Add tests for the eigenvalue solvers

eigenvivek · Aug 8, 2024 · 3b1eec5 · 3b1eec5
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diff --git a/diptorch/linalg.py b/diptorch/linalg.py
@@ -84,7 +84,6 @@ def eigvalsh3(
     eig3 = q + 2 * p * phi.cos()
     eig1 = q + 2 * p * (phi + 2 * torch.pi / 3).cos()
     eig2 = 3 * q - eig1 - eig3
-    print(eig1.shape, eig2.shape, eig3.shape)
     return torch.concat([eig1, eig2, eig3], dim=1)
 
 # %% ../notebooks/01_linalg.ipynb 9

diff --git a/notebooks/01_linalg.ipynb b/notebooks/01_linalg.ipynb
@@ -159,7 +159,6 @@
     "    eig3 = q + 2 * p * phi.cos()\n",
     "    eig1 = q + 2 * p * (phi + 2 * torch.pi / 3).cos()\n",
     "    eig2 = 3 * q - eig1 - eig3\n",
-    "    print(eig1.shape, eig2.shape, eig3.shape)\n",
     "    return torch.concat([eig1, eig2, eig3], dim=1)"
    ]
   },
@@ -181,6 +180,129 @@
     "    )"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "339315e4-4234-4a83-bb49-f5fa302d0371",
+   "metadata": {},
+   "source": [
+    "### Testing\n",
+    "\n",
+    "Our closed-form solvers are numerically equivalent to `torch.linalg.eigvalsh`.\n",
+    "Unsurprisingly, our implementation is also much faster than PyTorch's solver."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "532bfdff-1dd5-4e4a-8902-e6ff20b77590",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Test the 2×2 implementation is equivalent to torch's eigvalsh\n",
+    "A = torch.randn(100, 2, 2, 30, 30)\n",
+    "A = A + A.transpose(1, 2)  # Make A Hermitian\n",
+    "\n",
+    "torch.testing.assert_close(\n",
+    "    eigvalsh(A),\n",
+    "    torch.linalg.eigvalsh(A.permute(0, -2, -1, 1, 2)).permute(0, -1, 1, 2),\n",
+    "    rtol=1e-5,\n",
+    "    atol=1e-4,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0b654569-01b7-4d66-8653-e38ad8ff3629",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3.09 ms ± 157 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%timeit eigvalsh(A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "58d45054-3dac-4ac2-8cd9-786541854deb",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "46.7 ms ± 836 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "B = A.permute(0, -2, -1, 1, 2)\n",
+    "%timeit torch.linalg.eigvalsh(B)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11f5a9e6-a1e1-43cd-93c7-afa87de88b92",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Test the 3×3 implementation is equivalent to torch's eigh\n",
+    "A = torch.randn(100, 3, 3, 30, 30)\n",
+    "A = A + A.transpose(1, 2)  # Make A Hermitian\n",
+    "\n",
+    "torch.testing.assert_close(\n",
+    "    eigvalsh(A),\n",
+    "    torch.linalg.eigvalsh(A.permute(0, -2, -1, 1, 2)).permute(0, -1, 1, 2),\n",
+    "    rtol=1e-5,\n",
+    "    atol=1e-4,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3eac5bd1-9704-43c7-9aba-131e95790fcd",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5.52 ms ± 51.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%timeit eigvalsh(A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1ceecc93-e204-41fe-9c3a-3cf2bbaccb7e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "98.2 ms ± 635 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "B = A.permute(0, -2, -1, 1, 2)\n",
+    "%timeit torch.linalg.eigvalsh(B)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,