zima 0.1.0-alpha.0

An attempt to create a modern package for the needs of applied statistics
Documentation 
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use num_traits::Float;
use std::ops::{Add, Mul};

trait Vector:
    Add<Output = Self> +
    Mul<Self::Field, Output = Self> +
    Sized
{
    type Field: Float + Copy;
    fn zero() -> Self;
}

trait Metric<V>
where
    V: Vector,
{

    fn sqrt(&self) -> impl Vielbein<V>;
    fn dot(&self, v: V, w: V) -> V::Field;
    fn det(&self) -> V::Field;
    fn dvol(&self) -> V::Field
    where
        V::Field: Float,
    {
        self.det().sqrt()
    }

    fn norm(&self, v: V) -> V::Field
    where
        V: Copy,
        V::Field: Float,
    {
        self.dot(v, v).sqrt()
    }

    fn angle(&self, v: V, w: V) -> V::Field
    where
        V: Copy,
        V::Field: Float,
    {
        self.dot(v, w) / (self.norm(v) * self.norm(w))
    }
}

trait Sym<V>
where
    V: Vector,
{
    fn metric(&self) -> impl Metric<V>;
    fn otimes(v: V, w: V) -> Self;
}



trait Vielbein<V>
where
    V: Vector,
{
    ///  Induce metric
    fn metric(&self) -> impl Metric<V>;
}