GEO-INFER-MATH

Instructions

Foundation module with zero internal dependencies. Provides mathematical primitives consumed by all other modules.

Core Capabilities

• Spatial statistics: Moran's I, Geary's C, Getis-Ord G*, LISA, semivariograms
• Topology: Voronoi tessellation, Delaunay triangulation, spatial indexing
• Graph theory: Network analysis, shortest paths, centrality measures
• Kernel density: Gaussian, Epanechnikov, adaptive bandwidth KDE
• Distance metrics: Haversine, Vincenty, geodesic on WGS84 ellipsoid

Key Imports

# Spatial statistics
from geo_infer_math.core.spatial_statistics import (
    MoranI, SpatialDescriptiveStats,
    getis_ord_g, ripley_k, semivariogram,
    spatial_descriptive_statistics, spatial_entropy,
    local_indicators_spatial_association,
)
# Interpolation
from geo_infer_math.core.interpolation import (
    InterpolationConfig, SpatialInterpolator,
    IDWInterpolator, KrigingInterpolator, RBFInterpolator,
    InterpolationManager, create_interpolation_manager,
    interpolate_spatial_data, create_interpolation_grid,
)
# Optimization
from geo_infer_math.core.optimization import (
    OptimizationConfig, Optimizer,
    GradientDescentOptimizer, GeneticAlgorithmOptimizer,
    ScipyOptimizer, MultiObjectiveOptimizer,
    OptimizationManager, create_optimization_manager,
    optimize_function, compare_optimization_methods,
)
# Geometry / distance
from geo_infer_math.core.geometry import (
    Point, LineString, Polygon,
    haversine_distance, vincenty_distance,
    bearing, destination_point,
    point_in_polygon, buffer_point,
    line_intersection, polygon_area_spherical,
)

Examples

import numpy as np
from geo_infer_math.core.spatial_statistics import (
    MoranI, getis_ord_g, ripley_k, semivariogram,
    spatial_descriptive_statistics,
)

# Moran's I spatial autocorrelation
values = np.random.randn(100)
weights = np.random.rand(100, 100)
moran = MoranI(values, weights)
result = moran.compute()
print(f"Moran's I: {result.statistic}, p-value: {result.p_value}")

# Getis-Ord G* hot-spot statistic
g_stat = getis_ord_g(values, weights)
print(f"Getis-Ord G: {g_stat}")

# Ripley's K function
coords = np.random.rand(50, 2)
k_values = ripley_k(coords, distances=np.linspace(0.01, 1.0, 20))
print(f"Ripley K at first distance: {k_values[0]:.4f}")

# Semivariogram
semivar = semivariogram(values, coords)
print(f"Semivariogram computed: {len(semivar)} lag bins")

# Descriptive spatial statistics
stats = spatial_descriptive_statistics(values, coords)
print(stats)

Guidelines

• All distance calculations default to WGS84 ellipsoid
• Weight matrices should be row-standardized for spatial statistics
• This module has no external geo-dependencies — pure numpy/scipy
• Test: uv run python -m pytest GEO-INFER-MATH/tests/ -v

Integrations

• BAYES → Spatial statistics feeding Bayesian priors
• SPACE → H3 spatial weights for autocorrelation
• SPM → Statistical parametric map computation
• AI → Spatial feature engineering for ML
• EDU → Spatial statistics teaching exercises