inclusion exclusion

Author: alanedelman

notebooks/Determinantal Point Process.ipynb

@@ -515,27 +515,65 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 133,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "5×5 Array{Int64,2}:\n",
-       " 2  3  4  5   6\n",
-       " 3  4  5  6   7\n",
-       " 4  5  6  7   8\n",
-       " 5  6  7  8   9\n",
-       " 6  7  8  9  10"
+       "16-element Array{Float64,1}:\n",
+       "  9.99800009997195e-9  \n",
+       " -3.154713209048903e-5 \n",
+       " -4.1959963993950273e-5\n",
+       " -9.673304874165397e-5 \n",
+       " -2.9739851173984944e-5\n",
+       "  0.004466845396684257 \n",
+       "  0.3052207002111089   \n",
+       "  0.005815309274792625 \n",
+       "  0.39288415577467783  \n",
+       "  0.022290584536740973 \n",
+       "  0.2693223448055833   \n",
+       "  7.026419854489945e-5 \n",
+       "  3.2576007333799057e-6\n",
+       "  5.8041641398580314e-5\n",
+       "  6.845655600048237e-5 \n",
+       "  1.0002000170600884e-8"
+      ]
+     },
+     "execution_count": 133,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# This shows what happens if you perturb just a bit\n",
+    "KK = L + .0001I\n",
+    "LL = KK / (I - KK)\n",
+    "[det(LL[A,A])/det(LL+I) for A ∈ 𝒫 ]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 143,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4×4 Array{Float64,2}:\n",
+       " -3155.34    -3577.11     23.1725   2967.18\n",
+       " -3577.11    -4196.84  -1144.17     3202.24\n",
+       "    23.1725  -1144.17  -9675.24    -1357.26\n",
+       "  2967.18     3202.24  -1357.26    -2974.58"
       ]
      },
-     "execution_count": 99,
+     "execution_count": 143,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "[i+j for i=1:5,j=1:5]"
+    "LL"
    ]
   },
   {