Address PR review: improve cholesky comment and add upper=true test

- Reword THSTensor_cholesky comment to clarify we use the default
  lower-triangular form and conjugate-transpose for upper=true
- Add CholeskyUpperTest to validate upper=true path after migration
  from deprecated torch::cholesky to torch::linalg_cholesky

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: alinpahontu2912

src/Native/LibTorchSharp/THSLinearAlgebra.cpp

@@ -359,7 +359,8 @@ Tensor THSLinalg_lu_solve(const Tensor B, const Tensor LU, const Tensor pivots,
 Tensor THSTensor_cholesky(const Tensor tensor, const bool upper)
 {
     // torch::cholesky is deprecated in favor of torch::linalg_cholesky.
-    // linalg_cholesky always returns lower-triangular; use .mH() for upper.
+    // Here we call torch::linalg_cholesky with its default (lower-triangular) output,
+    // and return its conjugate transpose via .mH() when upper is true.
     CATCH_TENSOR(upper ? torch::linalg_cholesky(*tensor).mH() : torch::linalg_cholesky(*tensor))
 }
 

test/TorchSharpTest/LinearAlgebra.cs

@@ -305,6 +305,20 @@ public void CholeskyTest()
             Assert.True(a.allclose(l.matmul(l.swapaxes(-2, -1)))); // Worked this in to get it tested. Alias for 'transpose'
         }
 
+        [Fact]
+        [TestOf(nameof(Tensor.cholesky))]
+        public void CholeskyUpperTest()
+        {
+            var a = randn(new long[] { 3, 2, 2 }, float64);
+            a = a.matmul(a.swapdims(-2, -1));
+#pragma warning disable CS0618 // Obsolete
+            var u = a.cholesky(upper: true);
+#pragma warning restore CS0618
+
+            // U should be upper-triangular: U^T * U == A
+            Assert.True(a.allclose(u.swapaxes(-2, -1).matmul(u)));
+        }
+
         [Fact]
         [TestOf(nameof(linalg.cholesky_ex))]
         public void CholeskyExTest()