From 7e671657116b75010bcb2c9af4bae13b013ddfca Mon Sep 17 00:00:00 2001
From: Johan Larsson <johan@jolars.co>
Date: Thu, 27 Aug 2026 09:00:48 +0200
Subject: [PATCH] fix: center the dual before computing the gap

---
 objective.py            |  5 ++++-
 tests/conftest.py       |  5 +++++
 tests/test_objective.py | 15 +++++++++++++++
 3 files changed, 24 insertions(+), 1 deletion(-)
 create mode 100644 tests/conftest.py
 create mode 100644 tests/test_objective.py

diff --git a/objective.py b/objective.py
index b654eb0..b7bffad 100644
--- a/objective.py
+++ b/objective.py
@@ -47,7 +47,10 @@ def evaluate_result(self, beta):
         )
 
         # compute dual
-        theta = diff
+        theta = diff.copy()
+        if self.fit_intercept:
+            # An unpenalized intercept imposes sum(theta) = 0 in the dual.
+            theta -= np.mean(theta)
         theta /= max(1, self._dual_norm_slope(theta, self.alphas))
         d_obj = (norm(y) ** 2 - norm(y - theta * n_samples) ** 2) / (2 * n_samples)
 
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 0000000..26ab220
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,5 @@
+import sys
+from pathlib import Path
+
+
+sys.path.insert(0, str(Path(__file__).parents[1]))
diff --git a/tests/test_objective.py b/tests/test_objective.py
new file mode 100644
index 0000000..64ca9f3
--- /dev/null
+++ b/tests/test_objective.py
@@ -0,0 +1,15 @@
+import numpy as np
+
+from objective import Objective
+
+
+def test_intercept_dual_point_is_centered():
+    objective = Objective(fit_intercept=True)
+    objective.X = np.array([[-1.0], [1.0]])
+    objective.y = np.ones(2)
+    objective.alphas = np.ones(1)
+
+    result = objective.evaluate_result(beta=np.array([0.75, 0.0]))
+
+    np.testing.assert_allclose(result["duality_gap"], 0.03125)
+    assert result["duality_gap"] >= 0.0