exponentially decay message frequency in live_info

This way, you would not have to wait for all messages to be displayed after you open your laptop in the morning when you run an simulation overnight on the cluster.

notice this is a proof of concept, the randomness is not really important, but could be removed with if we keep track of the last printed message. Also it depends on status.comm.kernel.iopub_thread._events which I suppose is meant for internal usage (indicated by the underscore before _events.

Both these should be possible to mitigate when more time is spend on those parts.

adaptive/notebook_integration.py

@@ -3,6 +3,7 @@ import importlib
 import asyncio
 from contextlib import suppress
 import datetime
+import random
 import warnings
 
 
@@ -150,6 +151,24 @@ def live_plot(runner, *, plotter=None, update_interval=2, name=None):
     return dm
 
 
+def should_update(status):
+    try:
+        # Get the length of the write buffer size
+        buffer_size = len(status.comm.kernel.iopub_thread._events)
+
+        # Make sure to only keep all the messages when the notebook
+        # is viewed, this means 'buffer_size == 1'. However, when not
+        # viewing the notebook the buffer fills up. When this happens
+        # we decide to only add messages to it when a certain probability.
+        # i.e. we're offline for 12h, with an update_interval of 0.5s,
+        # and without the reduced probability, we have buffer_size=86400.
+        # With the correction this is np.log(86400) / np.log(1.1) = 119.2
+        return 1.1**buffer_size * random.random() < 1
+    except Exception:
+        # We catch any Exception because we are using a private API.
+        return True
+
+
 def live_info(runner, *, update_interval=0.5):
     """Display live information about the runner.
 
@@ -172,7 +191,12 @@ def live_info(runner, *, update_interval=0.5):
     async def update():
         while not runner.task.done():
             await asyncio.sleep(update_interval)
-            status.value = _info_html(runner)
+
+            if should_update(status):
+                status.value = _info_html(runner)
+            else:
+                await asyncio.sleep(0.05)
+
         status.value = _info_html(runner)
         cancel.layout.display = 'none'