Crate scirs2_interpolate

Interpolation module

This module provides implementations of various interpolation methods. These methods are used to estimate values at arbitrary points based on a set of known data points.

Overview

• 1D interpolation methods (interp1d module)
  • Linear, nearest, cubic interpolation
  • PCHIP (Piecewise Cubic Hermite Interpolating Polynomial) - shape-preserving interpolation
• Spline interpolation (spline module)
• B-spline basis functions and interpolation (bspline module):
  • BSpline - B-spline basis functions and interpolation
  • Support for derivatives, antiderivatives, and integration
  • Knot generation with different styles (uniform, average, clamped)
  • Least-squares fitting with B-splines
• NURBS curves and surfaces (nurbs module):
  • NurbsCurve - Non-Uniform Rational B-Spline curves
  • NurbsSurface - Non-Uniform Rational B-Spline surfaces
  • Utility functions for creating common NURBS shapes (circles, spheres)
  • Support for control point weights and derivatives
• Bezier curves and surfaces (bezier module):
  • BezierCurve - Parametric curves with control points
  • BezierSurface - Parametric surfaces with control points
  • Bernstein polynomial basis functions
  • Curve/surface evaluation, derivatives, and curve splitting
• Bivariate splines (bivariate module):
  • BivariateSpline - Base class for bivariate splines
  • SmoothBivariateSpline - Smooth bivariate spline approximation
  • RectBivariateSpline - Bivariate spline approximation over a rectangular mesh
• Multivariate interpolation (interpnd module)
• Advanced interpolation methods (advanced module):
  • Akima spline interpolation - robust to outliers
  • Radial Basis Function (RBF) interpolation - for scattered data
  • Enhanced RBF interpolation - with automatic parameter selection and multi-scale capabilities
  • Kriging (Gaussian process regression) - with uncertainty quantification
  • Barycentric interpolation - stable polynomial interpolation
  • Thin-plate splines - special case of RBF for smooth interpolation
• GPU-accelerated interpolation (gpu_accelerated module):
  • GPU-accelerated RBF interpolation for large datasets
  • Batch spline evaluation using GPU parallelism
  • Mixed CPU/GPU workloads for optimal performance
  • Multi-GPU support and memory-efficient operations
• Grid transformation and resampling (grid module):
  • Resample scattered data onto regular grids
  • Convert between grids of different resolutions
  • Map grid data to arbitrary points
• Tensor product interpolation (tensor module):
  • Efficient high-dimensional interpolation on structured grids
  • Higher-order interpolation using Lagrange polynomials
• Penalized splines (penalized module):
  • P-splines with various penalty types (ridge, derivatives)
  • Cross-validation for optimal smoothing parameter selection
• Constrained splines (constrained module):
  • Splines with explicit monotonicity and convexity constraints
  • Support for regional constraints and multiple constraint types
  • Constraint-preserving interpolation and least squares fitting
• Tension splines (tension module):
  • Splines with adjustable tension parameters
  • Control over the “tightness” of interpolation curves
  • Smooth transition between cubic splines and linear interpolation
• Hermite splines (hermite module):
  • Cubic and quintic Hermite interpolation with derivative constraints
  • Direct control over function values and derivatives at data points
  • Multiple derivative specification options (automatic, fixed, zero, periodic)
  • C1 and C2 continuity options (continuous first/second derivatives)
• Multiscale B-splines (multiscale module):
  • Hierarchical B-splines with adaptive refinement
  • Different refinement criteria (error-based, curvature-based, combined)
  • Multi-level representation with control over precision-complexity tradeoffs
  • Efficient representation of functions with varying detail across the domain
• Active learning for adaptive sampling (adaptive_learning module):
  • Intelligent sampling strategies for reducing function evaluations
  • Uncertainty-based, error-based, and gradient-based sampling
  • Exploration vs exploitation balance for optimal data collection
  • Expected improvement and combined sampling strategies
  • Statistics tracking and convergence monitoring
• Physics-informed interpolation (physics_informed module):
  • Interpolation methods that respect physical constraints and conservation laws
  • Mass, energy, and momentum conservation enforcement
  • Positivity-preserving and monotonicity-preserving interpolation
  • Boundary condition enforcement and smoothness constraints
  • Multi-physics coupling and constraint satisfaction monitoring
• Gaussian process regression with adaptive kernels (adaptive_gp module):
  • Automatic kernel selection and hyperparameter optimization
  • Multiple kernel types (RBF, Matérn, Periodic, Linear, Polynomial)
  • Uncertainty quantification and probabilistic interpolation
  • Model comparison and Bayesian model selection
  • Sparse GP methods for scalability to large datasets
• Neural network enhanced interpolation (neural_enhanced module):
  • Hybrid interpolation combining traditional methods with neural networks
  • Residual learning to improve base interpolation accuracy
  • Multiple neural architectures (MLP, Bayesian, PINN, Transformer)
  • Adaptive training with early stopping and regularization
  • Uncertainty-aware neural interpolation with Bayesian networks
• Advanced extrapolation methods (extrapolation module):
  • Configurable extrapolation beyond domain boundaries
  • Multiple methods: constant, linear, polynomial, periodic, reflected
  • Physics-informed extrapolation (exponential, power law)
  • Customizable for specific domain knowledge
• Enhanced boundary handling (boundarymode module):
  • Physical boundary conditions for PDEs (Dirichlet, Neumann)
  • Domain extension via symmetry, periodicity, and custom mappings
  • Separate control of upper and lower boundary behavior
  • Support for mixed boundary conditions
• Optimization-based parameter fitting (optimization module):
  • Cross-validation based model selection (K-fold, leave-one-out)
  • Regularization parameter optimization with grid search
  • Hyperparameter tuning for RBF kernels and spline smoothing
  • Model comparison and validation metrics (MSE, MAE, R²)
  • Bayesian optimization for efficient parameter search
• Time series specific interpolation (timeseries module):
  • Temporal pattern recognition (trends, seasonality, irregularities)
  • Missing data handling with forward/backward fill and interpolation
  • Seasonal decomposition and trend-aware interpolation
  • Outlier detection and robust temporal smoothing
  • Uncertainty estimation for time-dependent predictions
  • Holiday and event-aware interpolation strategies
• Geospatial interpolation methods (geospatial module):
  • Geographic coordinate handling (latitude/longitude, projections)
  • Spherical interpolation with great circle distances
  • Spatial autocorrelation and kriging for Earth science data
  • Multi-scale interpolation from local to global coverage
  • Elevation-aware 3D interpolation and topographic considerations
  • Boundary handling for coastal and land/water transitions
• Utility functions (utils module):
  • Error estimation with cross-validation
  • Parameter optimization
  • Differentiation and integration of interpolated functions

Re-exports

pub use error::InterpolateError;

pub use error::InterpolateResult;

pub use adaptive_gp::make_adaptive_gp;

pub use adaptive_gp::AdaptiveGPConfig;

pub use adaptive_gp::AdaptiveGaussianProcess;

pub use adaptive_gp::GPStats;

pub use adaptive_gp::KernelHyperparameters;

pub use adaptive_gp::KernelModel;

pub use adaptive_gp::KernelType as GPKernelType;

pub use adaptive_learning::make_active_learner;

pub use adaptive_learning::ActiveLearner;

pub use adaptive_learning::ActiveLearningConfig;

pub use adaptive_learning::LearningStats;

pub use adaptive_learning::SamplingCandidate;

pub use adaptive_learning::SamplingStrategy;

pub use adaptive_singularity::apply_singularity_handling;

pub use adaptive_singularity::SingularityDetector;

pub use adaptive_singularity::SingularityDetectorConfig;

pub use adaptive_singularity::SingularityInfo;

pub use adaptive_singularity::SingularityType;

pub use adaptive_singularity::TreatmentStrategy;

pub use advanced::akima::make_akima_spline;

pub use advanced::akima::AkimaSpline;

pub use advanced::barycentric::make_barycentric_interpolator;

pub use advanced::barycentric::BarycentricInterpolator;

pub use advanced::barycentric::BarycentricTriangulation;

pub use advanced::enhanced_kriging::make_bayesian_kriging;

pub use advanced::enhanced_kriging::make_enhanced_kriging;

pub use advanced::enhanced_kriging::make_universal_kriging;

pub use advanced::enhanced_kriging::AnisotropicCovariance;

pub use advanced::enhanced_kriging::BayesianKrigingBuilder;

pub use advanced::enhanced_kriging::BayesianPredictionResult;

pub use advanced::enhanced_kriging::EnhancedKriging;

pub use advanced::enhanced_kriging::EnhancedKrigingBuilder;

pub use advanced::enhanced_kriging::TrendFunction;

pub use advanced::enhanced_rbf::make_accurate_rbf;

pub use advanced::enhanced_rbf::make_auto_rbf;

pub use advanced::enhanced_rbf::make_fast_rbf;

pub use advanced::enhanced_rbf::EnhancedRBFInterpolator;

pub use advanced::enhanced_rbf::EnhancedRBFKernel;

pub use advanced::enhanced_rbf::KernelType;

pub use advanced::enhanced_rbf::KernelWidthStrategy;

pub use advanced::fast_kriging::make_fixed_rank_kriging;

pub use advanced::fast_kriging::make_hodlr_kriging;

pub use advanced::fast_kriging::make_local_kriging;

pub use advanced::fast_kriging::make_tapered_kriging;

pub use advanced::fast_kriging::FastKriging;

pub use advanced::fast_kriging::FastKrigingBuilder;

pub use advanced::fast_kriging::FastKrigingMethod;

pub use advanced::fast_kriging::FastPredictionResult;

pub use advanced::kriging::make_kriging_interpolator;

pub use advanced::kriging::CovarianceFunction;

pub use advanced::kriging::KrigingInterpolator;

pub use advanced::rbf::RBFInterpolator;

pub use advanced::rbf::RBFKernel;

pub use advanced::thinplate::make_thinplate_interpolator;

pub use advanced::thinplate::ThinPlateSpline;

pub use bezier::bernstein;

pub use bezier::compute_bernstein_all;

pub use bezier::BezierCurve;

pub use bezier::BezierSurface;

pub use bivariate::BivariateInterpolator;

pub use bivariate::BivariateSpline;

pub use bivariate::RectBivariateSpline;

pub use bivariate::SmoothBivariateSpline;

pub use bivariate::SmoothBivariateSplineBuilder;

pub use boundarymode::make_antisymmetric_boundary;

pub use boundarymode::make_linear_gradient_boundary;

pub use boundarymode::make_periodic_boundary;

pub use boundarymode::make_symmetric_boundary;

pub use boundarymode::make_zero_gradient_boundary;

pub use boundarymode::make_zero_value_boundary;

pub use boundarymode::BoundaryMode;

pub use boundarymode::BoundaryParameters;

pub use boundarymode::BoundaryResult;

pub use bspline::generate_knots;

pub use bspline::make_interp_bspline;

pub use bspline::make_lsq_bspline;

pub use bspline::BSpline;

pub use bspline::BSplineWorkspace;

pub use bspline::ExtrapolateMode as BSplineExtrapolateMode;

pub use bspline::WorkspaceMemoryStats;

pub use cache::make_cached_bspline;

pub use cache::make_cached_bspline_with_config;

pub use cache::BSplineCache;

pub use cache::CacheConfig;

pub use cache::CacheStats;

pub use cache::CachedBSpline;

pub use cache::DistanceMatrixCache;

pub use cache_aware::make_cache_aware_rbf;

pub use cache_aware::CacheAwareBSpline;

pub use cache_aware::CacheAwareRBF;

pub use cache_aware::CacheOptimizedConfig;

pub use cache_aware::CacheOptimizedStats;

pub use cache_aware::CacheSizes;

pub use constrained::ConstrainedSpline;

pub use constrained::Constraint;

pub use constrained::ConstraintRegion;

pub use constrained::ConstraintType;

pub use constrained::FittingMethod;

pub use extrapolation::make_cubic_extrapolator;

pub use extrapolation::make_exponential_extrapolator;

pub use extrapolation::make_linear_extrapolator;

pub use extrapolation::make_periodic_extrapolator;

pub use extrapolation::make_reflection_extrapolator;

pub use extrapolation::ExtrapolationMethod;

pub use extrapolation::ExtrapolationParameters;

pub use extrapolation::Extrapolator;

pub use fast_bspline::make_cached_fast_bspline_evaluator;

pub use fast_bspline::make_fast_bspline_evaluator;

pub use fast_bspline::FastBSplineEvaluator;

pub use fast_bspline::TensorProductFastEvaluator;

pub use geospatial::make_climate_interpolator;

pub use geospatial::make_elevation_interpolator;

pub use geospatial::CoordinateSystem;

pub use geospatial::GeospatialConfig;

pub use geospatial::GeospatialInterpolator;

pub use geospatial::GeospatialResult;

pub use geospatial::InterpolationModel;

pub use geospatial::SpatialStats;

pub use gpu_accelerated::get_gpu_device_info;

pub use gpu_accelerated::is_gpu_acceleration_available;

pub use gpu_accelerated::make_gpu_rbf_interpolator;

pub use gpu_accelerated::GpuBatchSplineEvaluator;

pub use gpu_accelerated::GpuConfig;

pub use gpu_accelerated::GpuDeviceInfo;

pub use gpu_accelerated::GpuRBFInterpolator;

pub use gpu_accelerated::GpuRBFKernel;

pub use gpu_accelerated::GpuStats;

pub use grid::create_regular_grid;

pub use grid::map_grid_to_points;

pub use grid::resample_grid_to_grid;

pub use grid::resample_to_grid;

pub use grid::GridTransformMethod;

pub use hermite::make_hermite_spline;

pub use hermite::make_hermite_spline_with_derivatives;

pub use hermite::make_natural_hermite_spline;

pub use hermite::make_periodic_hermite_spline;

pub use hermite::make_quintic_hermite_spline;

pub use hermite::DerivativeSpec;

pub use hermite::HermiteSpline;

pub use high_dimensional::make_knn_interpolator;

pub use high_dimensional::make_local_rbf_interpolator;

pub use high_dimensional::make_pca_interpolator;

pub use high_dimensional::DimensionReductionMethod;

pub use high_dimensional::HighDimensionalInterpolator;

pub use high_dimensional::HighDimensionalInterpolatorBuilder;

pub use high_dimensional::InterpolatorStats;

pub use high_dimensional::LocalMethod;

pub use high_dimensional::LocalRBFType;

pub use high_dimensional::SparseStrategy;

pub use high_dimensional::SpatialIndexType;

pub use interp1d::cubic_interpolate;

pub use interp1d::hyman_interpolate;

pub use interp1d::linear_interpolate;

pub use interp1d::modified_akima_interpolate;

pub use interp1d::monotonic_interpolate;

pub use interp1d::nearest_interpolate;

pub use interp1d::pchip_interpolate;

pub use interp1d::steffen_interpolate;

pub use interp1d::Interp1d;

pub use interp1d::InterpolationMethod;

pub use interp1d::MonotonicInterpolator;

pub use interp1d::MonotonicMethod;

pub use interp1d::PchipInterpolator;

pub use interpnd::make_interp_nd;

pub use interpnd::make_interp_scattered;

pub use interpnd::map_coordinates;

pub use interpnd::ExtrapolateMode;

pub use interpnd::GridType;

pub use interpnd::RegularGridInterpolator;

pub use interpnd::ScatteredInterpolator;

pub use local::mls::MovingLeastSquares;

pub use local::mls::PolynomialBasis;

pub use local::mls::WeightFunction;

pub use local::polynomial::make_loess;

pub use local::polynomial::make_robust_loess;

pub use local::polynomial::LocalPolynomialConfig;

pub use local::polynomial::LocalPolynomialRegression;

pub use local::polynomial::RegressionResult;

pub use multiscale::make_adaptive_bspline;

pub use multiscale::MultiscaleBSpline;

pub use multiscale::RefinementCriterion;

pub use neural_enhanced::make_neural_enhanced_interpolator;

pub use neural_enhanced::ActivationType;

pub use neural_enhanced::EnhancementStrategy;

pub use neural_enhanced::NeuralArchitecture;

pub use neural_enhanced::NeuralEnhancedInterpolator;

pub use neural_enhanced::NeuralTrainingConfig;

pub use neural_enhanced::TrainingStats;

pub use numerical_stability::apply_tikhonov_regularization;

pub use numerical_stability::assess_matrix_condition;

pub use numerical_stability::check_safe_division;

pub use numerical_stability::machine_epsilon;

pub use numerical_stability::safe_reciprocal;

pub use numerical_stability::solve_with_stability_monitoring;

pub use numerical_stability::ConditionReport;

pub use numerical_stability::StabilityDiagnostics;

pub use numerical_stability::StabilityLevel;

pub use nurbs::make_nurbs_circle;

pub use nurbs::make_nurbs_sphere;

pub use nurbs::NurbsCurve;

pub use nurbs::NurbsSurface;

pub use optimization::grid_search;

pub use optimization::make_cross_validator;

pub use optimization::CrossValidationResult;

pub use optimization::CrossValidationStrategy;

pub use optimization::CrossValidator;

pub use optimization::ModelSelector;

pub use optimization::OptimizationConfig;

pub use optimization::OptimizationResult;

pub use optimization::ValidationMetric;

pub use parallel::make_parallel_loess;

pub use parallel::make_parallel_mls;

pub use parallel::make_parallel_robust_loess;

pub use parallel::ParallelConfig;

pub use parallel::ParallelEvaluate;

pub use parallel::ParallelLocalPolynomialRegression;

pub use parallel::ParallelMovingLeastSquares;

pub use penalized::cross_validate_lambda;

pub use penalized::pspline_with_custom_penalty;

pub use penalized::PSpline;

pub use penalized::PenaltyType;

pub use physics_informed::make_mass_conserving_interpolator;

pub use physics_informed::make_monotonic_physics_interpolator;

pub use physics_informed::make_smooth_physics_interpolator;

pub use physics_informed::ConservationLaw;

pub use physics_informed::PhysicalConstraint;

pub use physics_informed::PhysicsInformedConfig;

pub use physics_informed::PhysicsInformedInterpolator;

pub use physics_informed::PhysicsInformedResult;

pub use scattered_optimized::make_optimized_scattered_interpolator;

pub use scattered_optimized::OptimizedScatteredInterpolator;

pub use scattered_optimized::OptimizedScatteredStats;

pub use scattered_optimized::ScatteredConfig;

pub use simd_optimized::get_simd_config;

pub use simd_optimized::is_simd_available;

pub use simd_optimized::simd_bspline_basis_functions;

pub use simd_optimized::simd_bspline_batch_evaluate;

pub use simd_optimized::simd_distance_matrix;

pub use simd_optimized::simd_rbf_evaluate;

pub use simd_optimized::RBFKernel as SimdRBFKernel;

pub use simd_optimized::SimdConfig;

pub use smoothing::make_adaptive_smoothing_spline;

pub use smoothing::make_error_based_smoothing_spline;

pub use smoothing::make_optimized_smoothing_spline;

pub use smoothing::KnotStrategy;

pub use smoothing::VariableKnotSpline;

pub use sparse_grid::make_adaptive_sparse_grid_interpolator;

pub use sparse_grid::make_sparse_grid_from_data;

pub use sparse_grid::make_sparse_grid_interpolator;

pub use sparse_grid::GridPoint;

pub use sparse_grid::MultiIndex;

pub use sparse_grid::SparseGridBuilder;

pub use sparse_grid::SparseGridInterpolator;

pub use sparse_grid::SparseGridStats;

pub use spatial::balltree::BallTree;

pub use spatial::kdtree::KdTree;

pub use spline::make_interp_spline;

pub use spline::BoundaryCondition;

pub use spline::CubicSpline;

pub use structured_matrix::create_bspline_band_matrix;

pub use structured_matrix::solve_band_system;

pub use structured_matrix::solve_sparse_system;

pub use structured_matrix::solve_structured_least_squares;

pub use structured_matrix::BandMatrix;

pub use structured_matrix::CSRMatrix;

pub use tension::make_tension_spline;

pub use tension::TensionSpline;

pub use tensor::lagrange_tensor_interpolate;

pub use tensor::tensor_product_interpolate;

pub use tensor::LagrangeTensorInterpolator;

pub use tensor::TensorProductInterpolator;

pub use timeseries::backward_fill;

pub use timeseries::forward_fill;

pub use timeseries::make_daily_interpolator;

pub use timeseries::make_weekly_interpolator;

pub use timeseries::MissingDataStrategy;

pub use timeseries::SeasonalityType;

pub use timeseries::TemporalPattern;

pub use timeseries::TemporalStats;

pub use timeseries::TimeSeriesConfig;

pub use timeseries::TimeSeriesInterpolator;

pub use timeseries::TimeSeriesResult;

pub use voronoi::constant_value_extrapolation;

pub use voronoi::inverse_distance_extrapolation;

pub use voronoi::linear_gradient_extrapolation;

pub use voronoi::make_laplace_interpolator;

pub use voronoi::make_natural_neighbor_interpolator;

pub use voronoi::make_parallel_laplace_interpolator;

pub use voronoi::make_parallel_natural_neighbor_interpolator;

pub use voronoi::make_parallel_sibson_interpolator;

pub use voronoi::make_sibson_interpolator;

pub use voronoi::nearest_neighbor_extrapolation;

pub use voronoi::Extrapolation;

pub use voronoi::ExtrapolationMethod as VoronoiExtrapolationMethod;

pub use voronoi::ExtrapolationParams;

pub use voronoi::GradientEstimation;

pub use voronoi::InterpolateWithGradient;

pub use voronoi::InterpolateWithGradientResult;

pub use voronoi::InterpolationMethod as VoronoiInterpolationMethod;

pub use voronoi::NaturalNeighborInterpolator;

pub use voronoi::ParallelNaturalNeighborInterpolator;

Modules

adaptive_gp

Gaussian process regression with adaptive kernels

adaptive_learning

Active learning approaches for adaptive sampling in interpolation

adaptive_singularity

Automatic singularity detection and handling for interpolation

advanced

Advanced interpolation methods for specialized use cases.

bezier

Bezier curve and surface implementations

bivariate

Bivariate interpolation modules

boundarymode

bspline

B-spline basis functions and B-spline curves

cache

Cache-aware algorithm implementations for interpolation

cache_aware

Cache-aware algorithm implementations for high-performance interpolation

constrained

Constrained splines with monotonicity and convexity constraints

error

Error types for the SciRS2 interpolation module

extrapolation

fast_bspline

Fast evaluation of B-splines using recursive algorithms

geospatial

Geospatial interpolation methods

gpu_accelerated

GPU-accelerated interpolation methods

grid

Grid transformation and resampling utilities

griddata

Grid data interpolation - SciPy-compatible griddata implementation

hermite

high_dimensional

High-dimensional interpolation methods

interp1d

One-dimensional interpolation methods

interp2d

2D interpolation - SciPy-compatible interp2d implementation

interpnd

N-dimensional interpolation methods

local

Local interpolation methods

multiscale

neural_enhanced

Neural network enhanced interpolation

numerical_stability

Numerical Stability Monitoring and Condition Assessment

nurbs

NURBS (Non-Uniform Rational B-Splines) implementation

optimization

Optimization-based parameter fitting for interpolation

parallel

Parallel processing utilities for interpolation

penalized

Penalized splines (P-splines) with various penalty terms

physics_informed

Physics-informed interpolation methods

scattered_optimized

Optimized scattered data interpolation for large datasets

simd_optimized

SIMD-optimized interpolation functions

smoothing

Variable knot smoothing splines

sparse_grid

Sparse grid interpolation methods

spatial

Spatial data structures for efficient nearest neighbor search

spline

Spline interpolation methods

structured_matrix

Structured coefficient matrix operations for interpolation algorithms

tension

tensor

Tensor product interpolation

timeseries

Time series specific interpolation methods

utils

Utility functions for interpolation

voronoi

Voronoi-based interpolation methods