 | 3 | 29 | 3 | A small computer algebra system over expression trees. |
| `fem/mod.rs` | `fem` | 25 | 0 | 0 | 0 | Finite elements, finite-difference time domain, and spectral methods. |
| `fem/fdtd.rs` | `fem::fdtd` | 1,154 | 7 | 1 | 3 | Finite-difference time domain: Maxwell's equations on a Yee grid. |
| `fem/fem1d.rs` | `fem::fem1d` | 952 | 7 | 6 | 2 | One-dimensional finite elements for `-(p u')' + q u = f`. |
| `fem/fem2d.rs` | `fem::fem2d` | 1,901 | 16 | 8 | 1 | Triangular finite elements in the plane. |
| `fem/spectral_pde.rs` | `fem::spectral_pde` | 693 | 7 | 0 | 0 | Spectral methods: global basis functions instead of local ones. |
| `fields.rs` | `fields` | 211 | 0 | 10 | 2 | Uniform-grid scalar fields. |
| `finance/mod.rs` | `finance` | 25 | 0 | 0 | 0 | Quantitative finance: derivative pricing, interest rates, portfolio construction and risk measurement. |
| `finance/options.rs` | `finance::options` | 2,090 | 17 | 0 | 3 | Option pricing: closed forms, lattices, Monte Carlo and a PDE solver. |
| `finance/portfolio.rs` | `finance::portfolio` | 865 | 16 | 0 | 0 | Portfolio construction and performance measurement. |
| `finance/rates.rs` | `finance::rates` | 1,388 | 19 | 1 | 2 | Interest rates: discounting, bonds, curves and short-rate models. |
| `finance/risk.rs` | `finance::risk` | 751 | 7 | 0 | 1 | Risk measurement: value at risk, expected shortfall, backtesting. |
| `fluid_instabilities.rs` | `fluid_instabilities` | 451 | 19 | 0 | 0 | When a fluid configuration stops being stable, and how fast it comes apart. |
| `fluids.rs` | `fluids` | 709 | 45 | 0 | 0 | Fluid statics and single-phase flow. |
| `fractals/mod.rs` | `fractals` | 642 | 10 | 5 | 1 | Fractals: escape-time sets, attractors, automata and noise. |
| `fractals/attractors.rs` | `fractals::attractors` | 1,104 | 42 | 8 | 3 | Strange attractors: 3-D chaotic flows and 2-D chaotic maps with trajectory integration, Lyapunov spectra (Benettin renormalization), Kaplan-Yorke… |
| `fractals/automata.rs` | `fractals::automata` | 2,881 | 29 | 63 | 16 | Cellular automata and growth models: elementary 1-D rules, life-like 2-D automata with pattern/RLE placement, cyclic CA, Langton's ant and… |
| `fractals/escape_time.rs` | `fractals::escape_time` | 1,044 | 24 | 0 | 3 | Escape-time fractals: a generic iteration engine with smooth coloring, orbit traps, and distance estimation, the classic quadratic families… |
| `fractals/ifs.rs` | `fractals::ifs` | 924 | 18 | 12 | 3 | Iterated function systems: the chaos game and deterministic attractor construction (Barnsley, "Fractals Everywhere", 1988), Moran similarity… |
| `fractals/lsystem.rs` | `fractals::lsystem` | 1,056 | 25 | 12 | 4 | Lindenmayer systems: parallel string rewriting with simple, stochastic, and context-sensitive rules, 2-D and 3-D turtle interpretation of the ABOP… |
| `fractals/noise.rs` | `fractals::noise` | 1,803 | 19 | 21 | 8 | Coherent noise: Perlin gradient noise (Perlin 2002), OpenSimplex2 (ported from K.jpg's reference implementation), value noise, Worley cellular… |
| `general_relativity.rs` | `general_relativity` | 427 | 23 | 0 | 0 | General relativity: black holes and cosmology. |
| `geometry/mod.rs` | `geometry` | 453 | 30 | 0 | 0 | Areas, volumes and surface areas of the standard shapes. |
| `geometry/delaunay.rs` | `geometry::delaunay` | 262 | 3 | 0 | 0 | Delaunay triangulation and Voronoi diagrams in the plane. |
| `geometry/geodesy.rs` | `geometry::geodesy` | 342 | 5 | 2 | 1 | Geodesy on a reference ellipsoid. |
| `geometry/hull.rs` | `geometry::hull` | 310 | 4 | 0 | 0 | Convex hulls and polygon predicates. |
| `geometry/mesh.rs` | `geometry::mesh` | 155 | 0 | 5 | 2 | Minimal indexed triangle mesh with ray intersection, backfilling the Part 2 `Mesh` type consumed by acoustics ray tracing and display helpers. |
| `geophysics.rs` | `geophysics` | 483 | 22 | 0 | 0 | The solid Earth: gravity, seismology, and heat. |
| `graph/mod.rs` | `graph` | 12 | 0 | 0 | 0 | Graphs: representation and structure, shortest paths, network flow, matchings, spectral graph theory, colouring, and drawing. |
| `graph/coloring.rs` | `graph::coloring` | 1,649 | 20 | 0 | 1 | Colouring, cliques, independent sets, and covers. |
| `graph/core.rs` | `graph::core` | 2,862 | 24 | 41 | 1 | Graphs: representation, structural queries, generators, and products. |
| `graph/flow.rs` | `graph::flow` | 1,519 | 14 | 0 | 0 | Network flow: maximum flow, minimum cut, and the problems that reduce to them. |
| `graph/layout.rs` | `graph::layout` | 1,935 | 15 | 0 | 0 | Graph drawing: where to put the vertices. |
| `graph/matching.rs` | `graph::matching` | 1,399 | 10 | 0 | 0 | Matchings: bipartite, general, weighted, and stable. |
| `graph/paths.rs` | `graph::paths` | 2,133 | 26 | 0 | 1 | Shortest paths, spanning trees, and tours. |
| `graph/spectral.rs` | `graph::spectral` | 1,984 | 32 | 0 | 0 | Spectral graph theory: Laplacians, centralities, resistances, and community detection. |
| `gravitation.rs` | `gravitation` | 236 | 14 | 0 | 0 | Newtonian gravity and two-body orbits. |
| `information_theory.rs` | `information_theory` | 367 | 16 | 0 | 0 | Shannon information: entropy, divergence, and channel capacity. |
| `learn/mod.rs` | `learn` | 16 | 0 | 0 | 0 | Learning algorithms, written to be read rather than to be fast. |
| `learn/cluster.rs` | `learn::cluster` | 1,295 | 13 | 2 | 3 | Clustering, mixture models and nearest neighbours. |
| `learn/gp.rs` | `learn::gp` | 839 | 1 | 12 | 2 | Gaussian process regression. |
| `learn/nn.rs` | `learn::nn` | 1,163 | 2 | 14 | 4 | Feed-forward networks, trained by backpropagation. |
| `learn/tree.rs` | `learn::tree` | 900 | 11 | 0 | 4 | Decision trees, random forests and gradient boosting. |
| `linalg/mod.rs` | `linalg` | 970 | 10 | 24 | 2 | Dense and sparse linear algebra. |
| `linalg/cholesky.rs` | `linalg::cholesky` | 147 | 2 | 0 | 0 | Cholesky factorization of symmetric positive-definite matrices. |
| `linalg/eigen.rs` | `linalg::eigen` | 492 | 2 | 0 | 1 | Eigenvalue solvers. |
| `linalg/lu.rs` | `linalg::lu` | 223 | 2 | 4 | 1 | LU decomposition with partial pivoting (Doolittle form). |
| `linalg/matrix.rs` | `linalg::matrix` | 344 | 0 | 16 | 1 | Dense row-major matrix of `f64`. |
| `linalg/qr.rs` | `linalg::qr` | 205 | 2 | 0 | 1 | QR decomposition by Householder reflections and least-squares solve. |
| `linalg/sparse.rs` | `linalg::sparse` | 360 | 2 | 4 | 1 | Compressed sparse row (CSR) matrices and conjugate-gradient solvers. |
| `linalg/svd.rs` | `linalg::svd` | 321 | 4 | 0 | 1 | Singular value decomposition by one-sided Jacobi rotations. |
| `linalg/tridiagonal.rs` | `linalg::tridiagonal` | 233 | 2 | 0 | 0 | Tridiagonal linear solve (Thomas algorithm). |
| `magnetohydrodynamics.rs` | `magnetohydrodynamics` | 359 | 19 | 0 | 0 | Magnetohydrodynamics: a conducting fluid and the field frozen into it. |
| `manifold/mod.rs` | `manifold` | 105 | 0 | 0 | 0 | Manifolds and higher-dimensional geometry: generic n-dimensional vectors and tensors, metric-driven curvature, and (in later modules) geodesics,… |
| `manifold/clifford.rs` | `manifold::clifford` | 2,830 | 93 | 45 | 2 | Clifford (geometric) algebras Cl(p, q, r): a dense multivector type over any signature, with the geometric/outer/inner products, versors and… |
| `manifold/dec.rs` | `manifold::dec` | 1,618 | 3 | 30 | 1 | Discrete exterior calculus on triangle meshes: exterior derivatives, diagonal Hodge stars, Laplacians, Hodge decomposition, harmonic forms and… |
| `manifold/embedding.rs` | `manifold::embedding` | 1,624 | 40 | 0 | 0 | Manifold learning and dimensionality reduction: spectral embeddings (MDS, Isomap, LLE, Laplacian eigenmaps, diffusion maps), PCA and kernel PCA,… |
| `manifold/geodesic.rs` | `manifold::geodesic` | 1,422 | 8 | 22 | 2 | Geodesics, parallel transport, Jacobi fields, and relativistic orbits, all driven by the finite-difference [`Metric`] machinery. |
| `manifold/hyperbolic.rs` | `manifold::hyperbolic` | 1,710 | 43 | 9 | 2 | Hyperbolic geometry across the standard models: Poincare disk/ball, upper half-plane/space, Klein disk, and the hyperboloid, with isometries,… |
| `manifold/lie.rs` | `manifold::lie` | 3,225 | 17 | 108 | 15 | Lie groups and algebras: rotation and rigid-motion groups in 2/3/4 dimensions, SU(2) and SL(2) groups, matrix exponentials and logarithms,… |
| `manifold/metric.rs` | `manifold::metric` | 1,382 | 5 | 49 | 2 | Metric geometry on n-dimensional manifolds: a metric is a function from coordinates to a matrix g_ij, and everything else — Christoffel symbols,… |
| `manifold/polytope4.rs` | `manifold::polytope4` | 2,142 | 27 | 41 | 2 | Four-dimensional polytopes: the six regular 4-polytopes with their full combinatorics, prisms and products, projections and cross-sections, duals,… |
| `manifold/spacetime.rs` | `manifold::spacetime` | 1,556 | 30 | 30 | 5 | Special and general relativity: four-vectors and Lorentz transforms, Rindler and Kruskal coordinates, Schwarzschild and Kerr geodesics,… |
| `manifold/spherical.rs` | `manifold::spherical` | 1,671 | 67 | 0 | 0 | Spherical geometry: n-sphere maps, spherical trigonometry, map projections, the Hopf fibration, spherical harmonics and their transforms, sky… |
| `manifold/vecn.rs` | `manifold::vecn` | 1,146 | 3 | 50 | 2 | n-dimensional vectors and arbitrary-rank tensors: the generic machinery behind the metric-driven differential geometry in this module tree. |
| `materials/mod.rs` | `materials` | 17 | 0 | 0 | 0 | Reference property tables. |
| `materials/common.rs` | `materials::common` | 349 | 2 | 0 | 1 | Engineering solids: metals, alloys, polymers and ceramics. |
| `materials/elements.rs` | `materials::elements` | 2,632 | 5 | 0 | 3 | The 118 chemical elements. |
| `materials/fluids.rs` | `materials::fluids` | 308 | 2 | 0 | 1 | Common liquids. |
| `materials/gases.rs` | `materials::gases` | 242 | 2 | 0 | 1 | Common gases. |
| `math.rs` | `math` | 621 | 0 | 23 | 2 | Vectors and the crate's table of physical constants. |
| `mesh/mod.rs` | `mesh` | 1,071 | 0 | 32 | 1 | Indexed triangle meshes: construction, mass properties, cleanup, spatial queries, and OBJ/STL interchange. |
| `mesh/analyze.rs` | `mesh::analyze` | 1,201 | 20 | 0 | 1 | Mesh analysis: topology (manifoldness, orientation, boundary, components, genus), quality statistics, QEM decimation, discrete curvatures, and… |
| `mesh/generate.rs` | `mesh::generate` | 881 | 14 | 0 | 0 | Procedural mesh generators. |
| `mesh/isosurface.rs` | `mesh::isosurface` | 1,052 | 8 | 9 | 2 | Isosurface and isocontour extraction from sampled scalar fields: marching squares/cubes/tetrahedra, surface nets, dual contouring, and metaballs. |
| `mesh/parameterize.rs` | `mesh::parameterize` | 652 | 7 | 0 | 1 | Mesh parameterization: closed-form spherical/planar/cylindrical projections, harmonic (cotangent-Laplace) disk parameterization with fixed… |
| `mesh/subdivide.rs` | `mesh::subdivide` | 616 | 9 | 3 | 1 | Subdivision surfaces (Loop, Catmull-Clark, sqrt(3), midpoint) and Laplacian-family smoothing. |
| `mesh/surfaces.rs` | `mesh::surfaces` | 1,043 | 19 | 15 | 4 | Parametric surfaces: Bézier/B-spline/NURBS patches, classic surface constructions, differential geometry via fundamental forms, and a catalogue of… |
| `monte_carlo/mod.rs` | `monte_carlo` | 700 | 15 | 5 | 1 | Monte Carlo methods and the random number generator behind them. |
| `monte_carlo/quasi.rs` | `monte_carlo::quasi` | 282 | 2 | 6 | 2 | Quasi-random (low-discrepancy) sequences: Sobol and Halton. |
| `neutronics.rs` | `neutronics` | 409 | 22 | 0 | 0 | Reactor physics: criticality, neutron diffusion, and shielding. |
| `nonlinear.rs` | `nonlinear` | 432 | 13 | 0 | 0 | Chaos in low-dimensional systems. |
| `nuclear.rs` | `nuclear` | 303 | 20 | 0 | 0 | Radioactive decay, nuclear binding, and dosimetry. |
| `numerical/mod.rs` | `numerical` | 424 | 0 | 0 | 0 | Numerical methods: quadrature, root finding, ODE solvers, and interpolation. |
| `numerical/bvp.rs` | `numerical::bvp` | 201 | 2 | 0 | 0 | Two-point boundary value problems. |
| `numerical/integrate.rs` | `numerical::integrate` | 270 | 8 | 0 | 1 | Numerical integration (quadrature) rules. |
| `numerical/interpolate.rs` | `numerical::interpolate` | 648 | 6 | 9 | 2 | Interpolation routines. |
| `numerical/ode/mod.rs` | `numerical::ode` | 11 | 0 | 0 | 0 | Ordinary differential equation solvers. |
| `numerical/ode/adaptive.rs` | `numerical::ode::adaptive` | 309 | 2 | 0 | 1 | Adaptive Runge-Kutta integration: Dormand-Prince 5(4). |
| `numerical/ode/explicit.rs` | `numerical::ode::explicit` | 63 | 4 | 0 | 0 | Explicit fixed-step ODE integrators. |
| `numerical/ode/implicit.rs` | `numerical::ode::implicit` | 232 | 2 | 0 | 0 | Implicit (stiff-stable) ODE steps: backward Euler and BDF2. |
| `numerical/ode/symplectic.rs` | `numerical::ode::symplectic` | 125 | 3 | 0 | 0 | Symplectic integrators for second-order systems x'' = a(x). |
| `numerical/roots.rs` | `numerical::roots` | 280 | 7 | 0 | 0 | Scalar and polynomial root finding. |
| `optics.rs` | `optics` | 348 | 20 | 0 | 0 | Geometric and wave optics. |
| `optimization/mod.rs` | `optimization` | 828 | 11 | 0 | 0 | Optimization: continuous, combinatorial, and strategic. |
| `optimization/convex.rs` | `optimization::convex` | 2,410 | 35 | 0 | 0 | Convex optimisation: gradient methods, quasi-Newton methods, proximal splitting, and constrained solvers. |
| `optimization/game_theory.rs` | `optimization::game_theory` | 3,326 | 41 | 0 | 11 | Game theory: equilibria, dynamics, cooperative solution concepts, auctions, and two-player search. |
| `optimization/integer.rs` | `optimization::integer` | 2,694 | 33 | 0 | 1 | Integer programming, dynamic programming, and combinatorial search. |
| `optimization/least_squares.rs` | `optimization::least_squares` | 371 | 3 | 0 | 1 | Nonlinear least squares: Levenberg-Marquardt. |
| `optimization/lp.rs` | `optimization::lp` | 2,600 | 13 | 8 | 3 | Linear programming: the simplex method, interior point methods, duality, and the classical models that reduce to a linear program. |
| `optimization/metaheuristics.rs` | `optimization::metaheuristics` | 1,577 | 15 | 0 | 2 | Derivative-free and population-based optimisation, and the benchmark landscapes used to tell one method from another. |
| `optimization/network.rs` | `optimization::network` | 1,383 | 17 | 1 | 1 | Network models and scheduling: project planning, flows on networks, and the sequencing rules that provably optimise a stated objective. |
| `particle_physics.rs` | `particle_physics` | 402 | 20 | 0 | 0 | Relativistic kinematics and scattering for particle collisions. |
| `patterns/mod.rs` | `patterns` | 14 | 0 | 0 | 0 | Geometric patterns: polygon algorithms, sampling distributions, phyllotaxis, tilings, symmetry groups, packings, space-filling curves, polyhedra,… |
| `patterns/aperiodic.rs` | `patterns::aperiodic` | 1,807 | 13 | 0 | 2 | Aperiodic tilings: Penrose P2 (kite/dart) and P3 (rhombs) by Robinson-triangle deflation, de Bruijn multigrid projection, Ammann-Beenker, the hat… |
| `patterns/knots.rs` | `patterns::knots` | 831 | 20 | 0 | 0 | Knots and space curves: parametric knot families, Frenet and rotation-minimizing frames, curvature/torsion estimates, and the classical knot… |
| `patterns/packing.rs` | `patterns::packing` | 1,130 | 17 | 0 | 0 | Circle and sphere packings: Descartes/Apollonian circles, lattice packings, random sequential adsorption, Doyle spirals, Ford circles, Steiner… |
| `patterns/phyllotaxis.rs` | `patterns::phyllotaxis` | 490 | 18 | 0 | 0 | Phyllotactic patterns and spirals: Vogel sunflowers, Fibonacci point sets, the classical spiral family, and parastichy analysis. |
| `patterns/polygon_ops.rs` | `patterns::polygon_ops` | 2,022 | 29 | 0 | 1 | 2-D polygon algorithms: triangulation, simplification, offsetting, Minkowski sums, boolean operations, clipping, decomposition, hulls, skeletons,… |
| `patterns/polyhedra.rs` | `patterns::polyhedra` | 2,032 | 32 | 14 | 2 | Polyhedra: Platonic/Archimedean/Catalan/Johnson solids, Goldberg and geodesic polyhedra, and Conway polyhedron operators. |
| `patterns/sampling.rs` | `patterns::sampling` | 1,220 | 27 | 0 | 0 | Random and low-discrepancy sampling: Poisson disk (Bridson), blue-noise ranking, stratified jitter, uniform samplers over shapes, random polygons… |
| `patterns/space_filling.rs` | `patterns::space_filling` | 755 | 20 | 0 | 0 | Space-filling curves and locality-preserving orders: Hilbert (2-D and 3-D), Peano, Morton/Z-order, Gray codes, and L-system curves (Sierpiński… |
| `patterns/symmetry.rs` | `patterns::symmetry` | 996 | 14 | 7 | 4 | Plane symmetry groups (the 17 wallpaper groups and 7 frieze groups), lattices, 3-D point groups, symmetry detection, and Hankin-style Islamic star… |
| `patterns/tilings.rs` | `patterns::tilings` | 1,107 | 10 | 18 | 3 | Plane tilings: regular and Archimedean (uniform) tilings, their Laves duals, hex-grid coordinate algebra, and a few classic non-edge-to-edge… |
| `photonics.rs` | `photonics` | 485 | 26 | 0 | 0 | Laser beams, optical fibre, and interferometry. |
| `plasma.rs` | `plasma` | 297 | 16 | 0 | 0 | Plasma parameters: the characteristic lengths, frequencies and speeds. |
| `propulsion.rs` | `propulsion` | 361 | 15 | 0 | 0 | Rocket propulsion and impulsive orbital transfers. |
| `quantum/mod.rs` | `quantum` | 411 | 27 | 0 | 0 | Quantum mechanics: the elementary relations here, with the wavefunction machinery and the Schrodinger solvers in submodules. |
| `quantum/algorithms.rs` | `quantum::algorithms` | 1,707 | 24 | 0 | 0 | Quantum algorithms on the state-vector simulator. |
| `quantum/circuit.rs` | `quantum::circuit` | 2,460 | 15 | 77 | 5 | A state-vector quantum circuit simulator, with density matrices and noise channels. |
| `quantum/schrodinger.rs` | `quantum::schrodinger` | 2,607 | 25 | 0 | 1 | Solvers for the Schrodinger equation, stationary and time dependent. |
| `quantum/solid_state.rs` | `quantum::solid_state` | 1,685 | 38 | 0 | 0 | Electrons and phonons in crystals: bands, densities of states, transport, and the standard model systems. |
| `quantum/spin.rs` | `quantum::spin` | 1,703 | 19 | 10 | 1 | Spin operators, quantum magnets, and magnetic resonance. |
| `quantum/wavefunction.rs` | `quantum::wavefunction` | 1,368 | 13 | 19 | 1 | One-dimensional wavefunctions, the standard eigenstates, and phase-space distributions. |
| `quaternion.rs` | `quaternion` | 562 | 2 | 16 | 1 | Unit quaternions for 3-D rotation. |
| `radiation.rs` | `radiation` | 335 | 14 | 0 | 0 | Thermal radiation and radiative transfer. |
| `relativity.rs` | `relativity` | 302 | 18 | 0 | 0 | Special relativity. |
| `resonance/mod.rs` | `resonance` | 42 | 0 | 0 | 0 | Resonance and vibration: single and coupled oscillators, acoustic and electromagnetic cavities, nonlinear resonance, and structural dynamics. |
| `resonance/cavity.rs` | `resonance::cavity` | 931 | 32 | 13 | 3 | Resonant cavities and structures: RLC circuits, Helmholtz resonators, strings, air columns, membranes, plates, beams, rooms, optical etalons, and… |
| `resonance/coupled.rs` | `resonance::coupled` | 828 | 6 | 18 | 1 | Coupled linear oscillators: normal modes, modal superposition, receptance, classic two-body systems, Kuramoto synchronization, and… |
| `resonance/nonlinear.rs` | `resonance::nonlinear` | 704 | 22 | 0 | 0 | Nonlinear resonance: the Duffing and van der Pol oscillators, parametric (Mathieu) stability, Fano interference, synchronization pulling/locking,… |
| `resonance/oscillator.rs` | `resonance::oscillator` | 636 | 9 | 19 | 2 | The damped harmonic oscillator m·x″ + c·x′ + k·x = F(t): closed-form responses in every damping regime, frequency-domain descriptions, and… |
| `resonance/structural.rs` | `resonance::structural` | 1,134 | 6 | 19 | 1 | Structural dynamics: finite-element bars and beams, modal analysis with general (consistent) mass matrices, Rayleigh damping, implicit time… |
| `rf.rs` | `rf` | 440 | 28 | 0 | 0 | Radio-frequency engineering: links, lines and noise. |
| `signal_processing/mod.rs` | `signal_processing` | 708 | 16 | 0 | 0 | Time-domain signal operations and test waveforms. |
| `sim/mod.rs` | `sim` | 21 | 0 | 0 | 0 | Time-stepping simulation engines. |
| `sim/cloth_sim.rs` | `sim::cloth_sim` | 970 | 2 | 10 | 3 | Verlet cloth and rope with spring constraints. |
| `sim/em_sim.rs` | `sim::em_sim` | 638 | 0 | 15 | 2 | FDTD electromagnetic simulation in one and two dimensions. |
| `sim/fluid_sim.rs` | `sim::fluid_sim` | 1,161 | 0 | 17 | 3 | Compact fluid solvers: column, shallow water, and 2-D Euler. |
| `sim/heat_sim.rs` | `sim::heat_sim` | 774 | 0 | 22 | 3 | Heat conduction and convection-diffusion on a grid. |
| `sim/rigid_body.rs` | `sim::rigid_body` | 681 | 2 | 19 | 2 | Rigid body dynamics in three dimensions. |
| `sim/wave_sim.rs` | `sim::wave_sim` | 682 | 0 | 14 | 2 | The wave equation in one and two dimensions. |
| `solid_mechanics.rs` | `solid_mechanics` | 380 | 23 | 0 | 0 | Strength of materials: stress, strain, elastic constants and beams. |
| `spatial/mod.rs` | `spatial` | 33 | 0 | 0 | 0 | Spatial data structures, transforms, geometric primitives, and queries. |
| `spatial/bvh.rs` | `spatial::bvh` | 513 | 0 | 10 | 1 | Bounding volume hierarchy over axis-aligned boxes. |
| `spatial/contain.rs` | `spatial::contain` | 527 | 20 | 0 | 0 | Orientation predicates and containment tests. |
| `spatial/distance.rs` | `spatial::distance` | 495 | 18 | 0 | 0 | Closest-point queries and set distances. |
| `spatial/frame.rs` | `spatial::frame` | 215 | 0 | 15 | 1 | Rigid coordinate frames (origin + unit-quaternion rotation). |
| `spatial/intersect.rs` | `spatial::intersect` | 908 | 23 | 0 | 1 | Intersection tests between the spatial primitives. |
| `spatial/kdtree.rs` | `spatial::kdtree` | 510 | 0 | 9 | 2 | k-d trees (3-D and 2-D) with median splits, plus a uniform spatial hash for broadphase neighbor queries. |
| `spatial/mat4.rs` | `spatial::mat4` | 504 | 0 | 21 | 1 | 4×4 homogeneous transform matrix (row-major storage, column-vector convention: p' = M·p). |
| `spatial/octree.rs` | `spatial::octree` | 342 | 1 | 2 | 1 | Barnes-Hut octree for N-body force approximation. |
| `spatial/primitives.rs` | `spatial::primitives` | 1,128 | 0 | 63 | 15 | Geometric primitive types shared by the intersection, distance, containment, and acceleration modules. |
| `spatial/projective.rs` | `spatial::projective` | 447 | 8 | 5 | 1 | Homogeneous 2-D projective geometry: points, lines, cross ratios, and plane homographies (Hartley & Zisserman, *Multiple View Geometry*, ch. |
| `spatial/quadtree.rs` | `spatial::quadtree` | 359 | 0 | 7 | 1 | Point quadtree with bucket capacity and depth limit. |
| `spatial/sdf.rs` | `spatial::sdf` | 731 | 37 | 0 | 0 | Signed distance fields: primitives, combinators, domain operators, and queries (sphere tracing, normals, AO, soft shadows). |
| `spatial/transform2d.rs` | `spatial::transform2d` | 308 | 0 | 15 | 1 | 2-D affine transforms stored as 3×3 homogeneous matrices (last row 0 0 1), column-vector convention: p' = M·p. |
| `special/mod.rs` | `special` | 26 | 0 | 0 | 0 | Special functions: error function family, gamma family, and beta functions. |
| `special/bessel.rs` | `special::bessel` | 528 | 12 | 0 | 0 | Bessel functions of integer order. |
| `special/beta.rs` | `special::beta` | 145 | 2 | 0 | 0 | Beta function and regularized incomplete beta. |
| `special/elliptic.rs` | `special::elliptic` | 333 | 7 | 0 | 0 | Elliptic integrals and physical applications. |
| `special/erf.rs` | `special::erf` | 335 | 3 | 0 | 0 | Error function family. |
| `special/expint.rs` | `special::expint` | 126 | 2 | 0 | 0 | Exponential integrals Ei(x) and E1(x). |
| `special/gamma.rs` | `special::gamma` | 219 | 4 | 0 | 0 | Gamma function family. |
| `special/legendre.rs` | `special::legendre` | 243 | 4 | 0 | 0 | Legendre polynomials, associated Legendre functions, real spherical harmonics, and Gauss-Legendre quadrature nodes. |
| `statistical_mechanics/mod.rs` | `statistical_mechanics` | 441 | 21 | 0 | 0 | Statistical mechanics: the elementary relations here, with lattice models and Monte Carlo in submodules. |
| `statistical_mechanics/ising.rs` | `statistical_mechanics::ising` | 2,004 | 13 | 23 | 4 | The Ising model and its relatives, by Monte Carlo. |
| `statistical_mechanics/kinetics.rs` | `statistical_mechanics::kinetics` | 2,806 | 36 | 3 | 2 | Chemical kinetics: rate laws, deterministic and stochastic reaction networks, enzyme saturation, equilibrium composition, oscillating mechanisms,… |
| `statistical_mechanics/lattice_models.rs` | `statistical_mechanics::lattice_models` | 1,199 | 17 | 0 | 0 | Lattice models: percolation, walks, growth, and avalanches. |
| `statistical_mechanics/md.rs` | `statistical_mechanics::md` | 3,237 | 12 | 36 | 3 | Molecular dynamics: pair potentials, a cell-list force evaluation, a symplectic integrator, thermostats and barostats, and the structural and… |
| `statistics/mod.rs` | `statistics` | 288 | 2 | 0 | 0 | Statistics: descriptive measures, probability distributions, and Fourier utilities. |
| `statistics/descriptive.rs` | `statistics::descriptive` | 114 | 12 | 0 | 0 | Descriptive statistics, error propagation, and weighted means. |
| `statistics/distributions.rs` | `statistics::distributions` | 1,013 | 7 | 13 | 12 | Probability distributions: densities, mass functions, and CDFs. |
| `statistics/fourier.rs` | `statistics::fourier` | 56 | 4 | 0 | 0 | Discrete Fourier transform utilities. |
| `statistics/inference.rs` | `statistics::inference` | 415 | 10 | 0 | 1 | Hypothesis tests and confidence intervals. |
| `statistics/resampling.rs` | `statistics::resampling` | 239 | 4 | 0 | 1 | Resampling methods: bootstrap, BCa bootstrap, permutation tests, and the jackknife. |
| `stochastic/mod.rs` | `stochastic` | 11 | 0 | 0 | 0 | Stochastic processes: Markov chains, Markov chain Monte Carlo, and hidden state models. |
| `stochastic/extreme.rs` | `stochastic::extreme` | 1,852 | 27 | 0 | 1 | Extreme value theory and copulas: the distribution of maxima, the distribution of exceedances, and the dependence structure between them. |
| `stochastic/hmm.rs` | `stochastic::hmm` | 1,451 | 4 | 26 | 4 | Hidden state models: hidden Markov models, smoothing, and particle filters. |
| `stochastic/markov.rs` | `stochastic::markov` | 1,952 | 0 | 37 | 3 | Finite Markov chains and Markov chain Monte Carlo. |
| `stochastic/point_process.rs` | `stochastic::point_process` | 1,373 | 25 | 0 | 0 | Point processes: random collections of points in time or space. |
| `stochastic/queueing.rs` | `stochastic::queueing` | 1,933 | 16 | 8 | 4 | Queueing theory: birth-death queues, Erlang loss and delay formulas, networks of queues, and continuous-time Markov chains. |
| `stochastic/rmt.rs` | `stochastic::rmt` | 1,217 | 18 | 0 | 0 | Random matrix theory: the classical ensembles, their limiting spectral laws, and the local statistics that distinguish correlated spectra from… |
| `stochastic/sde.rs` | `stochastic::sde` | 1,939 | 32 | 0 | 1 | Stochastic differential equations: simulation, convergence, and the densities the paths are distributed by. |
| `stochastic/timeseries.rs` | `stochastic::timeseries` | 3,979 | 28 | 32 | 6 | Time series analysis: correlation structure, stationarity, ARMA models, smoothing, volatility, and change detection. |
| `thermodynamics.rs` | `thermodynamics` | 808 | 52 | 0 | 0 | Thermodynamics: gases, heat transfer, cycles and phase change. |
| `transforms/mod.rs` | `transforms` | 54 | 0 | 0 | 0 | Discrete transforms: FFT (any length), DCT/DST, STFT, wavelets, Hilbert, Laplace inversion, Radon, and spectral estimation. |
| `transforms/dct.rs` | `transforms::dct` | 489 | 12 | 0 | 1 | Discrete cosine, sine, and Hartley transforms. |
| `transforms/fft.rs` | `transforms::fft` | 962 | 21 | 5 | 1 | Fast Fourier transforms. |
| `transforms/hilbert.rs` | `transforms::hilbert` | 570 | 13 | 0 | 0 | Hilbert transform, analytic signals, modulation, empirical mode decomposition, and causality (Kramers-Kronig) tools. |
| `transforms/laplace.rs` | `transforms::laplace` | 435 | 8 | 0 | 0 | Laplace-domain tools: numerical inverse transforms (fixed-Talbot and Gaver-Stehfest), the z-transform, transfer-function responses, and a discrete… |
| `transforms/radon.rs` | `transforms::radon` | 619 | 9 | 0 | 1 | Radon transform and tomographic reconstruction, plus Hankel/Abel transforms and Hough voting. |
| `transforms/spectral.rs` | `transforms::spectral` | 808 | 18 | 0 | 0 | Spectral estimation: periodogram, Welch averaging, multitaper (DPSS), parametric AR models (Burg, Yule-Walker), MUSIC, cross-spectra, coherence,… |
| `transforms/stft.rs` | `transforms::stft` | 695 | 10 | 8 | 1 | Short-time Fourier transform, spectrograms, Goertzel, chirp-z, and constant-Q analysis. |
| `transforms/wavelet.rs` | `transforms::wavelet` | 1,022 | 16 | 0 | 4 | Discrete and continuous wavelet transforms. |
| `transforms/wavelet_tables.rs` | `transforms::wavelet_tables` | 699 | 0 | 0 | 0 | Canonical orthogonal/biorthogonal scaling-filter tables (values from PyWavelets `wavelets_coeffs.template.h`, which in turn credits the classical… |
| `trigonometry.rs` | `trigonometry` | 493 | 33 | 0 | 0 | Triangle solving, trigonometric identities, and hyperbolic functions. |
| `units/mod.rs` | `units` | 813 | 54 | 0 | 0 | Unit conversions, dimensional analysis and the CODATA constants. |
| `units/dimensional.rs` | `units::dimensional` | 974 | 7 | 0 | 0 | Dimensional analysis: Buckingham's theorem, the named groups, natural units and the Planck scale. |
| `units/quantity.rs` | `units::quantity` | 998 | 7 | 17 | 3 | Values that carry their dimensions. |
| `vector_calculus.rs` | `vector_calculus` | 1,195 | 14 | 0 | 0 | Vector calculus operators and field theory for physics grids. |
| `verification/mod.rs` | `verification` | 63 | 0 | 0 | 0 | Kani proof harnesses. |
| `verification/core.rs` | `verification::core` | 27 | 0 | 0 | 0 | Kani harnesses for `crate::core`. |
| `verification/linalg.rs` | `verification::linalg` | 27 | 0 | 0 | 0 | Kani harnesses for `crate::linalg`. |
| `verification/physics.rs` | `verification::physics` | 236 | 0 | 0 | 0 | Kani harnesses for the Part 1 physics and numerics core. |
| `verification/spatial.rs` | `verification::spatial` | 41 | 0 | 0 | 0 | Kani harnesses for `crate::spatial`. |
| `waves.rs` | `waves` | 784 | 48 | 0 | 0 | Wave propagation: mechanical, acoustic and seismic. |