From 759c2c47781680d765da9467613adea66601b3cb Mon Sep 17 00:00:00 2001
From: RunasSudo <runassudo@yingtongli.me>
Date: Tue, 26 Dec 2023 19:18:38 +1100
Subject: [PATCH] turnbull: Use Illinois method rather than interval bisection
 for likelihood-ratio confidence intervals

27% speedup
NB: Regula falsi alone without Illinois adjustment was slower than interval bisection
---
 src/root_finding.rs | 45 ++++++++++++++++++++++++++++++++++++---------
 src/turnbull.rs     | 10 +++++-----
 2 files changed, 41 insertions(+), 14 deletions(-)

diff --git a/src/root_finding.rs b/src/root_finding.rs
index 99c10d4..d712b14 100644
--- a/src/root_finding.rs
+++ b/src/root_finding.rs
@@ -14,48 +14,75 @@
 // You should have received a copy of the GNU Affero General Public License
 // along with this program.  If not, see <https://www.gnu.org/licenses/>.
 
-pub struct BisectionRootFinder {
+pub struct IllinoisRootFinder {
 	bound_lower: f64,
 	bound_upper: f64,
 	value_lower: f64,
-	value_upper: f64
+	value_upper: f64,
+	last_sign: f64  // Sign of the function at last evaluation (1.0 or -1.0) or 0.0 if first iteration
 }
 
-impl BisectionRootFinder {
-	pub fn new(bound_lower: f64, bound_upper: f64, value_lower: f64, value_upper: f64,) -> BisectionRootFinder {
-		return BisectionRootFinder {
+impl IllinoisRootFinder {
+	pub fn new(bound_lower: f64, bound_upper: f64, value_lower: f64, value_upper: f64) -> IllinoisRootFinder {
+		return IllinoisRootFinder {
 			bound_lower: bound_lower,
 			bound_upper: bound_upper,
 			value_lower: value_lower,
-			value_upper: value_upper
+			value_upper: value_upper,
+			last_sign: 0.0
 		}
 	}
 	
-	pub fn update(&mut self, guess: f64, value: f64) {
+	pub fn update(&mut self, guess: f64, mut value: f64) {
 		if value > 0.0 {
 			if self.value_lower > 0.0 || self.value_upper < 0.0 {
 				self.bound_lower = guess;
 				self.value_lower = value;
+				
+				if self.last_sign == 1.0 {
+					// Illinois adjustment: Halve the y-value of the retained end point (the other end point) when the new y-value has the same sign as the previous one
+					self.value_upper *= 0.5;
+				}
 			} else {
 				self.bound_upper = guess;
 				self.value_upper = value;
+				
+				if self.last_sign == 1.0 {
+					self.value_lower *= 0.5;
+				}
 			}
+			self.last_sign = 1.0;
 		} else {
 			if self.value_lower < 0.0 || self.value_upper > 0.0 {
 				self.bound_lower = guess;
 				self.value_lower = value;
+				
+				if self.last_sign == -1.0 {
+					self.value_upper *= 0.5;
+				}
 			} else {
 				self.bound_upper = guess;
 				self.value_upper = value;
+				
+				if self.last_sign == -1.0 {
+					self.value_lower *= 0.5;
+				}
 			}
+			self.last_sign = -1.0;
 		}
 	}
 	
 	pub fn next_guess(&self) -> f64 {
-		return (self.bound_lower + self.bound_upper) / 2.0;
+		if self.value_lower.is_nan() || self.value_upper.is_nan() {
+			// Fall back to interval bisection
+			return (self.bound_lower + self.bound_upper) / 2.0;
+		} else {
+			// Regula falsi
+			return (self.bound_lower * self.value_upper - self.bound_upper * self.value_lower) / (self.value_upper - self.value_lower);
+		}
 	}
 	
 	pub fn precision(&self) -> f64 {
-		return self.bound_upper - self.bound_lower;
+		return (self.bound_upper - self.bound_lower).abs();
 	}
 }
diff --git a/src/turnbull.rs b/src/turnbull.rs
index 3b71566..3c32b61 100644
--- a/src/turnbull.rs
+++ b/src/turnbull.rs
@@ -29,7 +29,7 @@ use serde::{Serialize, Deserialize};
 
 use crate::csv::read_csv;
 use crate::pava::monotonic_regression_pava;
-use crate::root_finding::BisectionRootFinder;
+use crate::root_finding::IllinoisRootFinder;
 use crate::term::UnconditionalTermLike;
 
 #[derive(Args)]
@@ -622,7 +622,7 @@ fn compute_hessian(data: &TurnbullData, p: &Vec<f64>) -> DMatrix<f64> {
 
 fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: ProgressBar, max_iterations: u32, ll_tolerance: f64, ci_precision: f64, p: &Vec<f64>, ll_model: f64, s: &Vec<f64>, oim_se: &Vec<f64>, time_index: usize) -> (f64, f64) {
 	// Compute lower confidence limit
-	let mut root_finder = BisectionRootFinder::new(
+	let mut root_finder = IllinoisRootFinder::new(
 		0.0, s[time_index],
 		f64::NAN, -CHI2_1DF_95  // Value of (lr_statistic - CHI2_1DF_95), which we are seeking the roots of
 	);
@@ -660,14 +660,14 @@ fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: Progress
 	let ci_lower = ci_estimate;
 	
 	// Compute upper confidence limit
-	root_finder = BisectionRootFinder::new(
+	root_finder = IllinoisRootFinder::new(
 		s[time_index], 1.0,
-		-CHI2_1DF_95, f64::NAN
+		-CHI2_1DF_95, f64::NAN  // Value of (lr_statistic - CHI2_1DF_95), which we are seeking the roots of
 	);
 	
 	ci_estimate = s[time_index] + Z_97_5 * oim_se[time_index - 1];
 	if ci_estimate > 1.0 {
-		ci_estimate = root_finder.next_guess();
+		ci_estimate = root_finder.next_guess();  // Returns interval midpoint in this case
 	}
 	
 	let mut iteration = 1;