Fix divide by zero error in eigvalsh3

diptorch/linalg.py

@@ -62,6 +62,7 @@ def eigvalsh3(
     jj: torch.Tensor,
     jk: torch.Tensor,
     kk: torch.Tensor,
+    eps: float = 1e-8,
 ) -> torch.Tensor:
     """
     Compute the eigenvalues of a batched Hermitian 3×3 tensor
@@ -70,14 +71,15 @@ def eigvalsh3(
     Returns eigenvalues in a tensor with shape [1 3 H W D]
     sorted in ascending order.
     """
-    q = (ii + jj + kk) / 3
-    p1 = torch.concat([ij, ik, jk], dim=1).square().sum(1, keepdim=True)
-    p2 = (torch.concat([ii, jj, kk], dim=1) - q).square().sum(
-        dim=1, keepdim=True
-    ) + 2 * p1
-    p = (p2 / 6).sqrt()
-
-    r = deth3(ii - q, ij, ik, jj - q, jk, kk - q) / p.pow(3) / 2
+    diag = torch.concat([ii, jj, kk], dim=1)
+    triu = torch.concat([ij, ik, jk], dim=1)
+
+    q = diag.sum(dim=1, keepdim=True) / 3
+    p1 = triu.square().sum(dim=1, keepdim=True)
+    p2 = (diag - q).square().sum(dim=1, keepdim=True)
+    p = ((2 * p1 + p2) / 6).sqrt()
+
+    r = deth3(ii - q, ij, ik, jj - q, jk, kk - q) / (p.pow(3) + eps) / 2
     r = r.clamp(-1, 1)
     phi = r.arccos() / 3
 

notebooks/01_linalg.ipynb

@@ -139,6 +139,7 @@
     "    jj: torch.Tensor,\n",
     "    jk: torch.Tensor,\n",
     "    kk: torch.Tensor,\n",
+    "    eps: float = 1e-8,\n",
     ") -> torch.Tensor:\n",
     "    \"\"\"\n",
     "    Compute the eigenvalues of a batched Hermitian 3×3 tensor\n",
@@ -147,12 +148,15 @@
     "    Returns eigenvalues in a tensor with shape [1 3 H W D]\n",
     "    sorted in ascending order.\n",
     "    \"\"\"\n",
-    "    q = (ii + jj + kk) / 3\n",
-    "    p1 = torch.concat([ij, ik, jk], dim=1).square().sum(1, keepdim=True)\n",
-    "    p2 = (torch.concat([ii, jj, kk], dim=1) - q).square().sum(dim=1, keepdim=True) + 2 * p1\n",
-    "    p = (p2 / 6).sqrt()\n",
+    "    diag = torch.concat([ii, jj, kk], dim=1)\n",
+    "    triu = torch.concat([ij, ik, jk], dim=1)\n",
+    "    \n",
+    "    q = diag.sum(dim=1, keepdim=True) / 3\n",
+    "    p1 = triu.square().sum(dim=1, keepdim=True)\n",
+    "    p2 = (diag - q).square().sum(dim=1, keepdim=True)\n",
+    "    p = ((2 * p1 + p2) / 6).sqrt()\n",
     "\n",
-    "    r = deth3(ii - q, ij, ik, jj - q, jk, kk - q) / p.pow(3) / 2\n",
+    "    r = deth3(ii - q, ij, ik, jj - q, jk, kk - q) / (p.pow(3) + eps) / 2\n",
     "    r = r.clamp(-1, 1)\n",
     "    phi = r.arccos() / 3\n",
     "\n",
@@ -220,11 +224,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "3.09 ms ± 157 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
+      "1.61 ms ± 14.8 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
      ]
     }
    ],
    "source": [
+    "# Time diptorch's implementation\n",
     "%timeit eigvalsh(A)"
    ]
   },
@@ -238,11 +243,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "46.7 ms ± 836 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+      "43.7 ms ± 40.7 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
      ]
     }
    ],
    "source": [
+    "# Time torch's implementation\n",
     "B = A.permute(0, -2, -1, 1, 2)\n",
     "%timeit torch.linalg.eigvalsh(B)"
    ]
@@ -276,11 +282,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "5.52 ms ± 51.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
+      "5.78 ms ± 11 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
      ]
     }
    ],
    "source": [
+    "# Time diptorch's implementation\n",
     "%timeit eigvalsh(A)"
    ]
   },
@@ -294,11 +301,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "98.2 ms ± 635 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+      "97.8 ms ± 766 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
      ]
     }
    ],
    "source": [
+    "# Time torch's implementation\n",
     "B = A.permute(0, -2, -1, 1, 2)\n",
     "%timeit torch.linalg.eigvalsh(B)"
    ]