Add determinant and sign-log-determinant functions to mlx.core.linalg (#3416)

Co-authored-by: Lucas Fernandes Martins <[email protected]>

tests/linalg_tests.cpp

@@ -637,3 +637,68 @@ TEST_CASE("test solve_triangluar") {
   expected = array({-3., 2., 3.});
   CHECK(allclose(expected, result).item<bool>());
 }
+
+TEST_CASE("test det") {
+  // 1x1 fast path
+  {
+    array a = array({5.0f}, {1, 1});
+    auto d = det(a, Device::cpu);
+    CHECK_EQ(d.item<float>(), doctest::Approx(5.0f));
+  }
+
+  // 2x2 fast path: det([[1,2],[3,4]]) = -2
+  {
+    array a = array({1.0f, 2.0f, 3.0f, 4.0f}, {2, 2});
+    auto d = det(a, Device::cpu);
+    CHECK_EQ(d.item<float>(), doctest::Approx(-2.0f));
+  }
+
+  // 3x3 fast path: det([[1,2,3],[0,1,4],[5,6,0]]) = 1
+  {
+    array a =
+        array({1.0f, 2.0f, 3.0f, 0.0f, 1.0f, 4.0f, 5.0f, 6.0f, 0.0f}, {3, 3});
+    auto d = det(a, Device::cpu);
+    CHECK_EQ(d.item<float>(), doctest::Approx(1.0f));
+  }
+
+  // 4x4 LU path: identity matrix det = 1
+  {
+    array a = eye(4);
+    auto d = det(a, Device::cpu);
+    CHECK_EQ(d.item<float>(), doctest::Approx(1.0f));
+  }
+
+  // Non-square should throw
+  CHECK_THROWS(
+      det(array({1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f}, {2, 3}), Device::cpu));
+
+  // 1D should throw
+  CHECK_THROWS(det(array({1.0f, 2.0f}), Device::cpu));
+}
+
+TEST_CASE("test slogdet") {
+  // 2x2: det = -2, so sign = -1, logabsdet = log(2)
+  {
+    array a = array({1.0f, 2.0f, 3.0f, 4.0f}, {2, 2});
+    auto [s, logabs] = slogdet(a, Device::cpu);
+    CHECK_EQ(s.item<float>(), doctest::Approx(-1.0f));
+    CHECK_EQ(logabs.item<float>(), doctest::Approx(std::log(2.0f)));
+  }
+
+  // Identity: sign = 1, logabsdet = 0
+  {
+    array a = eye(4);
+    auto [s, logabs] = slogdet(a, Device::cpu);
+    CHECK_EQ(s.item<float>(), doctest::Approx(1.0f));
+    CHECK_EQ(logabs.item<float>(), doctest::Approx(0.0f));
+  }
+
+  // Singular: sign = 0, logabsdet = -inf
+  {
+    array a = array({1.0f, 2.0f, 2.0f, 4.0f}, {2, 2});
+    auto [s, logabs] = slogdet(a, Device::cpu);
+    CHECK_EQ(s.item<float>(), 0.0f);
+    CHECK(std::isinf(logabs.item<float>()));
+    CHECK(logabs.item<float>() < 0);
+  }
+}