Core geometry
Visible precision and information conservation
Exact split-frame geometry: visible precision, canonical lift, and the conservation law vis + hid = amb, verified to machine precision.
Python Kernel - Exact Geometry - Information Conservation - Observer Steering
Exact observer geometry for real data.
nomogeo computes what an observer can and cannot see about a system. Given a precision matrix and an observer, it returns exact information budgets, adapted observers, and certified diagnostics. Two companion packages, nomocomp and nomoselect, apply this to model comparison and dimensionality reduction.
Python >= 3.11
BSD-3-Clause
PyPI
Minimal dependencies
Overview
What the package includes
Observer steering
From data to adapted observer in one call
Pass (X, y) or a covariance matrix. Get the adapted observer, capture curve, exact-sector diagnostics, and comparison against PCA.
Companion packages
Model comparison and subspace selection
nomocomp replaces AIC/BIC with exact geometry. nomoselect replaces PCA with task-aware selection.
Start Here
Documentation
Quick Example
import numpy as np
from nomogeo import information_budget, steer
# Information budget: where does the information go?
H = np.array([[3.0, 1.0], [1.0, 2.0]])
C = np.array([[1.0, 0.0]])
Hdot = np.array([[0.1, -0.2], [-0.2, 0.3]])
b = information_budget(H, C, Hdot)
print(f"vis={b.visible_rate:.3f} hid={b.hidden_rate:.3f}")
# One-call steering from data
from sklearn.datasets import load_iris
X, y = load_iris(return_X_y=True)
r = steer(X=X, y=y, rank=2, task="fisher")
print(f"vis_frac={r.visible_fraction:.2f} vs PCA: +{r.advantage_over_pca:.2f}")Examples
Released examples
Released examples and companion packages. Each has clear scope and declared boundaries.
nomogeo
Observer steering on Iris
One call to steer(): extract geometry, find the adapted observer, compare against PCA, report diagnostics.
nomocomp
AIC/BIC reversal on collinear data
When predictors are correlated, AIC and BIC pick the wrong model. The geometric correction identifies the right one.
Learn morenomoselect
Task-aware beats PCA on Wine
PCA ignores class labels. The task-aware observer captures class structure that PCA misses entirely.
Learn moreConservation law
The observer splits information, never creates it.
The visible rate plus the hidden rate always equals the ambient rate. This is an exact algebraic identity, verified to machine precision on every tested configuration.
Honest boundary
The exact domain is finite-dimensional SPD geometry.
nomogeo is exact for linear observers on symmetric positive-definite matrices. It is not a generic non-Gaussian engine. Outside the exact sector, it provides local quadratic geometry.