From 2424aa6d7284cb9e40057bb92d22857967baaa65 Mon Sep 17 00:00:00 2001
From: Sibo Wang-Chen <sibo.wang@epfl.ch>
Date: Mon, 27 Jul 2026 13:57:50 +0200
Subject: [PATCH] reuse preallocated buffer for \delta x solution in Cholesky
 solver

---
 benchmark/plot/results/comparison-2d.svg | 528 ++++++++-------
 benchmark/plot/results/comparison.svg    | 782 +++++++++++------------
 benchmark/plot/results/scaling.svg       |  64 +-
 src/solver.rs                            |  16 +-
 4 files changed, 672 insertions(+), 718 deletions(-)

diff --git a/benchmark/plot/results/comparison-2d.svg b/benchmark/plot/results/comparison-2d.svg
index ae14701..c225da5 100644
--- a/benchmark/plot/results/comparison-2d.svg
+++ b/benchmark/plot/results/comparison-2d.svg
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index 83962b8..70e7b8b 100644
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+    <text style="font-size: 10px; font-family: 'Open Sans', '-apple-system', 'BlinkMacSystemFont', 'Helvetica', 'Arial', 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Avant Garde', sans-serif; text-anchor: start" x="231.916298" y="144.804265" transform="rotate(-0 231.916298 144.804265)">3.46x</text>
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+    <text style="font-size: 10px; font-family: 'Open Sans', '-apple-system', 'BlinkMacSystemFont', 'Helvetica', 'Arial', 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Avant Garde', sans-serif; text-anchor: start" x="311.607211" y="101.953761" transform="rotate(-0 311.607211 101.953761)">6.76x</text>
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+    <text style="font-size: 10px; font-family: 'Open Sans', '-apple-system', 'BlinkMacSystemFont', 'Helvetica', 'Arial', 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Avant Garde', sans-serif; text-anchor: start" x="391.298124" y="94.706513" transform="rotate(-0 391.298124 94.706513)">7.57x</text>
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@@ -237,7 +237,7 @@ L 70.596289 60.832813
 L 80.596289 60.832813 
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      <g>
-      <use xlink:href="#mc76b5f6fed" x="70.596289" y="60.832813" style="fill: #4051b5; stroke: #4051b5"/>
+      <use xlink:href="#m897e18e8a6" x="70.596289" y="60.832813" style="fill: #4051b5; stroke: #4051b5"/>
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@@ -247,7 +247,7 @@ L 80.596289 60.832813
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  </g>
  <defs>
-  <clipPath id="p2a7bf0b2c6">
+  <clipPath id="p20b142b52a">
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  </defs>
diff --git a/src/solver.rs b/src/solver.rs
index 5190fcc..39f534c 100644
--- a/src/solver.rs
+++ b/src/solver.rs
@@ -79,6 +79,9 @@ pub struct Solver<M: Mapper3Dto2D = NoMapper> {
     joint_weight_scalers: Vec<f32>,
     jtj: DMatrix<f32>,
     jtr: DVector<f32>,
+    /// Gauss-Newton update step, reused across iterations and solved into in
+    /// place by `Cholesky::solve_mut` to avoid a per-iteration allocation.
+    delta: DVector<f32>,
     /// Per-keypoint Jacobian buffer in compact form: shape is 3 x state_dim,
     /// but nonzero columns are moved to the left, and the rest is ignored.
     jacobian_buffer: DMatrix<f32>,
@@ -114,6 +117,7 @@ impl<M: Mapper3Dto2D> Solver<M> {
             joint_weight_scalers,
             jtj: DMatrix::zeros(state_dim, state_dim),
             jtr: DVector::zeros(state_dim),
+            delta: DVector::zeros(state_dim),
             jacobian_buffer: DMatrix::zeros(3, state_dim),
             jacobian_2d_buffer: DMatrix::zeros(2, state_dim),
             config,
@@ -203,11 +207,11 @@ impl<M: Mapper3Dto2D> Solver<M> {
             // contains garbage value after decomposition. But this is fine
             // because jtj is zeroed at the start of each solver iteration.
             let jtj_owned = std::mem::replace(&mut self.jtj, DMatrix::zeros(0, 0));
-            let delta = match nalgebra::linalg::Cholesky::new(jtj_owned) {
+            match nalgebra::linalg::Cholesky::new(jtj_owned) {
                 Some(chol) => {
-                    let delta = chol.solve(&self.jtr);
+                    self.delta.copy_from(&self.jtr);
+                    chol.solve_mut(&mut self.delta);
                     self.jtj = chol.unpack();
-                    delta
                 }
                 None => {
                     // Not positive-definite (numerically unstable): no
@@ -215,12 +219,12 @@ impl<M: Mapper3Dto2D> Solver<M> {
                     // is observed (even if some are observed, the root might
                     // be underconstrained and matches the targets exactly).
                     self.jtj = DMatrix::zeros(state_dim, state_dim);
-                    DVector::zeros(state_dim)
+                    self.delta.as_mut_slice().fill(0.0);
                 }
             };
-            state.apply_delta(&delta);
+            state.apply_delta(&self.delta);
 
-            if self.has_converged(&delta) {
+            if self.has_converged(&self.delta) {
                 break;
             }
         }