replace Scott's rule fallback with \propto (max - min)

- to avoid "sharp" transitions from Silverman to Scott value
- make custom bandwidth value use that same fallback when "too small"
- rename "scott-rule" mock to "bandwidth-edge-cases"

Author: etpinard

src/traces/violin/calc.js

@@ -71,7 +71,7 @@ module.exports = function calc(gd, trace) {
     return cd;
 };
 
-// Default to Silveman's rule of thumb, but if 'too small' use Scott's rule
+// Default to Silveman's rule of thumb
 // - https://stats.stackexchange.com/a/6671
 // - https://en.wikipedia.org/wiki/Kernel_density_estimation#A_rule-of-thumb_bandwidth_estimator
 // - https://github.com/statsmodels/statsmodels/blob/master/statsmodels/nonparametric/bandwidths.py
@@ -80,21 +80,27 @@ function silvermanRule(len, ssd, iqr) {
     return 1.059 * a * Math.pow(len, -0.2);
 }
 
-function scottRule(len, ssd) {
-    return ssd * Math.pow(len, -0.2);
-}
-
 function calcBandwidth(trace, cdi, vals) {
-    if(trace.bandwidth) return trace.bandwidth;
-
-    var len = vals.length;
-    var ssd = Lib.stdev(vals, len - 1, cdi.mean);
-    var bw = silvermanRule(len, ssd, cdi.q3 - cdi.q1);
+    var bw;
 
-    if((cdi.max - cdi.min) / bw > 1e5) {
-        bw = scottRule(len, ssd);
+    if(trace.bandwidth) {
+        bw = trace.bandwidth;
+    } else {
+        var len = vals.length;
+        var ssd = Lib.stdev(vals, len - 1, cdi.mean);
+        bw = silvermanRule(len, ssd, cdi.q3 - cdi.q1);
     }
-    return bw;
+
+    // Limit how small the bandwidth can be.
+    //
+    // Silverman's rule of thumb can be "very" small
+    // when IQR does a poor job at describing the spread
+    // of the distribution.
+    // We also want to limit custom bandwidths
+    // to not blow up kde computations.
+    return ((cdi.max - cdi.min) / bw) < 1e5 ?
+        bw :
+        (cdi.max - cdi.min) / 100;
 }
 
 function calcSpan(trace, cdi, valAxis, bandwidth) {

test/image/baselines/violin_bandwidth-edge-cases.png

@@ -1,7 +1,7 @@
 {
   "data": [
     {
-      "name": "with scott rule bandwidth",
+      "name": "silverman value is too small",
       "type": "violin",
       "points": false,
       "y": [
@@ -227,7 +227,233 @@
     },
     {
       "bandwidth": 0.03364359551927969,
-      "name": "with custom bandwidth",
+      "name": "OK custom bandwidth",
+      "type": "violin",
+      "points": false,
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+    {
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+      "name": "custom bandwidth is too small",
       "type": "violin",
       "points": false,
       "y": [