Capability index
Every public name in finitevolX (346 of them), each listed once,
grouped by the module that defines it (names re-exported from
spectraldiffx, gaussx and integrix are grouped by library), with the
first sentence of its docstring; then the public API of spectraldiffx,
gaussx and integrix.march, which finitevolX builds on. 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).
finitevolx
finitevolx
Advection operators for Arakawa C-grids (finitevolx._src.advection.advection)
| Name | Kind | What it does |
|---|---|---|
Advection1D |
class | 1-D advection operator. |
Advection2D |
class | 2-D advection operator. |
Advection3D |
class | 3-D advection operator (horizontal plane per z-level). |
Public functional API for raw face fluxes on Arakawa C-grids (finitevolx._src.advection.face_flux)
| Name | Kind | What it does |
|---|---|---|
rusanov_flux |
function | Local Lax--Friedrichs (Rusanov) numerical flux at faces along axis. |
uv_center_flux |
function | Compute raw face fluxes for a cell-centred scalar on a C-grid. |
uv_node_flux |
function | Compute raw face fluxes for a node-centred tracer on a C-grid. |
Upwind flux with mask-aware stencil-width dispatch for non-rectangular domains (finitevolx._src.advection.flux)
| Name | Kind | What it does |
|---|---|---|
upwind_flux |
function | Compute upwind flux with automatic stencil fallback near boundaries. |
Flux limiter functions for TVD (Total Variation Diminishing) reconstruction (finitevolx._src.advection.limiters)
| Name | Kind | What it does |
|---|---|---|
mc |
function | Monotonized Central (MC) flux limiter. |
minmod |
function | Minmod flux limiter. |
superbee |
function | Superbee flux limiter. |
van_leer |
function | Van Leer flux limiter. |
Linear (polynomial) face-value reconstruction stencils (finitevolx._src.advection.linear)
| Name | Kind | What it does |
|---|---|---|
linear_2pts |
function | 2-point centred reconstruction at face i+1/2. |
linear_3pts_left |
function | 3-point left-biased reconstruction at face i+1/2. |
linear_3pts_right |
function | 3-point right-biased reconstruction at face i+1/2. |
linear_4pts |
function | 4-point centred reconstruction at face i+1/2. |
linear_5pts_left |
function | 5-point left-biased reconstruction at face i+1/2. |
linear_5pts_right |
function | 5-point right-biased reconstruction at face i+1/2. |
linear_6pts |
function | 6-point centred reconstruction at face i+1/2. |
Functional reconstruction dispatcher for upwind face-value computation (finitevolx._src.advection.reconstruct_fn)
| Name | Kind | What it does |
|---|---|---|
plusminus |
function | Split velocity into positive and negative parts. |
reconstruct |
function | Compute upwind face flux along dim using the given reconstruction method. |
upwind_1pt |
function | 1st-order upwind face value at interior faces along the last axis. |
upwind_3pt |
function | 3-point upwind face value at i+1/2 along the last axis. |
upwind_5pt |
function | 5-point upwind face value at i+1/2 along the last axis. |
Face-value reconstruction operators for advective fluxes on Arakawa C-grids (finitevolx._src.advection.reconstruction)
| Name | Kind | What it does |
|---|---|---|
Reconstruction1D |
class | 1-D face-value reconstruction. |
Reconstruction2D |
class | 2-D face-value reconstruction for advective fluxes. |
Reconstruction3D |
class | 3-D face-value reconstruction. |
Spherical-coordinate advection operators for Arakawa C-grids (finitevolx._src.advection.spherical_advection)
| Name | Kind | What it does |
|---|---|---|
SphericalAdvection2D |
class | 2-D tracer advection on a spherical Arakawa C-grid. |
SphericalAdvection3D |
class | 3-D tracer advection on a spherical Arakawa C-grid. |
weno (finitevolx._src.advection.weno)
| Name | Kind | What it does |
|---|---|---|
weno_3pts |
function | 3-points non-linear left-biased stencil reconstruction: |
weno_3pts_improved |
function | 3-points non-linear left-biased stencil reconstruction: |
weno_3pts_improved_right |
function | 3-points non-linear right-biased WENO-Z stencil reconstruction at face q0+1/2: |
weno_3pts_right |
function | 3-points non-linear right-biased stencil reconstruction at face q0+1/2: |
weno_5pts |
function | 5-points non-linear left-biased stencil reconstruction |
weno_5pts_improved |
function | 5-points non-linear left-biased stencil reconstruction |
weno_5pts_improved_right |
function | 5-points non-linear right-biased WENO-Z stencil reconstruction at face q0+1/2: |
weno_5pts_right |
function | 5-points non-linear right-biased stencil reconstruction at face q0+1/2: |
weno_7pts |
function | 7-points non-linear left-biased stencil reconstruction |
weno_7pts_right |
function | 7-points non-linear right-biased stencil reconstruction at face q0+1/2: |
weno_9pts |
function | 9-points non-linear left-biased stencil reconstruction |
weno_9pts_right |
function | 9-points non-linear right-biased stencil reconstruction at face q0+1/2: |
Single-face boundary condition atoms for 2-D ghost-ring arrays (finitevolx._src.boundary.bc_1d)
| Name | Kind | What it does |
|---|---|---|
Dirichlet1D |
class | Apply a Dirichlet value on one domain face. |
Extrapolation1D |
class | High-order polynomial extrapolation for ghost cells. |
Neumann1D |
class | Apply an outward-normal gradient on one domain face. |
Outflow1D |
class | Apply a one-face outflow boundary condition. |
Periodic1D |
class | Apply periodic wrapping on one domain face. |
Reflective1D |
class | Apply an even-symmetry reflective boundary on one face. |
Robin1D |
class | Robin (mixed) boundary condition: α·u + β·∂u/∂n = γ. |
Slip1D |
class | Slip boundary condition for tangential velocity at a solid wall. |
Sponge1D |
class | Relax one ghost face toward a background value. |
Boundary-condition dispatchers for state dictionaries (finitevolx._src.boundary.bc_field)
| Name | Kind | What it does |
|---|---|---|
FieldBCSet |
class | Dispatch per-face boundary conditions across multiple fields. |
Per-face boundary condition containers for 2-D ghost-ring arrays (finitevolx._src.boundary.bc_set)
| Name | Kind | What it does |
|---|---|---|
BoundaryConditionSet |
class | Apply a different boundary condition on each domain face. |
Boundary condition helpers for finitevolX (finitevolx._src.boundary.boundary)
| Name | Kind | What it does |
|---|---|---|
enforce_periodic |
function | Fill the ghost-cell ring with periodic boundary conditions. |
fix_boundary_corners |
function | Average corner ghost cells from their two face-adjacent ghost neighbours. |
free_slip_boundaries |
function | Fill ghost ring with symmetric reflection (free-slip wall). |
no_flux_boundaries |
function | Fill ghost ring with zeros for normal-flux variables. |
no_slip_boundaries |
function | Fill ghost ring with sign-flipped interior values (no-slip wall). |
pad_interior |
function | Extract physical interior and re-pad to original size. |
wall_boundaries |
function | Apply wall boundary conditions appropriate for a C-grid staggering. |
zero_boundaries |
function | Fill ghost ring with zeros (homogeneous Dirichlet). |
zero_gradient_boundaries |
function | Fill ghost ring by copying nearest interior value (zero gradient / Neumann). |
Harmonic and biharmonic diffusion operators (flux form) on Arakawa C-grids (finitevolx._src.diffusion.diffusion)
| Name | Kind | What it does |
|---|---|---|
BiharmonicDiffusion2D |
class | Biharmonic (∇⁴) diffusion operator on a 2-D Arakawa C-grid. |
BiharmonicDiffusion3D |
class | Biharmonic (nabla^4) diffusion operator on a 3-D Arakawa C-grid. |
Diffusion2D |
class | Horizontal diffusion operator (flux form) on a 2-D Arakawa C-grid. |
Diffusion3D |
class | Horizontal diffusion operator (flux form) on a 3-D Arakawa C-grid. |
diffusion_2d |
function | Horizontal tracer diffusion tendency at T-points (flux form). |
Energy-conserving momentum advection operators for Arakawa C-grids (finitevolx._src.diffusion.momentum)
| Name | Kind | What it does |
|---|---|---|
MomentumAdvection2D |
class | Energy-conserving momentum advection on a 2-D Arakawa C-grid. |
MomentumAdvection3D |
class | Energy-conserving momentum advection on a 3-D Arakawa C-grid. |
Spherical-coordinate harmonic diffusion operators (flux form) (finitevolx._src.diffusion.spherical_diffusion)
| Name | Kind | What it does |
|---|---|---|
SphericalBiharmonicDiffusion2D |
class | Biharmonic (spherical ∇⁴) diffusion on a 2-D spherical C-grid. |
SphericalBiharmonicDiffusion3D |
class | Biharmonic spherical diffusion on a 3-D Arakawa C-grid. |
SphericalDiffusion2D |
class | Horizontal tracer diffusion (flux form) on a 2-D spherical C-grid. |
SphericalDiffusion3D |
class | Horizontal tracer diffusion on a 3-D spherical Arakawa C-grid. |
Energy-conserving momentum advection operators on spherical C-grids (finitevolx._src.diffusion.spherical_momentum)
| Name | Kind | What it does |
|---|---|---|
SphericalMomentumAdvection2D |
class | Energy-conserving momentum advection on a 2-D spherical C-grid. |
SphericalMomentumAdvection3D |
class | Energy-conserving momentum advection on a 3-D spherical C-grid. |
Forcing base class (Layer 1) and composition wrappers (Layer 3) (finitevolx._src.forcing._base)
| Name | Kind | What it does |
|---|---|---|
AbstractForcing |
class | Base class for forcing operators. |
ForcingProduct |
class | Modulated forcing: F = alpha * F_inner. |
ForcingSum |
class | Additive composition of forcings: F = F_1 + F_2 + ... + F_n. |
TimeVaryingForcing |
class | Bundle a time-agnostic forcing with time-dependent input fields. |
Linear and quadratic bottom-drag operators for Arakawa C-grids (finitevolx._src.forcing.drag)
| Name | Kind | What it does |
|---|---|---|
LinearDrag2D |
class | Linear drag on a 2-D Arakawa C-grid. |
LinearDrag3D |
class | Linear bottom drag on a 3-D Arakawa C-grid. |
QuadraticDrag2D |
class | Quadratic bottom drag on a 2-D Arakawa C-grid. |
QuadraticDrag3D |
class | Quadratic bottom drag on a 3-D Arakawa C-grid. |
Raw functional forcing primitives (Layer 0) (finitevolx._src.forcing.functional)
| Name | Kind | What it does |
|---|---|---|
linear_drag_tendency |
function | Linear (Rayleigh-type) drag tendency on one velocity component. |
quadratic_drag_tendency |
function | Quadratic bottom-drag tendency on one velocity component. |
rayleigh_tendency |
function | Rayleigh damping tendency toward a reference state. |
wind_stress_tendency |
function | Momentum tendency from a surface wind stress. |
Rayleigh damping operator for Arakawa C-grids (finitevolx._src.forcing.rayleigh)
| Name | Kind | What it does |
|---|---|---|
RayleighDamping2D |
class | Rayleigh damping of a T-point field on a 2-D Arakawa C-grid. |
RayleighDamping3D |
class | Rayleigh damping of a T-point field on a 3-D Arakawa C-grid. |
Surface wind-stress forcing operators for Arakawa C-grids (finitevolx._src.forcing.wind)
| Name | Kind | What it does |
|---|---|---|
WindCurl2D |
class | Wind-stress curl forcing of the vorticity / QG potential vorticity. |
WindStress2D |
class | Surface wind-stress forcing on a 2-D Arakawa C-grid. |
WindStress3D |
class | Surface wind-stress forcing on a 3-D Arakawa C-grid. |
Abstract base classes for finitevolX grid containers (finitevolx._src.grid.base)
| Name | Kind | What it does |
|---|---|---|
ArakawaCGrid1D |
class | 1-D Arakawa C-grid topology (no metric). |
ArakawaCGrid2D |
class | 2-D Arakawa C-grid topology (no metric). |
ArakawaCGrid3D |
class | 3-D Arakawa C-grid topology (no metric). |
CurvilinearGrid1D |
class | 1-D curvilinear C-grid with a uniform metric. |
CurvilinearGrid2D |
class | 2-D curvilinear C-grid with a uniform metric. |
CurvilinearGrid3D |
class | 3-D curvilinear C-grid with a uniform metric. |
Cartesian Arakawa C-grid containers (1-D, 2-D, 3-D) (finitevolx._src.grid.cartesian)
| Name | Kind | What it does |
|---|---|---|
CartesianGrid1D |
class | 1-D Cartesian Arakawa C-grid (uniform spacing). |
CartesianGrid2D |
class | 2-D Cartesian Arakawa C-grid (uniform spacing). |
CartesianGrid3D |
class | 3-D Cartesian Arakawa C-grid (uniform spacing). |
Spherical Arakawa C-grid containers (2-D, 3-D) (finitevolx._src.grid.spherical)
| Name | Kind | What it does |
|---|---|---|
SphericalGrid2D |
class | 2-D Arakawa C-grid on a sphere. |
SphericalGrid3D |
class | 3-D Arakawa C-grid on a sphere. |
Shared mask infrastructure: StencilCapability1D / 2D / 3D classes (finitevolx._src.mask.base)
| Name | Kind | What it does |
|---|---|---|
StencilCapability1D |
class | Directional count of contiguous wet neighbours for each 1-D grid cell. |
StencilCapability2D |
class | Directional count of contiguous wet neighbours for each 2-D grid cell. |
StencilCapability3D |
class | Directional count of contiguous wet neighbours for each 3-D grid cell. |
Cartesian Arakawa C-grid masks (1-D / 2-D / 3-D) (finitevolx._src.mask.cartesian)
| Name | Kind | What it does |
|---|---|---|
Mask1D |
class | Unified Arakawa C-grid mask for a 1-D Cartesian domain. |
Mask2D |
class | Unified Arakawa C-grid mask for a 2-D Cartesian domain. |
Mask3D |
class | Unified Arakawa C-grid mask for a 3-D Cartesian domain. |
Ghost-ring zeroing utilities for Arakawa C-grid operators (finitevolx._src.operators._ghost)
| Name | Kind | What it does |
|---|---|---|
interior |
function | Create an array shaped like like, zero everywhere except the interior. |
Implicit barotropic-mode (external gravity wave) filter for multi-layer shallow water (finitevolx._src.operators.barotropic)
| Name | Kind | What it does |
|---|---|---|
barotropic_filter |
function | Implicit external-gravity-wave (barotropic) mode filter. |
Coriolis force operator for Arakawa C-grids (finitevolx._src.operators.coriolis)
| Name | Kind | What it does |
|---|---|---|
Coriolis2D |
class | Coriolis force operator for 2-D Arakawa C-grids. |
Coriolis3D |
class | Coriolis force operator for 3-D Arakawa C-grids. |
Class forms of the diagnostic operators, with operator-attribute masks (finitevolx._src.operators.diagnostic_operators)
| Name | Kind | What it does |
|---|---|---|
Energetics2D |
class | Energy diagnostics at T-points on a 2-D Arakawa C-grid. |
QGPotentialVorticity2D |
class | Quasi-geostrophic potential vorticity at T-points. |
Strain2D |
class | Strain diagnostics on a 2-D Arakawa C-grid. |
Diagnostic quantities on Arakawa C-grids (finitevolx._src.operators.diagnostics)
| Name | Kind | What it does |
|---|---|---|
available_potential_energy |
function | Available potential energy at T-points. |
bernoulli_potential |
function | Bernoulli potential at T-points on an Arakawa C-grid. |
beta_param |
function | Meridional gradient of the Coriolis parameter from latitude. |
coriolis_fn |
function | Beta-plane Coriolis field. |
coriolis_param |
function | Reference Coriolis parameter from latitude. |
enstrophy |
function | Enstrophy (pointwise). |
kinetic_energy |
function | Kinetic energy at T-points (cell centers) on an Arakawa C-grid. |
okubo_weiss |
function | Okubo-Weiss parameter (pointwise). |
potential_enstrophy |
function | Potential enstrophy (pointwise). |
potential_vorticity |
function | Potential vorticity (pointwise). |
potential_vorticity_multilayer |
function | Multi-layer QG potential vorticity. |
qg_potential_vorticity |
function | QG potential vorticity at T-points (single layer). |
relative_vorticity_cgrid |
function | Relative vorticity at X-points (corners) on an Arakawa C-grid. |
shear_strain |
function | Shear strain at X-points (corners) on an Arakawa C-grid. |
ssh_to_streamfn |
function | Convert sea surface height to streamfunction. |
strain_magnitude_squared |
function | Squared strain magnitude (pointwise). |
streamfn_to_ssh |
function | Convert streamfunction to sea surface height. |
stretching_term |
function | Cross-layer stretching term for multi-layer QG models. |
sw_potential_vorticity |
function | Shallow-water potential vorticity at X-points on an Arakawa C-grid. |
sw_potential_vorticity_multilayer |
function | Multi-layer shallow-water potential vorticity at X-points. |
tensor_strain |
function | Tensor (normal) strain at T-points on an Arakawa C-grid. |
total_energy |
function | Domain-integrated total energy. |
total_enstrophy |
function | Domain-integrated enstrophy. |
vertical_velocity |
function | Vertical velocity from the continuity equation. |
Finite-difference operators on Arakawa C-grids (finitevolx._src.operators.difference)
| Name | Kind | What it does |
|---|---|---|
Difference1D |
class | Finite-difference operators on a 1-D Arakawa C-grid. |
Difference2D |
class | Finite-difference operators on a 2-D Arakawa C-grid. |
Difference3D |
class | Finite-difference operators on a 3-D Arakawa C-grid. |
Differentiable surrogates for non-smooth operations (finitevolx._src.operators.differentiable)
| Name | Kind | What it does |
|---|---|---|
smooth_abs |
function | Smooth approximation of \|x\| with a nonzero gradient at the origin. |
smooth_clamp |
function | Smooth approximation of max(x, x_min) (a soft lower clamp). |
smooth_max |
function | Smooth approximation of the elementwise max(x, y). |
Standalone divergence operator on 2-D Arakawa C-grids (finitevolx._src.operators.divergence)
| Name | Kind | What it does |
|---|---|---|
Divergence2D |
class | Divergence operator on a 2-D Arakawa C-grid. |
divergence_2d |
function | Compute ∇·(u, v) at T-points on the 2-D Arakawa C-grid. |
Equation of state operators for ocean density from temperature and salinity (finitevolx._src.operators.eos)
| Name | Kind | What it does |
|---|---|---|
buoyancy |
function | Compute buoyancy from density. |
linear_density |
function | Compute density from temperature and salinity using a linear EOS. |
linear_density_anomaly |
function | Compute density anomaly ρ' = ρ − ρ₀ using a linear EOS. |
linear_drho_dS |
function | Partial derivative ∂ρ/∂S for the linear EOS (constant). |
linear_drho_dT |
function | Partial derivative ∂ρ/∂T for the linear EOS (constant). |
reduced_gravity |
function | Compute reduced gravity between two layers. |
Interpolation (averaging) operators on Arakawa C-grids (finitevolx._src.operators.interpolation)
| Name | Kind | What it does |
|---|---|---|
Interpolation1D |
class | 1-D averaging operators on an Arakawa C-grid. |
Interpolation2D |
class | 2-D averaging operators on an Arakawa C-grid. |
Interpolation3D |
class | 3-D averaging operators on an Arakawa C-grid. |
Arakawa (1966) Jacobian operator for energy- and enstrophy-conserving advection (finitevolx._src.operators.jacobian)
| Name | Kind | What it does |
|---|---|---|
ArakawaJacobian2D |
class | Arakawa (1966) Jacobian J(f, g) at T-points, on the full grid. |
arakawa_jacobian |
function | Arakawa (1966) discretization of J(f, g). |
Area- and volume-weighted reduction helpers for Arakawa C-grids (finitevolx._src.operators.reductions)
| Name | Kind | What it does |
|---|---|---|
area_mean |
function | Area-weighted mean over physical interior T-cells. |
area_sum |
function | Area-weighted sum over physical interior T-cells. |
area_weights |
function | Dispatch to cartesian_area_weights or spherical_area_weights. |
cartesian_area_mean |
function | Cartesian area-weighted mean. |
cartesian_area_sum |
function | Cartesian area-weighted sum (area_sum with Cartesian grid). |
cartesian_area_weights |
function | T-cell areas on a Cartesian grid. |
cartesian_volume_mean |
function | Cartesian volume-weighted mean. |
cartesian_volume_sum |
function | Cartesian volume-weighted sum. |
cartesian_volume_weights |
function | T-cell volumes on a Cartesian 3-D grid: dx · dy · dz. |
masked_mean |
function | Mean over axis, excluding dry cells. |
masked_moments |
function | (mean, std) in one call — see masked_mean, masked_std. |
masked_std |
function | Standard deviation over axis, excluding dry cells, floored at eps. |
spherical_area_mean |
function | Spherical area-weighted mean. |
spherical_area_sum |
function | Spherical area-weighted sum. |
spherical_area_weights |
function | T-cell areas on a spherical grid. |
spherical_volume_mean |
function | Spherical volume-weighted mean. |
spherical_volume_sum |
function | Spherical volume-weighted sum. |
spherical_volume_weights |
function | T-cell volumes on a spherical 3-D grid. |
volume_mean |
function | Volume-weighted mean over physical interior T-cells (3-D). |
volume_sum |
function | Volume-weighted sum over physical interior T-cells (3-D). |
volume_weights |
function | Dispatch to Cartesian/spherical volume weights based on grid type. |
Linear drag and Rayleigh-sponge relaxation tendency operators (finitevolx._src.operators.relaxation)
| Name | Kind | What it does |
|---|---|---|
linear_drag |
function | Rayleigh (linear) bottom-drag tendency -\text{coef}\cdot u. |
rayleigh_relaxation |
function | Sponge / relaxation tendency -\text{coef}\cdot W\cdot(x - x_\text{ref}). |
Compound spherical operators on Arakawa C-grids (finitevolx._src.operators.spherical_compound)
| Name | Kind | What it does |
|---|---|---|
SphericalDivergence2D |
class | Horizontal divergence on a 2-D spherical Arakawa C-grid. |
SphericalDivergence3D |
class | 3-D spherical divergence (vmap over z-levels). |
SphericalLaplacian2D |
class | Spherical Laplacian on a 2-D Arakawa C-grid. |
SphericalLaplacian3D |
class | 3-D spherical Laplacian (vmap over z-levels). |
SphericalVorticity2D |
class | Vorticity and PV-flux operators on a 2-D spherical Arakawa C-grid. |
SphericalVorticity3D |
class | 3-D spherical vorticity (vmap over z-levels). |
Spherical finite-difference operators on Arakawa C-grids (finitevolx._src.operators.spherical_difference)
| Name | Kind | What it does |
|---|---|---|
SphericalDifference2D |
class | Spherical finite-difference operators on a 2-D Arakawa C-grid. |
SphericalDifference3D |
class | Spherical finite-difference operators on a 3-D Arakawa C-grid. |
Raw finite-difference and averaging stencils for Arakawa C-grids (finitevolx._src.operators.stencils)
| Name | Kind | What it does |
|---|---|---|
avg_x_bwd |
function | Backward average in x (east face → centre). |
avg_x_bwd_1d |
function | Backward average in x (east face → centre), 1-D. |
avg_x_bwd_3d |
function | Backward average in x over all z-levels (east face → centre). |
avg_x_fwd |
function | Forward average in x (centre → east face). |
avg_x_fwd_1d |
function | Forward average in x (centre → east face), 1-D. |
avg_x_fwd_3d |
function | Forward average in x over all z-levels (centre → east face). |
avg_xbwd_yfwd |
function | Bilinear average: U-points → V-points (backward-x, forward-y). |
avg_xfwd_ybwd |
function | Bilinear average: V-points → U-points (forward-x, backward-y). |
avg_xy_bwd |
function | Bilinear average from corners to centre (backward in both x and y). |
avg_xy_fwd |
function | Bilinear average to NE corner (forward in both x and y). |
avg_y_bwd |
function | Backward average in y (north face → centre). |
avg_y_bwd_3d |
function | Backward average in y over all z-levels (north face → centre). |
avg_y_fwd |
function | Forward average in y (centre → north face). |
avg_y_fwd_3d |
function | Forward average in y over all z-levels (centre → north face). |
diff_x_bwd |
function | Backward difference in x (east face → centre). |
diff_x_bwd_1d |
function | Backward difference in x (east face → centre), 1-D. |
diff_x_bwd_3d |
function | Backward difference in x over all z-levels (east face → centre). |
diff_x_fwd |
function | Forward difference in x (centre → east face). |
diff_x_fwd_1d |
function | Forward difference in x (centre → east face), 1-D. |
diff_x_fwd_3d |
function | Forward difference in x over all z-levels (centre → east face). |
diff_y_bwd |
function | Backward difference in y (north face → centre). |
diff_y_bwd_3d |
function | Backward difference in y over all z-levels (north face → centre). |
diff_y_fwd |
function | Forward difference in y (centre → north face). |
diff_y_fwd_3d |
function | Forward difference in y over all z-levels (centre → north face). |
Vorticity and potential-vorticity flux operators on Arakawa C-grids (finitevolx._src.operators.vorticity)
| Name | Kind | What it does |
|---|---|---|
Vorticity2D |
class | 2-D vorticity and PV-flux operators. |
Vorticity3D |
class | 3-D vorticity operators (horizontal plane per z-level). |
pv_flux_arakawa_lamb |
function | Deprecated alias of pv_flux_blend (not Arakawa-Lamb 1981). |
pv_flux_blend |
function | Blend of the energy- and enstrophy-conserving PV fluxes (grid-free). |
vorticity_flux_upwind |
function | Dissipative upwind vortex-force fluxes on a C-grid. |
Capacitance matrix solver and convenience wrappers for 2-D elliptic PDEs (finitevolx._src.solvers.elliptic)
| Name | Kind | What it does |
|---|---|---|
build_capacitance_solver |
function | Pre-compute the capacitance matrix and return a ready-to-use solver. |
pressure_from_divergence |
function | Solve ∇²p = ∇·u for the pressure correction. |
pv_inversion |
function | QG potential-vorticity inversion: solve (∇² − λ)ψ = q. |
streamfunction_from_vorticity |
function | Invert the vorticity–streamfunction relation ∇²ψ − λψ = ζ. |
Known-value lifting for inhomogeneous Dirichlet boundary conditions (finitevolx._src.solvers.inhomogeneous)
| Name | Kind | What it does |
|---|---|---|
KnownValueLifting |
class | Pre/post-processing wrapper for the lifting trick. |
SolveDomain |
class | Derived masks for the lifting trick. |
boundary_ring |
function | Wet cells adjacent to at least one dry cell (the inner ring). |
coast_ring |
function | Dry cells adjacent to at least one wet cell (the coast ring). |
Iterative solvers for 2-D elliptic PDEs (finitevolx._src.solvers.iterative)
| Name | Kind | What it does |
|---|---|---|
CGInfo |
class | Convergence diagnostics returned by solve_cg. |
masked_laplacian |
function | Apply the masked discrete Helmholtz operator (∇² − λ)·ψ. |
solve_cg |
function | Preconditioned Conjugate Gradient solver for symmetric linear operators. |
The C-grid Helmholtz operator as a structured gaussx linear operator (finitevolx._src.solvers.linear_operators)
| Name | Kind | What it does |
|---|---|---|
helmholtz_operator |
function | The rectangular Helmholtz operator (∇² − λ) as a gaussx operator. |
masked_helmholtz_operator |
function | The masked Helmholtz operator of masked_laplacian as a gaussx operator. |
Geometric multigrid solver for variable-coefficient Helmholtz equations (finitevolx._src.solvers.multigrid)
| Name | Kind | What it does |
|---|---|---|
MultigridSolver |
class | Geometric multigrid V-cycle solver for the variable-coefficient Helmholtz equation:: |
build_multigrid_solver |
function | Build a multigrid solver with precomputed level hierarchies. |
Preconditioners for iterative elliptic solvers (finitevolx._src.solvers.preconditioners)
| Name | Kind | What it does |
|---|---|---|
make_gaussx_multigrid_preconditioner |
function | The multigrid V-cycle as a symmetric gaussx preconditioner. |
make_multigrid_preconditioner |
function | Return a preconditioner closure that applies a single multigrid V-cycle. |
make_nystrom_preconditioner |
function | Build a randomized Nyström preconditioner for a symmetric operator. |
make_preconditioner |
function | Convenience factory that builds a preconditioner by name. |
make_spectral_preconditioner |
function | Return a spectral-solve preconditioner for PCG. |
Deprecated time steppers, kept for one release after the move to integrix (finitevolx._src.timestepping._deprecated)
| Name | Kind | What it does |
|---|---|---|
AB2Solver |
class | Deprecated: use integrix.march.AB2Solver with integrix.march.run. |
LeapfrogRAFSolver |
class | Deprecated: use integrix.march.LeapfrogRAFSolver with integrix.march.run. |
SplitExplicitRKSolver |
class | Deprecated: use integrix.march.SplitExplicitRKSolver with integrix.march.run. |
Convenience wrapper around diffeqsolve for ocean PDEs (finitevolx._src.timestepping._solve)
| Name | Kind | What it does |
|---|---|---|
solve_ocean_pde |
function | Integrate an ocean PDE using diffrax. |
Semi-Lagrangian advection: a pure step and its diffrax solver (finitevolx._src.timestepping.semi_lagrangian)
| Name | Kind | What it does |
|---|---|---|
SemiLagrangianSolver |
class | Semi-Lagrangian advection solver for diffrax. |
SemiLagrangianTerm |
class | Velocity term for SemiLagrangianSolver in diffeqsolve. |
semi_lagrangian_step |
function | Advect a 2D scalar field using semi-Lagrangian backtracking. |
Convenience wrapper to lift 2D horizontal operators to multilayer fields (finitevolx._src.vertical.multilayer)
| Name | Kind | What it does |
|---|---|---|
multilayer |
function | Lift a 2D horizontal operator to multilayer/multimode fields. |
Vertical coupling matrix and layer/mode transforms for multi-layer ocean models (finitevolx._src.vertical.vertical_modes)
| Name | Kind | What it does |
|---|---|---|
build_coupling_matrix |
function | Build the tridiagonal vertical coupling (stratification) matrix A. |
decompose_vertical_modes |
function | Eigendecompose the coupling matrix A to get Rossby radii and transforms. |
layer_to_mode |
function | Transform a field from layer space to mode space. |
mode_to_layer |
function | Transform a field from mode space to layer space. |
Re-exported from spectraldiffx
| Name | Kind | What it does |
|---|---|---|
BoundaryCondition |
type alias | typing.Union[typing.Literal['periodic', 'dirichlet', 'dir... |
CapacitanceSolver |
class | Spectral Poisson/Helmholtz solver for masked irregular domains. |
DirichletHelmholtzSolver2D |
class | 2D Helmholtz/Poisson/Laplace solver with homogeneous Dirichlet BCs. |
MixedBCHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with per-axis boundary conditions. |
MixedBCHelmholtzSolver3D |
class | 3D Helmholtz/Poisson solver with per-axis boundary conditions. |
NeumannHelmholtzSolver2D |
class | 2D Helmholtz/Poisson/Laplace solver with homogeneous Neumann BCs. |
RegularNeumannHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with Neumann BCs on a regular grid. |
SpectralHelmholtzSolver1D |
class | 1D Helmholtz/Poisson solver with periodic BCs using FFT. |
SpectralHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with periodic BCs using FFT. |
SpectralHelmholtzSolver3D |
class | 3D Helmholtz/Poisson solver with periodic BCs using FFT. |
StaggeredDirichletHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with Dirichlet BCs on a staggered grid. |
dct |
function | Discrete Cosine Transform of a 1-D vector. |
dct1_eigenvalues |
function | 1-D Laplacian eigenvalues for the DCT-I basis (Neumann BCs, regular grid). |
dct1_eigenvalues_ps |
function | PS eigenvalues for DCT-I (Neumann BCs, regular grid). |
dct2_eigenvalues |
function | 1-D Laplacian eigenvalues for the DCT-II basis (homogeneous Neumann BCs). |
dct2_eigenvalues_ps |
function | PS eigenvalues for DCT-II (Neumann BCs, staggered grid). |
dct3_eigenvalues |
function | 1-D Laplacian eigenvalues for Neumann-left + Dirichlet-right on a regular grid. |
dct3_eigenvalues_ps |
function | PS eigenvalues for Neumann-left + Dirichlet-right on a regular grid. |
dct4_eigenvalues |
function | 1-D Laplacian eigenvalues for Neumann-left + Dirichlet-right on a staggered grid. |
dct4_eigenvalues_ps |
function | PS eigenvalues for Neumann-left + Dirichlet-right on a staggered grid. |
dctn |
function | N-dimensional DCT: apply DCT sequentially along each axis. |
dst |
function | Discrete Sine Transform of a 1-D vector. |
dst1_eigenvalues |
function | 1-D Laplacian eigenvalues for the DST-I basis (homogeneous Dirichlet BCs). |
dst1_eigenvalues_ps |
function | PS eigenvalues for DST-I (Dirichlet BCs, regular grid). |
dst2_eigenvalues |
function | 1-D Laplacian eigenvalues for the DST-II basis (Dirichlet BCs, staggered grid). |
dst2_eigenvalues_ps |
function | PS eigenvalues for DST-II (Dirichlet BCs, staggered grid). |
dst3_eigenvalues |
function | 1-D Laplacian eigenvalues for Dirichlet-left + Neumann-right on a regular grid. |
dst3_eigenvalues_ps |
function | PS eigenvalues for Dirichlet-left + Neumann-right on a regular grid. |
dst4_eigenvalues |
function | 1-D Laplacian eigenvalues for Dirichlet-left + Neumann-right on a staggered grid. |
dst4_eigenvalues_ps |
function | PS eigenvalues for Dirichlet-left + Neumann-right on a staggered grid. |
dstn |
function | N-dimensional DST: apply DST sequentially along each axis. |
fft_eigenvalues |
function | 1-D Laplacian eigenvalues for the FFT basis (periodic BCs). |
fft_eigenvalues_ps |
function | PS eigenvalues for the FFT basis (periodic BCs). |
idct |
function | Inverse Discrete Cosine Transform of a 1-D vector. |
idctn |
function | N-dimensional inverse DCT: apply IDCT sequentially along each axis. |
idst |
function | Inverse Discrete Sine Transform of a 1-D vector. |
idstn |
function | N-dimensional inverse DST: apply IDST sequentially along each axis. |
modify_rhs_1d |
function | Apply boundary source terms for inhomogeneous BCs to a 1-D RHS. |
modify_rhs_2d |
function | Apply boundary source terms for inhomogeneous BCs to a 2-D RHS. |
modify_rhs_3d |
function | Apply boundary source terms for inhomogeneous BCs to a 3-D RHS. |
solve_helmholtz_2d |
function | Solve (nabla^2 - lambda)psi = f in 2-D with per-axis boundary conditions. |
solve_helmholtz_3d |
function | Solve (nabla^2 - lambda)psi = f in 3-D with per-axis boundary conditions. |
solve_helmholtz_dct |
function | Solve (∇² − λ)ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_helmholtz_dct1 |
function | Solve (∇² − λ)ψ = f with Neumann BCs on a regular grid (DCT-I). |
solve_helmholtz_dct1_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Neumann BCs on a regular grid (DCT-I). |
solve_helmholtz_dct1_3d |
function | Solve (∇² − λ)ψ = f with Neumann BCs on a regular 3-D grid (DCT-I). |
solve_helmholtz_dct2 |
function | Solve (∇² − λ)ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_helmholtz_dct2_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Neumann BCs on a staggered grid (DCT-II). |
solve_helmholtz_dct2_3d |
function | Solve (∇² − λ)ψ = f with Neumann BCs on a staggered 3-D grid (DCT-II). |
solve_helmholtz_dst |
function | Solve (∇² − λ)ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_helmholtz_dst1 |
function | Solve (∇² − λ)ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_helmholtz_dst1_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Dirichlet BCs on a regular grid (DST-I). |
solve_helmholtz_dst1_3d |
function | Solve (∇² − λ)ψ = f with Dirichlet BCs on a regular 3-D grid (DST-I). |
solve_helmholtz_dst2 |
function | Solve (∇² − λ)ψ = f with Dirichlet BCs on a staggered grid (DST-II). |
solve_helmholtz_dst2_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Dirichlet BCs on a staggered grid (DST-II). |
solve_helmholtz_dst2_3d |
function | Solve (∇² − λ)ψ = f with Dirichlet BCs on a staggered 3-D grid (DST-II). |
solve_helmholtz_fft |
function | Solve (∇² − λ)ψ = f with periodic BCs using the 2-D FFT. |
solve_helmholtz_fft_1d |
function | Solve (∇² − λ)ψ = f in 1-D with periodic BCs using the FFT. |
solve_helmholtz_fft_3d |
function | Solve (∇² − λ)ψ = f with periodic BCs using the 3-D FFT. |
solve_poisson_2d |
function | Solve nabla^2 psi = f in 2-D with per-axis boundary conditions. |
solve_poisson_3d |
function | Solve nabla^2 psi = f in 3-D with per-axis boundary conditions. |
solve_poisson_dct |
function | Solve ∇²ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_poisson_dct1 |
function | Solve ∇²ψ = f with Neumann BCs on a regular grid (DCT-I). |
solve_poisson_dct1_1d |
function | Solve ∇²ψ = f in 1-D with Neumann BCs on a regular grid (DCT-I). |
solve_poisson_dct1_3d |
function | Solve ∇²ψ = f with Neumann BCs on a regular 3-D grid (DCT-I). |
solve_poisson_dct2 |
function | Solve ∇²ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_poisson_dct2_1d |
function | Solve ∇²ψ = f in 1-D with Neumann BCs on a staggered grid (DCT-II). |
solve_poisson_dct2_3d |
function | Solve ∇²ψ = f with Neumann BCs on a staggered 3-D grid (DCT-II). |
solve_poisson_dst |
function | Solve ∇²ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_poisson_dst1 |
function | Solve ∇²ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_poisson_dst1_1d |
function | Solve ∇²ψ = f in 1-D with Dirichlet BCs on a regular grid (DST-I). |
solve_poisson_dst1_3d |
function | Solve ∇²ψ = f with Dirichlet BCs on a regular 3-D grid (DST-I). |
solve_poisson_dst2 |
function | Solve ∇²ψ = f with Dirichlet BCs on a staggered grid (DST-II). |
solve_poisson_dst2_1d |
function | Solve ∇²ψ = f in 1-D with Dirichlet BCs on a staggered grid (DST-II). |
solve_poisson_dst2_3d |
function | Solve ∇²ψ = f with Dirichlet BCs on a staggered 3-D grid (DST-II). |
solve_poisson_fft |
function | Solve ∇²ψ = f with periodic BCs using the 2-D FFT. |
solve_poisson_fft_1d |
function | Solve ∇²ψ = f in 1-D with periodic BCs using FFT. |
solve_poisson_fft_3d |
function | Solve ∇²ψ = f with periodic BCs using the 3-D FFT. |
Re-exported from gaussx
| Name | Kind | What it does |
|---|---|---|
solve_tridiagonal |
function | Solve a tridiagonal system A x = d. |
solve_tridiagonal_batched |
function | Solve independent tridiagonal systems over leading batch dimensions. |
Re-exported from integrix
| Name | Kind | What it does |
|---|---|---|
AB3Solver |
class | Third-order Adams–Bashforth as a diffrax solver, with an SSP-RK3 start. |
ForwardEulerDfx |
class | Forward Euler as a diffrax solver: yₙ₊₁ = yₙ + h F(tₙ, yₙ). |
IMEX_SSP2 |
class | IMEX-SSP2(2,2,2) for a diffrax.MultiTerm of an explicit and an implicit term. |
RK2Heun |
class | Heun's method (RK2), with an embedded forward-Euler error estimate. |
RK3SSP |
class | Third-order strong-stability-preserving Runge–Kutta (Shu–Osher). |
RK4Classic |
class | The classical fourth-order Runge–Kutta method, fixed steps only. |
SSP_RK104 |
class | Ketcheson's ten-stage, fourth-order SSP Runge–Kutta, fixed steps only. |
SSP_RK2 |
class | Second-order SSP Runge–Kutta, the same scheme as RK2Heun. |
ab2_step |
function | One second-order Adams–Bashforth step. |
ab3_step |
function | One third-order Adams–Bashforth step. |
euler_step |
function | One forward-Euler step: yₙ₊₁ = yₙ + h f(yₙ). |
heun_step |
function | One Heun (RK2) step, order 2, SSP with C = 1. |
imex_ssp2_step |
function | One IMEX-SSP2(2,2,2) step, with the caller's implicit solve. |
leapfrog_raf_step |
function | One leapfrog step with a Robert–Asselin filter on the middle level. |
rk3_ssp_step |
function | One third-order SSP Runge–Kutta step in Shu–Osher form, C = 1. |
rk4_step |
function | One classical fourth-order Runge–Kutta step. |
split_explicit_step |
function | One split-explicit barotropic/baroclinic step. |
Listed at spectraldiffx 0.1.1, gaussx 0.6.5, integrix 0.0.3.
Upstream: spectraldiffx
Spectral transforms (DCT / DST / FFT), the rectangular spectral Poisson / Helmholtz solvers and their eigenvalues, and the spectral capacitance solver. finitevolX re-exports most of the solver API (listed above); the rest — spectral derivatives, spherical-harmonic and Chebyshev machinery — is used from here, never re-implemented.
spectraldiffx
| Name | Kind | What it does |
|---|---|---|
BoundaryCondition |
type alias | typing.Union[typing.Literal['periodic', 'dirichlet', 'dir... |
CapacitanceSolver |
class | Spectral Poisson/Helmholtz solver for masked irregular domains. |
ChebyshevDerivative1D |
class | 1D Chebyshev derivative operator using the precomputed differentiation matrix. |
ChebyshevDerivative2D |
class | 2D Chebyshev derivative operators on [−Lx, Lx] × [−Ly, Ly]. |
ChebyshevDerivative3D |
class | 3D Chebyshev derivative operators on [−Lz, Lz] × [−Ly, Ly] × [−Lx, Lx]. |
ChebyshevFilter1D |
class | 1D Chebyshev spectral filter for smoothing and numerical stabilisation. |
ChebyshevFilter2D |
class | 2D Chebyshev spectral filter on [−Lx, Lx] × [−Ly, Ly]. |
ChebyshevGrid1D |
class | 1D Chebyshev grid on the domain [-L, L]. |
ChebyshevGrid2D |
class | 2D Chebyshev grid on [-Lx, Lx] × [-Ly, Ly]. |
ChebyshevGrid3D |
class | 3D Chebyshev grid on [-Lz, Lz] × [-Ly, Ly] × [-Lx, Lx]. |
ChebyshevHelmholtzSolver1D |
class | 1D Chebyshev-collocation Helmholtz/Poisson solver with Dirichlet or Neumann BCs. |
ChebyshevHelmholtzSolver2D |
class | 2D Chebyshev-collocation Helmholtz/Poisson solver with Dirichlet BCs. |
ChebyshevPoissonSolver1D |
class | 1D Chebyshev Poisson solver: d²u/dx² = f on [−L, L]. |
ChebyshevPoissonSolver2D |
class | 2D Chebyshev Poisson solver: ∇²u = f with Dirichlet BCs. |
ChebyshevTransform1D |
class | Forward/inverse 1D Chebyshev transform. |
ChebyshevTransform2D |
class | Forward/inverse 2D Chebyshev transform (tensor product of 1D). |
DirichletHelmholtzSolver2D |
class | 2D Helmholtz/Poisson/Laplace solver with homogeneous Dirichlet BCs. |
FourierGrid1D |
class | Fourier grid setup for periodic domain. |
FourierGrid2D |
class | 2D Fourier grid for doubly periodic domain. |
FourierGrid3D |
class | 3D Fourier grid for triply periodic domain. |
MixedBCHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with per-axis boundary conditions. |
MixedBCHelmholtzSolver3D |
class | 3D Helmholtz/Poisson solver with per-axis boundary conditions. |
NeumannHelmholtzSolver2D |
class | 2D Helmholtz/Poisson/Laplace solver with homogeneous Neumann BCs. |
RegularNeumannHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with Neumann BCs on a regular grid. |
SpectralDerivative1D |
class | 1D Spectral derivative operator using the Fast Fourier Transform (FFT). |
SpectralDerivative2D |
class | 2D Spectral derivative operators for doubly periodic rectangular domains. |
SpectralDerivative3D |
class | 3D Spectral derivative operators for triply periodic domains. |
SpectralFilter1D |
class | 1D Spectral filter for smoothing and numerical stabilization. |
SpectralFilter2D |
class | 2D Spectral filter for doubly periodic domains. |
SpectralFilter3D |
class | 3D Spectral filter for triply periodic domains. |
SpectralHelmholtzSolver1D |
class | 1D Helmholtz/Poisson solver with periodic BCs using FFT. |
SpectralHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with periodic BCs using FFT. |
SpectralHelmholtzSolver3D |
class | 3D Helmholtz/Poisson solver with periodic BCs using FFT. |
SphericalDerivative1D |
class | 1D spectral derivative operator on Gauss-Legendre latitude grid. |
SphericalDerivative2D |
class | 2D pseudo-spectral derivative operators on the sphere. |
SphericalDivergenceInversionSolver |
class | Divergence-inversion solver on the sphere. |
SphericalFilter1D |
class | 1D spectral filter on the Gauss–Legendre latitude grid. |
SphericalFilter2D |
class | 2D spectral filter on the full sphere lat-lon grid. |
SphericalGrid1D |
class | Gauss-Legendre grid for the latitude (colatitude) direction. |
SphericalGrid2D |
class | Full sphere latitude-longitude pseudo-spectral grid. |
SphericalHarmonicTransform |
class | Full 2D Spherical Harmonic Transform (SHT). |
SphericalHelmholtzDecomposition |
class | Helmholtz decomposition of a horizontal vector field on the sphere. |
SphericalHelmholtzSolver |
class | Spectral Helmholtz solver on the sphere: (∇² − α) φ = f. |
SphericalPoissonSolver |
class | Spectral Poisson solver on the sphere: ∇²φ = f. |
SphericalVorticityInversionSolver |
class | Vorticity-inversion solver on the sphere. |
StaggeredDirichletHelmholtzSolver2D |
class | 2D Helmholtz/Poisson solver with Dirichlet BCs on a staggered grid. |
build_capacitance_solver |
function | Pre-compute the capacitance factorisation and return a solver. |
cheb_dealias_product |
function | Compute the dealiased pointwise product a·b on a Chebyshev grid. |
chebyshev_antiderivative_coeffs |
function | Indefinite integral of a Chebyshev series, vanishing at x = −L. |
chebyshev_derivative_coeffs |
function | Differentiate a Chebyshev series in coefficient space (last axis). |
chebyshev_integral_coeffs |
function | Definite integral ∫_{−L}^{L} u(x) dx from Chebyshev coefficients. |
clenshaw_curtis_integrate_1d |
function | Integrate a 1D nodal field over [−L, L] using Clenshaw–Curtis. |
clenshaw_curtis_integrate_2d |
function | Integrate a 2D nodal field over [−Lx, Lx] × [−Ly, Ly]. |
clenshaw_curtis_weights |
function | Clenshaw–Curtis quadrature weights on Gauss–Lobatto nodes of [−L, L]. |
dct |
function | Discrete Cosine Transform of a 1-D vector. |
dct1_eigenvalues |
function | 1-D Laplacian eigenvalues for the DCT-I basis (Neumann BCs, regular grid). |
dct1_eigenvalues_ps |
function | PS eigenvalues for DCT-I (Neumann BCs, regular grid). |
dct2_eigenvalues |
function | 1-D Laplacian eigenvalues for the DCT-II basis (homogeneous Neumann BCs). |
dct2_eigenvalues_ps |
function | PS eigenvalues for DCT-II (Neumann BCs, staggered grid). |
dct3_eigenvalues |
function | 1-D Laplacian eigenvalues for Neumann-left + Dirichlet-right on a regular grid. |
dct3_eigenvalues_ps |
function | PS eigenvalues for Neumann-left + Dirichlet-right on a regular grid. |
dct4_eigenvalues |
function | 1-D Laplacian eigenvalues for Neumann-left + Dirichlet-right on a staggered grid. |
dct4_eigenvalues_ps |
function | PS eigenvalues for Neumann-left + Dirichlet-right on a staggered grid. |
dctn |
function | N-dimensional DCT: apply DCT sequentially along each axis. |
dst |
function | Discrete Sine Transform of a 1-D vector. |
dst1_eigenvalues |
function | 1-D Laplacian eigenvalues for the DST-I basis (homogeneous Dirichlet BCs). |
dst1_eigenvalues_ps |
function | PS eigenvalues for DST-I (Dirichlet BCs, regular grid). |
dst2_eigenvalues |
function | 1-D Laplacian eigenvalues for the DST-II basis (Dirichlet BCs, staggered grid). |
dst2_eigenvalues_ps |
function | PS eigenvalues for DST-II (Dirichlet BCs, staggered grid). |
dst3_eigenvalues |
function | 1-D Laplacian eigenvalues for Dirichlet-left + Neumann-right on a regular grid. |
dst3_eigenvalues_ps |
function | PS eigenvalues for Dirichlet-left + Neumann-right on a regular grid. |
dst4_eigenvalues |
function | 1-D Laplacian eigenvalues for Dirichlet-left + Neumann-right on a staggered grid. |
dst4_eigenvalues_ps |
function | PS eigenvalues for Dirichlet-left + Neumann-right on a staggered grid. |
dstn |
function | N-dimensional DST: apply DST sequentially along each axis. |
fft_eigenvalues |
function | 1-D Laplacian eigenvalues for the FFT basis (periodic BCs). |
fft_eigenvalues_ps |
function | PS eigenvalues for the FFT basis (periodic BCs). |
idct |
function | Inverse Discrete Cosine Transform of a 1-D vector. |
idctn |
function | N-dimensional inverse DCT: apply IDCT sequentially along each axis. |
idst |
function | Inverse Discrete Sine Transform of a 1-D vector. |
idstn |
function | N-dimensional inverse DST: apply IDST sequentially along each axis. |
modify_rhs_1d |
function | Apply boundary source terms for inhomogeneous BCs to a 1-D RHS. |
modify_rhs_2d |
function | Apply boundary source terms for inhomogeneous BCs to a 2-D RHS. |
modify_rhs_3d |
function | Apply boundary source terms for inhomogeneous BCs to a 3-D RHS. |
solve_helmholtz_2d |
function | Solve (nabla^2 - lambda)psi = f in 2-D with per-axis boundary conditions. |
solve_helmholtz_3d |
function | Solve (nabla^2 - lambda)psi = f in 3-D with per-axis boundary conditions. |
solve_helmholtz_dct |
function | Solve (∇² − λ)ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_helmholtz_dct1 |
function | Solve (∇² − λ)ψ = f with Neumann BCs on a regular grid (DCT-I). |
solve_helmholtz_dct1_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Neumann BCs on a regular grid (DCT-I). |
solve_helmholtz_dct1_3d |
function | Solve (∇² − λ)ψ = f with Neumann BCs on a regular 3-D grid (DCT-I). |
solve_helmholtz_dct2 |
function | Solve (∇² − λ)ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_helmholtz_dct2_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Neumann BCs on a staggered grid (DCT-II). |
solve_helmholtz_dct2_3d |
function | Solve (∇² − λ)ψ = f with Neumann BCs on a staggered 3-D grid (DCT-II). |
solve_helmholtz_dst |
function | Solve (∇² − λ)ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_helmholtz_dst1 |
function | Solve (∇² − λ)ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_helmholtz_dst1_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Dirichlet BCs on a regular grid (DST-I). |
solve_helmholtz_dst1_3d |
function | Solve (∇² − λ)ψ = f with Dirichlet BCs on a regular 3-D grid (DST-I). |
solve_helmholtz_dst2 |
function | Solve (∇² − λ)ψ = f with Dirichlet BCs on a staggered grid (DST-II). |
solve_helmholtz_dst2_1d |
function | Solve (∇² − λ)ψ = f in 1-D with Dirichlet BCs on a staggered grid (DST-II). |
solve_helmholtz_dst2_3d |
function | Solve (∇² − λ)ψ = f with Dirichlet BCs on a staggered 3-D grid (DST-II). |
solve_helmholtz_fft |
function | Solve (∇² − λ)ψ = f with periodic BCs using the 2-D FFT. |
solve_helmholtz_fft_1d |
function | Solve (∇² − λ)ψ = f in 1-D with periodic BCs using the FFT. |
solve_helmholtz_fft_3d |
function | Solve (∇² − λ)ψ = f with periodic BCs using the 3-D FFT. |
solve_poisson_2d |
function | Solve nabla^2 psi = f in 2-D with per-axis boundary conditions. |
solve_poisson_3d |
function | Solve nabla^2 psi = f in 3-D with per-axis boundary conditions. |
solve_poisson_dct |
function | Solve ∇²ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_poisson_dct1 |
function | Solve ∇²ψ = f with Neumann BCs on a regular grid (DCT-I). |
solve_poisson_dct1_1d |
function | Solve ∇²ψ = f in 1-D with Neumann BCs on a regular grid (DCT-I). |
solve_poisson_dct1_3d |
function | Solve ∇²ψ = f with Neumann BCs on a regular 3-D grid (DCT-I). |
solve_poisson_dct2 |
function | Solve ∇²ψ = f with homogeneous Neumann BCs using DCT-II. |
solve_poisson_dct2_1d |
function | Solve ∇²ψ = f in 1-D with Neumann BCs on a staggered grid (DCT-II). |
solve_poisson_dct2_3d |
function | Solve ∇²ψ = f with Neumann BCs on a staggered 3-D grid (DCT-II). |
solve_poisson_dst |
function | Solve ∇²ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_poisson_dst1 |
function | Solve ∇²ψ = f with homogeneous Dirichlet BCs using DST-I. |
solve_poisson_dst1_1d |
function | Solve ∇²ψ = f in 1-D with Dirichlet BCs on a regular grid (DST-I). |
solve_poisson_dst1_3d |
function | Solve ∇²ψ = f with Dirichlet BCs on a regular 3-D grid (DST-I). |
solve_poisson_dst2 |
function | Solve ∇²ψ = f with Dirichlet BCs on a staggered grid (DST-II). |
solve_poisson_dst2_1d |
function | Solve ∇²ψ = f in 1-D with Dirichlet BCs on a staggered grid (DST-II). |
solve_poisson_dst2_3d |
function | Solve ∇²ψ = f with Dirichlet BCs on a staggered 3-D grid (DST-II). |
solve_poisson_fft |
function | Solve ∇²ψ = f with periodic BCs using the 2-D FFT. |
solve_poisson_fft_1d |
function | Solve ∇²ψ = f in 1-D with periodic BCs using FFT. |
solve_poisson_fft_3d |
function | Solve ∇²ψ = f with periodic BCs using the 3-D FFT. |
Upstream: gaussx
Structured linear algebra and solver strategies. finitevolX delegates the tridiagonal solve and the Nyström preconditioner to it; use it for any other structured solve, preconditioner or low-rank approximation instead of writing one here.
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 |
type alias | <class 'gaussx._quadrature._psi_statistics.AnalyticalPsiS... |
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 | diagonal_tag |
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 | Returns whether an operator is marked as diagonal. |
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 | 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_upper_triangular |
function | Returns whether an operator is marked as upper triangular. |
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 | lower_triangular_tag |
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 | negative_semidefinite_tag |
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 | positive_semidefinite_tag |
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 | symmetric_tag |
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 | tridiagonal_tag |
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 | unit_diagonal_tag |
unwhiten |
function | Unwhiten variational mean: m = L @ m_tilde. |
unwhiten_covariance |
function | Unwhiten variational covariance: S = L S̃ Lᵀ. |
upper_triangular_tag |
constant | upper_triangular_tag |
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: integrix
Time steppers: the diffrax solvers, the pure step functions and the history-carrying AbstractSteppers run by integrix.march.run. The finitevolX names of these are deprecated aliases (listed above) for one release; new code imports them from integrix.march.
integrix.march
| Name | Kind | What it does |
|---|---|---|
AB2Solver |
class | Second-order Adams–Bashforth, run by integrix.march.run. |
AB3Solver |
class | Third-order Adams–Bashforth as a diffrax solver, with an SSP-RK3 start. |
AbstractStepper |
class | A fixed-step scheme whose history lives in the loop carry. |
ForwardEulerDfx |
class | Forward Euler as a diffrax solver: yₙ₊₁ = yₙ + h F(tₙ, yₙ). |
IMEX_SSP2 |
class | IMEX-SSP2(2,2,2) for a diffrax.MultiTerm of an explicit and an implicit term. |
LeapfrogRAFSolver |
class | Leapfrog with a Robert–Asselin filter, run by integrix.march.run. |
RK2Heun |
class | Heun's method (RK2), with an embedded forward-Euler error estimate. |
RK3SSP |
class | Third-order strong-stability-preserving Runge–Kutta (Shu–Osher). |
RK4Classic |
class | The classical fourth-order Runge–Kutta method, fixed steps only. |
SSP_RK104 |
class | Ketcheson's ten-stage, fourth-order SSP Runge–Kutta, fixed steps only. |
SSP_RK2 |
class | Second-order SSP Runge–Kutta, the same scheme as RK2Heun. |
SplitExplicitRKSolver |
class | Split-explicit stepping as an AbstractStepper, for integrix.march.run. |
SplitExplicitTerms |
class | The vector fields of a split-explicit model, passed to run as rhs. |
ab2_step |
function | One second-order Adams–Bashforth step. |
ab3_step |
function | One third-order Adams–Bashforth step. |
euler_step |
function | One forward-Euler step: yₙ₊₁ = yₙ + h f(yₙ). |
heun_step |
function | One Heun (RK2) step, order 2, SSP with C = 1. |
imex_solver |
function | A KenCarp3 IMEX solver whose implicit stage is matrix-free. |
imex_ssp2_step |
function | One IMEX-SSP2(2,2,2) step, with the caller's implicit solve. |
imex_stepsize_controller |
function | An adaptive PID step-size controller for an IMEX solve. |
leapfrog_raf_step |
function | One leapfrog step with a Robert–Asselin filter on the middle level. |
rk3_ssp_step |
function | One third-order SSP Runge–Kutta step in Shu–Osher form, C = 1. |
rk4_step |
function | One classical fourth-order Runge–Kutta step. |
run |
function | March y₀ through n_steps constant steps of h from t₀. |
split_explicit_step |
function | One split-explicit barotropic/baroclinic step. |
stable_step |
function | The largest stable forward-Euler step for advection and diffusion together. |