tensor/CHANGELOG.md

Changelog

All notable changes to Tensor are documented in this file.

The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.

[development]

Fixed

Linear algebra.

• Cholesky, Eigen, EigenComplex and the Cholesky rank-one update refuse a matrix or vector holding a NaN or infinity instead of returning an all-NaN factor or spectrum with a nil error, the refusal the sparse solvers already make.
• EigenComplex converges on a Hermitian matrix whose off-diagonal entries all sit just under the per-entry skip level: the sweep no longer exhausts its passes on a matrix it should have declared converged.

Statistics.

• FitHiddenMarkovModel fits a single-observation sequence instead of crashing the process: a transition row with no evidence keeps its previous estimate rather than dividing by zero.
• Viterbi refuses a sequence of probability zero under the model, the same refusal Forward makes, instead of returning a meaningless path beside a log probability of -Inf.
• The Student-t tails stay accurate past the point t squared overflows float64: StudentTCDF, the regression coefficient p-values and NoncentralTCDF at extreme t answer the tail the format still holds instead of a silent zero or an error naming a NaN.
• LinearRegression and WeightedLinearRegression keep their inference alive when the squared deviations underflow to zero: the standard errors, t and F statistics read factored sums of squares instead of reporting infinity beside zero evidence.

Integration and optimisation.

• TriangleMesh2D.BoundaryEdges returns the mesh's own edges: the boundary pairs sort as pairs, never as one flat index list that interleaves the endpoints of unrelated edges.
• IntegrateFunction names itself in its errors; the adaptive quadrature no longer reports under a name absent from the surface.

[1.0.0] - 2026-09-03

The initial release of Tensor, a scientific computing library in pure Go: immutable n-dimensional arrays over a wide element-type set, dense and sparse linear algebra, differential equations, quadrature, signal transforms, statistics up to mixed models and hidden Markov models, optimisation from simplex to stochastic global search, a reverse-mode differentiable core, deterministic SVG plotting and an experimental SPMD package, with no third-party dependencies and a deterministic, parallel execution model.

The module is one core package plus one package per domain: sourcedock.dev/petrbalvin/tensor carries the Array core with element-wise math, special functions and the reproducible generator, re-exporting the whole surface of every domain package; linalg the dense and sparse solvers; signal the transforms, filters and stencils; integrate the differential equations and quadrature; stats the distributions and inference; optim the fitting and root finding; io the CSV, FITS, HDF5, NetCDF and memory-mapped readers and writers; grad the differentiable core; plot the deterministic figures. Import what you use: the domain packages depend on the core, never on each other except through five one-directional edges, and nothing below the root imports the root. The experimental spmd package stands beside them, imported explicitly: a distributed program names it, the facade does not.

Added

Core arrays.

• Immutable, shape-checked n-dimensional arrays over int64, float32, float64, complex128, IEEE 754 float16 and the narrow integer types Int8, Uint8, Int16, Uint16, Int32 and Uint32, with Bool beside them, under a strict promotion ladder, row-major layout and multi-rank text formatting. Constructors cover literals (FromInts, FromFloat32s, FromFloats, FromComplexes, FromFloat16s, FromInt8s and the family around them), filled and ranged builders (Zeros, Ones, FullI/FullF/FullC, Range, RangeBy, Linspace, Grid), byte loading and dtype conversions (WithInt/WithFloat/WithComplex, and Astype, which range-checks every conversion into a narrow target with an error naming the value and its index).
• Element-wise arithmetic with scalar variants, transcendentals, comparisons that answer a bool mask of one byte per element composing through And, Or, Xor and Not (Where and Select keep the int mask), and reductions from Sum, Mean, Min/Max, Prod and Dot through axis variants, ArgMax, TopK, CumSum and CumProd to SumKahan compensated summation. Every float fold cuts its line through a canonical partition fixed by the length alone and combines the partials through a balanced tree, so a reduction's answer is a function of the data alone, never of the machine, and CumSum carries a Neumaier compensation term so a long prefix sheds no small addend.
• Shape operations (Reshape, Flatten, Squeeze, Transpose, TransposeAxes, MoveAxis, Pad, Tile, Repeat, Flip, Roll, Diag, triangular extractions), indexing (contiguous Slice selections as read-only payload views, Gather, Scatter, Take, Nonzero, Argwhere, SearchSorted), and the toolkit pieces Einsum, Unique, OneHot, CrossProduct, Sort, ArgSort, and the numeric Jacobian of a vector function by central differences.
• MatMul2D, the parallel cache-friendly kernel; sparse matrices as SparseCOO; interpolation (Interpolate, the Fritsch-Carlson InterpolateMonotone, Interpolate2D, InterpolateGrid, natural cubic splines); and special functions: the gamma and beta families, error functions, Bessel of integer order and, through BesselJRealOrder, of any real order, Airy and Fresnel families, exponential integrals, orthogonal polynomials, spherical harmonics, elliptic integrals and Jacobi functions, and Cosm1 for cos(x) − 1 at the arguments where the direct subtraction has no correct significant bit.
• Quasirandom sequences for Monte Carlo integration: HaltonPoints and the base-2 digital SobolPoints (Joe and Kuo initialisation, 40 dimensions).
• Parallel execution across every core with a fixed reduction order, SetNumCPU to pin the worker count, and pooled scratch buffers whose borrow path zeroes the window.
• The reproducible Generator: xoshiro256++ seeded through splitmix64, stable across Go releases, with uniform, normal and truncated-normal draws, shuffles and permutations; Splitmix64 and Substream are exported for callers who seed their own streams. The distribution draws of the stats package take the same generator, so a seeded program replays exactly.

Linear algebra.

• Dense factorisations and solves: LU (Solve, Inv, Det), QR beside RRQR, the rank-revealing column-pivoted factorisation with RRQRRank and SolveRRQR, whose rank-deficient path answers the minimum-norm solution, Cholesky with rank-one update and downdate, LeastSquares, the tridiagonal and cyclic-tridiagonal solvers, Pinverse, MatrixRank, Cond.
• Eigenproblems in the symmetric, Hermitian-complex, general and generalised forms; SVD and SVDComplex in real and complex arithmetic; SchurComplex; the matrix functions MatrixExp, MatrixSqrt and MatrixLog.
• Regularised and truncated solves for ill-posed systems: SolveTruncated (rank truncation of the singular spectrum) and SolveTikhonov (Tikhonov damping through the SVD).
• Sparse direct factorisations: CSCFromCOO and the SparseCSC view with ToCSR/ToCSC conversions, NewSparseCholesky, the sparse Cholesky with the elimination tree, the natural, reverse Cuthill-McKee and minimum-degree orderings and the rank-one Update and Downdate, and NewSparseLU, the Gilbert-Peierls left-looking elimination with partial pivoting. One factorisation solves any number of right-hand sides.
• Sparse iterative methods on the CSR view: SpSolve (conjugate gradient), SpSolveBiCGSTAB, SpLSQR and SpLSMR for overdetermined systems, the ILU(0) preconditioner, the Lanczos eigensolver SpEigen with its general Arnoldi form, and SpExpApply, the Krylov action of a matrix exponential. The complex side mirrors it for Hermitian positive-definite and general non-Hermitian operators, the shape Helmholtz and electromagnetics problems need.
• Polynomial fitting, roots through the companion matrix, and the fluent Pipeline chain over the element-wise surface.

Signal and transforms.

• Fourier transforms of any length: FFT/IFFT, FFT2, FFT3, FFTN/IFFTN, the real-input RFFT/IRFFT pair and FFTFreq.
• Cosine and sine transforms (orthonormal types I to IV), the type-1 non-uniform FFT by Gaussian gridding, and the short-time Fourier transform with window choice.
• Spectral estimation: WelchPSD, Spectrogram, LombScargle for unevenly sampled data, and the spectral Poisson solves in periodic, Dirichlet and Neumann boundaries.
• Sample-rate conversion: Decimate behind a Kaiser anti-alias filter, rational Resample and exact band-limited ResampleFourier; the Hilbert AnalyticSignal and Envelope; and Chirp, the linear frequency sweep synthesised from the closed-form phase at each sample.
• Filter design: Butterworth, Chebyshev, inverse Chebyshev and elliptic (Cauer) responses in low-pass, high-pass, band-pass and band-stop forms with explicit ripple and attenuation budgets, applied through FilterApply and, zero phase, through Filtfilt.
• Correlation and wavelets: FFT-based Autocorrelate and CrossCorrelate, PartialAutocorrelate, the Haar DWT/IDWT and the Daubechies families db2 to db8, and the analytic CWT (Morlet and Mexican hat).
• Convolutions, pooling and windows: Conv1D/Conv2D/Conv3D with groups and dilation, ConvTranspose2D, the max, average, adaptive and global pooling families, the MedianFilter and RankFilter families in one and two dimensions, the SavitzkyGolay smoother, the Gradient1D/Laplacian stencils, and the public window catalogue WindowHann through WindowBox, each in the symmetric and the periodic convention.
• Time-series estimation: KalmanFilter, ExtendedKalmanFilter and UnscentedKalmanFilter with the filtered states, covariance history, innovations and the summed log likelihood; EstimateAR through Yule-Walker over the Levinson recursion, EstimateARMA through Hannan-Rissanen innovations, SelectARMA over a lag grid by information criterion, and ARMASpectrum for the theoretical one-sided spectrum.

Differential equations and quadrature.

• Initial value problems: IntegrateODE (adaptive Dormand-Prince 4(5)) with path and step recording, IntegrateBDF2 and IntegrateBDFVar (variable order 1 to 5, VODE-style step and order adaptation) for stiff systems, IntegrateROS4, the L-stable Rosenbrock-Wanner solver, IntegrateBackwardEuler, IntegrateRK4, event detection with direction filters, IntegrateDAE for semi-explicit index-1 differential-algebraic systems in mass-matrix form, and the symplectic IntegrateVerlet beside IntegrateYoshida4 and IntegrateMidpoint for separable and general Hamiltonians.
• Boundary values: IntegrateBoundary by damped shooting with the root finder of optim, and SolveBoundaryCollocation by three-point Lobatto IIIA collocation on an adaptively refined mesh.
• Quadrature: adaptive Gauss-Legendre IntegrateFunction, fixed-node GaussLegendreNodes, IntegrateND, globally adaptive cubature over hyperrectangles, and IntegrateFilon for the oscillatory integrals of a smooth amplitude against a cosine or sine carrier.
• Turnkey PDE evolution: the heat equation by Crank-Nicolson in one dimension and Peaceman-Rachford ADI in two, the wave equation by velocity Verlet in one dimension and an explicit central stencil in two, advection by the monotone upwind and Koren-limited fluxes and their advection-diffusion combination, CFL enforced everywhere.
• Finite elements: structured and arbitrary triangular meshes in two dimensions and tetrahedral meshes in three, with SolvePoissonFEM2D and SolvePoissonFEM3D, the piecewise-linear Poisson assemblies through the sparse direct factorisation, with Dirichlet lifting and natural Neumann boundaries.

Statistics.

• Distributions: CDFs, quantiles and matched random draws for the normal, exponential, gamma, chi-square, Student t, F and their noncentral forms, Poisson, binomial, negative binomial, Weibull, lognormal, Pareto and Dirichlet laws, built on the incomplete gamma and beta functions.
• Descriptives: mean-free moments, Median, Quantile, histograms in one and two dimensions, the robust MedianAbsoluteDeviation and TrimmedMean, and the rolling windows.
• Inference: WelchTTest, KolmogorovSmirnovTest, MannWhitneyU, one-way ANOVAOneWay, ChiSquareGoodnessOfFit, BootstrapCI, the rank correlations SpearmanRho and KendallTau, the multiple-testing corrections Bonferroni, Holm and BenjaminiHochberg, and the contingency table analyses FisherExactTest, ChiSquareIndependence, McNemarTest and CramersV.
• Models: LinearRegression with standard errors, t-tests, p-values, R² and the model F-test, WeightedLinearRegression, LogisticRegression and PoissonRegression on the exact likelihood with Wald inference, HuberRegression, TheilSenRegression and QuantileRegression for the robust and distribution-free fits, lasso and elastic net over a documented regularisation path, PCA, KMeans with k-means++ seeding, GaussianMixture selected over a component grid by GaussianMixtureBIC, Gaussian-process regression over squared-exponential, Matern 3/2 and 5/2 and periodic kernels, multivariate normal densities and draws, Gaussian KernelDensity, LinearMixedModel, the Gaussian linear mixed model with grouped random effects estimated by residual maximum likelihood, the discrete hidden Markov model with its Forward, Smooth and Viterbi recursions and its Baum-Welch fit, and HierarchicalClustering, the agglomerative dendrogram with the single, complete, average, centroid and Ward linkages and the Dendrogram cuts into flat clusters.

Optimisation.

• Local: Minimise (Nelder-Mead simplex), MinimiseLBFGS with box bounds and a projected-gradient convergence measure, and LevenbergMarquardt with an optional analytic Jacobian. The LevenbergMarquardtFit form reports χ², a named FitStatus and, on request, the parameter covariance and per-residual weights through Sigma, and the least squares and system solvers take ParallelJacobian, an explicit opt-in that spreads the finite-difference columns across workers with bit-identical answers.
• Constrained: MinimiseConstrained, the augmented Lagrangian over the box, so equality and inequality rows of LinearConstraints compose with the walls, and MinimiseNonlinearConstrained for rows that are arbitrary functions.
• Global: MinimiseDifferentialEvolution for multimodal, derivative-free landscapes, MinimiseCMAES (the rank-one and rank-mu update set, seeded through the generator) and MinimiseSimulatedAnnealing (geometric cooling), all deterministic under a seed and all honest about an exhausted budget.
• Programming: MinimiseLinear and MinimiseLinearRows, the revised simplex with a two-phase start over standard-form and two-sided row programs, and MinimiseQP, the active-set method for the strictly convex program with the multipliers returned.
• Root finding: FindRoot (Brent), FindRootBrent for a scalar bracketed root, FindRootNewton and FindRootSystem (damped Newton with Armijo backtracking and an optional Broyden rank-one update in place of repeated Jacobian builds). A solver that exhausts its budget is refused with an error unless the best-effort exit is requested by name.

Automatic differentiation.

• A reverse-mode graph over the arithmetic surface, the matrix products (single and batched), the reductions, slicing, concatenation, axis permutation and the Fourier transforms; every float leaf accumulates through Backward.
• Complex tensors differentiate under the Wirtinger convention, the loss stays real, and mixed real-complex graphs compose exactly through the 2·Re narrowing.
• Second order: Hessian (forward-over-reverse) and HessianVectorProduct in two gradient evaluations.
• On top of the graph: MinimiseNewtonCG (truncated-CG Newton with an Armijo line search), SampleHMC (Hamiltonian Monte Carlo on any differentiable unnormalised density) and AdjointODE (adjoint sensitivities at the cost of one extra solve).

Plotting.

• The plot package: deterministic SVG line charts of computed series. Linear axes with five ticks, one legend line per series, a Line constructor straight from two rank-1 arrays through the promotion ladder, and a byte-identical file on every run, so a figure in a paper is compared exactly like any other computed number.

Distributed execution.

• The experimental spmd package: explicit SPMD worlds, one program on many ranks, over TCP between machines or in one process over channels, launched, listened for and joined through Launch, Listen and Join. The movement collectives Broadcast, Scatter, Gather and AllGather move arrays between ranks; the sharded reductions cut a global array on the canonical fold partition's block boundaries and combine the partials through the same balanced tree the single-array fold uses, so Sum, Min, Max, Any, All, Prod, the norm and the dot families answer the single-array reduction's exact bits at any world size, whatever the order the frames arrive in; Reduce and AllReduce fold the ranks' same-shaped arrays elementwise in rank index order. ExchangeHalos and ExchangeHalosOnGrid hand each rank's boundary slabs to the neighbours of a decomposition laid out on a row-major process grid. Every failure or deadline fails the whole world loudly, and no collective ever returns a partial numeric result.

Data I/O.

• CSV reading and writing, with or without a header row, every stored numeric dtype written and read.
• FITS images with header cards in both directions, and binary and ASCII table extensions.
• HDF5 in both directions: LoadHDF5 reads the default and the "latest" file formats (contiguous, compact and chunked storage, the deflate, shuffle and fletcher32 filters, superblocks of versions 2 and 3 with the lookup3 checksum of each verified, group attributes merged into each dataset), and SaveHDF5 with SaveHDF5Text writes every stored dtype at its native width, booleans through the HDF5 enumeration convention, nested groups, attributes and optional filters, byte-deterministic on every run. Unsupported format features are refused by name, and cyclic or over-deep group walks are refused.
• LoadNetCDF/SaveNetCDF for the NetCDF classic model (CDF-1 and CDF-2), with named dimensions, text attributes and record dimensions in both directions, and fixed-point variables landing at their own width and sign.
• Memory mapping: MapFloats, MapFloat32s and MapInts open native-endian files as read-only arrays without reading them, and SaveNativeFloats writes the format they read.

Examples.

• Thirteen runnable workflows in examples/: ODE parameter fitting by adjoint sensitivities, PSF deconvolution, HMC sampling, spectral analysis, wavelet denoising, the exact pendulum period through EllipticK, a Helmholtz system on the complex sparse solvers, quasi-Monte Carlo integration, heat and wave evolution, regression inference, a FITS star field, a NetCDF climate round trip and an FFT tour.

Project.

• A determinism oracle pinning fixed workloads through the facade by SHA-256 digest of the output bits, and a resource-leak harness holding the goroutine count and live heap to baseline under repeated heavy runs.
• Gitea Actions pipelines for test, race and release, with the release notes extracted from this file's matching section.
• The document set: this changelog, the README, the API reference, the architecture, the development guide, the benchmarking method, the contribution rules and the security policy, under the MIT licence.