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Capability index: GeoML

Layers: GeoStack · GeoNumerics · GeoML · GeoModels.

Every public name in the libraries geostack builds on, each listed once under the shortest module path that exports it, with the first sentence of its docstring. Search this page before writing a loader, a model, a training step or a helper in a script or a notebook: if what you need is here, use 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).

This page is the GeoML layer. It may import GeoNumerics, GeoStack.

Listed at geonnax 0.0.9, kernellib 0.0.21, optax-bayes 0.0.3, filterax 0.0.5, vardax 0.1.9, gauss-flows 0.1.9, xtremax 0.0.4, pyrox 0.1.1, pyrox-gp 0.1.9, pyrox-lgm 0.1.2, pyrox-nn 0.1.0.

Upstream: geonnax

Basis functions, neural layers and coordinate transforms in Equinox.

geonnax

NameKindWhat it does
AbstractConditionerclassDuck-typed protocol for (h, z) -> y conditioning layers.
AffineModulationclassFeature-wise Linear Modulation (FiLM): y = γ(z) ⊙ h + β(z).
AntiAliasedActivationclassA pointwise nonlinearity between band-limited function spaces.
AttentionclassPre-norm multi-head self-attention with cosine (QK-normalised) similarity.
BasisSpectralConvclassSpectral convolution in a precomputed basis: per-mode channel mixing.
BasisTransformclassFrozen analysis / synthesis pair for a precomputed basis.
BlockclassConv → GroupNorm → SiLU, the residual-block primitive.
CNOclassConvolutional Neural Operator: lift → U-Net of band-limited blocks → project.
CNOBlockclassConvolution then band-limited activation: the CNO I, D and U blocks.
CNOResBlockclassThe CNO residual (R) block, v↦v+K2 Σ K1vv \mapsto v + K_2\,\Sigma\,K_1 v.
CPTensorclassCanonical-Polyadic (CP / PARAFAC) factorization.
Cartesian3DEncoderclassLift a single lon/lat coordinate onto the unit sphere S2S^2.
ConcatConditionerclassConcatenate h and z then apply a single Linear.
ConditionedINRclassWrap an inner network’s per-layer activations with conditioners.
ConvNeXtBlockclassConvNeXt-V2 block: depthwise conv → norm → MLP with GRN (Woo et al., 2023).
CyclicEncoderclassEncode a single periodic input as concatenated cos/sin features.
DeepVSSGPCoreclassDeterministic deep RFF spectral core.
Deg2RadclassElement-wise degrees-to-radians conversion.
DenseRank1classRank-1 ensemble dense layer (deterministic BatchEnsemble core).
DenseTensorclassA full, un-factorised tensor.
DomainPaddingclassZero-pad spatial axes by a fraction of their size, then crop back.
DownsampleclassMemory-efficient factor-2 downsample: space-to-depth, then 1x1 conv.
FNOclassFourier Neural Operator: lifting → Fourier blocks → projection.
FNOBlockclassOne Fourier layer: spectral conv + pointwise skip, then an activation.
FourierFilterclassSingle Fourier filter: g(x)=sin⁡(Ωx+φ)g(x) = \sin(\Omega x + \varphi).
FourierNetclassMultiplicative Fourier Filter Network (Fathony et al., ICLR 2021).
GaborFilterclassSingle Gabor filter: g(x)=sin⁡(Ωx+φ)⊙exp⁡(−γ2∥x−μ∥2)g(x) = \sin(\Omega x + \varphi) \odot \exp(-\tfrac{\gamma}{2}\|x - \mu\|^2).
GaborNetclassMultiplicative Gabor Filter Network (Fathony et al., ICLR 2021).
GeneratedSirenclassWrapper around a SIREN whose layers consume generated weights.
GeoContextEncoderclassEncode geoscience metadata into a single context vector.
GeoFNOclassGeo-FNO: a Fourier neural operator on per-sample point clouds.
GlobalResponseNormclassGlobal Response Normalization (Woo et al., 2023, “ConvNeXt-V2”).
HeteroscedasticHeadclassShared state and init for the FA-noise heteroscedastic layers.
HybridSphericalSlepianEncoderclassConcatenate low-bandwidth global SHs with local Slepian cap modes.
HyperLinearclassGenerate a target Linear’s (W, b) from z, then apply.
HyperSIRENfunctionNIF-style ShapeNet/ParameterNet composite (Pan, Brunton, Kutz — JMLR 2023).
LNOclassLocal Neural Operator: pad → local core → crop, marched with jax.lax.scan.
LaplaceRandomFeatureCovarianceclassLaplace-approximation precision for an SNGP output head.
LayerNormEnsembleclassPer-ensemble-member LayerNorm (deterministic core).
LearnedDeformationclassA learned chart from the physical domain onto the latent torus (Geo-FNO).
LinearAttentionclassPre-norm linear attention — O(n) in the number of spatial positions.
LinearChainCRFclassDeterministic linear-chain CRF — forward algorithm plus Viterbi decoding.
LonLatScaleclassAffine-rescale a single lon/lat pair into [-1, 1].
MCSigmoidDenseFAclassHeteroscedastic multi-label output layer (FA noise + sigmoid).
MCSoftmaxDenseFAclassHeteroscedastic multi-class output layer (FA noise + softmax).
MSWTclassMulti-Scale Wavelet Transformer operator (Wang et al., 2026).
MSWTBlockclassPre-norm wavelet-attention block: an attention residual, then an FFN residual.
ManifoldNOclassManifold Neural Operator: lifting → basis blocks → projection.
ManifoldNOBlockclassOne manifold-operator layer: basis spectral conv + pointwise skip.
MixtureOfGaussiansDenseHeadclassDeterministic mixture-density-network output head.
MultiHeadAttentionBEclassMulti-head attention with BatchEnsemble rank-1 projections.
MultiScaleSIRENclassParallel frequency-banded SIRENs summed at the readout.
NCPContinuousPerturbclassInput perturbation for the Noise Contrastive Prior pattern.
NestedResidualUNetclassA small residual U-Net used as one stage block (Qin et al., 2020, “U²-Net”).
OrthogonalRandomFeaturesclassOrthogonal Random Features (Yu et al., 2016) — variance-reduced RFF.
RandomFeatureGaussianProcessclassSNGP output layer (Liu et al., 2020) — deterministic core.
Rank1ProjInitclassPer-projection BatchEnsemble inits used by MultiHeadAttentionBE.
ResnetBlockclassTwo Blocks with squeeze-excitation and a residual skip.
SFNOclassSpherical Fourier Neural Operator: lift → spherical blocks → project.
SIRENclassMulti-layer sinusoidal representation network (Sitzmann et al., NeurIPS 2020).
SirenDenseclassSine-activated dense layer: y = sin(ω · (W x + b)) or y = W x + b.
SirenLayerSpecclassStatic per-layer metadata shared by deterministic and Bayesian SIRENs.
SirenLayerTypefunctionRe-exported from typing.
SlepianEncoderclassDeterministic Slepian-cap positional encoder on S2S^2.
SpectralConvclassFourier spectral convolution over num_spatial_dims = len(n_modes) axes.
SpectralNormalizationclassWrap an Equinox linear layer to be cc-Lipschitz via power iteration.
SphericalFNOBlockclassOne spherical Fourier layer: spherical spectral conv + pointwise skip.
SphericalHarmonicEncoderclassReal spherical-harmonic features on the unit 2-sphere for a single point.
SphericalHarmonicTransformclassDense, differentiable spherical harmonic analysis/synthesis on a grid.
SphericalSpectralConvclassSpherical spectral convolution: per-degree channel mixing in SH space.
SphericalWaveletConvclassPer-scale channel mixing in the spherical-wavelet domain.
SphericalWaveletTransformclassScale-discretised (needlet) wavelet analysis/synthesis on the sphere.
SqueezeExcitationclassSqueeze-and-Excitation channel gating (Hu et al., 2018).
StageclassOne encoder/decoder stage: a leaf block, then an optional nested U-Net.
StandardizedConvclassConvolution with optional on-the-fly weight standardization.
TTTensorclassTensor-Train (Matrix-Product) factorization.
TuckerTensorclassTucker factorization: a small core contracted with per-mode factor matrices.
UNetclassDimension-flexible U-Net with modern blocks, attention, and nested stages.
UpsampleclassFactor-2 upsample via pixel-shuffle: 1x1 conv, then depth-to-space.
WNOclassWavelet Neural Operator: lifting → wavelet blocks → projection.
WNOBlockclassOne wavelet layer: wavelet conv + pointwise skip, then an activation.
WaveletAttentionclassSelf-attention performed inside the wavelet domain (Wang et al., 2026).
WaveletConvclassWavelet-domain channel mixing — the wavelet analogue of SpectralConv.
WindowedAttentionclassSwin-style windowed multi-head self-attention with cosine similarity.
apply_rank1_projfunctionApply y_i = ((x ⊙ s_i) @ W) ⊙ r_i + b_i per ensemble member.
band_limited_resizefunctionResample a periodic field onto a new grid by Fourier truncation / zero-padding.
build_siren_specsfunctionProduce per-layer specs for a depth-depth SIREN, first + hidden… + last.
cno_receptive_radiusfunctionEffective receptive radius, in grid points, of a CNO run on its input grid.
hetero_noisy_logitsfunctionSample num_mc_samples heteroscedastic logits for one example.
init_factorized_tensorfunctionConstruct a factorized tensor of the requested kind.
init_rank1_projfunctionGlorot-init shared kernel + per-member rank-1 vectors + zero bias.
log_spaced_omegasfunctionReturn num_scales log-spaced frequencies spanning the closed band.
mfn_forwardfunctionPure-JAX MFN forward pass given user-supplied filter and linear callables.
orthogonal_blocksfunctionBuild the ORF frequency matrix as [Q_1 S_1, ..., Q_K S_K].
rff_cosine_forwardfunctionShared single-cosine RFF feature map: sqrt(2/D) cos(xW/l + b).
rff_forwardfunctionShared RFF feature map: sqrt(1/D) [cos(xW/l), sin(xW/l)].
siren_W_limitfunctionReturn the half-width a of the U(-a, a) weight init for a SIREN layer.

Upstream: kernellib

Covariance kernels and scalable kernel methods on gaussx.

kernellib

NameKindWhat it does
AbstractEstimatorclassConfigure, fit, predict.
AbstractFeatureMapclassA finite-dimensional approximation k(x, x') ≈ φ(x)ᵀ φ(x').
AbstractGraphclassWeighted, undirected graph without self-loops.
AbstractGreatCircleKernelclassk(x,x′)=σ2 ψ(θ(x,x′)/c)k(x, x') = \sigma^2\,\psi(\theta(x, x') / c) on (lon, lat) inputs.
AbstractKernelclassAnything that produces a Gram matrix.
AbstractMeshKernelclassA kernel on a triangle mesh given by its Laplace-Beltrami spectrum.
AbstractPointwiseKernelclassA kernel defined by k(x, x').
AbstractSphereSeriesKernelclassA kernel on S2S^2 given by its Laplace-Beltrami spectrum Φ(λ)\Phi(\lambda).
AbstractStationaryKernelclassk(x, x') = variance * shape(||(x - x') / lengthscale||²).
ActiveDimsclassApply a kernel to a subset of input dimensions.
AdvectedclassA frozen spatial field moving at a constant velocity.
CKAAccumulatorclassRunning mini-batch CKA (Nguyen, Raghu & Kornblith, 2021).
ChordalclassA Euclidean kernel on points of the sphere, k0(R u(x),R u(x′))k_0(R\,u(x), R\,u(x')).
ConstantclassConstant kernel, k(x, x') = sigma^2.
CosineclassCosine kernel, sigma^2 cos(2 pi ||x - x'|| / p).
CubicclassCubic covariance model, compactly supported.
CurlFreeclassCurl-free kernel: the covariance of a gradient field F=∇ΦF = \nabla\Phi.
CurlFreeFeaturesclassHilbert-space features of a curl-free 2-D vector field.
Derivativeclass∂xi∂xj′k(x,x′)\partial_{x_i} \partial_{x'_j} k(x, x') for fixed input dimensions.
DerivativeIndexedclassJoint covariance of a GP’s values and partial derivatives.
DistanceclassDistance-induced kernel, k(x, x') = σ² (|x|^a + |x'|^a - |x - x'|^a) / 2.
DivergenceFreeclassDivergence-free kernel: the covariance of a rotated gradient field.
DivergenceFreeFeaturesclassHilbert-space features of a divergence-free 2-D vector field.
EARTH_RADIUS_KMconstant6371.0088
EigenProclassKernel regression by EigenPro-preconditioned SGD (Ma & Belkin, 2017).
EigenProPreconditionerclassSpectral correction state for EigenPro kernel SGD.
FalkonclassNyström kernel ridge regression solved by Falkon (Rudi et al., 2017).
FalkonInfoclassConvergence report of a falkon_solve run.
FalkonPreconditionerclassThe two upper-triangular Cholesky factors of the Falkon preconditioner.
FastFoodFeaturesclassFastFood random features (Le, Sarlós & Smola, 2013) for any kernel with a spectral sampler.
FastFoodParamsclassThe random structure of a FastFood feature map.
FeatureKernelclassInner product of features, k(x,x′)=⟨ϕ(x),ϕ(x′)⟩k(x, x') = \langle \phi(x), \phi(x') \rangle.
GeneralizedCauchyclassGeneralized Cauchy covariance model.
GeometricAnisotropyclassA rotated, stretched stationary kernel: a correlation ellipse or ellipsoid.
GibbsclassGibbs kernel: a lengthscale that varies with location.
GneitingclassGneiting’s non-separable space-time covariance.
GraphclassSparse weighted graph: a static topology and traced edge weights.
GraphEigenFeaturesclassLow-rank features of GraphMatern / GraphHeat from Laplacian eigenpairs.
GraphHeatclassGraph heat (diffusion) kernel on node indices.
GraphMaternclassGraph Matérn kernel on node indices (Borovitskiy et al., 2021).
GraphTopologyclassStatic, hashable edge list of an undirected graph without self-loops.
GreatCircleAskeyclassAskey’s truncated power kernel, ψ(t)=(1−t)+τ\psi(t) = (1 - t)_+^\tau.
GreatCircleCauchyclassGeneralized Cauchy kernel, ψ(t)=(1+tα)−τ/α\psi(t) = (1 + t^\alpha)^{-\tau/\alpha}.
GreatCircleExponentialclassExponential kernel of the great-circle angle, ψ(t)=e−t\psi(t) = e^{-t}.
GreatCirclePoweredExponentialclassPowered exponential kernel, ψ(t)=e−tα\psi(t) = e^{-t^\alpha}.
GreatCircleSphericalclassThe geostatistics spherical model of the great-circle angle.
GreatCircleWendlandclassC²- or C⁴-Wendland kernel of the great-circle angle.
GridGraphclassRegular lattice graph that never stores its edges.
HelmholtzclassHelmholtz-decomposition kernel: curl-free plus divergence-free parts.
HelmholtzFeaturesclassHelmholtz features: curl-free plus divergence-free columns.
HoleEffectclassHole-effect (cardinal sine, “wave”) covariance model.
ImplicitCrossKernelOperatorclassMatrix-free rectangular kernel operator K(X, Z) \cdot v.
ImplicitKernelOperatorclassMatrix-free kernel operator: (K + sigma^2 I) v via sequential scan.
JunSteinclassAxially symmetric kernel of Jun & Stein (2008), LxLyk0(x,y)L_x L_y k_0(x, y).
KNNGraphclassA directed k-nearest-neighbour graph, self excluded.
KRRclassKernel ridge regression.
KernelLocalityPreservingProjectionsclassKernel locality preserving projections.
KernelOperatorclassKernel matrix operator with efficient first-order autodiff.
KernelPCAclassKernel principal component analysis.
KernelSchrodingerProjectionsclassKernel Schrödinger eigenmap projections.
KroneckerFeaturesclassFeatures of a separable kernel ksktk_s k_t as a product of two maps.
LaplaceEigenfunctionFeaturesclassHilbert-space (HSGP) approximation of a stationary kernel on a box.
LaplacianEigenmapsclassLaplacian eigenmaps (Belkin & Niyogi, 2003) of the k-NN graph of X.
LatitudeScaledclassAmplitude modulation by latitude, k(x,y)=s(ϕx) s(ϕy) k0(x,y)k(x, y) = s(\phi_x)\,s(\phi_y)\,k_0(x, y).
LegendreLatitudeFnclassA function of latitude, f(ϕ)=∑j=0J−1wj Pj(sin⁡ϕ)f(\phi) = \sum_{j=0}^{J-1} w_j\,P_j(\sin\phi).
LinearclassLinear kernel, k(x, x') = sigma^2 x^T x' + b.
LinearTransformclassA stationary kernel of a linearly transformed lag.
LocalityPreservingProjectionsclassLocality preserving projections (He & Niyogi, 2003).
MaternclassMatern kernel with closed-form nu in {0.5, 1.5, 2.5}.
MeshHeatclassHeat (diffusion) kernel on a triangulated surface.
MeshLaplaceFeaturesclassFEM Laplace-Beltrami eigenvector features of a mesh kernel.
MeshMaternclassMatérn kernel on a triangulated surface (Borovitskiy et al. 2020).
ModulatedclassA kernel with an input-dependent amplitude, k(x,x′)=a(x) k0(x,x′) a(x′)k(x, x') = a(x)\, k_0(x, x')\, a(x').
NystromFeaturesclassNyström features (Williams & Seeger, 2001) for any kernel.
OrthogonalRandomFeaturesclassOrthogonal random features (Yu et al., 2016).
PaciorekSchervishclassPaciorek-Schervish kernel: a location-dependent anisotropy matrix.
PentasphericalclassPentaspherical covariance model, compactly supported.
PeriodicclassPeriodic (MacKay) kernel on the Euclidean distance.
PeriodicFeaturesclassExact truncated Fourier features of a 1-D Periodic kernel.
PeriodisedclassMake any kernel periodic: apply it to inputs wrapped onto circles.
PermutationTestResultclassOutcome of permutation_test.
PolynomialclassPolynomial kernel, k(x, x') = sigma^2 (x^T x' + b)^d.
ProductclassElementwise product of kernels, k(x, x') = prod_i k_i(x, x').
RBFclassRadial basis function (squared exponential) kernel.
RandomAdvectionRBFclassThe frozen-field RBF averaged over a Gaussian velocity.
RandomFourierFeaturesclassRandom Fourier features (Rahimi & Recht, 2007).
RationalQuadraticclassRational quadratic kernel, a scale mixture of RBFs.
ResidualclassWhat an approximation misses, k(x,x′)−k~(x,x′)k(x, x') - \tilde k(x, x').
RootedTreeclassA tree with one root: every non-root node has exactly one parent.
ScaledclassA kernel times a scalar, k(x, x') = scale * k_0(x, x').
SchrodingerEigenmapProjectionsclassSchrödinger eigenmap projections (SEP): linear Schrödinger eigenmaps.
SchrodingerEigenmapsclassSchrödinger eigenmaps (Czaja & Ehler, 2013) of the k-NN graph of X.
ShiftclassInput warp x -> x - offset; offset is scalar or per dimension.
SlepianFeaturesclassFeatures of a zonal kernel concentrated on a spherical cap.
SphereHeatclassHeat (diffusion, squared-exponential) kernel on the sphere.
SphereMaternclassIntrinsic Matérn kernel on the sphere (Borovitskiy et al. 2020).
SphereSeriesclassA sphere kernel from any user spectrum Φ(λ)≥0\Phi(\lambda) \ge 0.
SphericalclassSpherical covariance model, compactly supported.
SphericalHarmonicFeaturesclassWeighted real spherical harmonics up to degree LL for a zonal kernel.
StableclassStable (powered exponential) covariance model.
StretchclassInput warp x -> x / scale; scale is scalar or per dimension.
SumclassSum of kernels, k(x, x') = sum_i k_i(x, x').
TailDownclassTail-down covariance on a rooted tree (Ver Hoef & Peterson, 2010).
TailUpclassTail-up covariance on a rooted tree (Ver Hoef & Peterson, 2010).
TanhclassHyperbolic-tangent kernel, k(x, x') = sigma^2 tanh(gamma x^T x' + c0).
TaperedclassA covariance multiplied by a compactly supported taper.
TaylorStatisticsclassThe sides and angle of a kernel Taylor-diagram triangle.
TreeSitesclassPairwise geometry of N sites on a RootedTree (host-computed).
VariogramclassA binned empirical semivariogram.
WarpedclassApply a kernel to warped inputs, k(x, x') = k_0(w(x), w(x')).
WendlandclassWendland covariance model, compactly supported.
WhiteclassWhite-noise kernel, sigma^2 delta(x, x').
adjacency_matrixfunctionSymmetric weighted adjacency matrix of a k-NN graph.
barrier_potentialfunctionDiagonal potential that is strength at indices and 0 elsewhere.
batched_kernel_matvecfunctionCompute K(X, Z) @ v in memory-efficient batches.
batched_kernel_rmatvecfunctionCompute K(X, Z)^T @ u in memory-efficient batches.
ckafunctionCentred kernel alignment, HSIC(x,y)/HSIC(x,x) HSIC(y,y)\mathrm{HSIC}(x, y) / \sqrt{\mathrm{HSIC}(x, x)\,\mathrm{HSIC}(y, y)}.
combine_potentialsfunctionSeveral Schrödinger potentials as one: ∑kαkckVk\sum_k \alpha_k c_k V_k.
commute_time_kernelfunctionCommute-time kernel K=L+K = L^{+}, the Laplacian’s pseudo-inverse.
cosine_graph_kernelfunctionInverse-cosine kernel K=cos⁡(πL/4)K = \cos(\pi L / 4) (Smola & Kondor, 2003).
curlfunctionPer-point curl of a 2-D or 3-D vector field.
delaunay_graphfunctionThe edge graph of the Delaunay triangulation of X.
derivative_inputsfunctionRows [x, i] for DerivativeIndexed: values, then partials.
diffusion_kernelfunctionDiffusion (heat) kernel K=exp⁡(−βL)K = \exp(-\beta L) (Kondor & Lafferty, 2002).
distance_correlation_squaredfunctionSquared distance correlation (Székely et al., 2007), cka.
distance_covariance_squaredfunctionSquared distance covariance (Székely et al., 2007), 4 * hsic.
divergencefunctionPer-point divergence ∇⋅F(xn)=tr⁡Jn\nabla \cdot F(x_n) = \operatorname{tr} J_n.
draw_rff_cosine_basisfunctionDraw (variance, lengthscale, omega, phase, weights) for a kernel.
edge_weightsfunctionReweight a graph’s edges by a kernel on the nodes’ features.
eigenpro_correctionfunctionCompute the EigenPro eigenspace correction for one SGD mini-batch.
eigenpro_preconditionerfunctionBuild an EigenPro spectral preconditioner from a kernel operator.
eigenpro_step_sizefunctionReturn the EigenPro preconditioned step size for a batch size.
empirical_variogramfunctionBinned empirical semivariogram of y observed at X.
energy_distancefunctionEnergy distance (Székely & Rizzo, 2004), 2 * mmd_squared.
estimate_lengthscalefunctionA data-driven lengthscale for an RBF-type kernel.
evaluate_rff_cosine_pathsfunctionEvaluate the zero-mean RFF prior path(s) at inputs X.
falkon_preconditionerfunctionBuild the Falkon preconditioner from the inducing-point kernel matrix.
falkon_predictfunctionPredict with Nyström KRR weights: f(x∗)=∑jαj k(x∗,zj)f(x_*) = \sum_j \alpha_j\, k(x_*, z_j).
falkon_solvefunctionNyström kernel ridge regression weights by Falkon’s preconditioned CG.
fastfood_featuresfunctionFastFood feature map, Φ(x)=D−1/2 [cos⁡(Vx),sin⁡(Vx)]\Phi(x) = D^{-1/2}\,[\cos(Vx), \sin(Vx)].
fastfood_frequenciesfunctionThe dense frequency matrix VV that FastFood applies implicitly.
fastfood_operatorfunctionFastFood approximation of the RBF Gram matrix, K≈ΦΦ⊤K \approx \Phi\Phi^\top.
fastfood_paramsfunctionDraw the random structure for a FastFood RBF feature map.
fit_variogramfunctionFit a stationary kernel plus a nugget to an empirical variogram.
funk_hecke_coefficientsfunctionPer-degree spherical-harmonic spectrum of a kernel on a sphere.
gabriel_graphfunctionThe Gabriel graph of X.
gamma_to_lengthscalefunctionlengthscale = 1 / sqrt(2 gamma), the inverse of lengthscale_to_gamma.
gradientfunctionPer-point gradient ∇f(xn)\nabla f(x_n) of a scalar field.
graph_from_adjacencyfunctionThe sparse graph of a dense, symmetric adjacency matrix.
graph_from_edgesfunctionThe sparse graph of an edge list: the seam for other graph libraries.
graph_from_neighborsfunctionThe sparse, symmetric graph of a k-nearest-neighbour relation.
graph_laplacianfunctionGraph Laplacian of a symmetric adjacency matrix.
graph_null_spacefunctionOrthonormal basis of the Laplacian’s null space.
grid_graphfunctionThe lattice graph of an array of shape shape.
hadamard_transformfunctionRe-exported from gaussx.
hessianfunctionPer-point Hessian Hn[j,k]=∂2f(xn)/∂xj∂xkH_n[j, k] = \partial^2 f(x_n) / \partial x^j \partial x^k.
hsicfunctionHilbert-Schmidt Independence Criterion between paired samples.
hsic_penaltyfunctionThe HSIC penalty operator M=HKsH/n2M = H K_s H / n^2 on protected attributes.
implicit_cross_kernelfunctionCreate a matrix-free rectangular cross-kernel operator.
jacobianfunctionPer-point Jacobian Jn[i,j]=∂Fi(xn)/∂xjJ_n[i, j] = \partial F_i(x_n) / \partial x^j.
kernel_alignmentfunctionUncentred kernel alignment, ⟨K,L⟩F/(∥K∥F∥L∥F)\langle K, L\rangle_F / (\|K\|_F \|L\|_F).
knn_graphfunctionThe k-nearest-neighbour graph of X.
label_potentialfunctionNon-diagonal potential pulling together points that share a label.
laplacianfunctionPer-point Laplacian Δf(xn)=tr⁡Hn\Delta f(x_n) = \operatorname{tr} H_n.
laplacian_eigenmapfunctionLaplacian eigenmap of a weighted graph: smallest solutions of Ly=λDyL y = \lambda D y.
laplacian_eigpairsfunctionThe n smallest eigenpairs of a graph Laplacian.
laplacian_penaltyfunctionThe graph-smoothness penalty operator M=L/n2M = L / n^2.
lengthscale_gridfunctionLog-spaced lengthscales within decades orders of magnitude of center.
lengthscale_to_gammafunctiongamma = 1 / (2 lengthscale^2), the scikit-learn RBF parameter.
matern_graph_kernelfunctionGraph Matérn kernel K=UΦ(Λ)U⊤K = U \Phi(\Lambda) U^\top (Borovitskiy et al., 2021).
mesh_graphfunctionThe edge graph of a triangle mesh.
mmd_squaredfunctionSquared maximum mean discrepancy between samples X and Y.
n_components_graphfunctionNumber of connected components (an isolated node is one).
nearest_neighborsfunctionThe n_neighbors nearest other points of every point in X.
nystrom_kernelfunctionThe Nyström kernel kZ(x,x′)=k(x,Z)KZZ−1k(Z,x′)k_Z(x, x') = k(x, Z) K_{ZZ}^{-1} k(Z, x').
nystrom_operatorfunctionNystrom low-rank kernel approximation.
permutation_testfunctionPermutation p-value for a statistic that is large under the alternative.
radius_graphfunctionThe graph joining points within radius of each other.
radius_neighborsfunctionThe other points within radius of every point, at most max_neighbors of them.
random_walk_kernelfunctionpp-step random-walk kernel K=(aI−L)pK = (aI - L)^p (Smola & Kondor, 2003).
regularized_laplacian_kernelfunctionRegularised Laplacian kernel K=(I+σ2L)−1K = (I + \sigma^2 L)^{-1}.
relative_neighborhood_graphfunctionThe relative neighbourhood graph of X.
rff_operatorfunctionRandom Fourier Features kernel approximation.
schrodinger_eigenmapfunctionSchrödinger eigenmap: smallest solutions of (L+αV)y=λDy(L + \alpha V) y = \lambda D y.
select_landmarksfunctionIndices into X of n_landmarks distinct landmarks.
spatial_spectral_graphfunctionSpatial-spectral graph for images (Cahill, Czaja & Messinger, 2014).
spatial_spectral_potentialfunctionSpatial-spectral potential for images (Cahill, Czaja & Messinger, 2014).
structure_matrixfunctionThe Besag (ICAR) structure matrix R=LR = L, optionally BYM2-scaled.
tapered_operatorfunctionThe tapered Gram K(X,X)∘T(X,X)K(X, X) \circ T(X, X) as a sparse gaussx operator.
taylor_statisticsfunctionRadii, correlation and distance for a kernel Taylor diagram.
to_cross_operatorfunctionK(X1, X2) as a rectangular linear operator.
to_operatorfunctionK(X, X) (+ noise * I) as a symmetric, PSD-tagged linear operator.
vector_inputsfunctionPoint-major rows [x_n, i] for the vector-field kernels.

Upstream: optax-bayes

The Bayesian learning rule as optax gradient transformations.

Upstream: filterax

Differentiable ensemble Kalman filters and smoothers.

Upstream: vardax

Variational data assimilation: BLUE/OI, 3D-Var, 4D-Var and kin.

vardax

NameKindWhat it does
AmortizedConfigclassConfiguration for an AmortizedPosterior.
AmortizedPosteriorclassAmortized variational posterior qϕ(x∣y)q_\phi(x \mid y).
AnalysisStepclassRe-exported from pipekit_cycle.
AveragingKernelclassRTM L2-style averaging-kernel obs operator.
Batch1DclassBatch of 1-D spatiotemporal data.
Batch2DclassBatch of 2-D spatiotemporal data.
Batch2DMultivarclassBatch of 2-D multivariate spatiotemporal data.
BilinAEPrior1DclassBilinear autoencoder prior for 1-D data.
BilinAEPrior2DclassBilinear autoencoder prior for 2-D data.
BilinAEPrior2DMultivarclassBilinear autoencoder prior for 2-D multivariate data.
CompositeBasisclassConcatenate several reduced bases into one control vector.
ConditionalFlowHeadclassConditional normalising flow head (stub).
ConvAEPrior1DclassConvolutional autoencoder prior for 1-D spatially-structured data.
ConvLSTMGradMod1Dclass1-D ConvLSTM-based gradient modulator.
ConvLSTMGradMod2Dclass2-D ConvLSTM-based gradient modulator.
CostFunctionclassVariational cost function J(x, batch, **kwargs) -> scalar.
DynIncrementsclassOne-step-increment dynamical prior.
DynTrajectoryclassFull-rollout dynamical prior.
DynamicalPriorclassBase class for ODE-based dynamical priors.
EnsembleCovarianceclassSample-covariance posterior from an ensemble of analyses.
ForwardModelclassRe-exported from pipekit_cycle.
FourDVarNet1DclassEnd-to-end 4DVarNet model for 1-D spatiotemporal reconstruction.
FourDVarNet2DclassEnd-to-end 4DVarNet model for 2-D spatiotemporal reconstruction.
GaussNewtonHessianclassGauss-Newton Hessian inversion at MAP.
GaussianMarkLikelihoodclassSerialise a Gaussian posterior into a mark-likelihood dict.
GradModulatorclassLearned gradient modulator for the FourDVarNet inner solver.
IdentityObsEncoderclassConcatenate input and mask into a flat context vector.
IdentityPriorclassTrivial identity prior: φ(x)=x\varphi(x) = x.
ImplicitAdjointclassRe-exported from optimistix.
Incremental4DVarclassReduced-basis 4DVar.
IncrementalConfigclassConfiguration for IncrementalFourDVar.
IncrementalFourDVarclassOperational incremental 4DVar (Decision D11).
InstrumentRegistryclassKeyed lookup of InstrumentSpec by instrument_id.
InstrumentSpecclassPer-instrument (obs_op, mask, R_op, id) bundle.
InterpObsclassGrid → scattered-obs sparse bilinear interpolation.
KStepAdjointclassK-step differentiation: warmup under stop_gradient, then k live steps.
L63PriorclassLearned prior for the Lorenz-63 system.
L96PriorclassLearned prior for the Lorenz-96 system.
LSTMState1DclassHidden state for a 1-D ConvLSTM gradient modulator.
LSTMState2DclassHidden state for a 2-D ConvLSTM gradient modulator.
LaplaceCovarianceclassLaplace approximation at MAP.
LinearBasisclassGeneric linear reduced basis with a diagonal-QQ prior.
LinearObsclassH(x) = H_mat @ x.
Lorenz63classLorenz-63 vector field as an Equinox module.
Lorenz96classLorenz-96 vector field as an Equinox module.
MLPAEPrior1DclassMLP autoencoder prior for 1-D data.
MLPObsEncoderclassTwo-layer MLP encoder from flat (input, mask) to context.
MaskedIdentityclassH(x)=m⊙xH(x) = m \odot x with optional element-wise mask.
MinimiserclassWrapper protocol around optimistix.AbstractMinimiser.
MultiInstrumentFusionclassCompose per-instrument operators at the likelihood level.
ObservationOperatorclassRe-exported from pipekit_cycle.
OneStepAdjointclassOne-step differentiation (Bolte et al., 2023).
OptimalInterpolationclassBLUE / OI — closed-form linear-Gaussian analysis.
PosteriorclassPosterior container — Decision D10.
PosteriorAdapterclassTurns an analysis output into a Posterior container.
PriorclassPrior model: maps state to its regularised reconstruction.
RecursiveCheckpointAdjointclassRe-exported from optimistix.
ReducedBasisclassReduced-basis control-vector operator.
RegressionHeadclassGaussian regression head: q_φ(x|y) = N(μ_φ(y), diag(σ²_φ(y))).
ScoreDiffusionHeadclassScore-based diffusion head (stub).
SoftBoundedForwardclassForwardModel adapter that softly confines states to a box.
SolverState1DclassMutable solver state for 1-D problems.
SolverState2DclassMutable solver state for 2-D problems.
StrongFourDVarclassStrong-constraint 4DVar.
TemporalPriorclassTime-dependent prior: dynamics-aware regularisation over a window.
ThreeDVarclass3D variational analysis.
VarDACyclefunctionBuild a pipekit_cycle.DACycle from a vardax model.
VarSmootherCyclefunctionBuild a pipekit_cycle.SmootherCycle from a vardax model.
WeakFourDVarclassWeak-constraint 4DVar with augmented control vector.
amortized_nll_loss_fnfunctionNegative log-likelihood for amortized inference (Epic 8).
amortized_train_stepfunctionSingle training step for AmortizedPosterior.
assert_adjoint_calibratedfunctionRandom-vector probe of the Jacobian agreement at y.
assert_posterior_agreementfunctionCheck that p_fast.mean lies within tolerance_sigma standard deviations of p_oracle.mean.
background_costfunctionBackground cost ∥x0−xb∥2\|x_0 - x_b\|^2.
composite_basisfunctionBuild a CompositeBasis from a sequence of ReducedBasis components.
decomposed_lossfunctionCompute the decomposed variational loss.
eof_basisfunctionData-driven EOF (PCA) reduced basis from a sample matrix.
eval_stepfunctionCompute the evaluation loss for a single batch (no gradient).
fourier_basisfunctionLaplacian-eigenfunction (Dirichlet/HSGP) reduced basis on a box.
fp_solver_step_1dfunctionPerform a single 1-D fixed-point projection step.
init_solver_state_1dfunctionInitialise a 1-D solver state from a batch.
init_solver_state_2dfunctionInitialise a 2-D solver state from a batch.
interp_obs_from_coordsfunctionBuild an InterpObs from grid axis arrays + obs locations.
linear_basisfunctionBuild a LinearBasis from an arbitrary precomputed design matrix.
obs_cost_1dfunctionObservation cost for 1-D data.
obs_cost_2dfunctionObservation cost for 2-D data.
one_step_solve_4dvarnet_1dfunctionSolve 4DVarNet-1D using k-step differentiation (Bolte et al., 2023).
one_step_solve_4dvarnet_2dfunctionSolve 4DVarNet-2D using k-step differentiation (Bolte et al., 2023).
plot_l96_gridfunctionHovmöller-style image of Lorenz-96 states over time.
plot_l96_trajectoriesfunctionLine plot of selected Lorenz-96 variables over time.
plot_reconstruction_comparisonfunctionSide-by-side comparison of target, masked input, and reconstruction.
prior_costfunctionPrior cost based on learned autoencoder reconstruction.
rbf_basisfunctionPlaceable radial-basis reduced basis (Gaussian or Wendland kernels).
reconstruction_lossfunctionMean-squared reconstruction loss.
simulate_lorenz63functionSimulate the Lorenz-63 system and return state trajectory.
simulate_lorenz96functionSimulate the Lorenz-96 system and return state trajectory.
simulation_based_calibrationfunctionPer Talts et al. 2018: rank histogram of true draws within posterior samples.
solve_4dvarnet_1dfunctionRun the full 1-D 4DVarNet solver for n_steps iterations.
solve_4dvarnet_1d_fixedpointfunctionRun n_fp_steps fixed-point projection steps using jax.lax.scan.
solve_4dvarnet_2dfunctionRun the full 2-D 4DVarNet solver for n_steps iterations.
solver_step_1dfunctionPerform a single 1-D solver iteration.
solver_step_2dfunctionPerform a single 2-D solver iteration.
strong_variational_costfunctionStrong-constraint variational cost U(x0)U(x_0).
time_patchesfunctionOverlapping consecutive time pairs for one-step increment losses.
to_optimistix_adjointfunctionMap an adjoint spec onto an optimistix.AbstractAdjoint.
train_loss_fnfunctionCompute the training loss for a single batch.
train_stepfunctionPerform a single training step (forward + backward + update).
variational_costfunctionCompute the variational cost U(x)U(x).
variational_cost_gradfunctionGradient of variational_cost w.r.t. x.
wavelet_basisfunctionOrthonormal wavelet (DWT) reduced basis on a periodic grid.

Upstream: gauss-flows

Gaussianization (RBIG) and normalizing flows.

gauss_flows

NameKindWhat it does
AbstractStochasticclassBase class for transforms that are stochastic in both directions.
AbstractSurjectionclassBase class for SurVAE surjective transforms.
ActNormclassActivation normalization (ActNorm) for image-shaped events.
ActNorm1DclassActivation normalization (ActNorm) for 1-D events.
AffineCouplingclassAffine coupling layer.
AugmentclassGenerative surjection that appends conditionally sampled dimensions.
BatchNormclassInvertible batch normalization layer for 1D inputs.
CircularRQSplineCouplingclassCoupling layer whose transformer is a circular rational quadratic spline.
CircularRationalQuadraticSplineclassScalar rational quadratic spline with tied endpoint derivatives.
ClassCondDiagGaussianclassClass-conditional diagonal Gaussian with learned per-class parameters.
ClassCondFlowclassClass-conditional flow built on a ClassCondDiagGaussian base.
ConditionalDiagGaussianclassDiagonal Gaussian whose (loc, log_scale) are produced by a single net.
ConditionerclassWrap an unconditional bijection with a context-amortised affine.
ConjugateTransformFilterclassEnsemble Kalman analysis performed in a Gaussianised latent space.
ContinuousAffineCouplingclassTime-gated affine coupling with optional control conditioning.
DeepSigmoidCouplingclassCoupling layer with a monotone single-layer sigmoidal transformer.
DiffeqConcatclassMLP vector field with a learnable scalar time embedding.
DiffeqMLPclassMLP vector field f(ode_time, x, condition) via concatenation.
FFJORDclassContinuous normalizing flow via a learned ODE.
FixedRotationclassFixed (non-trainable) orthogonal rotation matrix.
FlowDistclassWrap a flowjax Transformed distribution as a NumPyro distribution.
FlowGuideclassNumPyro variational guide using a Gaussianization flow.
GINCouplingclassVolume-preserving affine coupling from Sorrenson et al. (2020).
GaussianMixtureclassTrainable multivariate Gaussian-mixture base distribution.
GaussianPCAclassProbabilistic-PCA Gaussian base distribution (low-rank + diagonal Σ).
GeneralizedDivisiveNormalizationclassGeneralized divisive normalization for image-shaped events (..., C).
GeneralizedDivisiveNormalization1Dclass1-D Generalized divisive normalization with full D x D coupling.
HaarWaveletclassHaar wavelet transform bijection (1-D, last axis).
HistogramCDFclassMarginal Gaussianization via a per-dimension empirical histogram CDF.
HouseholderRotationclassOrthogonal rotation via a sequence of Householder reflections.
InverseGaussCDFclassApply the inverse Gaussian CDF (probit) element-wise.
Invertible1x1ConvclassInvertible 1×1 convolution with LU-parameterised weight (Glow).
LULinearPermuteclassInvertible linear layer via LU decomposition composed with a fixed permutation.
MatrixExponentialclassClosed-form linear neural flow parameterised by exp(W · t).
MixtureGaussianCDFclassMarginal Gaussianization via a mixture-of-Gaussians CDF.
MixtureGaussianCDFCouplingclassCoupling layer whose transformed half goes through a mixture-CDF.
MixtureLogisticCDFclassMarginal Gaussianization via a mixture-of-logistics CDF.
NumpyroBaseclassWrap any numpyro.distributions.Distribution as a flowjax base.
Orthogonal1x1ConvclassOrthogonal 1x1 convolution (Cayley-parameterised orthogonal mixing).
OrthogonalConvExponentialclassOrthogonal convolution via the exponential of a skew-symmetric operator.
OrthogonalRotationclassLearnable orthogonal rotation via the Cayley map.
PeriodicShiftclassLearnable circular shift on selected periodic dimensions.
PeriodicWrapclassCanonical projection of selected dimensions onto [−bound, bound].
PlanarFlowclassPlanar normalizing-flow bijection (Rezende & Mohamed 2015).
RQSplineCouplingclassRational quadratic spline coupling layer.
RQSplineMarginalclassMarginal Gaussianization via rational-quadratic splines.
SimpleAbsSurjectionclassElementwise absolute-value surjection with a random-sign inverse.
SimpleMaxPoolSurjection2dclass2D max-pooling surjection with a learned residual decoder.
SimpleSortSurjectionclassSort along one axis; invert via independent per-slice permutations.
SliceclassInference surjection that drops the trailing dimensions of a 1D event.
SqueezeclassVolume-preserving squeeze that trades spatial extent for channels.
StochasticPermutationclassUniform random permutation along one axis (zero log-det).
SurVAEFlowclassContainer that threads PRNG keys through a mixed bijection / surjection chain.
SylvesterFlowclassSylvester normalizing flow (van den Berg et al. 2018).
TimeFourierclassFourier-feature time gate with g(0) = 0 by construction.
TimeIdentityclassIdentity time gate g(t) = t.
TimeTanhclassTanh time gate with g(0) = 0 by construction.
TransformFilterclassRun a Gaussian filter in warped coordinates.
UniformOnSphereclassUniform distribution on the unit sphere Sᵈ ⊂ ℝ^{d+1}.
VAEclassVariational autoencoder as a SurVAE stochastic transform.
VonMisesFisherclassVon Mises–Fisher distribution on the unit sphere Sᵈ ⊂ ℝ^{d+1}.
coupling_gaussianization_flowfunctionConstruct a coupling-based Gaussianization flow.
entropyfunctionDifferential entropy of a flow (flow-based Monte-Carlo estimator).
entropy_reductionfunctionDifferential entropy of x via a Gaussianization flow (RBIG-way).
expmap_spherefunctionMap a tangent vector at x to the sphere via the exponential map.
fit_gaussianization_flowfunctionFit a Gaussianization flow to data by maximum likelihood.
fit_rbigfunctionFit an iterative-Gaussianization (RBIG) flow to data in closed form.
fit_rbig_couplingfunctionWarm-start an RBIG-style coupling flow in closed form.
gaussian_entropyfunctionDifferential entropy of a Gaussian (analytical Gaussian closed form).
gaussian_kl_divergencefunctionKL divergence of two Gaussians (analytical Gaussian closed form).
gaussian_mutual_informationfunctionMutual information of Gaussian blocks (analytical Gaussian closed form).
gaussian_total_correlationfunctionTotal correlation of a Gaussian (analytical Gaussian closed form).
gaussianization_flowfunctionConstruct a Gaussianization flow.
information_reductionfunctionTotal correlation removed between two representations (RBIG-way reduction).
iterative_rbigfunctionConstruct an iterative RBIG (Rotation-Based Iterative Gaussianization) flow.
kl_divergencefunctionKL divergence KL(P ‖ Q) of flows (flow-based Monte-Carlo estimator).
kl_divergence_reductionfunctionKL divergence KL(P || Q) via a reference Gaussianization (RBIG-way).
logmap_spherefunctionReturn the tangent vector at x whose exp-map reaches y.
mutual_informationfunctionMutual information I(X; Y) of flows (flow-based Monte-Carlo estimator).
negentropyfunctionNegentropy of a flow (flow-based Monte-Carlo estimator).
normalizing_kalman_filterfunctionCompose a state-space base with a per-timestep observation warp.
pack_time_controlfunctionPack time and optional control vector into one condition array.
rbig_conjugate_filterfunctionFit a Gaussianising warp to a prior ensemble with RBIG.
tangent_basisfunctionReturn an orthonormal basis of the tangent space Tₓ Sᵈ.
time_control_cond_shapefunctionReturn the FlowJax cond_shape for packed (time, control) inputs.
total_correlationfunctionTotal correlation of a flow (flow-based Monte-Carlo estimator).
total_correlation_reductionfunctionTotal correlation of x via a Gaussianization flow (RBIG-way).
unpack_time_controlfunctionUnpack a packed (time, control) condition.

Upstream: xtremax

Extreme-value and point-process models in NumPyro.

xtremax

NameKindWhat it does
FrechetType2GEVDclassFréchet Type II Generalized Extreme Value Distribution for NumPyro.
GeneralizedExtremeValueDistributionclassGeneralized Extreme Value Distribution (GEVD) for NumPyro.
GeneralizedParetoDistributionclassGeneralized Pareto Distribution (GPD) for NumPyro.
GumbelType1GEVDclassGumbel Type I Generalized Extreme Value Distribution for NumPyro.
WeibullType3GEVDclassWeibull Type III Generalized Extreme Value Distribution for NumPyro.
assemble_nonstationary_gev_fieldsfunctionBuild non-stationary spatio-temporal GEV parameter fields.
design_matrixfunctionPrepend an intercept column to a static-covariate matrix.
expected_exceedancesfunctionExpected number of block exceedances of a threshold.
frechet_cdffunctionFréchet CDF.
frechet_icdffunctionFréchet quantile function.
frechet_log_probfunctionFréchet log PDF (assumes shape > 0).
frechet_meanfunctionFréchet mean (+inf when shape >= 1).
frechet_return_levelfunctionT-period return level.
gev_cdffunctionCDF of the Generalized Extreme Value distribution.
gev_icdffunctionQuantile function (inverse CDF) of the GEV distribution.
gev_log_probfunctionLog PDF of the Generalized Extreme Value distribution.
gev_log_survivalfunctionLog survival function :math:\log S(x) = \log(1 - F(x)) of the GEV.
gev_meanfunctionMean of the GEV distribution (+inf when :math:\xi \ge 1).
gev_return_levelfunctionT-period return level: :math:z_T = F^{-1}(1 - 1/T).
gev_survivalfunctionSurvival function :math:S(x) = 1 - F(x) of the GEV distribution.
gpd_cdffunctionCDF of the Generalized Pareto Distribution.
gpd_icdffunctionQuantile function (inverse CDF) of the GPD.
gpd_log_probfunctionLog PDF of the Generalized Pareto Distribution (loc = 0).
gpd_log_survivalfunctionLog survival :math:\log S(x) = -\tfrac{1}{\xi}\log(1 + \xi x/\sigma).
gpd_meanfunctionGPD mean: :math:\sigma / (1 - \xi) for :math:\xi < 1, else +inf.
gpd_return_levelfunctionT-period return level: :math:Q(1 - 1/T).
gpd_survivalfunctionSurvival function :math:S(x) = (1 + \xi x/\sigma)^{-1/\xi} of the GPD.
gumbel_cdffunctionGumbel CDF: :math:F(x) = \exp(-\exp(-z)).
gumbel_icdffunctionGumbel quantile: :math:Q(p) = \mu - \sigma\log(-\log p).
gumbel_log_probfunctionGumbel log PDF: :math:-\log\sigma - z - e^{-z}, :math:z=(x-\mu)/\sigma.
gumbel_meanfunctionGumbel mean: :math:\mu + \sigma\gamma_E.
gumbel_return_levelfunctionT-period return level: :math:Q(1 - 1/T).
nonstationary_return_levelfunctionReturn level for stationary or non-stationary GEV parameter fields.
nonstationary_return_periodfunctionReturn period associated with a threshold under (non-)stationary GEV.
pairwise_distancesfunctionEuclidean distance matrix between sites.
two_range_correlationfunctionTwo-range exponential correlation matrix with unit diagonal.
weibull_cdffunctionReverse-Weibull CDF.
weibull_icdffunctionReverse-Weibull quantile function.
weibull_log_probfunctionReverse-Weibull log PDF (assumes shape < 0).
weibull_meanfunctionReverse-Weibull mean (always finite for shape < 0).
weibull_return_levelfunctionT-period return level.

xtremax.extraction

NameKindWhat it does
XarrayQuantileRegressorclassQuantile regressor that operates on :class:xr.DataArray inputs.
constant_thresholdfunctionReturn a constant threshold value.
decluster_runsfunctionDecluster exceedances using the runs method.
decluster_separationfunctionDecluster by enforcing minimum separation between peaks.
declustered_block_maximafunctionExtract declustered block maxima by identifying independent extreme events.
estimate_extremal_indexfunctionEstimate the extremal index (theta), a measure of clustering.
quantile_regression_thresholdfunctionEstimate a time-varying threshold via linear quantile regression.
quantile_thresholdfunctionCalculate threshold based on a percentile of the data.
r_largest_block_maximafunctionExtract r-largest order statistics from each block.
rolling_thresholdfunctionCalculate time-varying threshold using a rolling window.
seasonal_thresholdfunctionCalculate seasonal threshold (backward compatibility wrapper).
sliding_block_maximafunctionExtract block maxima using a sliding window approach.
spatial_block_maximafunctionExtract spatial block maximum values from an xarray DataArray.
temporal_block_maximafunctionExtract temporal block maximum values from an xarray DataArray.
temporal_thresholdfunctionCalculate time-varying threshold based on temporal grouping.

xtremax.point_processes

NameKindWhat it does
EventHistoryclassFixed-size buffer of events + optional marks.
GoodnessOfFitclassBundle of diagnostics returned by goodness_of_fit.
MarkedSampleResultclassMarked temporal sample: (times, mask, marks).
MarkedSpatialSampleResultclassMarked spatial sample: (locations, mask, marks).
MarkedSpatiotemporalSampleResultclassMarked spatiotemporal sample: (locations, times, mask, marks).
RectangularDomainclassAxis-aligned rectangle [lo, hi] ⊂ ℝᵈ.
SampleResultclassUnmarked temporal sample: (times, mask, n_events).
SpatialSampleResultclassUnmarked spatial sample: (locations, mask, n_events).
SpatiotemporalSampleResultclassUnmarked spatiotemporal sample: (locations, times, mask, n_events).
TemporalDomainclassHalf-open temporal interval [t0, t1) ⊂ ℝ.
constant_mark_distributionfunctionMark distribution that ignores time and history and returns d.
constant_retentionfunctionRetention that always returns the same probability p.
cumulative_log_intensityfunctionShorthand for :math:\Lambda(t) = \int_0^t \lambda(s) ds.
integrate_log_intensityfunctionCompute :math:\int_{t_0}^{t_1} \exp(\log\lambda(s))\, ds.
integrate_log_intensity_spatialfunctionCompute :math:\int_D \exp(\log\lambda(s))\, ds.
integrate_log_intensity_spatiotemporalfunctionCompute :math:\int_{t_0}^{t_1} \int_D \exp(\log\lambda(s, t))\, ds\, dt.
time_varying_marksfunctionWrap a time → Distribution callable into the full signature.
time_varying_retentionfunctionWrap a pure function of time into the full retention signature.

xtremax.simulations

NameKindWhat it does
SpatialFeatureExtractorclassStatic methods to derive physical features from a Digital Elevation Model (DEM).
augment_spatial_featuresfunctionPipeline to run all extractors and merge into Dataset.
compute_advanced_climate_signalfunctionGenerates Tmax and Precip Mean fields using advanced physics proxies.
compute_climate_signalfunctionCombines Spatial and Temporal fields to create a mean climate signal (Mu).
create_iberian_domainfunctionCreates the master spatial dataset with Lat, Lon, Elevation, and Land Mask.
generate_fractal_terrainfunctionGenerates coherent terrain using Fractal Brownian Motion (fBm).
generate_gmst_trajectoryfunctionGenerates a synthetic Global Mean Surface Temperature (GMST) anomaly curve.
generate_iberia_maskfunctionProcedurally generates a boolean mask approximating the Iberian Peninsula and Balearic Islands using geometrical primitives.
generate_physical_gmstfunctionSimulates Global Mean Surface Temperature (GMST) using a 0-D Energy Balance Model.
generate_spatial_fieldfunctionGenerates static spatial data: Lat, Lon, Elevation, Distance to Coast.
simulate_precip_extremesfunctionSimulates Precipitation Extremes: 1.
simulate_temp_extremesfunctionSimulates Block Maxima Temperature via the GEV distribution.
simulate_wind_extremesfunctionSimulates Extreme Wind Speeds (Gusts) using Weibull distribution.

Upstream: pyrox

Equinox modules with NumPyro sample and param sites.

pyrox.inference

NameKindWhat it does
EnsembleMAPclassNumPyro-like ensemble MAP/MLE runner.
EnsembleResultclassOutput of a full EnsembleMAP.run / EnsembleVI.run.
EnsembleStateclassStacked state for an ensemble of optimizer runs.
EnsembleVIclassNumPyro-like ensemble variational-inference runner.
ensemble_initfunctionInitialize an ensemble of (params, opt_state) by vmap over keys.
ensemble_lossfunctionBuild the filter_value_and_grad loss from a log-joint.
ensemble_mapfunctionOne-shot wrapper around EnsembleMAP.
ensemble_predictfunctionVmap predict_fn over the leading ensemble axis of params.
ensemble_stepfunctionPerform one ensemble update step on a batch.
ensemble_vifunctionOne-shot wrapper around EnsembleVI.
param_group_optimizerfunctionApply a different optimizer to each labelled parameter group.

Upstream: pyrox-gp

Gaussian processes for pyrox.

pyrox_gp

NameKindWhat it does
BernoulliLikelihoodclassBinary classification likelihood with logit link.
ConditionedGPclassGP conditioned on Gaussian-likelihood training observations.
ConditionedLatentFactorGPclassLatent-factor posterior — MAP latents plus the decoder posterior.
ConditionedMarkovGPclassMarkov GP conditioned on Gaussian-likelihood observations.
ConditionedOILMMGPclassOILMM posterior — Q conditioned scalar GPs plus the mixing.
ConjugateVIclassNatural-gradient / CVI update for sparse variational GPs.
ConstantclassConstant kernel k(x, x') = sigma^2.
ConstantSDEclassRe-exported from gaussx.
CosineclassCosine kernel sigma^2 cos(2 pi ||x - x'|| / period).
CosineSDEclassRe-exported from gaussx.
DecoupledInducingFeaturesclassDecoupled mean / covariance inducing-feature bases (Cheng & Boots 2017).
DecoupledPathwiseSamplerclassSparse/decoupled pathwise sampler with RFF prior + inducing update.
DeltaGuideclassPoint-mass (MAP-style) variational posterior over inducing values.
DistLikelihoodclassGeneric likelihood wrapping any numpyro.distributions.Distribution.
ExpectationPropagationclassParallel expectation propagation (Minka 2001) with damping.
ExpectationPropagationMarkovclassParallel Expectation Propagation for MarkovGPPrior.
FourierInducingFeaturesclassVFF — Variational Fourier inducing features on [−L,L]D[-L, L]^D.
FullRankGuideclassFull-rank Gaussian variational posterior over inducing values u.
GPPriorclassFinite-dimensional GP prior over a fixed training input set.
GaussNewtonInferenceclassGauss-Newton inference: Newton loop with PSD-projected curvature.
GaussNewtonMarkovInferenceclassGauss-Newton (Markov) inference: Newton with a strict PSD floor.
GaussianLikelihoodclassGaussian observation model p(y∣f)=N(y∣f,σ2)p(y \mid f) = N(y \mid f, \sigma^2).
GuideclassAbstract base for variational posterior families.
HeteroscedasticGaussianLikelihoodclassGaussian regression with input-dependent noise.
ICMKernelclassIntrinsic coregionalization model with one shared latent kernel.
InducingFeaturesclassProtocol for inter-domain inducing features.
IntegratedWienerSDEclassRe-exported from gaussx.
LMCKernelclassLinear model of coregionalization for vector-valued GPs.
LaplaceInferenceclassLaplace approximation via Newton iteration on the log posterior.
LaplaceMarkovInferenceclassLaplace approximation for MarkovGPPrior.
LaplacianInducingFeaturesclassInducing features from low-frequency graph Laplacian eigenvectors.
LatentFactorGPPriorclassGP latent factors with an analytically marginalized linear decoder.
LikelihoodclassAbstract base for observation models.
LinearclassLinear kernel sigma^2 x^T x' + bias.
MarkovGPPriorclassLinear-time temporal GP prior over a sorted 1-D grid.
MaternclassMatern kernel with nu in {0.5, 1.5, 2.5}.
MaternSDEclassRe-exported from gaussx.
MeanFieldGuideclassDiagonal Gaussian variational posterior over inducing values u.
MultiOutputConditionedGPclassMulti-output GP conditioned on Gaussian-likelihood observations.
MultiOutputGPPriorclassFinite-dimensional multi-output GP prior over fixed training inputs.
MultiOutputInducingVariablesclassShared inducing-point structure for LMC-style sparse workflows.
MultiOutputSparseGPPriorclassSparse multi-output GP prior over shared inducing inputs.
NaturalGuideclassNatural-parameter Gaussian variational posterior over inducing values.
NonGaussConditionedGPclassGP conditioned on a non-Gaussian likelihood via an advanced strategy.
NonGaussConditionedMarkovGPclassMarkov GP conditioned on a non-Gaussian likelihood via a site-based strategy.
NormalizingKalmanPriorclassNormalizing Kalman Filter prior over a multivariate time grid.
OILMMGPPriorclassOrthogonal-mixing multi-output GP prior with a projected exact posterior.
OILMMKernelclassOrthogonal instantaneous linear mixing model.
PathwiseFunctionclassCallable posterior function draw(s) produced by a pathwise sampler.
PathwiseSamplerclassExact-GP pathwise posterior sampler using Matheron’s rule.
PeriodicclassPeriodic (MacKay) kernel.
PeriodicSDEclassRe-exported from gaussx.
PoissonLikelihoodclassCount likelihood with log-link.
PolynomialclassPolynomial kernel sigma^2 (x^T x' + bias)^degree.
PosteriorLinearizationclassIterated statistical-linearization site updates.
PosteriorLinearizationMarkovclassPosterior linearization for MarkovGPPrior (Markov IPLF).
ProductSDEclassRe-exported from gaussx.
QuasiNewtonInferenceclassMAP optimization via L-BFGS, Laplace covariance at convergence.
QuasiPeriodicSDEclassRe-exported from gaussx.
RBFclassRadial basis function (squared exponential) kernel.
RationalQuadraticclassRational quadratic kernel.
SDEKernelclassRe-exported from gaussx.
SDEParamsclassRe-exported from gaussx.
SharedInducingPointsclassShared inducing inputs for multi-output latent GP collections.
SlepianInducingFeaturesclassRegion-localized Slepian inducing features on S2S^2.
SoftmaxLikelihoodclassMulti-class classification likelihood with softmax link.
SparseConditionedMarkovGPclassSparse Markov GP fitted to a guide.
SparseGPPriorclassGP prior parameterized over inducing inputs Z.
SparseMarkovGPPriorclassSparse variational GP prior over an SDE kernel and inducing time grid.
SphericalHarmonicInducingFeaturesclassVISH — inducing harmonics on S2S^2 (Dutordoir et al. 2020).
StudentTLikelihoodclassHeavy-tailed regression: p(y | f) = StudentT(nu, f, sigma).
SumSDEclassRe-exported from gaussx.
WarpedGaussianLikelihoodclassp(y∣f)=N(y∣G(f),σ2)p(y \mid f) = N(y \mid G(f), \sigma^2) -- the transformed-GP model.
WhiteclassWhite-noise kernel sigma^2 delta(x, x').
WhitenedGuideclassWhitened-coordinate Gaussian variational posterior over inducing values.
collapsed_lfr_log_probfunctionLog-likelihood with the linear decoder marginalized analytically.
decoder_posteriorfunctionClosed-form matrix-normal posterior over the decoder.
funk_hecke_coefficientsfunctionFunk-Hecke coefficients of a zonal kernel on S2S^2.
gp_factorfunctionRegister the collapsed GP log marginal likelihood with NumPyro.
gp_samplefunctionSample a latent function f at the prior’s training inputs.
init_inducingfunctionInducing inputs (M, D): rows of X picked by kernellib.select_landmarks.
latent_initfunctionInitial latents (N, n_latent) for a GPLVM or latent-factor model.
latent_total_correlationfunctionTotal correlation of the fitted latent factors.
lfr_factorfunctionRegister the collapsed latent-factor log-likelihood with NumPyro.
lfr_modelfunctionMAP-over-latents collapsed latent-factor regression model.
lfr_predictive_momentsfunctionExact moments of the product of two independent Gaussians.
markov_gp_factorfunctionRegister the collapsed Markov-GP marginal log-likelihood with NumPyro.
markov_gp_samplefunctionSample a latent function f at the prior’s training times.
mo_gp_factorfunctionRegister the collapsed multi-output GP marginal likelihood with NumPyro.
mo_svgp_elbofunctionStructured multi-output SVGP ELBO as a differentiable scalar.
mo_svgp_factorfunctionRegister the multi-output SVGP ELBO as a NumPyro factor site.
normalizing_kalman_factorfunctionRegister the NKF marginal log-likelihood with NumPyro.
preconditioned_cg_solverfunctionA gaussx solver strategy for exact GPs: preconditioned CG plus SLQ.
sparse_markov_elbofunctionSparse variational ELBO for SparseMarkovGPPrior.
sparse_markov_factorfunctionRegister sparse_markov_elbo as a NumPyro factor site.
svgp_elbofunctionStructured SVGP ELBO as a differentiable scalar.
svgp_factorfunctionRegister the structured SVGP ELBO as a NumPyro factor site.
warp_to_basefunctionMap observations into the space where the factor model is linear.
warped_decoder_posteriorfunctionMatrix-normal decoder posterior, read in the warped space.
warped_lfr_log_probfunctionCollapsed latent-factor log-likelihood on warped observations.
warped_predictive_momentsfunctionMoments of y=G(f)+ϵy = G(f) + \epsilon under q(f)q(f), by quadrature.

Upstream: pyrox-lgm

Latent Gaussian models for pyrox.

pyrox_lgm

NameKindWhat it does
AR1classStationary AR(1), xt=ρxt−1+εtx_t = \rho x_{t-1} + \varepsilon_t.
AbstractComponentclassA latent field with hyperpriors and a projector to observations.
AbstractObservationclassy | eta for an LGM, with its own hyperparameters.
BYM2classBYM2 (Riebler et al., 2016), a mixture of unstructured and ICAR effects.
Bernoulliclassy ~ Bernoulli(sigmoid(eta)), y in {0, 1}.
BesagclassIntrinsic CAR (ICAR / Besag): precision τR\tau R, R=D−WR = D - W.
Binomialclassy ~ Binomial(n, sigmoid(eta)) with n = data["n_trials"].
CARclassProper CAR: precision τ(D−ρW)\tau(D - \rho W), ρ∈[0,1)\rho \in [0, 1).
DiagnosticsclassLeave-one-out and information criteria of an INLAResult.
FixedEffectsclassFixed effects β∼N(0,λ−1I)\beta \sim \mathcal N(0, \lambda^{-1} I), columns of XX.
Gaussianclassy ~ N(eta, 1/prec); prec under PCPrecision(1, 0.01).
GenericclassA field with precision τR\tau R for a user-supplied structure RR.
IIDclassIndependent effects xi∼N(0,1/τ)x_i \sim \mathcal N(0, 1/\tau), i<ni < n.
INLAResultclassWhat inla() returns.
KroneckerclassSeparable product Q=Qmain⊗QgroupQ = Q_\text{main} \otimes Q_\text{group} (R-INLA group).
LGMclassA latent Gaussian model: components, fixed effects and an observation model.
LerouxclassLeroux CAR: precision τ(ρR+(1−ρ)I)\tau(\rho R + (1 - \rho) I), ρ∈[0,1]\rho \in [0, 1].
NegativeBinomialclassy ~ NegBin(mean exp(eta), size); size under Gamma(1, 0.1).
PCAR1RhoclassPC prior on the lag-one correlation ρ\rho of an AR(1) process.
PCBYM2PhiclassPC prior on the BYM2 mixing parameter ϕ∈(0,1)\phi \in (0, 1).
PCMaternclassJoint PC prior on the range ρ\rho and marginal sd σ\sigma of a Matérn field.
PCPrecisionclassPC prior on the precision τ\tau of a Gaussian effect.
Poissonclassy ~ Poisson(exp(eta)); put the log exposure in data["offset"].
RW1classFirst-order random walk, xt+1−xt∼N(0,1/τ)x_{t+1} - x_t \sim \mathcal N(0, 1/\tau).
RW2classSecond-order random walk, xt+1−2xt+xt−1∼N(0,1/τ)x_{t+1} - 2x_t + x_{t-1} \sim \mathcal N(0, 1/\tau).
Replicateclassn_rep independent copies of a component, sharing its hyperparameters.
SPDEclassMatérn field via the SPDE, on a triangle mesh or a regular grid.
StructureSpectrumclassSpectral measure of R∗+R_\ast^{+}, the generalised inverse of a structure.
SummaryclassPosterior summary: mean, sd and the 2.5 / 50 / 97.5 % quantiles.
diagnosticsfunctionDIC, WAIC, CPO and PIT of an INLAResult, with no refits.
ffunctionBuild a latent component named after the data column it indexes.
inlafunctionIntegrated nested Laplace approximation of a latent Gaussian model.
structure_spectrumfunctionThe spectrum of R+R^{+} that PCBYM2Phi needs, computed once.

Upstream: pyrox-nn

Bayesian neural networks for pyrox.

pyrox_nn

NameKindWhat it does
ArcCosineFourierFeaturesclassRandom features for the arc-cosine kernel (Cho & Saul, 2009).
BayesianAffineModulationclassgeonnax.AffineModulation with Normal priors on the FiLM generator.
BayesianConcatConditionerclassgeonnax.ConcatConditioner with Normal priors on the projection.
BayesianFourierNetclassFourierNet with Bayesian priors on all filter and linear weights.
BayesianGaborNetclassGaborNet with Bayesian priors on all filter and linear weights.
BayesianHyperLinearclassgeonnax.HyperLinear with Normal priors on the generator only.
BayesianNeuralFieldclassThe full Bayesian Neural Field architecture.
BayesianSIRENclassSIREN with regime-scaled Normal priors on all layer weights.
BayesianSlepianEncoderclassSlepian encoder with NumPyro sites for cap radius and centre.
ConditionedRFFNetclassConditional analogue of pyrox_nn.RandomKitchenSinks.
DeepVSSGPclassDeep Random Feature Expansion for Variational SSGP (Cutajar et al. 2017).
DenseDVIclassDeterministic Variational Inference dense layer (Wu et al., 2018).
DenseFlipoutclassBayesian dense layer with Flipout sign-flip structure.
DenseHierarchicalclassHierarchical Bayesian dense layer with multiplicative shrinkage.
DenseNCPclassNoise Contrastive Prior dense layer (Hafner et al., 2019).
DenseRank1classRank-1 ensemble dense layer.
DenseReparameterizationclassBayesian dense layer via the reparameterization trick.
DenseVariationalclassDense layer with a user-supplied prior factory.
DenseVariationalDropoutclassSparse variational dropout dense layer.
FourierFeaturesclassPer-input dyadic-frequency Fourier basis.
HSGPFeaturesclassHilbert-Space Gaussian Process feature layer (Riutort-Mayol et al., 2023).
HyperFourierFeaturesclassRandom Fourier features with (W, b, log_lengthscale) from a parameter net.
InteractionFeaturesclassElement-wise products on selected pairs of input columns.
LaplaceCosineFeaturesclassCosine-bias variant of random Fourier features for the Laplace kernel.
LaplaceFourierFeaturesclassSSGP-style RFF layer with Laplace (Matern-1/2) spectral density.
LayerNormEnsembleclassPer-ensemble-member LayerNorm.
MCSigmoidDenseFAclassHeteroscedastic multi-label output layer (FA noise + sigmoid).
MCSoftmaxDenseFAclassHeteroscedastic multi-class output layer (FA noise + softmax).
MaternCosineFeaturesclassCosine-bias variant of random Fourier features for the Matern kernel.
MaternFourierFeaturesclassSSGP-style RFF layer with Matern spectral density.
MultiHeadAttentionBEclassMulti-head attention with BatchEnsemble rank-1 projections.
NCPNormalOutputclassOutput-side Noise Contrastive Prior layer (Hafner et al., 2018).
RBFCosineFeaturesclassCosine-bias variant of random Fourier features for the RBF kernel.
RBFFourierFeaturesclassSSGP-style RFF layer with RBF spectral density.
RandomFeatureGaussianProcessclassSNGP output layer (Liu et al., 2020).
RandomKitchenSinksclassRandom Kitchen Sinks: RFF + a learned linear head.
SeasonalFeaturesclassPeriod-and-harmonic cos/sin basis on a scalar time axis.
StandardizationclassApply a fixed-coefficient affine standardization.
VariationalFourierFeaturesclassVSSGP — RFF with a learnable variational posterior over frequencies.
cyclic_encodefunctionRe-exported from geonnax.
deg2radfunctionRe-exported from geonnax.
fourier_featuresfunctionRe-exported from geonnax.
interaction_featuresfunctionRe-exported from geonnax.
lonlat_scalefunctionRe-exported from geonnax.
lonlat_to_cartesian3dfunctionRe-exported from geonnax.
seasonal_featuresfunctionRe-exported from geonnax.
seasonal_frequenciesfunctionRe-exported from geonnax.
spherical_harmonic_encodefunctionRe-exported from geonnax.
standardizefunctionRe-exported from geonnax.
unstandardizefunctionRe-exported from geonnax.