alice/groups/
gl.rs

1use alloc::vec::Vec;
2use core::marker::PhantomData;
3use crate::core::ops::{Group, Magma, Monoid, Semigroup, TopologicalGroup};
4use crate::groups::matrix_group::{GroupError, MatrixGroup};
5use crate::topology::manifold::{Atlas, Dim, Manifold};
6use crate::core::scalar::FiniteF64;
7use crate::maps::exp_log::HasExpMap;
8
9#[derive(Debug, Clone, PartialEq, Eq)]
10pub struct Gl<D: Dim> {
11    inner: MatrixGroup,
12    _dim: PhantomData<D>,
13}
14
15#[derive(Debug, Clone, PartialEq, Eq)]
16pub struct GlAlgebra<D: Dim> {
17    inner: MatrixGroup,
18    _dim: PhantomData<D>,
19}
20
21impl<D: Dim> Gl<D> {
22    pub fn new(data: Vec<f64>, dim: D) -> Result<Self, GroupError> {
23        let n = dim.value();
24        let inner = MatrixGroup::new(data, n)?;
25        if libm::fabs(inner.det()) < 1e-14 {
26            return Err(GroupError::ConstraintViolated("matrix must be invertible"));
27        }
28        Ok(Self { inner, _dim: PhantomData })
29    }
30
31    pub fn identity(dim: D) -> Self {
32        Self { inner: MatrixGroup::identity(dim.value()), _dim: PhantomData }
33    }
34
35    pub fn n(&self) -> usize { self.inner.n() }
36    pub fn data(&self) -> Vec<f64> { self.inner.data() }
37    pub fn det(&self) -> f64 { self.inner.det() }
38}
39
40impl<D: Dim> GlAlgebra<D> {
41    pub fn new(data: Vec<f64>, dim: D) -> Result<Self, GroupError> {
42        let inner = MatrixGroup::new(data, dim.value())?;
43        Ok(Self { inner, _dim: PhantomData })
44    }
45
46    pub fn zero(dim: D) -> Self {
47        Self {
48            inner: MatrixGroup::new(alloc::vec![0.0; dim.value() * dim.value()], dim.value()).unwrap(),
49            _dim: PhantomData,
50        }
51    }
52
53    pub fn data(&self) -> Vec<f64> { self.inner.data() }
54    pub fn n(&self) -> usize { self.inner.n() }
55}
56
57impl<D: Dim> Magma for Gl<D> {
58    fn op(&self, other: &Self) -> Self {
59        Self {
60            inner: self.inner.mul(&other.inner).expect("GL multiplication must succeed"),
61            _dim: PhantomData,
62        }
63    }
64}
65
66impl<D: Dim> Semigroup for Gl<D> {}
67
68impl<D: Dim> Monoid for Gl<D> {
69    fn identity() -> Self {
70        panic!("GL identity requires dimension; use Gl::identity(dim)")
71    }
72}
73
74impl<D: Dim> Group for Gl<D> {
75    fn inverse(&self) -> Self {
76        Self {
77            inner: self.inner.inverse().expect("GL element must be invertible"),
78            _dim: PhantomData,
79        }
80    }
81}
82
83impl<D: Dim> TopologicalGroup for Gl<D> {}
84
85impl<D: Dim> Manifold for Gl<D> {
86    type Scalar = FiniteF64;
87    fn dim(&self) -> usize { self.inner.n() * self.inner.n() }
88    fn atlas(&self) -> &Atlas<FiniteF64> { unimplemented!("GL atlas not yet constructed") }
89}
90
91impl<D: Dim> HasExpMap for Gl<D> {
92    type Algebra = GlAlgebra<D>;
93    fn exp(x: &GlAlgebra<D>) -> Self {
94        Self { inner: x.inner.exp(), _dim: PhantomData }
95    }
96    fn log(&self) -> Option<GlAlgebra<D>> {
97        Some(GlAlgebra { inner: self.inner.log()?, _dim: PhantomData })
98    }
99}
alice/groups/gl.rs

alice/groups/
gl.rs
