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Record optimization history

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This commit is contained in:
Aaron Fenyes 2024-10-26 00:02:06 -07:00
parent 9f8632efb3
commit ce33bbf418
1 changed files with 69 additions and 25 deletions
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94
app-proto/src/engine.rs
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@ -62,6 +62,30 @@ impl PartialMatrix {
}
}
// --- descent history ---
struct DescentHistory {
config: Vec<DMatrix<f64>>,
scaled_loss: Vec<f64>,
neg_grad: Vec<DMatrix<f64>>,
min_eigval: Vec<f64>,
base_step: Vec<DMatrix<f64>>,
backoff_steps: Vec<i32>
}
impl DescentHistory {
fn new() -> DescentHistory {
DescentHistory {
config: Vec::<DMatrix<f64>>::new(),
scaled_loss: Vec::<f64>::new(),
neg_grad: Vec::<DMatrix<f64>>::new(),
min_eigval: Vec::<f64>::new(),
base_step: Vec::<DMatrix<f64>>::new(),
backoff_steps: Vec::<i32>::new(),
}
}
}
// --- gram matrix realization ---
// the Lorentz form
@ -108,14 +132,14 @@ fn seek_better_config(
min_efficiency: f64,
backoff: f64,
max_backoff_steps: i32
) -> Option<SearchState> {
) -> Option<(SearchState, i32)> {
let mut rate = 1.0;
for _ in 0..max_backoff_steps {
for backoff_steps in 0..max_backoff_steps {
let trial_config = &state.config + rate * base_step;
let trial_state = SearchState::from_config(gram, trial_config);
let improvement = state.loss - trial_state.loss;
if improvement >= min_efficiency * rate * base_target_improvement {
return Some(trial_state);
return Some((trial_state, backoff_steps));
}
rate *= backoff;
}
@ -134,7 +158,10 @@ fn realize_gram(
reg_scale: f64,
max_descent_steps: i32,
max_backoff_steps: i32
) -> (DMatrix<f64>, bool) {
) -> (DMatrix<f64>, bool, DescentHistory) {
// start the descent history
let mut history = DescentHistory::new();
// find the dimension of the search space
let element_dim = guess.nrows();
let assembly_dim = guess.ncols();
@ -153,13 +180,14 @@ 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!("scaled loss: {}", state.loss / scale_adjustment);
/* println!("projected error: {}", state.err_proj); */
history.config.push(state.config.clone());
history.scaled_loss.push(state.loss / scale_adjustment);
if state.loss < tol { break; }
// find the negative gradient of the loss function
let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
history.neg_grad.push(neg_grad.clone());
// find the negative Hessian of the loss function
let mut hess_cols = Vec::<DVector<f64>>::with_capacity(total_dim);
@ -182,10 +210,10 @@ 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);
}
history.min_eigval.push(min_eigval);
// project the negative gradient and negative Hessian onto the
// orthogonal complement of the frozen subspace
@ -207,17 +235,21 @@ fn realize_gram(
*/
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));
history.base_step.push(base_step.clone());
// use backtracking line search to find a better configuration
match seek_better_config(
gram, &state, &base_step, neg_grad.dot(&base_step),
min_efficiency, backoff, max_backoff_steps
) {
Some(better_state) => state = better_state,
None => return (state.config, false)
Some((better_state, backoff_steps)) => {
state = better_state;
history.backoff_steps.push(backoff_steps);
},
None => return (state.config, false, history)
};
}
(state.config, state.loss < tol)
(state.config, state.loss < tol, history)
}
// --- tests ---
@ -329,29 +361,33 @@ mod tests {
);
let frozen: [(usize, usize); 4] = array::from_fn(|k| (3, k));
const SCALED_TOL: f64 = 1.0e-12;
let (config, success) = realize_gram(
let (config, success, history) = realize_gram(
&gram, guess, &frozen,
SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
);
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!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
}
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);
println!("Steps: {}", history.scaled_loss.len() - 1);
println!("Loss: {}", history.scaled_loss.last().unwrap());
if success {
println!("\nChain diameters:");
println!(" {} sun (given)", 1.0 / final_state.config[(3, 3)]);
println!(" {} sun (given)", 1.0 / config[(3, 3)]);
for k in 4..9 {
println!(" {} sun", 1.0 / final_state.config[(3, k)]);
println!(" {} sun", 1.0 / 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);
println!("\nStep │ Loss\n─────┼────────────────────────────────");
for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
println!("{:<4} │ {}", step, scaled_loss);
}
}
@ -385,18 +421,22 @@ mod tests {
])
};
println!();
let (config, success) = realize_gram(
let (config, success, history) = realize_gram(
&gram, guess, &[],
1.0e-12, 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);
println!("Steps: {}", history.scaled_loss.len() - 1);
println!("Loss: {}", history.scaled_loss.last().unwrap());
println!("\nStep │ Loss\n─────┼────────────────────────────────");
for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
println!("{:<4} │ {}", step, scaled_loss);
}
}
#[test]
@ -419,18 +459,22 @@ mod tests {
]);
let frozen = [(3, 0)];
println!();
let (config, success) = realize_gram(
let (config, success, history) = realize_gram(
&gram, guess, &frozen,
1.0e-12, 0.5, 0.9, 1.1, 200, 110
);
print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
print!("Configuration:{}", 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);
println!("Steps: {}", history.scaled_loss.len() - 1);
println!("Loss: {}", history.scaled_loss.last().unwrap());
println!("\nStep │ Loss\n─────┼────────────────────────────────");
for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
println!("{:<4} │ {}", step, scaled_loss);
}
}
}