Port the Irisawa hexlet test to Rust
In the process, notice that the tolerance scale adjustment was ported wrong, and correct it.
This commit is contained in:
Aaron Fenyes
parent
9fe03264ab
commit
9f8632efb3
@ -3,5 +3,6 @@
|
||||
# https://jonalmeida.com/posts/2015/01/23/print-cargo/
|
||||
#
|
||||
|
||||
cargo test -- --nocapture engine::tests::irisawa_hexlet_test
|
||||
cargo test -- --nocapture engine::tests::three_spheres_example
|
||||
cargo test -- --nocapture engine::tests::point_on_sphere_example
|
||||
|
||||
@ -37,7 +37,7 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
|
||||
|
||||
struct MatrixEntry {
|
||||
index: (usize, usize),
|
||||
val: f64
|
||||
value: f64
|
||||
}
|
||||
|
||||
struct PartialMatrix(Vec<MatrixEntry>);
|
||||
@ -56,7 +56,7 @@ impl PartialMatrix {
|
||||
let mut result = DMatrix::<f64>::zeros(rhs.nrows(), rhs.ncols());
|
||||
let PartialMatrix(entries) = self;
|
||||
for ent in entries {
|
||||
result[ent.index] = ent.val - rhs[ent.index];
|
||||
result[ent.index] = ent.value - rhs[ent.index];
|
||||
}
|
||||
result
|
||||
}
|
||||
@ -141,7 +141,7 @@ fn realize_gram(
|
||||
let total_dim = element_dim * assembly_dim;
|
||||
|
||||
// scale the tolerance
|
||||
let scale_adjustment = ((guess.ncols() - frozen.len()) as f64).sqrt();
|
||||
let scale_adjustment = (gram.0.len() as f64).sqrt();
|
||||
let tol = scale_adjustment * scaled_tol;
|
||||
|
||||
// convert the frozen indices to stacked format
|
||||
@ -153,8 +153,8 @@ fn realize_gram(
|
||||
let mut state = SearchState::from_config(gram, guess);
|
||||
for _ in 0..max_descent_steps {
|
||||
// stop if the loss is tolerably low
|
||||
println!("loss: {}", state.loss);
|
||||
/*println!("projected error: {}", state.err_proj);*/
|
||||
println!("scaled loss: {}", state.loss / scale_adjustment);
|
||||
/* println!("projected error: {}", state.err_proj); */
|
||||
if state.loss < tol { break; }
|
||||
|
||||
// find the negative gradient of the loss function
|
||||
@ -182,6 +182,7 @@ fn realize_gram(
|
||||
|
||||
// regularize the Hessian
|
||||
let min_eigval = hess.symmetric_eigenvalues().min();
|
||||
/* println!("lowest eigenvalue: {}", min_eigval); */
|
||||
if min_eigval <= 0.0 {
|
||||
hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
|
||||
}
|
||||
@ -198,6 +199,12 @@ fn realize_gram(
|
||||
}
|
||||
|
||||
// compute the Newton step
|
||||
/*
|
||||
we need to either handle or eliminate the case where the minimum
|
||||
eigenvalue of the Hessian is zero, so the regularized Hessian is
|
||||
singular. right now, this causes the Cholesky decomposition to return
|
||||
`None`, leading to a panic when we unrap
|
||||
*/
|
||||
let base_step_stacked = hess.cholesky().unwrap().solve(&neg_grad_stacked);
|
||||
let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
|
||||
|
||||
@ -217,17 +224,17 @@ fn realize_gram(
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use std::f64;
|
||||
use std::{array, f64::consts::PI};
|
||||
|
||||
use super::*;
|
||||
|
||||
#[test]
|
||||
fn sub_proj_test() {
|
||||
let target = PartialMatrix(vec![
|
||||
MatrixEntry { index: (0, 0), val: 19.0 },
|
||||
MatrixEntry { index: (0, 2), val: 39.0 },
|
||||
MatrixEntry { index: (1, 1), val: 59.0 },
|
||||
MatrixEntry { index: (1, 2), val: 69.0 }
|
||||
MatrixEntry { index: (0, 0), value: 19.0 },
|
||||
MatrixEntry { index: (0, 2), value: 39.0 },
|
||||
MatrixEntry { index: (1, 1), value: 59.0 },
|
||||
MatrixEntry { index: (1, 2), value: 69.0 }
|
||||
]);
|
||||
let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
|
||||
1.0, 2.0, 3.0,
|
||||
@ -248,7 +255,7 @@ mod tests {
|
||||
for k in 0..3 {
|
||||
entries.push(MatrixEntry {
|
||||
index: (j, k),
|
||||
val: if j == k { 1.0 } else { -1.0 }
|
||||
value: if j == k { 1.0 } else { -1.0 }
|
||||
});
|
||||
}
|
||||
}
|
||||
@ -266,6 +273,88 @@ mod tests {
|
||||
assert!(state.loss.abs() < f64::EPSILON);
|
||||
}
|
||||
|
||||
// this problem is from a sangaku by Irisawa Shintarō Hiroatsu. the article
|
||||
// below includes a nice translation of the problem statement, which was
|
||||
// recorded in Uchida Itsumi's book _Kokon sankan_ (_Mathematics, Past and
|
||||
// Present_)
|
||||
//
|
||||
// "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki
|
||||
// https://www.nippon.com/en/japan-topics/c12801/
|
||||
//
|
||||
#[test]
|
||||
fn irisawa_hexlet_test() {
|
||||
let gram = PartialMatrix({
|
||||
let mut entries = Vec::<MatrixEntry>::new();
|
||||
for s in 0..9 {
|
||||
// each sphere is represented by a spacelike vector
|
||||
entries.push(MatrixEntry { index: (s, s), value: 1.0 });
|
||||
|
||||
// the circumscribing sphere is tangent to all of the other
|
||||
// spheres, with matching orientation
|
||||
if s > 0 {
|
||||
entries.push(MatrixEntry { index: (0, s), value: 1.0 });
|
||||
entries.push(MatrixEntry { index: (s, 0), value: 1.0 });
|
||||
}
|
||||
|
||||
if s > 2 {
|
||||
// each chain sphere is tangent to the "sun" and "moon"
|
||||
// spheres, with opposing orientation
|
||||
for n in 1..3 {
|
||||
entries.push(MatrixEntry { index: (s, n), value: -1.0 });
|
||||
entries.push(MatrixEntry { index: (n, s), value: -1.0 });
|
||||
}
|
||||
|
||||
// each chain sphere is tangent to the next chain sphere,
|
||||
// with opposing orientation
|
||||
let s_next = 3 + (s-2) % 6;
|
||||
entries.push(MatrixEntry { index: (s, s_next), value: -1.0 });
|
||||
entries.push(MatrixEntry { index: (s_next, s), value: -1.0 });
|
||||
}
|
||||
}
|
||||
entries
|
||||
});
|
||||
let guess = DMatrix::from_columns(
|
||||
[
|
||||
sphere(0.0, 0.0, 0.0, 15.0),
|
||||
sphere(0.0, 0.0, -9.0, 5.0),
|
||||
sphere(0.0, 0.0, 11.0, 3.0)
|
||||
].into_iter().chain(
|
||||
(1..=6).map(
|
||||
|k| {
|
||||
let ang = (k as f64) * PI/3.0;
|
||||
sphere(9.0 * ang.cos(), 9.0 * ang.sin(), 0.0, 2.5)
|
||||
}
|
||||
)
|
||||
).collect::<Vec<_>>().as_slice()
|
||||
);
|
||||
let frozen: [(usize, usize); 4] = array::from_fn(|k| (3, k));
|
||||
const SCALED_TOL: f64 = 1.0e-12;
|
||||
let (config, success) = realize_gram(
|
||||
&gram, guess, &frozen,
|
||||
SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
|
||||
);
|
||||
print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
|
||||
let final_state = SearchState::from_config(&gram, config);
|
||||
if success {
|
||||
println!("Target accuracy achieved!");
|
||||
} else {
|
||||
println!("Failed to reach target accuracy");
|
||||
}
|
||||
println!("Loss: {}", final_state.loss);
|
||||
if success {
|
||||
println!("\nChain diameters:");
|
||||
println!(" {} sun (given)", 1.0 / final_state.config[(3, 3)]);
|
||||
for k in 4..9 {
|
||||
println!(" {} sun", 1.0 / final_state.config[(3, k)]);
|
||||
}
|
||||
}
|
||||
let entry_tol = SCALED_TOL.sqrt();
|
||||
let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
|
||||
for (k, diam) in solution_diams.into_iter().enumerate() {
|
||||
assert!((final_state.config[(3, k)] - 1.0 / diam).abs() < entry_tol);
|
||||
}
|
||||
}
|
||||
|
||||
// --- process inspection examples ---
|
||||
|
||||
// these tests are meant for human inspection, not automated use. run them
|
||||
@ -281,7 +370,7 @@ mod tests {
|
||||
for k in 0..3 {
|
||||
entries.push(MatrixEntry {
|
||||
index: (j, k),
|
||||
val: if j == k { 1.0 } else { -1.0 }
|
||||
value: if j == k { 1.0 } else { -1.0 }
|
||||
});
|
||||
}
|
||||
}
|
||||
@ -318,7 +407,7 @@ mod tests {
|
||||
for k in 0..2 {
|
||||
entries.push(MatrixEntry {
|
||||
index: (j, k),
|
||||
val: if (j, k) == (1, 1) { 1.0 } else { 0.0 }
|
||||
value: if (j, k) == (1, 1) { 1.0 } else { 0.0 }
|
||||
});
|
||||
}
|
||||
}
|
||||
@ -328,9 +417,10 @@ mod tests {
|
||||
point(0.0, 0.0, 2.0),
|
||||
sphere(0.0, 0.0, 0.0, 1.0)
|
||||
]);
|
||||
let frozen = [(3, 0)];
|
||||
println!();
|
||||
let (config, success) = realize_gram(
|
||||
&gram, guess, &[(3, 0)],
|
||||
&gram, guess, &frozen,
|
||||
1.0e-12, 0.5, 0.9, 1.1, 200, 110
|
||||
);
|
||||
print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
|
||||
|
||||
Loading…
Reference in New Issue
Block a user