Feature 181 & 242 - improve auto window detection (#243)

* Add ema calculation class, calculate an emo temperature, use the ema_temperature in auto_window dectection

* Removes circular dependency error

* Fix ema_temp unknown and remove slope smoothing

* 15 sec between two slope calculation

* Take Maia feedbacks on the algo.

* Maia comments: change MAX_ALPHA to 0.5, add slope calculation at each cycle.

* With EMA entity and slope calculation optimisations

* Change open_window_detection fake datapoint threshold

* Try auto window new algo

* Don't store datetime of fake datapoint

* Change auto window threshold in °/hour

---------

Co-authored-by: Jean-Marc Collin <jean-marc.collin-extern@renault.com>

custom_components/versatile_thermostat/ema.py

@@ -0,0 +1,85 @@
+# pylint: disable=line-too-long
+"""The Estimated Mobile Average calculation used for temperature slope
+and maybe some others feature"""
+
+import logging
+import math
+from datetime import datetime, tzinfo
+
+_LOGGER = logging.getLogger(__name__)
+
+MIN_TIME_DECAY_SEC = 0
+# As for the EMA calculation of irregular time series, I've seen that it might be useful to
+# have an upper limit for alpha in case the last measurement was too long ago.
+# For example when using a half life of 10 minutes a measurement that is 60 minutes ago
+# (if there's nothing inbetween) would contribute to the smoothed value with 1,5%,
+# giving the current measurement 98,5% relevance. It could be wise to limit the alpha to e.g. 4x the half life (=0.9375).
+MAX_ALPHA = 0.5
+
+
+class ExponentialMovingAverage:
+    """A class that will do the Estimated Mobile Average calculation"""
+
+    def __init__(
+        self, vterm_name: str, halflife: float, timezone: tzinfo, precision: int = 3
+    ):
+        """The halflife is the duration in secondes of a normal cycle"""
+        self._halflife: float = halflife
+        self._timezone = timezone
+        self._current_ema: float = None
+        self._last_timestamp: datetime = datetime.now(self._timezone)
+        self._name = vterm_name
+        self._precision = precision
+
+    def __str__(self) -> str:
+        return f"EMA-{self._name}"
+
+    def calculate_ema(self, measurement: float, timestamp: datetime) -> float | None:
+        """Calculate the new EMA from a new measurement measured at timestamp
+        Return the EMA or None if all parameters are not initialized now
+        """
+
+        if measurement is None or timestamp is None:
+            _LOGGER.warning(
+                "%s - Cannot calculate EMA: measurement and timestamp are mandatory. This message can be normal at startup but should not persist",
+                self,
+            )
+            return measurement
+
+        if self._current_ema is None:
+            _LOGGER.debug(
+                "%s - First init of the EMA",
+                self,
+            )
+            self._current_ema = measurement
+            self._last_timestamp = timestamp
+            return self._current_ema
+
+        time_decay = (timestamp - self._last_timestamp).total_seconds()
+        if time_decay < MIN_TIME_DECAY_SEC:
+            _LOGGER.debug(
+                "%s - time_decay %s is too small (< %s). Forget the measurement",
+                self,
+                time_decay,
+                MIN_TIME_DECAY_SEC,
+            )
+            return self._current_ema
+
+        alpha = 1 - math.exp(math.log(0.5) * time_decay / self._halflife)
+        # capping alpha to avoid gap if last measurement was long time ago
+        alpha = min(alpha, MAX_ALPHA)
+        new_ema = alpha * measurement + (1 - alpha) * self._current_ema
+
+        self._last_timestamp = timestamp
+        self._current_ema = new_ema
+        _LOGGER.debug(
+            "%s - timestamp=%s alpha=%.2f measurement=%.2f current_ema=%.2f new_ema=%.2f",
+            self,
+            timestamp,
+            alpha,
+            measurement,
+            self._current_ema,
+            new_ema,
+        )
+
+        return round(self._current_ema, self._precision)