viva_math

viva_math - Mathematical foundations for VIVA’s sentient digital life.

A specialized math library for the BEAM, designed to sit between gleam_community_maths (primitives) and viva_tensor (tensors + NIF).

Modules

Foundations

• viva_math/scalar - Scalar math: erf, gelu, silu, mish, logsumexp…
• viva_math/constants - High-precision constants (pi, e, sqrt_2pi…)
• viva_math/common - Generic helpers: clamp, lerp, sigmoid, softmax

Geometry & linear algebra

• viva_math/vector - Vec3 (PAD emotional space) + ops
• viva_math/vec2 - 2-D vectors (polar, planar)
• viva_math/vec4 - 4-D vectors (RGBA, homogeneous, quaternions)
• viva_math/vecn - N-D vectors as List(Float)
• viva_math/matrix - Mat2, Mat3, Mat4 and generic MatN

Stochastic & inference

• viva_math/random - PRNG with opaque Seed (Erlang :rand backed)
• viva_math/statistics - mean, var, ema, percentile, correlation
• viva_math/distributions - gaussian/uniform/exponential/categorical
• viva_math/entropy - Shannon, KL, JS, Rényi, Tsallis, Fisher

Dynamical systems

• viva_math/cusp - Catastrophe theory (Thom)
• viva_math/free_energy - Friston FEP + active inference
• viva_math/attractor - Mehrabian PAD attractors + OU dynamics
• viva_math/ode - Euler / RK2 / RK4 / Euler-Maruyama / Milstein
• viva_math/calculus - Finite differences + Simpson / Romberg
• viva_math/scheduler - Cosine annealing, warmup, decay schedules

Quick start

import viva_math/scalar
import viva_math/vector
import viva_math/attractor
import viva_math/random

// PAD emotional state
let state = vector.pad(-0.3, 0.7, -0.2)

// Classify nearest emotion
let emotion = attractor.classify_emotion(state)
// -> "fear"

// Scalar activations for ML
let y = scalar.gelu(0.5)

// Seedable, reproducible normal sample
let seed = random.from_int(42)
let #(x, _) = random.normal(seed, 0.0, 1.0)

pub fn clamp_bipolar(x: Float) -> Float

pub fn classify(state: vector.Vec3) -> String

pub fn entropy(probabilities: List(Float)) -> Float

pub fn erf(x: Float) -> Float

pub fn free_energy(
  expected: vector.Vec3,
  actual: vector.Vec3,
) -> free_energy.FreeEnergyState

pub fn gelu(x: Float) -> Float

pub fn is_volatile(arousal: Float, dominance: Float) -> Bool

pub fn pad(
  pleasure: Float,
  arousal: Float,
  dominance: Float,
) -> vector.Vec3

pub fn sigmoid(x: Float) -> Float

pub const version: String