binjamin

Derive artifact-free, perfectly nested multiscale analysis windows from any discrete data. Also includes every major bin width estimation method in one place.

Install

pip install binjamin

Quick Start

Lattice geometry — the main feature

Standard multiscale analysis requires choosing window sizes. Those choices introduce boundary artifacts, inconsistent nesting, and results that depend on the analyst. Binjamin derives the measurement space from arithmetic — the windows are forced by the math, not chosen.

import binjamin as bj

geo = bj.lattice([10, 30, 60, 360])

That's it. You get a complete measurement space:

geo.cbin        # 10 — computational resolution (gcd of windows)
geo.horizon     # 360 — lcm of windows
geo.windows     # (10, 12, 15, 18, 20, 30, 36, 40, 60, 90, 120, 180, 360)
geo.prime_basis # {2: 2, 3: 2} — the geometry of scale

Every window divides the horizon. Every window nests perfectly into every larger window. No boundary artifacts. The structure comes from the divisibility lattice — the unique maximal family of window sizes with these properties.

From real data

# EEG at 256 Hz — windows in samples
geo = bj.lattice([256, 1024, 4096, 15360], data=sample_indices)
geo.data_grain  # estimated from data
geo.cbin        # 256 — analysis resolution
geo.grain       # 1 — can zoom finer later

Bin width estimation

bj.freedman_diaconis(intervals)   # robust, no assumption
bj.auto(intervals)                # good default
edges, counts = bj.bin(data)      # bin and count

Features

Lattice geometry

Derive a complete measurement space from analysis windows.

geo = bj.lattice(
    windows=[10, 30, 60, 360],   # desired analysis scales
    grain=1,                      # finest resolution (optional)
    cbin=10,                      # materialized resolution (optional)
    data=orders,                  # data for grain estimation (optional)
    horizon=720,                  # override horizon (optional)
)

Usually you just pass windows. Everything else is derived. See docs/lattice.md for details.

LatticeGeometry fields:

Field	Meaning
data_grain	Estimated from data (raw cadence)
grain	Finest admissible resolution
cbin	Materialized resolution (divides all windows)
horizon	Outer boundary of coordinate space
windows	All valid scales in the active domain
prime_basis	Prime factorization of horizon // cbin
coordinates	Prime exponent vector per window
members	Full set of lattice members

Coordinates

Every integer has a unique prime factorization. Binjamin exposes this as a coordinate system.

bj.factorize(360)                  # {2: 3, 3: 2, 5: 1}
bj.divisors(12)                    # (1, 2, 3, 4, 6, 12)
bj.lattice_members(360, 10)        # (10, 20, 30, ..., 360)
bj.smallest_divisor_gte(360, 50)   # 60
bj.to_int({2: 3, 3: 2, 5: 1})     # 360

Vector arithmetic mirrors integer operations:

bj.vec_add({2: 1}, {3: 1})        # {2: 1, 3: 1}  — multiplication
bj.vec_sub({2: 2, 3: 1}, {2: 1})  # {2: 1, 3: 1}  — division
bj.vec_le({2: 1}, {2: 2, 3: 1})   # True           — divisibility
bj.vec_min({2: 3}, {2: 1, 5: 2})  # {2: 1}         — gcd
bj.vec_max({2: 3}, {2: 1, 5: 2})  # {2: 3, 5: 2}   — lcm

See docs/coordinates.md for the full API and the math behind it.

Bin width estimation

Every major method. All scalar methods take a 1-D array, return a float.

Method	Best for
auto	General default
freedman_diaconis	Unknown distribution, outliers
scott	Near-normal data
sturges	Small, near-normal
rice	Simple, no assumption
sqrt	Quick exploratory
doane	Skewed or multimodal
stone	Accuracy over speed
knuth	Optimal uniform bins
gcd_interval	Integer sequences, regular data
bayesian_blocks	Non-stationary event data (variable-width)

See docs/methods.md for formulas and usage guidance.

Grain estimation

bj.grain_from_orders(orders)                        # Freedman-Diaconis default
bj.grain_from_orders(orders, method="gcd_interval")  # exact for regular data
bj.suggest_cbin(grain=60, windows=[3600, 86400])     # → 60

Documentation

Doc	What it covers
Lattice geometry	LatticeGeometry, derivation logic, grain/cbin/horizon
Coordinates	Prime factorization, divisors, vector arithmetic
Methods	Bin width estimation formulas and guidance

Used by

SignalForge — multiscale signal analysis on the p-adic divisibility lattice. Binjamin provides the mathematical substrate; SignalForge provides signals, surfaces, and the exploration tools.

License

MIT