plot error probabilities

docs/wfm.ipynb

@@ -388,8 +388,9 @@
    ]
   },
   {
+   "attachments": {},
    "cell_type": "markdown",
-   "id": "f97e9772-7aa8-426a-a0ba-3a0d0b6babf0",
+   "id": "ce1df677-098e-4bec-9278-07fe16d0379f",
    "metadata": {},
    "source": [
     "We can see that the WFM estimate clearly outperforms the naive computation.\n",
@@ -556,7 +557,34 @@
    "id": "1d28f370-dd84-41f9-af44-d1363a069772",
    "metadata": {},
    "source": [
-    "This once again illustrates the superiority of the WFM estimate."
+    "This once again illustrates the superiority of the WFM estimate.\n",
+    "\n",
+    "An alternative way of comparing the accuracy of the methods is to look at the probability that a computed wavelength has relative error above $x$,\n",
+    "as a function of $x$:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "23dde7e5-c2d2-4601-bf1e-fc3b85be7c85",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "true_wavs = events.flatten(to='event').coords['wavelength']\n",
+    "\n",
+    "err_wfm = sc.abs(true_wavs - flat.coords['wavelength']) / true_wavs\n",
+    "err_naive = sc.abs(true_wavs - naive.coords['wavelength']) / true_wavs\n",
+    "\n",
+    "bins = sc.geomspace('relative_error', 1e-3, 0.2, 101)\n",
+    "err_wfm = sc.cumsum(err_wfm.hist(relative_error=bins))\n",
+    "err_naive = sc.cumsum(err_naive.hist(relative_error=bins))\n",
+    "\n",
+    "p = pp.plot(\n",
+    "    {'naive': 1 - err_naive / sc.max(err_naive), 'wfm': 1 - err_wfm / sc.max(err_wfm)},\n",
+    "    scale={'relative_error': 'log'},\n",
+    ")\n",
+    "p.canvas.ylabel = 'Probability of $rel. err. > x$'\n",
+    "p"
    ]
   }
  ],