Capability index

Every public name in radtrax (255 of them), each listed once at its public home and grouped by the module that defines it, with the first sentence of its docstring; then the public API of gaussx, lineax, optimistix. Search this page before writing a helper: if what you need is here, compose it; if it is almost here, extend it where it lives. Regenerate with make capabilities after changing a public API (tests/test_capabilities.py checks it is current).

radtrax

Exception hierarchy for radtrax. (radtrax.exceptions)

Name	Kind	What it does
ArgumentTypeError	class	An argument is of a type the function does not accept.
DegenerateInputError	class	Well-shaped input that cannot be used: too few samples, no data yet, or a zero norm.
GridError	class	A grid is not strictly monotone, has too few points, or does not match another grid.
MissingExtraError	class	An optional dependency is not installed; the message names the extra.
MissingFileError	class	An input file or glob pattern matched nothing.
MissingKeyError	class	A gas, band or variable is missing from a state, table or dataset.
MissingTableError	class	A table (cross sections, a solar spectrum) is not in the cache; its message names the command that builds or fetches it.
ParameterError	class	A scalar or option is outside its allowed range or set, or a required one is missing.
RadtraxError	class	Base class for every exception raised by radtrax.
ShapeError	class	An array has the wrong shape or rank, or two arrays disagree in shape.
TableBuildError	class	Building a cross-section table failed: a HITRAN fetch or a line-by-line computation.

The layered forward model. (radtrax.forward_model)

Name	Kind	What it does
ForwardModel	class	State → opacity → solver → instrument: band values for one pixel.

Target signature construction from the radiance forward model. (radtrax.retrieval.matched_filter.target)

Name	Kind	What it does
unit_absorption_target	function	Matched-filter target t = ∂ ln y / ∂ΔX at ΔX = 0 [per mol/m²].

radtrax.atmosphere

AFGL reference atmospheres (Anderson et al., 1986). (radtrax.atmosphere.afgl)

Name	Kind	What it does
afgl_us_standard	function	The AFGL US Standard atmosphere as layers between its levels.

Ideal-gas constants and the total number density. (radtrax.atmosphere.gas)

Name	Kind	What it does
number_density	function	Total number density from the ideal-gas law [molecules / cm³].

Viewing geometry: the air-mass factor and the geometry a solver sees. (radtrax.atmosphere.geometry)

Name	Kind	What it does
ViewingGeometry	class	Sun and sensor directions as seen from the surface.
air_mass_factor	function	Plane-parallel two-way air-mass factor, sun → surface → sensor.

Layers from levels by hydrostatic balance. (radtrax.atmosphere.hydrostatics)

Name	Kind	What it does
layers_from_levels	function	An :class:AtmosphericState of L layers from L + 1 levels.

The layered atmospheric state: the input of every forward model. (radtrax.atmosphere.state)

Name	Kind	What it does
AtmosphericState	class	Pressure, temperature, altitude, thickness and gases, per layer.

Re-exported from other libraries

Name	Kind	What it does
AFGL_GASES	constant	Re-exported from builtins.
ATM_TO_PA	constant	Re-exported from builtins.
AVOGADRO_PER_MOL	constant	Re-exported from builtins.
BOLTZMANN_J_PER_K	constant	Re-exported from builtins.
CM2_PER_M2	constant	Re-exported from builtins.
CM3_PER_M3	constant	Re-exported from builtins.
DRY_AIR_MOLAR_MASS_KG_PER_MOL	constant	Re-exported from builtins.
STANDARD_GRAVITY_M_PER_S2	constant	Re-exported from builtins.

radtrax.atmosphere.gas

Name	Kind	What it does
ATM_TO_PA	constant	Re-exported from builtins.
AVOGADRO_PER_MOL	constant	Re-exported from builtins.
BOLTZMANN_J_PER_K	constant	Re-exported from builtins.
CM2_PER_M2	constant	Re-exported from builtins.
CM3_PER_M3	constant	Re-exported from builtins.
DRY_AIR_MOLAR_MASS_KG_PER_MOL	constant	Re-exported from builtins.
STANDARD_GRAVITY_M_PER_S2	constant	Re-exported from builtins.

radtrax.geo

ECOSTRESS: band set, SRF, instrument, noise, radiance and geometry. (radtrax.geo.ecostress)

Name	Kind	What it does
ecostress_bands	function	The TIR bands with data in a granule.
ecostress_geometry	function	Per-pixel viewing geometry from the L1B geolocation angles.
ecostress_instrument	function	ECOSTRESS bands as a :class:~radtrax.instrument.BandInstrument.
ecostress_noise	function	NEΔT as a noise model on instrument's bands.
ecostress_radiance	function	L1B radiance per band and pixel, fill values as NaN.
ecostress_srf	function	Build the ECOSTRESS SRF from the bundled science-team responses.

EMIT L1B on radtrax's terms: instrument and per-pixel geometry. (radtrax.geo.emit)

Name	Kind	What it does
emit_geometry	function	Per-pixel viewing geometry of an EMIT image, on its grid (H, W).
emit_instrument	function	EMIT bands as a :class:~radtrax.instrument.BandInstrument on a wavenumber grid.

Landsat 8/9 OLI and TIRS: SRF, instrument, noise, radiance and geometry. (radtrax.geo.landsat)

Name	Kind	What it does
landsat_geometry	function	Per-pixel viewing geometry from the Collection 2 angle bands.
landsat_instrument	function	Landsat 8/9 bands as a :class:~radtrax.instrument.BandInstrument.
landsat_noise	function	The thermal bands' NEΔT as a noise model on instrument's bands.
landsat_radiance	function	TOA radiance from Level-1 digital numbers, per band and pixel.
landsat_srf	function	Build a Landsat 8/9 SRF from the bundled USGS band-average RSRs.

GeoTensor operators for the matched filter (behind the [geo] extra). (radtrax.geo.matched_filter)

Name	Kind	What it does
AdaptiveBackground	class	Local window statistics, in the layout of the cube they came from.
AdaptiveWindowBackground	class	Per-pixel local mean and variance over a square window.
ApplyAdaptiveMF	class	Matched filter against each pixel's local diagonal background.
ApplyClusterMF	class	Matched filter with each pixel's own cluster background.
ColumnEnhancement	class	Trace-gas enhancement map: mean, covariance, target and matched filter.
DetectionThreshold	class	Score threshold with a given false-alarm rate under the Gaussian null.
EstimateCovEmpirical	class	Empirical (1/n) covariance operator of a cube's valid pixels.
EstimateCovLowRank	class	Low-rank plus Tikhonov covariance λI + V D Vᵀ of a cube's valid pixels.
EstimateCovShrunk	class	Ledoit–Wolf or OAS covariance operator of a cube's valid pixels.
EstimateMean	class	Background mean spectrum (B,) of a cube's valid pixels.
GMMClusterBackground	class	Per-cluster backgrounds from a Gaussian mixture over the valid pixels.
LinearTargetFromObs	class	Tangent-linear target signature (B,) from an observation model.
MatchedFilter	class	Per-pixel matched-filter score map.
MatchedFilterPixel	class	Matched-filter score of one pixel spectrum, as a float.
MatchedFilterSNR	class	Theoretical detection SNR amplitude · √(tᵀ Σ⁻¹ t).
NonlinearTargetFromObs	class	Finite-amplitude target H(x_b + α δx) − H(x_b), (B,).
StreamingBackground	class	Mean and covariance accumulated over an iterable of cubes.
StreamingBackgroundResult	class	Background from :class:StreamingBackground.
UnitAbsorptionTarget	class	Target (B,) from v0's layered :class:~radtrax.ForwardModel.
ValidateMFInputs	class	Pass-through guard: fail early on a zero target or a singular covariance.

The multi-pass operators on GeoTensors (behind the [geo] extra). (radtrax.geo.mbmp)

Name	Kind	What it does
MBMP	class	Sentinel-2 multi-band multi-pass methane signal, with or without scale factors.
MBSP	class	Sentinel-2 multi-band single-pass signal, −ln(c R₁₂ / R₁₁).
SBMP	class	Sentinel-2 single-band multi-pass signal, −ln(c_s R₁₂ / R′₁₂).

Sentinel-2 L1C on radtrax's terms: instrument, geometry and radiance. (radtrax.geo.sentinel2)

Name	Kind	What it does
sentinel2_geometry	function	Per-pixel viewing geometry of an L1C image, on its grid (H, W).
sentinel2_instrument	function	Sentinel-2 bands as a :class:~radtrax.instrument.BandInstrument.
sentinel2_radiance	function	TOA radiance from an L1C image's reflectance, per band and pixel.

Sentinel-2 spectral response functions from georeader's bundled table. (radtrax.geo.srf)

Name	Kind	What it does
sentinel2_band_responses	function	Sentinel-2 band 11 and 12 responses, interpolated onto a wavelength grid.
sentinel2_srf	function	Build a Sentinel-2 SRF from the agency table georeader bundles.

Re-exported from other libraries

Name	Kind	What it does
ECOSTRESS_3BAND	constant	Re-exported from builtins.
ECOSTRESS_3BAND_PERIOD	constant	Re-exported from builtins.
ECOSTRESS_BANDS	constant	Re-exported from builtins.
ECOSTRESS_BAND_CENTRES_UM	constant	Re-exported from builtins.
ECOSTRESS_NETD_K	constant	Re-exported from builtins.
LANDSAT_CALIBRATION_K	constant	Re-exported from builtins.
LANDSAT_NETD_K	constant	Re-exported from builtins.

radtrax.instrument

The NoiseModel protocol: the measurement-noise covariance S_ε. (radtrax.instrument.noise)

Name	Kind	What it does
DiagonalNoise	class	Independent noise with a fixed standard deviation per band, S_ε = diag(σ²).
NEdTNoise	class	Thermal-band noise from a noise-equivalent temperature difference.
NoiseModel	class	Protocol: the measurement-noise covariance S_ε(y) and draws from it.
SNRNoise	class	Signal-dependent noise from a signal-to-noise ratio and a floor.

JAX point-spread + ground-sampling instrument operators. (radtrax.instrument.psf)

Name	Kind	What it does
GroundSamplingDistance	class	Block-mean down-sampling operator for a fixed integer factor.
PointSpreadFunction	class	2D PSF blur applied independently per spectral channel.

The Instrument protocol and a band instrument with a spectral shift. (radtrax.instrument.spectral)

Name	Kind	What it does
BandInstrument	class	Band integration with a spectral shift, y_b = Σ_g f_bg L(ν_g + δ).
GaussianInstrument	class	Gaussian bands built in JAX, shifted analytically in cm⁻¹ or in nm.
Instrument	class	Protocol: radiance on a wavenumber grid in, one value per band out.

Spectral Response Function — band integration of hyperspectral radiance. (radtrax.instrument.srf)

Name	Kind	What it does
SpectralResponseFunction	class	Band-integration operator for a multispectral / hyperspectral instrument.

radtrax.instrument.srf

Spectral Response Function — band integration of hyperspectral radiance. (radtrax.instrument.srf)

Name	Kind	What it does
check_srf_lut_coverage	function	Warn when SRF bands respond outside the LUT's wavelength coverage.

Re-exported from other libraries

Name	Kind	What it does
FWHM_PER_SIGMA	constant	Re-exported from builtins.

radtrax.optics

Name	Kind	What it does
OpticalProperties	class	Per-layer optical depth on a wavenumber grid.

radtrax.radiometry

Brightness temperature: Planck inverted, per wavenumber and per band. (radtrax.radiometry.brightness)

Name	Kind	What it does
band_brightness_temperature	function	Band brightness temperature: the \(T_b\) with \(\bar B_b(T_b) = y_b\) [K].
band_planck_radiance	function	Band-integrated Planck radiance \(\bar B_b(T_b) = \sum_g A_{bg} B(\tilde\nu_g, T_b)\).
brightness_temperature	function	Monochromatic brightness temperature [K], the inverse of planck_radiance.

Planck spectral radiance in wavenumber, its derivatives and its unit views. (radtrax.radiometry.planck)

Name	Kind	What it does
from_per_ghz	function	A spectral density per GHz as one per cm⁻¹: \(L_{\tilde\nu} = c L_f\).
from_per_um	function	A spectral density per µm as one per cm⁻¹: \(L_{\tilde\nu} = 10^4 L_\lambda / \tilde\nu^2\).
log_planck_radiance	function	Natural log of the Planck radiance, finite wherever \(\tilde\nu, T > 0\).
planck_radiance	function	Planck spectral radiance per unit wavenumber [W m⁻² sr⁻¹ (cm⁻¹)⁻¹].
to_per_ghz	function	A spectral density per cm⁻¹ as one per GHz: \(L_f = L_{\tilde\nu} / c\).
to_per_um	function	A spectral density per cm⁻¹ as one per µm: \(L_\lambda = L_{\tilde\nu} \tilde\nu^2 / 10^4\).

Re-exported from other libraries

Name	Kind	What it does
C1_W_M2_SR_CM4	constant	Re-exported from builtins.
C2_CM_K	constant	Re-exported from builtins.
PLANCK_J_S	constant	Re-exported from builtins.
SPEED_OF_LIGHT_M_PER_S	constant	Re-exported from builtins.
STEFAN_BOLTZMANN_W_M2_K4	constant	Re-exported from builtins.

radtrax.radiometry.planck

Name	Kind	What it does
C1_W_M2_SR_CM4	constant	Re-exported from builtins.
C2_CM_K	constant	Re-exported from builtins.
PLANCK_J_S	constant	Re-exported from builtins.
SPEED_OF_LIGHT_M_PER_S	constant	Re-exported from builtins.
STEFAN_BOLTZMANN_W_M2_K4	constant	Re-exported from builtins.

radtrax.retrieval.absorption

The profile fit of the ratio spectrum and its score, D_norm. (radtrax.retrieval.absorption.fit)

Name	Kind	What it does
TransmittanceFit	class	The profile fit of R ≈ P(λ; c) E(λ; ΔX).
d_norm	function	Xiang et al.'s eq. 11: the fit's misfit relative to the ratio's spread.
fit_transmittance	function	Fit a Legendre continuum times the transmittance, profiling over ΔX.

One-to-one spectral pairs and the ratio of their mean radiances. (radtrax.retrieval.absorption.pairing)

Name	Kind	What it does
pair_pixels	function	One-to-one pairs of in-pixels and out-pixels, the best-matched kept.
ratio_spectrum	function	The ratio of the pairs' mean in-pixel and mean out-pixel radiances.

The gas's transmittance: a scene's band transmittance on a grid of columns. (radtrax.retrieval.absorption.transmittance)

Name	Kind	What it does
transmittance_table	function	The band transmittance E_b(ΔX) of a column enhancement, on a grid.

A gas's absorption window: its fitting bands, its pairing bands and its background cut. (radtrax.retrieval.absorption.window)

Name	Kind	What it does
AbsorptionWindow	class	A gas's fitting bands, the bands kept out of pairing, and the background cut.

radtrax.retrieval.band_table

Name	Kind	What it does
BandTable	class	A band observable g(m[, h], ΔΩ), monotone in ΔΩ, and its inverse.
band_table_from_model	function	A :class:BandTable from the layered forward model.

radtrax.retrieval.matched_filter

Background mean and covariance estimators for the matched filter. (radtrax.retrieval.matched_filter.background)

Name	Kind	What it does
estimate_cov_empirical	function	Empirical covariance via :class:sklearn.covariance.EmpiricalCovariance.
estimate_cov_lowrank	function	Low-rank + Tikhonov covariance: Σ = λI + V D Vᵀ.
estimate_cov_shrunk	function	Shrinkage covariance estimator.
estimate_mean	function	Estimate the per-band background mean μ from a scene.
shrink_covariance	function	Shrink a 1/n empirical covariance toward a scaled identity.

Cluster-based and spatially-adaptive background estimators. (radtrax.retrieval.matched_filter.cluster)

Name	Kind	What it does
ClusterBackground	class	Per-cluster background model.
adaptive_window_background	function	Per-pixel local mean and per-band variance over a square window.
apply_adaptive_mf	function	Matched filter against a local diagonal-covariance background.
apply_cluster_mf	function	Matched-filter scores with each pixel's own cluster background.
gmm_cluster_background	function	Fit a Gaussian mixture and build per-cluster background models.

Matched-filter kernel — one implementation for any covariance structure. (radtrax.retrieval.matched_filter.core)

Name	Kind	What it does
apply_image	function	Matched-filter score map for a hyperspectral cube.
apply_pixel	function	Matched-filter score for a single pixel spectrum.
detection_threshold	function	Gaussian detection threshold on the MF score for a given FAR.
matched_filter_snr	function	Theoretical SNR of the matched filter at a given plume amplitude.
validate_mf_inputs	function	Public fail-fast check for (Σ, t) compatibility.

xarray glue: apply the matched filter to DataArrays and multi-file stores. (radtrax.retrieval.matched_filter.io)

Name	Kind	What it does
apply_image_xarray	function	Apply the matched filter to an xarray DataArray.
open_multi_scene	function	Yield (n_pixels, n_bands) batches from a sequence of scene files.

Streaming background estimation via Welford's algorithm. (radtrax.retrieval.matched_filter.streaming)

Name	Kind	What it does
WelfordAccumulator	class	Online mean, covariance and fourth moment for (n_samples, n_bands) streams.
streaming_background	function	Streamed (μ, Σ) from an iterable of batches.

Target signature construction from the radiance forward model. (radtrax.retrieval.matched_filter.target)

Name	Kind	What it does
linear_target_from_obs	function	Matched-filter target via the tangent-linear of the forward operator.
nonlinear_target_from_obs	function	Matched-filter target via a finite-amplitude difference.

radtrax.retrieval.matched_filter.background

Name	Kind	What it does
lowrank_factors	function	Jittable randomised-SVD core: (V, d) of centred samples Xc.

radtrax.retrieval.mbmp

Name	Kind	What it does
background_mask	function	Background pixels: outside a first-pass detection grown by a Gaussian.
mbmp_log_signal	function	MBMP log signal ln(R₁₁/R₁₂) − ln(R′₁₁/R′₁₂), no scale factors.
mbmp_signal	function	Multi-band multi-pass signal −ln((1 + δ) / (1 + δ′)), δ = c R₁₂ / R₁₁ − 1.
mbsp_signal	function	Multi-band single-pass signal −ln(c R₁₂ / R₁₁), R₁₁ ≈ c R₁₂ on mask.
sbmp_signal	function	Single-band multi-pass signal −ln(c_s R₁₂ / R′₁₂), R′₁₂ ≈ c_s R₁₂ on mask.
scale_factor	function	The least-squares c with y ≈ c x through the origin, Σ x y / Σ x².
swir_contrast	function	Single-pass normalised SWIR contrast (R₁₁ − R₁₂) / (R₁₁ + R₁₂ + ε).

radtrax.retrieval.var3d

Background-error covariance B constructors for 3D-Var. (radtrax.retrieval.var3d.background)

Name	Kind	What it does
build_diagonal_background	function	Build B = diag(σ²) as a :class:lineax.DiagonalLinearOperator.
build_kronecker_background	function	Build B = σ² · (ρ_y ⊗ ρ_x) using :class:gaussx.Kronecker.
build_lowrank_background	function	Estimate B from a stack of state samples and wrap as λI + U D Uᵀ.

Control-variable transforms for variational data assimilation. (radtrax.retrieval.var3d.control)

Name	Kind	What it does
IdentityTransform	class	Pass-through transform.
WhiteningTransform	class	δx = U ξ where B = U Uᵀ.

3D-Var cost functions and gradients. (radtrax.retrieval.var3d.cost)

Name	Kind	What it does
Cost	class	Bundle of (value, gradient, Hessian-vector product) for an optimiser.
build_cost_x	function	Build J(δx) = ½ δxᵀ B⁻¹ δx + ½ (y − H(x_b + δx))ᵀ R⁻¹ (y − H(x_b + δx)).
build_cost_xi	function	Build J(ξ) = ½ ξᵀ ξ + ½ (y − H(x_b + U ξ))ᵀ R⁻¹ (…).
finite_difference_grad	function	Central finite differences — used only by tests to validate jax.grad.

Posterior diagnostics for a converged 3D-Var solution. (radtrax.retrieval.var3d.diagnostics)

Name	Kind	What it does
degrees_of_freedom_for_signal	function	Estimate DFS = trace(I − Bₐ B⁻¹) (Rodgers 2000, §2.5).
posterior_covariance_proxy	function	Return a callable v → Bₐ v (model-space posterior covariance) via CG.
reduced_chi_squared	function	χ²_red = (y - H(x̂))ᵀ R⁻¹ (y - H(x̂)) / dim(y).

JAX observation operator for the methane VMR retrieval. (radtrax.retrieval.var3d.obs_operator)

Name	Kind	What it does
RadianceObservationModel	class	Bundle of precomputed pieces that defines the forward operator H.

Optimisers for 3D-Var: primal LBFGS, Gauss-Newton, and a dual PSAS path. (radtrax.retrieval.var3d.solve)

Name	Kind	What it does
SolveResult	class	Common result type for all three solvers.
run_dual_psas	function	Solve the dual 3D-Var system in observation space.
run_gauss_newton	function	Run :class:optimistix.GaussNewton for min ½ ‖r(y)‖².
run_lbfgs	function	Minimise cost.value via :class:optimistix.LBFGS.

radtrax.slab

Observation-geometry and instrument configuration for radtran. (radtrax.slab.config)

Name	Kind	What it does
InstrumentSpec	class	Multispectral instrument description.
ObservationGeometry	class	Viewing geometry for a single pixel.
number_density_cm3	function	Ideal-gas total number density [molecules / cm³].

Beer-Lambert forward models for atmospheric retrieval. (radtrax.slab.forward)

Name	Kind	What it does
ForwardResult	class	Bundle of (radiance, Jacobian, transmittance) returned by the forward models.
forward_maclaurin	function	Maclaurin-series forward model: expand exp(-τ(VMR)) around VMR = 0.
forward_maclaurin_normalized	function	Maclaurin expansion of exp(-Δτ) around ΔVMR = 0.
forward_nonlinear	function	Exact Beer-Lambert forward model.
forward_nonlinear_normalized	function	Exact Beer-Lambert normalised by the background radiance.
forward_taylor	function	First-order Taylor expansion around vmr_background.
forward_taylor_normalized	function	Taylor expansion of L_norm around ΔVMR = 0.

Normalised-brightness LUT for fast per-pixel plume injection. (radtrax.slab.nb_lut)

Name	Kind	What it does
NBLookup	class	Pre-computed normalised-brightness table, indexed by band and ΔX.
build_nb_lut	function	Pre-tabulate band-integrated nB over a column-enhancement grid.
inject_plume	function	Multiplicative plume injection: scene_plume = scene · nB(ΔX).
lookup_nb	function	Look up per-band nB for every pixel of a 2-D column map.

Re-exported from other libraries

Name	Kind	What it does
ATM_TO_PA	constant	Re-exported from builtins.
BOLTZMANN_J_PER_K	constant	Re-exported from builtins.
CM3_PER_M3	constant	Re-exported from builtins.

radtrax.solvers

Name	Kind	What it does
BeerLambert	class	Beer–Lambert along the two-way path; no scattering, no emission.
RTSolver	class	Protocol: optical properties, a surface and a geometry in, radiance out.

radtrax.spectroscopy

Per-layer optical depth: the OpacityProvider protocol and table opacity. (radtrax.spectroscopy.opacity)

Name	Kind	What it does
CrossSectionTable	class	One gas's cross sections σ(ν; p, T) on a (ln p, T) grid.
OpacityProvider	class	Protocol: an atmospheric state in, per-layer optical depth out.
SumOpacity	class	Optical depth from several sources on one wavenumber grid.
TableOpacity	class	Optical depth from per-gas cross-section tables.

The solar irradiance at the top of the atmosphere, on the model grid. (radtrax.spectroscopy.solar)

Name	Kind	What it does
earth_sun_distance	function	The Earth–Sun distance [AU] on a day of the year.
fetch_solar_spectrum	function	Download a solar spectrum into the cache, once, and check its SHA-256.
solar_irradiance	function	Solar irradiance \(E_0(\nu)\) at 1 AU, interpolated onto a wavenumber grid.

The cross-section tables of v0: where they live and how to load them. (radtrax.spectroscopy.table_cache)

Name	Kind	What it does
TableGrid	class	The (ν, p, T) grid a cross-section table is built on.
V0_GRID	constant	TableGrid(name='v0', nu_min_cm=4000.0, nu_max_cm=6500.0, ...
load_opacity	function	A :class:~radtrax.spectroscopy.TableOpacity from cached tables.
load_table	function	Open gas's cached table (lazily, with xarray).
table_cache_dir	function	Where tables are cached.

LUT interpolation + Beer-Lambert transmittance for one-shot forward models. (radtrax.spectroscopy.tables)

Name	Kind	What it does
absorption_coefficient	function	α(ν) = σ(ν) · N_gas [1/cm].
beers_law_from_lut	function	End-to-end: σ-from-LUT → α → τ(ν) for a single homogeneous layer.
interpolate_cross_section	function	Return σ(ν) at a given (T, p) via bilinear LUT interpolation.
plume_ratio_spectrum	function	Differential-Beer-Lambert ratio τ_total(ν) / τ_bg(ν).
transmittance	function	τ(ν) = exp(-α · L_vert · AMF).

radtrax.spectroscopy.hitran

Build v0's cross-section tables into the cache (the [hitran] extra). (radtrax.spectroscopy.hitran.build)

Name	Kind	What it does
build_table	function	Build gas's table on grid and write it to the table cache.

Gas + grid configuration for HAPI absorption-cross-section look-up tables. (radtrax.spectroscopy.hitran.config)

Name	Kind	What it does
GasConfig	class	Configuration for a single HITRAN gas species.
LUTGridConfig	class	Grid configuration shared across gases for a single LUT build.

Single-gas absorption-cross-section LUT builder. (radtrax.spectroscopy.hitran.generator)

Name	Kind	What it does
build_lut_dataset	function	Wrap the raw LUT arrays in a CF-conformant xarray.Dataset.
compute_absorption_lut	function	Evaluate σ(ν, T, P) on the full LUT grid.
default_cache_dir	function	Return the HITRAN line-data cache directory.
fetch_hitran_data	function	Fetch HITRAN line parameters for gas_config into cache_dir.
generate_single_gas_lut	function	End-to-end single-gas pipeline: fetch → compute → wrap → (optionally) save.
save_lut	function	Persist ds to <output_dir>/<filename> (zlib, σ as float32).

Multi-gas LUT orchestration — separate-per-gas and combined builds. (radtrax.spectroscopy.hitran.multi)

Name	Kind	What it does
create_combined_lut	function	Build a single NetCDF with one cross-section variable per gas.
create_multi_gas_luts	function	Build one separate <gas>_absorption_lut.nc per gas.

Re-exported from other libraries

Name	Kind	What it does
ATMOSPHERIC_GASES	constant	Re-exported from builtins.
DEFAULT_VMR_NOMINAL	constant	Re-exported from builtins.
HAPI_CACHE_ENV	constant	Re-exported from builtins.

radtrax.spectroscopy.hitran.build

Build v0's cross-section tables into the cache (the [hitran] extra). (radtrax.spectroscopy.hitran.build)

Name	Kind	What it does
fetch_lines	function	Download gas's HITRAN lines over the grid plus a margin ([hitran]).
gas_config_for	function	gas's HITRAN configuration over grid's wavenumber range.
main	function	python -m radtrax.spectroscopy.hitran GAS [GAS ...] [--grid v0].

Re-exported from other libraries

Name	Kind	What it does
LINE_MARGIN_CM	constant	Re-exported from builtins.

radtrax.spectroscopy.hitran.config

Name	Kind	What it does
annotations	constant	Re-exported from __future__.
dataclass	function	Re-exported from dataclasses.
field	function	Re-exported from dataclasses.

radtrax.spectroscopy.hitran.generator

Name	Kind	What it does
HAPI_CACHE_ENV	constant	Re-exported from builtins.

radtrax.spectroscopy.hitran.multi

Name	Kind	What it does
Path	class	Re-exported from pathlib.
logger	constant	Re-exported from logging.

radtrax.spectroscopy.solar

The solar irradiance at the top of the atmosphere, on the model grid. (radtrax.spectroscopy.solar)

Name	Kind	What it does
SolarSource	class	A published solar reference spectrum that radtrax can download.
solar_spectrum_path	function	The cache file of a solar spectrum (it may not exist yet).

Re-exported from other libraries

Name	Kind	What it does
SOLAR_SOURCES	constant	Re-exported from builtins.

radtrax.spectroscopy.synthetic

Synthetic methane spectra for docs, notebooks and tests, without HITRAN. (radtrax.spectroscopy.synthetic)

Name	Kind	What it does
band_mean	function	⟨x⟩_b = ∫ x f dλ / ∫ f dλ on a shared uniform grid.
methane_cross_section	function	radtrax · 1 and · 2's synthetic CH₄ cross-section σ(λ) on :data:WL_NM [m²/kg].
synthetic_table	function	radtrax · 3's σ(ν; T, p) [cm²/molecule] on (wavenumber, temperature, pressure [atm]).

Re-exported from other libraries

Name	Kind	What it does
CH4_MASS_U	constant	Re-exported from builtins.
NU_CM	constant	Re-exported from numpy.
P_ATM	constant	Re-exported from numpy.
T_K	constant	Re-exported from numpy.
WL_NM	constant	Re-exported from numpy.

radtrax.spectroscopy.table_cache

The cross-section tables of v0: where they live and how to load them. (radtrax.spectroscopy.table_cache)

Name	Kind	What it does
build_command	function	The shell command that builds gases on grid.
table_path	function	The cache file of gas on grid: <gas>_<grid key>_<HITRAN>_v<table>.nc.

Re-exported from other libraries

Name	Kind	What it does
GRIDS	constant	Re-exported from builtins.
HITRAN_VERSION	constant	Re-exported from builtins.
TABLE_DIR_ENV	constant	Re-exported from builtins.
TABLE_VERSION	constant	Re-exported from builtins.

radtrax.spectroscopy.tables

Name	Kind	What it does
ATM_TO_PA	constant	Re-exported from builtins.
BOLTZMANN_J_PER_K	constant	Re-exported from builtins.
CM3_PER_M3	constant	Re-exported from builtins.

radtrax.surface

The Surface protocol and the Lambertian surface. (radtrax.surface.lambertian)

Name	Kind	What it does
Lambertian	class	A Lambertian surface: R = A in every direction.
Surface	class	Protocol: the surface's bidirectional reflectance factor.

A spectral albedo: a low-order Legendre series in wavenumber. (radtrax.surface.polynomial)

Name	Kind	What it does
PolynomialAlbedo	class	A Lambertian surface whose albedo is a Legendre series in wavenumber.

The Ross–Li kernel BRDF: RossThick and LiSparse-Reciprocal. (radtrax.surface.ross_li)

Name	Kind	What it does
RossLi	class	The Ross–Li kernel BRDF: R = f_iso + f_vol K_vol + f_geo K_geo.

radtrax.surface.ross_li

Name	Kind	What it does
li_sparse_reciprocal	function	The LiSparse-Reciprocal geometric kernel K_geo (dimensionless), MODIS's shape.
ross_thick	function	The RossThick volume-scattering kernel K_vol (dimensionless).

Listed at gaussx 0.6.5, lineax 0.1.1, optimistix 0.1.0.

Upstream: gaussx

Structured Gaussian linear algebra for JAX: low-rank updates and Woodbury solves, block-tridiagonal operators, structured Cholesky. radtrax uses it for matched-filter and retrieval covariances.

gaussx

Name	Kind	What it does
AbstractIntegrator	class	Protocol for Gaussian integral approximation.
AbstractLikelihood	class	Base class for likelihood functions with optional analytical ELL.
AbstractLogdetStrategy	class	Protocol for log-determinant strategies.
AbstractPreconditioner	class	Protocol for preconditioners producing an approximate inverse.
AbstractSketch	class	A random sketching matrix \(S \in \mathbb{R}^{d \times m}\), sampled once.
AbstractSolveStrategy	class	Protocol for linear solve strategies.
AbstractSolverStrategy	class	Protocol for solver strategies that pair solve + logdet.
AnalyticalPsiStatistics	class	Protocol for kernels with closed-form Ψ statistics.
AssumedDensityFilter	class	KL-optimal Gaussian projection via moment matching.
AutoSolver	class	Automatic solver selection based on operator type and size.
BBMMSolver	class	CG solve and SLQ logdet with BBMM's defaults (Gardner et al. 2018).
BernoulliLikelihood	class	Bernoulli likelihood with logit link.
BinomialLikelihood	class	Binomial likelihood with logit link.
BlockDiag	class	Block diagonal operator diag(A₁, A₂, …, Aₖ).
BlockTriDiag	class	Block-tridiagonal operator with a symmetric off-diagonal band.
CGSolver	class	Iterative CG solver with stochastic log-determinant.
CUR	class	CUR decomposition \(A \approx C\,U\,R\), \(C = A_{:,J}\), \(R = A_{I,:}\).
CapacitanceSolver	class	Solve a base system subject to homogeneous point constraints.
Chandrupatla	class	Chandrupatla's hybrid inverse-quadratic / bisection root finder.
ColumnID	class	Column interpolative decomposition \(A \approx A_{:,J}\,X\).
ComposedSolver	class	Mix-and-match solve and logdet from different strategies.
ConstantSDE	class	State-space representation of a constant kernel.
CosineSDE	class	State-space representation of the cosine kernel.
CubatureIntegrator	class	Third-order spherical-radial cubature.
DAREResult	class	Result of DARE solver.
DenseFallbackWarning	class	Warning emitted when a structured primitive materialises an operator.
DenseLogdet	class	Dense log-determinant via gaussx structural dispatch.
DenseSolver	class	Dense solver strategy using gaussx structural dispatch.
DiagonalizedOperator	class	Linear operator A x = V⁻¹(Λ ⊙ V x) given by a transform pair.
EigenDecomposition	class	Precomputed eigendecomposition A = V diag(λ) V⁻¹ of a square matrix.
EmissionModel	class	Observation (emission) model wrapping a linear observation matrix.
FifthOrderCubatureIntegrator	class	Fifth-order fully symmetric cubature (McNamee & Stenger).
FilterState	class	Output of kalman_filter.
GaussHermiteIntegrator	class	Gauss-Hermite quadrature integrator.
GaussianExpFam	class	Gaussian in natural (exponential family) parameters.
GaussianLikelihood	class	Gaussian likelihood log N(y \| f, noise_var * I).
GaussianSites	class	Time-varying Gaussian likelihood sites in natural parameterization.
GaussianSketch	class	Gaussian sketch: i.i.d. entries \(S_{ij} \sim \mathcal{N}(0, 1/d)\).
GaussianState	class	Gaussian distribution as (mean, covariance operator) pair.
HeteroscedasticGaussianLikelihood	class	Heteroscedastic Gaussian likelihood with input-dependent noise.
IndefiniteSLQLogdet	class	Stochastic log\|det(A)\| for symmetric (possibly indefinite) operators.
IntegratedWienerSDE	class	State-space representation of an integrated Wiener process.
InterpolatedOperator	class	Structured Kernel Interpolation: K \approx W K_{uu} W^T.
JacobiPreconditioner	class	Diagonal preconditioner M^{-1} = diag(1 / \|diag(A)\|).
KeyedSolver	class	Bind a PRNG key to a strategy's stochastic log-determinant (gh-384).
Kronecker	class	Kronecker product operator A₁ ⊗ A₂ ⊗ … ⊗ Aₖ.
KroneckerSum	class	Kronecker sum A \oplus B = A \otimes I_b + I_a \otimes B.
KroneckerSumSqrt	class	Symmetric square root of A \oplus B via per-factor eigenvectors.
LOOResult	class	Result of leave-one-out cross-validation.
LOVECache	class	Cached rank-k Lanczos approximation of K^{-1}.
LSMRSolver	class	LSMR iterative least-squares solver (Fong & Saunders 2011).
LinearizedSDE	class	Linear surrogate \(dx = (A_t x + b_t)\,dt + Q_t^{1/2}\,dW\) of an SDE.
LineaxSolver	class	A lineax solver as a gaussx solve strategy.
LowRankUpdate	class	Low-rank update operator L + U diag(d) Vᵀ.
LowerBlockTriDiag	class	Lower triangular block-bidiagonal Cholesky factor.
MINRESSolver	class	MINRES solver for symmetric (possibly indefinite) systems.
MaskedOperator	class	Row/column-masked view of a base operator.
MaternSDE	class	State-space representation of the Matern kernel.
MomentMatchResult	class	Tilted log-normaliser and its derivatives w.r.t. the cavity mean.
MonteCarloIntegrator	class	Monte Carlo moment matching: sample, propagate, compute moments.
NegativeBinomialLikelihood	class	Negative-binomial likelihood with log link (NB2, a gamma-Poisson mixture).
NystromLogdet	class	Nyström-preconditioned log-determinant of \(A + \mu I\) (Wenger et al., 2022).
NystromPreconditioner	class	Randomized Nyström preconditioner for A + μ I.
OperatorPreconditioner	class	Use an externally supplied approximate inverse as a preconditioner.
OrthonormalSketch	class	Gaussian sketch with orthonormal rows, \(S S^\top = I_d\).
PartialCholeskyPreconditioner	class	Preconditioner from a pivoted partial Cholesky factor.
PeriodicSDE	class	State-space representation of the periodic (MacKay) kernel.
PoissonLikelihood	class	Poisson likelihood with log link.
PreconditionedCGSolver	class	CG solver with pivoted partial Cholesky preconditioner.
PredictionCache	class	Cached training solve (and factor) for amortized predictions.
ProductSDE	class	Product of two SDE kernels via Kronecker composition.
PropagationResult	class	Output of uncertainty propagation through a nonlinear function.
QuasiPeriodicSDE	class	Quasi-periodic kernel: product of Matern and Periodic SDE.
RootDecomposition	class	Tall factor R with R Rᵀ ≈ A semantics.
RowSamplingSketch	class	Weighted row-sampling sketch.
SDEKernel	class	Abstract base class for state-space kernel representations.
SDEParams	class	Continuous-time SDE parameters for a linear SDE.
SLQLogdet	class	Stochastic log-determinant via Lanczos quadrature (SLQ).
SLRResult	class	Linear-Gaussian surrogate produced by statistical linear regression.
SRHTSketch	class	Subsampled randomized Hadamard transform sketch.
SVDLowRankUpdate	class	Deprecated subclass of LowRankUpdate with orthonormal=True.
SketchAndPrecondLSMR	class	Sketch-and-precondition LSMR for tall least squares (Rokhlin & Tygert, 2008).
SoftmaxLikelihood	class	Softmax (categorical) likelihood for multi-class classification.
SparseCholeskyFactor	class	Sparse Cholesky factor P Q Pᵀ = L Lᵀ on a static symbolic pattern.
SparseCholeskySolver	class	Exact solve / logdet / diag_inv through a sparse Cholesky factor.
SparseOperator	class	Sparse matrix with a static SparsityPattern and traced values.
SparseSignSketch	class	Sparse sign sketch (sparse Johnson-Lindenstrauss transform).
SparsityPattern	class	Static, hashable sparsity pattern of a (m, n) matrix.
SpectralFunction	class	f(B) for a symmetric B with a factored eigenbasis.
StudentTLikelihood	class	Student-t likelihood for robust regression.
SumKronecker	class	Deprecated alias for SumOfKroneckers.
SumKroneckerSqrt	class	Deprecated alias for SumOfKroneckersSqrt (gh-297).
SumOfKroneckers	class	Sum of Kronecker products Σ_k A_k \otimes B_k.
SumOfKroneckersSqrt	class	Lazy Lanczos square-root operator for SumOfKroneckers covariances.
SumSDE	class	Sum of SDE kernels via block-diagonal composition.
SymbolicCholesky	class	Symbolic Cholesky factor of a symmetric sparsity pattern.
TaylorIntegrator	class	1st or 2nd order Taylor expansion for uncertainty propagation.
Toeplitz	class	Symmetric Toeplitz matrix from its first column.
ToeplitzCholesky	class	Circulant-embedding sample factor for a symmetric positive Toeplitz matrix.
UDLDecomposition	class	Banded factorisation \(\Lambda = U \tilde{D} U^{\top}\) of a BlockTriDiag.
UnscentedIntegrator	class	Unscented transform: deterministic sigma points.
UpperBlockTriDiag	class	Upper triangular block-bidiagonal (transpose of LowerBlockTriDiag).
add_jitter	function	Add diagonal jitter for numerical stability: A + eps * I.
ar1_precision	function	Precision of a stationary AR(1) process with marginal precision τ.
as_diagonalized	function	Express operator as one DiagonalizedOperator, if possible.
as_linear_operator	function	Wrap a raw matvec callable as a tagged lineax operator.
base_conditional	function	Deprecated: use sparse_conditional (note K_xz = K_mn.T).
besag_structure	function	Validate a graph Laplacian as a Besag (ICAR) structure matrix.
block_diagonal_tag	constant	block_diagonal_tag
block_tridiagonal_tag	constant	block_tridiagonal_tag
blr_diag_update	function	Diagonal natural parameter BLR update step.
blr_full_update	function	Full-rank natural parameter BLR update step.
build_prediction_cache	function	Solve K_y alpha = y and cache the result.
bym2_precision	function	Joint precision of the BYM2 pair (b, u*) (Riebler et al., 2016).
cavity_distribution	function	Compute EP cavity distribution by removing a site.
cavity_from_marginal	function	Compute cavity distribution by removing a site from the marginal.
cholesky	function	Compute Cholesky factor L such that A = L L^T.
cholesky_logdet	function	Compute log|A| from Cholesky factor L where A = L Lᵀ.
circulant	function	(Block-)circulant operator from its first column.
circulant_from_symbol	function	(Block-)circulant operator from its DFT symbol.
collapsed_elbo	function	Collapsed ELBO (Titsias bound) for sparse GP regression.
column_id	function	Randomized column interpolative decomposition (Voronin & Martinsson, 2017).
compute_psi_statistics	function	Compute Ψ statistics, dispatching to analytical or numerical.
conditional	function	Compute p(x_A \| x_B = b) from a joint Gaussian p(x_A, x_B).
conditional_interpolate	function	Two-filter fusion at t from a filtered state and a backward message.
conditional_variance	function	Predictive variance: Schur complement diagonal plus optional variational correction.
cost_expectation	function	Compute E[Cost(f(x), target)] where x ~ N(mu, Sigma).
cov_transform	function	Covariance propagation through a linear map: J @ Sigma @ J^T.
create_grid	function	Create a regular grid from per-dimension sizes and bounds.
cubature_points	function	Spherical-radial cubature points and weights.
cubic_interpolation_weights	function	Compute cubic interpolation indices and weights for SKI.
cur	function	Randomized CUR decomposition (Voronin & Martinsson, 2017, §4).
cvi_update_sites	function	Natural gradient update for CVI sites.
damped_natural_update	function	Damped update in natural parameter space.
dare	function	Steady-state Kalman filter covariance and gain (the filtering DARE).
diag	function	Extract the diagonal of an operator as a 1D array.
diag_conditional_variance	function	Diagonal of Schur complement: diag(K_XX - A K_ZX).
diag_inv	function	Compute the diagonal of the inverse of a linear operator.
diagonal_tag	constant	Re-exported from lineax.
discrepancy_step_size	function	Adaptive EKI tempering step: the data misfit controller.
discrete_lyapunov_solve	function	Solve the discrete Lyapunov equation P - G P G^T = Q.
discretize_mfd	function	Discretise a linear SDE by matrix-fraction decomposition.
discretize_mfd_sequence	function	Vectorised gaussx.discretize_mfd over a vector of time steps.
eig	function	Compute eigenvalues and eigenvectors.
eigh_generalized	function	Solve \(A v = \lambda B v\) for symmetric \(A\) and symmetric PSD \(B\).
eigvals	function	Compute eigenvalues only.
eki_step	function	One ensemble Kalman inversion (EKI) update.
elbo	function	Evidence lower bound (ELBO).
enkf_analysis	function	Stochastic (perturbed-observation) ensemble Kalman analysis step.
ensemble_covariance	function	Empirical covariance from an ensemble as a low-rank operator.
ensemble_cross_covariance	function	Cross-covariance between two ensemble sets.
ensemble_kalman_gain	function	Kalman gain from an ensemble and its image in observation space.
ep_tilted_moments	function	Moments of the scalar EP tilted distribution, elementwise over a batch.
estimate_spectral_bounds	function	Estimate \((\lambda_{\min}, \lambda_{\max})\) of a symmetric operator.
etkf_transform	function	Ensemble Transform Kalman Filter (ETKF) analysis weights.
euclidean_distance	function	Pairwise Euclidean distances \|\|a_i - b_j\|\|.
expectation_to_mean_chol	function	Convert expectation parameters to mean/variance (Cholesky).
expectation_to_natural	function	Convert expectation parameters to natural parameters.
expectations_to_ssm	function	Convert expectation parameters back to SSM marginals.
expected_log_likelihood	function	Unified expected log-likelihood with analytical dispatch.
fem_matrices	function	Lumped mass C̃ and stiffness G of P1 elements on a triangle mesh.
fem_projector	function	Observation matrix A of P1 interpolation: (A w)_k = Σ_i ψ_i(s_k) w_i.
fifth_order_cubature_points	function	Fifth-order fully symmetric cubature points and weights.
fisher_info	function	Fisher information with respect to the mean, \(F_\mu = \Sigma^{-1}\).
frobenius_norm	function	Compute the Frobenius norm \|\|A\|\|_F with structural dispatch.
gaspari_cohn	function	Gaspari-Cohn (1999) fifth-order compactly-supported taper.
gauss_hermite_points	function	Gauss-Hermite quadrature points and weights.
gauss_kl	function	KL(first ‖ second): KL[q(u) \|\| p(u)] with p(u) = N(0, K).
gauss_newton_precision	function	Gauss-Newton precision matrix J^T J, optionally plus a prior.
gaussian_entropy	function	Entropy of a multivariate normal N(mu, Sigma).
gaussian_expected_log_lik	function	Expected log-likelihood E_q[log N(y \| f, R)].
gaussian_kl	function	KL(first ‖ second): KL(p \|\| q) between two multivariate normals.
gaussian_log_prob	function	Multivariate normal log-probability.
generalized_variance_scale	function	Generalized variance of an intrinsic GMRF (Sørbye & Rue, 2014).
ggn_diagonal	function	Generalized Gauss-Newton diagonal approximation.
gradient_expectation	function	Compute E[nabla f(x)] via Stein's lemma.
grid_coupling_indices	function	Flat indices of masked-out grid cells adjacent to the masked-in region.
grid_data	function	Expand a grid to the full Cartesian product of grid points.
hadamard_transform	function	Unnormalized Walsh-Hadamard transform along the last axis.
haversine_distance	function	Pairwise great-circle (haversine) distances on a sphere.
hutchinson_hessian_diag	function	Stochastic Hessian diagonal via Hutchinson with Rademacher probes.
iid_precision	function	Precision τ I of n independent effects with variance 1/τ.
infinite_horizon_filter	function	Infinite-horizon Kalman filter with fixed steady-state gain.
infinite_horizon_smoother	function	Infinite-horizon RTS smoother with fixed steady-state gain.
inflate_multiplicative	function	Multiplicative ensemble inflation about the mean.
inflate_rtpp	function	Relaxation to prior perturbations (RTPP; Zhang et al. 2004).
inflate_rtps	function	Relaxation to prior spread (RTPS; Whitaker & Hamill 2012).
inv	function	Return a lazy inverse operator A^{-1}.
inv_quad_logdet	function	Joint inverse-quadratic and log-determinant via shared BBMM CG.
is_block_diagonal	function	Check whether operator carries the block-diagonal tag.
is_block_tridiagonal	function	Check whether operator carries the block-tridiagonal tag.
is_diagonal	function	Re-exported from lineax.
is_eigen_reducible	function	Whether a sum of Kronecker products has the exact two-term reduction.
is_kronecker	function	Check whether operator carries the Kronecker tag.
is_kronecker_sum	function	Check whether operator carries the Kronecker sum tag.
is_low_rank	function	Check whether operator carries the low-rank tag.
is_lower_triangular	function	Re-exported from lineax.
is_negative_semidefinite	function	Re-exported from lineax.
is_positive_semidefinite	function	Re-exported from lineax.
is_symmetric	function	Re-exported from lineax.
is_upper_triangular	function	Re-exported from lineax.
joseph_update	function	Numerically stable Joseph-form covariance update.
kalman_filter	function	Kalman filter forward pass via jax.lax.scan.
kalman_gain	function	Compute Kalman gain K = P @ H^T @ (H @ P @ H^T + R)^{-1}.
kernel_expectations	function	Compute kernel expectations Psi_0, Psi_1, Psi_2 for uncertain inputs.
kl_divergence	function	KL(first ‖ second): KL(q \|\| p) via the Bregman form on natural parameters.
kl_standard_normal	function	KL(first ‖ second): KL(N(m, S) \|\| N(0, I)).
kronecker_mll	function	Exact marginal log-likelihood for a Kronecker-structured GP.
kronecker_posterior_predictive	function	Posterior mean and variance for a Kronecker GP at test points.
kronecker_sum_sample	function	Sample from 𝒩(0, A ⊕ B) using per-factor eigendecompositions.
kronecker_sum_solve	function	Solve a shifted Kronecker-sum system in tensor (unvectorized) form.
kronecker_sum_tag	constant	kronecker_sum_tag
kronecker_tag	constant	kronecker_tag
leave_one_out_cv	function	LOO-CV via the bordered-system identity.
linear_solve	function	Solve A x = b through the unified front door.
linearize_sde	function	Optimal linear drift of a nonlinear SDE along a Gaussian path.
localization_matrix	function	Pairwise Gaspari-Cohn taper rho(dist(a_i, b_j); c).
localized_kalman_gain	function	Ensemble Kalman gain with Hadamard (Schur-product) localization.
log_likelihood_expectation	function	Compute E[log p(y_{obs} \| f(x))] where x ~ N(mu, Sigma).
log_marginal_likelihood	function	GP log marginal likelihood.
log_partition	function	Log-partition function A(eta).
logdet	function	Compute log |det(A)| with structural dispatch.
love_cache	function	Precompute a Lanczos approximation of K^{-1} for fast variance.
love_residual	function	Relative solve residual of a LOVE cache for one cross-covariance.
love_variance	function	Approximate k_*^\top K^{-1} k_* from a LOVE cache.
love_variance_error_bound	function	Upper bound on the variance over-estimate of a LOVE cache.
low_rank_plus_diag	function	Construct diag(diag) + U diag(d) Vᵀ.
low_rank_plus_identity	function	Construct scale * I + U diag(d) Vᵀ.
low_rank_tag	constant	low_rank_tag
lower_triangular_tag	constant	Re-exported from lineax.
masked_moment_inputs	function	Make masked observation channels inert in a moment-matched update.
matern_spde_params	function	SPDE parameters (κ, τ, α) of a Matérn field.
matheron_update	function	Posterior samples via Matheron's-rule correction.
mean_chol_to_expectation	function	Convert mean/variance (Cholesky) to expectation parameters.
mean_chol_to_natural	function	Convert mean/variance (Cholesky) to natural parameters.
mean_cov_to_natural	function	Convert mean/covariance to natural parameters (operator form).
mean_expectation	function	Compute E[f(x)] where x ~ N(mu, Sigma).
meanfield_kalman_filter	function	Mean-field Kalman filter over L = D // block_size state blocks.
meanfield_rts_smoother	function	Mean-field RTS smoother over L = D // block_size state blocks.
mixture_quantile	function	Invert a CDF at one or more quantile levels by bracketed root finding.
mixture_quantile_gaussian_approx	function	Quantiles of the Gaussian matched to an ensemble's first two moments.
moment_match	function	EP moment matching: tilted log-normaliser and its first two derivatives.
moment_transform	function	Moment triple of (x, fn(x)) for x Gaussian.
natural_to_expectation	function	Convert natural parameters to expectation parameters.
natural_to_mean_chol	function	Convert natural parameters to mean/variance (Cholesky).
natural_to_mean_cov	function	Convert natural parameters to mean/covariance (operator form).
naturals_to_ssm	function	Convert natural parameters back to SSM parameters.
negative_semidefinite_tag	constant	Re-exported from lineax.
newton_update	function	Convert a Newton step to natural pseudo-likelihood parameters.
nonlinear_kalman_filter	function	Moment-matched nonlinear Kalman filter.
nonlinear_kalman_predict	function	One moment-matched predict step.
nonlinear_kalman_update	function	One moment-matched update step.
nonlinear_rts_smoother	function	Moment-matched nonlinear Rauch-Tung-Striebel smoother.
nonlinear_rts_step	function	One moment-matched RTS backward step.
oilmm_back_project	function	Back-project latent GP predictions to the observation space.
oilmm_project	function	Project multi-output data to independent latent GPs via OILMM.
pairwise_marginals	function	Joint p(x_k, x_{k+1}) for each consecutive pair.
parallel_kalman_filter	function	Parallel Kalman filter via jax.lax.associative_scan.
parallel_rts_smoother	function	Parallel RTS smoother via reverse jax.lax.associative_scan.
positive_semidefinite_tag	constant	Re-exported from lineax.
predict_mean	function	Predictive mean: mu* = K_*f @ alpha.
predict_variance	function	Predictive variance sigma^2_* = k_** - diag(K_*f K_y^{-1} K_f*).
process_noise_covariance	function	Compute process noise from stationary covariance.
product_operator	function	Lazy matmul (A B) v = A (B v).
project	function	Compute A_X = K_XZ @ K_ZZ^{-1} via Cholesky solve.
pseudo_logdet	function	Log pseudo-determinant: the log of the product of the non-zero eigenvalues.
qb	function	Randomized QB factorisation \(A \approx QB\) with \(B = Q^\top A\).
quadratic_form	function	Compute x^T A^{-1} x via a single solve.
randomized_eigh	function	Partial eigendecomposition of a symmetric operator by Rayleigh-Ritz.
randomized_nystrom	function	Randomized Nyström approximation \(\hat A = U\hat\Lambda U^\top\) of a PSD \(A\).
randomized_svd	function	Truncated SVD \(A \approx U \operatorname{diag}(s) V^\top\) by randomized QB.
range_finder	function	Orthonormal basis \(Q\) for the dominant range of \(A\).
riemannian_psd_correction	function	Riemannian gradient correction for PSD precision updates.
root_decomposition	function	Compute a tall factor R such that R Rᵀ ≈ A.
root_inv_decomposition	function	Compute a tall factor R⁻ such that R⁻ (R⁻)ᵀ ≈ A⁻¹.
rp_cholesky	function	Randomly pivoted partial Cholesky of a PSD matrix A.
rts_interpolate	function	Smoothed marginal at an unobserved t from filtered and smoothed states.
rts_smoother	function	Rauch-Tung-Striebel backward smoother.
rw1_structure	function	Structure matrix R = D₁ᵀ W D₁ of a first-order random walk.
rw2_structure	function	Structure matrix R = D₂ᵀ D₂ of a second-order random walk.
safe_cholesky	function	Cholesky decomposition with adaptive jitter for near-singular matrices.
sample_joint_conditional	function	Joint draws of a partitioned Gaussian, and conditional draws from them.
sample_mvn	function	Draw samples from \(\mathcal{N}(\mu, K)\), dispatching on \(K\)'s structure.
sandwich	function	Return A @ P @ A.T exploiting compatible operator structure.
scaled_operator	function	Lazy scalar multiply (c A) v = c (A v).
schur_complement	function	Schur complement: K_XX - K_XZ @ K_ZZ^{-1} @ K_ZX.
sde_autocovariance	function	Compute the stationary autocovariance of an SDE kernel.
sde_kl_divergence	function	Drift path-KL between a linear and a nonlinear SDE along a Gaussian path.
selected_inverse	function	The band of Σ = Q⁻¹ for a symmetric positive-definite BlockTriDiag.
sigma_points	function	Unscented transform sigma points and weights.
site_mean_var_from_natural	function	Convert per-site natural parameters to mean/variance.
site_natural_from_tilted	function	Compute site natural parameters from tilted and cavity moments.
sites_to_precision	function	Convert Gaussian sites to a block-tridiagonal precision.
sketch_and_solve	function	Approximate least squares from a sketch.
solve	function	Solve A x = b with structural dispatch.
solve_columns	function	Solve A X = B column-by-column via vmap.
solve_matrix	function	Solve A X = B with a single factorization on the matrix RHS.
solve_rows	function	Solve A x = bᵢ for each row bᵢ of a matrix via vmap.
sparse_cholesky	function	Sparse Cholesky factorisation of a symmetric positive-definite operator.
sparse_conditional	function	Sparse-GP conditional q(f_x) = \int p(f_x \| u) q(u) du.
spde_precision	function	SPDE precision Q_α = τ² K (C̃⁻¹K)^{α−1} with K = κ²C̃ + G.
spde_precision_grid	function	SPDE precision on a regular grid: a function of a Kronecker sum.
spingp_log_likelihood	function	Log marginal likelihood via sparse inverse GP formulation.
spingp_posterior	function	Posterior mean and precision via SpInGP.
sqrt	function	Compute matrix square root S such that S @ S = A.
sqrt_inv_matmul	function	Compute \(A^{-1/2} b\) via contour-integral quadrature.
sqrt_matmul	function	Compute \(A^{1/2} b\) via contour-integral quadrature.
ssm_to_expectations	function	Convert SSM marginals to expectation parameters.
ssm_to_naturals	function	Convert SSM parameters to natural parameters.
stable_squared_distances	function	Squared Euclidean distances with mixed-precision stability.
statistical_linear_regression	function	Moment-match a nonlinear conditional to a linear-Gaussian surrogate.
submatrix	function	Extract A[row_idx, col_idx] without forming the full matrix.
sufficient_stats	function	Compute sufficient statistics T(x) = [x, x x^T].
sum_of_kroneckers_sample	function	Sample from 𝒩(0, op) with matrix-free Lanczos square roots.
sum_operator	function	Lazy sum (A + B + …) v = A v + B v + ….
sumkronecker_sample	function	Deprecated alias for sum_of_kroneckers_sample (gh-297).
svd	function	Compute the singular value decomposition A = U diag(s) V^T.
svd_low_rank_plus_diag	function	Construct diag(diag) + U diag(S) Vᵀ from a truncated SVD.
svgp_variance_adjustment	function	Compute the SVGP variance adjustment operator.
symbolic_cholesky	function	Symbolic analysis of a sparse Cholesky factorisation (host, cached).
symmetric_tag	constant	Re-exported from lineax.
symmetrize	function	Symmetrize the trailing two axes: 0.5 * (X + X^T).
theta_design	function	Integration points and log-weights over hyperparameters \(\theta\).
tikhonov_augment	function	Observation augmentation for Tikhonov-regularised EKI (TEKI).
to_expectation	function	Deprecated alias of to_mean_cov.
to_mean_cov	function	Convert natural parameters to the mean and covariance.
to_natural	function	Deprecated alias of gaussx.mean_cov_to_natural.
toeplitz_sample	function	Sample from 𝒩(0, Toeplitz(column)) via FFT circulant embedding.
trace	function	Compute the trace of an operator.
trace_and_diag	function	Jointly estimate the trace and diagonal from one probe pass.
trace_correction	function	Trace term in Titsias collapsed ELBO.
trace_product	function	Trace of a matrix product: tr(A @ B) with structural dispatch.
tridiagonal_solve	function	Solve a tridiagonal system A x = d.
tridiagonal_solve_batched	function	Solve independent tridiagonal systems over leading batch dimensions.
tridiagonal_tag	constant	Re-exported from lineax.
udl_decomposition	function	Factorise a symmetric block-tridiagonal precision as \(U \tilde{D} U^{\top}\).
udl_from_ssm_params	function	Build the UDLDecomposition of a Gauss-Markov chain's precision.
udl_to_ssm_params	function	Read the equivalent Gauss-Markov chain off a UDLDecomposition.
uncertain_bgplvm_predict	function	Multi-output uncertain GP prediction for BGPLVM.
uncertain_gp_predict	function	Predictive mean and variance for GP with uncertain inputs.
uncertain_gp_predict_mc	function	Monte Carlo GP prediction with uncertain inputs.
uncertain_svgp_predict	function	Predictive mean and variance for SVGP with uncertain inputs.
uncertain_vgp_predict	function	Predictive mean and variance for dense VGP with uncertain inputs.
unit_diagonal_tag	constant	Re-exported from lineax.
unwhiten	function	Unwhiten variational mean: m = L @ m_tilde.
unwhiten_covariance	function	Unwhiten variational covariance: S = L S̃ Lᵀ.
upper_triangular_tag	constant	Re-exported from lineax.
variational_elbo_gaussian	function	Uncollapsed (SVGP) ELBO for a Gaussian likelihood.
variational_elbo_mc	function	Monte Carlo ELBO for non-conjugate likelihoods.
whiten_covariance	function	Unwhiten variational covariance: S = L S̃ Lᵀ.
whitened_svgp_predict	function	Whitened SVGP prediction: mean and variance at test points.
woodbury_solve	function	Standalone Woodbury identity solve: (L + U diag(D) U^T)^{-1} b.

Upstream: lineax

Linear solves in JAX with implicit differentiation. radtrax uses it for linear systems that are not covariances.

lineax

Name	Kind	What it does
AbstractLinearOperator	class	Abstract base class for all linear operators.
AbstractLinearSolver	class	Abstract base class for all linear solvers.
AddLinearOperator	class	A linear operator formed by adding two other linear operators together.
AutoLinearSolver	class	Automatically determines a good linear solver based on the structure of the operator.
BiCGStab	class	Biconjugate gradient stabilised method for linear systems.
CG	class	Conjugate gradient solver for linear systems.
Cholesky	class	Cholesky solver for linear systems.
ComposedLinearOperator	class	A linear operator formed by composing (matrix-multiplying) two other linear operators together.
Diagonal	class	Diagonal solver for linear systems.
DiagonalLinearOperator	class	A diagonal linear operator, e.g. for a diagonal matrix.
DivLinearOperator	class	A linear operator formed by dividing a linear operator by a scalar.
FunctionLinearOperator	class	Wraps a linear function fn: X -> Y into a linear operator. (So that self.mv(x) is defined by self.mv(x) == fn(x).)
GMRES	class	GMRES solver for linear systems.
IdentityLinearOperator	class	Represents the identity transformation X -> X, where each x in X is some PyTree of floating-point JAX arrays.
JacobianLinearOperator	class	Given a function fn: X -> Y, and a point x in X, then this defines the linear operator (also a function X -> Y) given by the Jacobian (d(fn)/dx)(x).
LSMR	class	LSMR solver for linear systems.
LU	class	LU solver for linear systems.
MatrixLinearOperator	class	Wraps a 2-dimensional JAX array into a linear operator.
MulLinearOperator	class	A linear operator formed by multiplying a linear operator by a scalar.
NegLinearOperator	class	A linear operator formed by computing the negative of a linear operator.
Normal	class	Wrapper for an inner solver of positive (semi)definite systems.
NormalCG	function	Deprecated helper function.
PyTreeLinearOperator	class	Represents a PyTree of floating-point JAX arrays as a linear operator.
QR	class	QR solver for linear systems.
RESULTS	class	An enumeration, with the following entries:
SVD	class	SVD solver for linear systems.
Solution	class	The solution to a linear solve.
TaggedLinearOperator	class	Wraps another linear operator and specifies that it has certain tags, e.g. representing symmetry.
TangentLinearOperator	class	Internal to lineax.
Triangular	class	Triangular solver for linear systems.
Tridiagonal	class	Tridiagonal solver for linear systems, uses the LAPACK/cusparse implementation of Gaussian elimination with partial pivotting (which increases stability). .
TridiagonalLinearOperator	class	As lineax.MatrixLinearOperator, but for specifically a tridiagonal matrix.
conj	function	Elementwise conjugate of a linear operator.
diagonal	function	Extracts the diagonal from a linear operator, and returns a vector.
diagonal_tag	constant	diagonal_tag
has_unit_diagonal	function	Returns whether an operator is marked as having unit diagonal.
invert	function	Returns a lineax.FunctionLinearOperator representing the (pseudo)inverse of operator.
is_diagonal	function	Returns whether an operator is marked as diagonal.
is_lower_triangular	function	Returns whether an operator is marked as lower triangular.
is_negative_semidefinite	function	Returns whether an operator is marked as negative semidefinite.
is_positive_semidefinite	function	Returns whether an operator is marked as positive semidefinite.
is_symmetric	function	Returns whether an operator is marked as symmetric.
is_tridiagonal	function	Returns whether an operator is marked as tridiagonal.
is_upper_triangular	function	Returns whether an operator is marked as upper triangular.
linear_solve	function	Solves a linear system.
linearise	function	Linearises a linear operator.
lower_triangular_tag	constant	lower_triangular_tag
materialise	function	Materialises a linear operator.
negative_semidefinite_tag	constant	negative_semidefinite_tag
positive_semidefinite_tag	constant	positive_semidefinite_tag
symmetric_tag	constant	symmetric_tag
transpose_tags	function	Lineax uses "tags" to declare that a particular linear operator exhibits some property, e.g. symmetry.
transpose_tags_rules	constant	Re-exported from builtins.
tridiagonal	function	Extracts the diagonal, lower diagonal, and upper diagonal, from a linear operator.
tridiagonal_tag	constant	tridiagonal_tag
unit_diagonal_tag	constant	unit_diagonal_tag
upper_triangular_tag	constant	upper_triangular_tag

Upstream: optimistix

Root finding, least squares and fixed points in JAX. radtrax uses its Gauss-Newton and Levenberg-Marquardt solvers for optimal estimation.

optimistix

Name	Kind	What it does
AbstractAdjoint	class	The abstract base class of all adjoints.
AbstractBFGS	class	Abstract version of the BFGS (Broyden–Fletcher–Goldfarb–Shanno) minimisation algorithm.
AbstractDFP	class	Abstract version of the DFP (Davidon–Fletcher–Powell) minimisation algorithm.
AbstractDescent	class	The abstract base class for descents.
AbstractFixedPointSolver	class	Abstract base class for all fixed point solvers.
AbstractGaussNewton	class	Abstract base class for all Gauss-Newton type methods.
AbstractGradientDescent	class	The gradient descent method for unconstrained minimisation.
AbstractIterativeSolver	class	Abstract base class for all iterative solvers.
AbstractLBFGS	class	Abstract version of the L-BFGS (limited memory Broyden–Fletcher–Goldfarb–Shanno) solver.
AbstractLeastSquaresSolver	class	Abstract base class for all least squares solvers.
AbstractMinimiser	class	Abstract base class for all minimisers.
AbstractQuasiNewton	class	Abstract quasi-Newton minimisation algorithm.
AbstractRootFinder	class	Abstract base class for all root finders.
AbstractSearch	class	The abstract base class for all searches. (Which are our generalisation of line searches, trust regions, and learning rates.)
BFGS	class	BFGS (Broyden–Fletcher–Goldfarb–Shanno) minimisation algorithm.
BacktrackingArmijo	class	Perform a backtracking Armijo line search.
BestSoFarFixedPoint	class	Wraps another fixed-point solver, to return the best-so-far value.
BestSoFarLeastSquares	class	Wraps another least-squares solver, to return the best-so-far value.
BestSoFarMinimiser	class	Wraps another minimiser, to return the best-so-far value.
BestSoFarRootFinder	class	Wraps another root-finder, to return the best-so-far value.
Bisection	class	The bisection method of root finding.
Chord	class	The Chord method of root finding.
ClassicalTrustRegion	class	The classic trust-region update algorithm which uses a quadratic approximation of the objective function to predict reduction.
DFP	class	DFP (Davidon–Fletcher–Powell) minimisation algorithm.
DampedNewtonDescent	class	The damped Newton (Levenberg--Marquardt) descent.
Dogleg	class	Dogleg algorithm.
DoglegDescent	class	The Dogleg descent step, which switches between the Cauchy and the Newton descent directions.
FixedPointIteration	class	Repeatedly calls a function in search of a fixed point.
FunctionInfo	class	Different solvers (BFGS, Levenberg--Marquardt, ...) evaluate different quantities of the objective function.
GaussNewton	class	Gauss-Newton algorithm, for solving nonlinear least-squares problems.
GoldenSearch	class	Golden-section search for finding the minimum of a univariate function in a given interval.
GradientDescent	class	Classic gradient descent with a learning rate learning_rate.
ImplicitAdjoint	class	Backpropagate via the implicit function theorem.
IndirectDampedNewtonDescent	class	The indirect damped Newton (Levenberg--Marquardt) trust-region descent.
IndirectLevenbergMarquardt	class	The Levenberg--Marquardt method as a true trust-region method.
LBFGS	class	L-BFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) minimisation algorithm.
LearningRate	class	Move downhill by taking a step of the fixed size learning_rate.
LevenbergMarquardt	class	The Levenberg--Marquardt method.
LinearTrustRegion	class	The trust-region update algorithm which uses a linear approximation of the objective function to predict reduction.
NelderMead	class	The Nelder-Mead minimisation algorithm. (Downhill simplex derivative-free method.)
Newton	class	Newton's method for root finding.
NewtonDescent	class	Newton descent direction.
NonlinearCG	class	The nonlinear conjugate gradient method.
NonlinearCGDescent	class	The nonlinear conjugate gradient step.
OptaxMinimiser	class	A wrapper to use Optax first-order gradient-based optimisers with optimistix.minimise.
RESULTS	class	An enumeration, with the following entries:
RecursiveCheckpointAdjoint	class	Backpropagate by differentiating through the iterates directly.
Solution	class	The solution to a nonlinear solve.
SteepestDescent	class	The descent direction given by locally following the gradient.
dai_yuan	function	The Dai--Yuan formula for β.
fixed_point	function	Find a fixed-point of a function.
fletcher_reeves	function	The Fletcher--Reeves formula for β.
hestenes_stiefel	function	The Hestenes--Stiefel formula for β.
least_squares	function	Solve a nonlinear least-squares problem.
max_norm	function	Compute the L-infinity norm of a PyTree of arrays.
minimise	function	Minimise a function.
polak_ribiere	function	The Polak--Ribière formula for β.
rms_norm	function	Compute the RMS (root-mean-squared) norm of a PyTree of arrays.
root_find	function	Solve a root-finding problem.
two_norm	function	Computes the L2 norm of a PyTree of arrays.