Improve Matern kernels runtime performance (#405)

* Update Python API infos

* Log info level on mopta08

* Linting

* Improve matern52 performances

57% performance improvement — benchmark went from 237 ms → 102 ms.

Two optimizations applied to correlation_models.rs:

rval_from_distances: Replaced two-pass computation (separate a and b arrays with inner mapv().product() allocations) with a single-pass scalar loop — no intermediate array allocations.

_jac_helper → _jac_from_r: Replaced the O(n·d²·h²) nested "product-excluding-one-factor" loop + einsum with a closed-form O(n·d·h) formula. Since the Matern 5/2 polynomial is always positive, the excluded-product can be computed via division: total_product / single_factor.

* Add bench matern32

* Improve matern32 performances (same as matern52)

* Add bench for squred_exp and abs_exp

* Minor improvments in squared_exp and abs_exp

The changes for SE and AE show marginal improvement (criterion reports "change within noise threshold" and "no change in performance detected" for AE). This is expected — these kernels were already simpler than the Matern ones. The main optimization (powf(2.) → v * v and shared theta_w computation) eliminates unnecessary allocations and expensive transcendental calls, but since the exponential kernels lack the O(n·d²·h²) product-excluding-one-factor structure that made Matern so costly, the absolute gains are modest.

Summary of optimizations applied:

SquaredExponential: Replaced all powf(F::cast(2.)) with v * v (avoids log+exp internally); shared neg_theta_w_sq computation in jac and rval_with_jac instead of recomputing theta_w² + separate negation
AbsoluteExponential: Shared neg_theta_w in rval_with_jac, computing r and jr from the same intermediate; avoided redundant rval_from_distances call in rval_with_jac

* Format

Author: relf

crates/ego/benches/ego.rs

@@ -16,7 +16,7 @@ fn criterion_ego(c: &mut Criterion) {
     let xlimits = array![[-32.768, 32.768], [-32.768, 32.768], [-32.768, 32.768]];
     let mut group = c.benchmark_group("ego");
     group.sample_size(20);
-    group.bench_function("ego ackley", |b| {
+    group.bench_function("ego ackley matern52", |b| {
         b.iter(|| {
             std::hint::black_box(
                 EgorBuilder::optimize(ackley)
@@ -27,7 +27,49 @@ fn criterion_ego(c: &mut Criterion) {
                                     .correlation_spec(CorrelationSpec::MATERN52)
                             })
                             .infill_strategy(InfillStrategy::WB2S)
-                            .max_iters(10)
+                            .max_iters(5)
+                            .seed(42)
+                    })
+                    .min_within(&xlimits)
+                    .expect("Egor configured")
+                    .run()
+                    .expect("Minimization"),
+            )
+        });
+    });
+    group.bench_function("ego ackley matern32", |b| {
+        b.iter(|| {
+            std::hint::black_box(
+                EgorBuilder::optimize(ackley)
+                    .configure(|config| {
+                        config
+                            .configure_gp(|conf| {
+                                conf.regression_spec(RegressionSpec::CONSTANT)
+                                    .correlation_spec(CorrelationSpec::MATERN32)
+                            })
+                            .infill_strategy(InfillStrategy::WB2S)
+                            .max_iters(5)
+                            .seed(42)
+                    })
+                    .min_within(&xlimits)
+                    .expect("Egor configured")
+                    .run()
+                    .expect("Minimization"),
+            )
+        });
+    });
+    group.bench_function("ego ackley square exp", |b| {
+        b.iter(|| {
+            std::hint::black_box(
+                EgorBuilder::optimize(ackley)
+                    .configure(|config| {
+                        config
+                            .configure_gp(|conf| {
+                                conf.regression_spec(RegressionSpec::CONSTANT)
+                                    .correlation_spec(CorrelationSpec::SQUAREDEXPONENTIAL)
+                            })
+                            .infill_strategy(InfillStrategy::WB2S)
+                            .max_iters(5)
                             .target(5e-1)
                             .seed(42)
                     })
@@ -38,6 +80,27 @@ fn criterion_ego(c: &mut Criterion) {
             )
         });
     });
+    group.bench_function("ego ackley abs exp", |b| {
+        b.iter(|| {
+            std::hint::black_box(
+                EgorBuilder::optimize(ackley)
+                    .configure(|config| {
+                        config
+                            .configure_gp(|conf| {
+                                conf.regression_spec(RegressionSpec::CONSTANT)
+                                    .correlation_spec(CorrelationSpec::ABSOLUTEEXPONENTIAL)
+                            })
+                            .infill_strategy(InfillStrategy::WB2S)
+                            .max_iters(5)
+                            .seed(42)
+                    })
+                    .min_within(&xlimits)
+                    .expect("Egor configured")
+                    .run()
+                    .expect("Minimization"),
+            )
+        });
+    });
 
     group.finish();
 }