225 lines
6.1 KiB
Rust
225 lines
6.1 KiB
Rust
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use nalgebra::DMatrix;
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pub fn extended_gram_matrix(g: &DMatrix<f64>, faces: Vec<Vec<usize>>) -> DMatrix<f64> {
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let n = g.row_iter().len();
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let m = faces.len();
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let mut b = DMatrix::zeros(n, m);
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for i in 0..n {
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for j in 0..m {
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let n = faces[j][0];
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let x = i;
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let one = faces[j][1];
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let two = faces[j][2];
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b[(i, j)] = (1.0
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- g[(n, x)].powi(2)
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- (g[(one, x)] + g[(n, x)]) / (1.0 - g[(two, n)])
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* (g[(two, n)] * g[(n, x)]
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- g[(two, n)] * g[(one, x)]
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- g[(one, x)]
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- g[(n, x)]
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- 2.0 * g[(two, x)]))
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.sqrt();
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}
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}
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let d = b.transpose()
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* g.clone()
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.pseudo_inverse(1e-8)
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.expect("Invalid gram matrix!")
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* &b;
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let mut gext = DMatrix::zeros(n + m, n + m);
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for i in 0..n + m {
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for j in 0..n + m {
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if i < n && j < n {
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gext[(i, j)] = g[(i, j)];
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} else if i < n && j >= n {
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gext[(i, j)] = b[(i, j - n)];
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} else if i >= n && j < n {
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gext[(i, j)] = b[(j, i - n)];
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} else {
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gext[(i, j)] = d[(i - n, j - n)];
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}
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}
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}
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gext
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}
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fn invert_matrix(bt: f64, b: f64, h1: f64, h2: f64) -> DMatrix<f64> {
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DMatrix::from_row_slice(
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4,
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4,
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&[
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h1 * h1 + h2 * h2,
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bt * bt,
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-2.0 * h1 * bt,
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-2.0 * h2 * bt,
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b * b,
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h1 * h1 + h2 * h2,
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-2.0 * b * h1,
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-2.0 * b * h2,
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b * h1,
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h1 * bt,
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1.0 - 2.0 * h1 * h1,
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-2.0 * h1 * h2,
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b * h2,
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h2 * bt,
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-2.0 * h1 * h2,
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1.0 - 2.0 * h2 * h2,
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],
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)
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}
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pub fn root_tuple(g: &DMatrix<f64>, face: (usize, usize, usize), invert: usize) -> DMatrix<f64> {
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let (c1, c2, c3) = face;
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let n = g.row_iter().len();
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let mut c = DMatrix::zeros(4, n);
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c[(0, c1)] = 2.0;
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c[(1, c1)] = 0.0;
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c[(2, c1)] = 0.0;
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c[(3, c1)] = 1.0;
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c[(0, c2)] = 0.0;
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c[(1, c2)] = 0.0;
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c[(2, c2)] = 0.0;
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c[(3, c2)] = -1.0;
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c[(0, c3)] = (1.0 - g[(c2, c3)].powi(2)) / (g[(c1, c3)] + g[(c2, c3)]);
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c[(1, c3)] = -g[(c1, c3)] - g[(c2, c3)];
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c[(2, c3)] = 0.0;
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c[(3, c3)] = -g[(c2, c3)];
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let a13 = g[(c1, c3)];
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let a23 = g[(c2, c3)];
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for i in 0..n {
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if i != c1 && i != c2 && i != c3 {
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let a1 = g[(i, c1)];
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let a2 = g[(i, c2)];
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let a3 = g[(i, c3)];
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// b-tilde
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c[(0, i)] = (a1 * (-1.0 + a23 * a23) - a2 * (1.0 + 2.0 * a13 * a23 + a23 * a23)
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+ 2.0 * (a13 + a23) * a3)
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/ (a13 + a23).powi(2);
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// b
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c[(1, i)] = -a1 - a2;
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// h1 (positive solution)
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c[(2, i)] = (a2 * a2 - a13 * a13 * (-1.0 + a2 * a2) + a23 * a23
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- a1 * a1 * (-1.0 + a23 * a23)
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- 2.0 * a2 * a23 * a3
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+ 2.0 * a13 * (a23 - a2 * a3)
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+ 2.0 * a1 * (a2 + a13 * a2 * a23 - (a13 + a23) * a3))
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.sqrt()
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/ (a13 + a23).abs();
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// h2
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c[(3, i)] = -a2;
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}
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}
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println!("{}", c);
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let newc = invert_matrix(
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c[(0, invert)],
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c[(1, invert)],
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c[(2, invert)],
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c[(3, invert)],
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) * &c;
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println!("{}", newc);
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newc
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}
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pub fn algebraic_generators(g: DMatrix<f64>) -> Vec<DMatrix<f64>> {
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}
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#[cfg(test)]
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#[rustfmt::skip]
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mod tests {
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use super::{root_tuple, extended_gram_matrix};
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use nalgebra::DMatrix;
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#[test]
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fn extended_gram_matrix_test() {
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let g = DMatrix::from_row_slice(4, 4,
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&[
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1.0, -1.0, -1.0, -1.0,
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-1.0, 1.0, -1.0, -1.0,
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-1.0, -1.0, 1.0, -1.0,
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-1.0, -1.0, -1.0, 1.0,
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],
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);
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assert_ne!(
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extended_gram_matrix(
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&g,
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vec![vec![0, 1, 2], vec![0, 1, 3], vec![0, 2, 3], vec![1, 2, 3]]
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),
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DMatrix::from_row_slice(8, 8,
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&[
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1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 2.0,
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-1.0, 1.0, -1.0, -1.0, 0.0, 2.0, 0.0, 0.0,
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-1.0, -1.0, 1.0, -1.0, 0.0, 0.0, 2.0, 0.0,
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-1.0, -1.0, -1.0, 1.0, 2.0, 0.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 2.0, 1.0, -1.0, -1.0, -1.0,
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0.0, 2.0, 0.0, 0.0, -1.0, 1.0, -1.0, -1.0,
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0.0, 0.0, 2.0, 0.0, -1.0, -1.0, 1.0, -1.0,
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2.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0, 1.0,
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])
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);
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let octahedron = DMatrix::from_row_slice(6, 6,
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&[
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1.0, -1.0, -1.0, -1.0, -3.0, -1.0,
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-1.0, 1.0, -1.0, -1.0, -1.0, -3.0,
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-1.0, -1.0, 1.0, -3.0, -1.0, -1.0,
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-1.0, -1.0, -3.0, 1.0, -1.0, -1.0,
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-3.0, -1.0, -1.0, -1.0, 1.0, -1.0,
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-1.0, -3.0, -1.0, -1.0, -1.0, 1.0,
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],
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);
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assert_ne!(
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extended_gram_matrix(
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&octahedron,
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vec![
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vec![0, 1, 3],
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vec![0, 2, 1],
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vec![0, 3, 5],
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vec![0, 5, 2],
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vec![1, 2, 4],
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vec![1, 4, 3],
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vec![2, 5, 4],
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vec![3, 4, 5],
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]
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),
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g
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);
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}
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#[test]
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fn root_tuple_test() {
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let octahedron = DMatrix::from_row_slice(6, 6,
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&[
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1.0, -1.0, -1.0, -1.0, -3.0, -1.0,
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-1.0, 1.0, -1.0, -1.0, -1.0, -3.0,
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-1.0, -1.0, 1.0, -3.0, -1.0, -1.0,
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-1.0, -1.0, -3.0, 1.0, -1.0, -1.0,
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-3.0, -1.0, -1.0, -1.0, 1.0, -1.0,
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-1.0, -3.0, -1.0, -1.0, -1.0, 1.0,
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],
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);
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assert_eq!(
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root_tuple(&octahedron, (0, 1, 3), 2),
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octahedron,
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);
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}
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}
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