Haskell modules¶

Select a module below or in the sidebar to read its public types, function signatures, input requirements, results, and failure conditions. Search accepts function names as well as descriptive terms. Module pages are generated from the same source revision as this site, including function, method, and record field documentation.

Area	Representative modules
Foundations	`HMath`, `HMath.Error`, `HMath.Numeric`, `HMath.Constants`, `HMath.Units`
Algebra	`HMath.Algebra`, `HMath.Polynomial`, `HMath.NumberTheory`, `HMath.Combinatorics`
Linear algebra	`HMath.Linear`, `HMath.Matrix`, `HMath.Matrix.LU`, `HMath.Matrix.QR`, `HMath.Sparse`
Calculus and solvers	`HMath.Calculus`, `HMath.Root`, `HMath.ODE`, `HMath.PDE`, `HMath.Interpolation`
Optimization	`HMath.Optimization`, `HMath.Autodiff`
Statistics	`HMath.Statistics`, `HMath.Probability`, `HMath.Random`, `HMath.TimeSeries`
Learning	`HMath.MachineLearning`, `HMath.DeepLearning`
Transforms and signals	`HMath.Fourier`, `HMath.Signal`
Geometry and images	`HMath.Geometry`, `HMath.Image`, `HMath.Rotation`, `HMath.Quaternion`
Discrete and symbolic	`HMath.Graph`, `HMath.Discrete`, `HMath.Symbolic`, `HMath.Expression`
Arrays and interchange	`HMath.Tensor`, `HMath.Interchange`, `HMath.API`

The HMath facade re-exports selected foundational modules. Import additional modules explicitly for other numerical domains. Checked APIs generally return Either MathError; consult the function signature for the exact error and result types.

Read a checked result¶

The Haskell API covers more numerical domains than the C, Wave, and Python bindings. Those bindings currently expose the native scalar/tensor interface; a Haskell-only function is not automatically available in Python.

import qualified HMath.Scalar as Scalar
import qualified HMath.Matrix as Matrix
import qualified HMath.Matrix.LU as LU

main :: IO ()
main = do
    print (Scalar.divide (6 :: Double) 2)  -- Right 3.0
    print (Scalar.divide (1 :: Double) 0)  -- Left (DomainError ...)
    let solution = do
            a <- Matrix.fromListChecked 2 2 [2, 0, 0, 4 :: Double]
            LU.solve a [6, 8]
    print solution  -- Right [3.0,2.0]

An Either result distinguishes input/numerical failure (Left) from an accepted result (Right). Solver report fields additionally distinguish a budget stop from convergence. Pure legacy functions such as HMath.Basic.factorial and HMath.Statistics.mean can raise errors on invalid input; their entries state those preconditions. IEEE/generic arithmetic APIs can retain host-type overflow or NaN behavior when their contract does not add finite checks.

Build the complete local site with:

python tools/build_docs.py

The dense linear algebra guide describes matrix shapes, checked operations, and zero-dimensional matrices in more detail.

All public modules¶

Select a module for its types, constructors, method signatures and function contracts.

Foundations¶

Module	Purpose
HMath.API.Algebra	Small law-oriented numeric interfaces.
HMath.API.Buffer	Checked containers and copying conversion boundaries.
HMath.API.Convergence	Uniform iteration reports retain the best current estimate on an exhausted budget.
HMath.API.Shape	Runtime-checked shapes and nominal type-indexed matrices/tensors.
HMath.Basic	Public types and operations.
HMath.Constants	Constants with machine-readable provenance and uncertainty.
HMath.Error	Errors shared by the checked linear algebra APIs.
HMath.Numeric	Numeric representations and deterministic IEEE utilities.
HMath.Scalar	Scalar utilities.
HMath.Trigonometry	Radian-based checked trigonometry.
HMath.Units	Exact rational unit conversion and API-level dimensional safety.

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Algebra and number theory¶

Module	Purpose
HMath.Algebra	Algebraic interfaces, exact law checks, checked modular rings, and finite extension fields GF(p^n).
HMath.Algorithms	Reference numerical search and ordering algorithms.
HMath.Combinatorics	Exact combinatorics.
HMath.Complex	Checked finite complex arithmetic over Data.Complex.
HMath.NumberTheory	Exact integer algorithms.
HMath.Polynomial	Univariate polynomials with ascending coefficients: [a0,a1,...] means a0+a1*x+....
HMath.Special	Real special functions with checked domains.

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Linear algebra¶

Module	Purpose
HMath.Backend	Checked dense CPU kernels with explicit, garbage-collected provider handles.
HMath.Linear	List-based vector operations.
HMath.Matrix	Dense matrices with finite, row-major storage and zero-based indices.
HMath.Matrix.Advanced	Matrix constructors, products, spaces, and matrix functions.
HMath.Matrix.Decomposition	Pure reference decompositions with explicit shape and tolerance contracts.
HMath.Matrix.Iterative	Bounded reference iterative solvers for dense real matrices.
HMath.Matrix.LAPACK	Double-precision optional, dynamically loaded LAPACKE spectral routines.
HMath.Matrix.LU	Dense real LU factorization with partial row pivoting.
HMath.Matrix.QR	Column-pivoted Householder QR.
HMath.Sparse	Sparse matrices use canonical sorted coordinates, coalesced duplicates and no explicit zeros.
HMath.Sparse.Spectral	Matrix-free sparse power algorithms.
HMath.Vector	Immutable dynamically sized and type-indexed vectors.

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Calculus and differential equations¶

Module	Purpose
HMath.Calculus	Checked, finite-difference differentiation and numerical quadrature for Double callbacks.
HMath.Interpolation	Checked reference interpolation and approximation.
HMath.ODE	Checked real ODE/DAE integration.
HMath.PDE	Structured-grid reference PDEs in one, two or three spatial dimensions.
HMath.Root	Checked Double root solvers.

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Optimization and differentiation¶

Module	Purpose
HMath.Autodiff	Pure CPU automatic differentiation.
HMath.Optimization.Common	Shared checked Double objective contracts.
HMath.Optimization.Constrained	Dense bounded reference constrained optimization.
HMath.Optimization.FirstOrder	Explicit optimizer state for deterministic gradients, SGD and minibatches.
HMath.Optimization.Global	Seeded bounded CPU global search.
HMath.Optimization.Local	Bounded CPU reference local solvers.

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Statistics and time series¶

Module	Purpose
HMath.Probability	Checked probability models.
HMath.Random	Explicit, immutable random streams.
HMath.Statistics	Public types and operations.
HMath.Statistics.Advanced	Finite-data checked statistics.
HMath.TimeSeries	Timestamped observations, bounded CPU forecasting, decomposition and diagnostics.
HMath.TimeSeries.Core	Timestamped finite observations.
HMath.TimeSeries.Diagnostics	Explicit-lag stationarity statistics, bounded change-point/warping reference algorithms, and forecast diagnostics.
HMath.TimeSeries.Models	Bounded Double forecasting models.

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Machine learning¶

Module	Purpose
HMath.DeepLearning.Core	Checked Double activations, losses, and real-coordinate reverse rules.
HMath.DeepLearning.Layers	Row-major CPU layers.
HMath.DeepLearning.Metrics	Classification metrics.
HMath.DeepLearning.Precision	Explicit INT8 quantization and software FP16/BF16 matrix multiplication.
HMath.MachineLearning	Reproducible dense CPU estimators, preprocessing, clustering, and manifold methods.
HMath.MachineLearning.Clustering	Dense, finite-budget clustering.
HMath.MachineLearning.Decomposition	Dense decomposition and manifold reference algorithms.
HMath.MachineLearning.Internal	Shared, deliberately small dense reference kernels for the ML estimators.
HMath.MachineLearning.Neighbors	Exact branch-and-bound KD/ball trees and budgeted approximate search.
HMath.MachineLearning.Preprocessing	Fitted preprocessing and index-based splits.
HMath.MachineLearning.Regression	Dense reference estimators.

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Signals and transforms¶

Module	Purpose
HMath.Fourier	CPU reference Fourier transforms.
HMath.Signal	CPU reference DSP.

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Geometry and images¶

Module	Purpose
HMath.Geometry	Checked Cartesian geometry and bounded CPU reference algorithms.
HMath.Geometry.Collision	Bounded two-dimensional convex collision reference algorithms.
HMath.Geometry.Internal	Shared finite Euclidean geometry.
HMath.Geometry.Polygon	Planar hulls, polygon measurements and Boolean arrangements.
HMath.Geometry.Primitives	Checked distances, containment, intersections and primitive signed distance functions.
HMath.Geometry.Spatial	Immutable point-cloud spatial indexes.
HMath.Geometry.Transform	Column-vector homogeneous transforms.
HMath.Geometry.Triangulation	Deterministic Bowyer-Watson Delaunay triangulation (at most 256 unique points), edge-flip constrained Delaunay triangulation, polygon ear clipping, and bounded Voronoi cells.
HMath.Image	Finite ND CPU images and bounded reference color, filtering, resampling, histogram, topology, and measurement operations.
HMath.Image.Color	Three-channel color conversion. sRGB uses the IEC piecewise transfer; XYZ is D65 with Y=1 for reference white; Lab uses that same D65 white (no implicit chromatic adaptation).
HMath.Image.Core	Finite CPU images with row-major spatial axes and interleaved channels (last axis).
HMath.Image.Filter	Direct ND reference filtering and 2D edge detection.
HMath.Image.Histogram	Unit-range, per-channel histograms, equalization, thresholds, and CLAHE.
HMath.Image.Measure	Image measurements use caller-declared intensity ranges and explicit local windows.
HMath.Image.Spatial	2D resampling/warps, ND binary topology, and exact bounded distance queries.
HMath.Quaternion	Finite Hamilton quaternions in scalar-first (w,x,y,z) order.
HMath.Rotation	SO(3), SE(3), and rigid dual quaternions.

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Graphs and symbolic mathematics¶

Module	Purpose
HMath.DataStructure	Persistent finite range, queue, heap and streaming structures.
HMath.Discrete	Finite-width bits, relations and propositional logic.
HMath.Expression	A pure, bounded real expression language shared with HMath.Symbolic.
HMath.Graph.Analysis	Finite graph analysis.
HMath.Graph.Core	Checked finite labeled multigraphs.
HMath.Graph.Flow	Exact integral network flow and assignment.
HMath.Graph.Paths	Checked graph paths.
HMath.Symbolic	Bounded symbolic real algebra over the common Expr language.

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Tensors and interchange¶

Module	Purpose
HMath.Interchange	Checked fixed-width numerical serialization and array exchange.
HMath.Interchange.Array	Fixed-width, typed array interchange.
HMath.Interchange.Binary	HMath array wire format version 1.
HMath.Interchange.Compression	Optional zlib codecs with an explicit hard decompression budget.
HMath.Interchange.IO	Bounded strict file codecs, fixed-chunk raw streaming, and read-only mapped arrays.
HMath.Interchange.Numpy	NPY v1v2v3 and NPZ (ZIP32 directory, stored or raw-DEFLATE members).
HMath.Interchange.Text	Bounded ASCII numeric formats.
HMath.Tensor	CPU tensors with immutable boxed backing arrays and shared, zero-copy strided views.
HMath.Tensor.Mutable	Pinned CPU storage with shared mutable views.

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