Use theory to calculate default corr threshold

Theory suggests a correlation threshold of 3/sqrt(ensemble_size)

src/ert/_c_wrappers/analysis/__init__.py

@@ -1,3 +1,3 @@
-from .analysis_module import AnalysisMode, AnalysisModule
+from .analysis_module import AnalysisMode, AnalysisModule, correlation_threshold
 
-__all__ = ["AnalysisModule", "AnalysisMode"]
+__all__ = ["AnalysisModule", "AnalysisMode", "correlation_threshold"]

src/ert/_c_wrappers/analysis/analysis_module.py

@@ -1,4 +1,5 @@
 import logging
+import math
 from enum import Enum
 from typing import TYPE_CHECKING, Dict, List, Type, TypedDict, Union
 
@@ -22,7 +23,22 @@ class VariableInfo(TypedDict):
 DEFAULT_ENKF_TRUNCATION = 0.98
 DEFAULT_IES_INVERSION = 0
 DEFAULT_LOCALIZATION = False
-DEFAULT_LOCALIZATION_CORRELATION_THRESHOLD = 0.4
+# Default threshold is a function of ensemble size which is not available here.
+DEFAULT_LOCALIZATION_CORRELATION_THRESHOLD = -1
+
+
+def correlation_threshold(ensemble_size: int, user_defined_threshold: float) -> float:
+    """Decides whether or not to use user-defined or default threshold.
+
+    Default threshold taken from luo2022,
+    Continuous Hyper-parameter OPtimization (CHOP) in an ensemble Kalman filter
+    Section 2.3 - Localization in the CHOP problem
+    """
+    default_threshold = 3 / math.sqrt(ensemble_size)
+    if user_defined_threshold == -1:
+        return default_threshold
+
+    return user_defined_threshold
 
 
 class AnalysisMode(str, Enum):
@@ -222,8 +238,10 @@ def get_truncation(self) -> float:
     def localization(self) -> bool:
         return self.get_variable_value("LOCALIZATION")
 
-    def localization_correlation_threshold(self) -> float:
-        return self.get_variable_value("LOCALIZATION_CORRELATION_THRESHOLD")
+    def localization_correlation_threshold(self, ensemble_size: int) -> float:
+        return correlation_threshold(
+            ensemble_size, self.get_variable_value("LOCALIZATION_CORRELATION_THRESHOLD")
+        )
 
     def get_steplength(self, iteration_nr: int) -> float:
         """

src/ert/analysis/_es_update.py

@@ -215,7 +215,7 @@ def analysis_ES(
                     responses_to_keep = _correlated_parameter_response_pairs(
                         A_chunk,
                         Y,
-                        module.localization_correlation_threshold(),
+                        module.localization_correlation_threshold(ensemble_size),
                     )
                     Y_loc = Y[responses_to_keep, :]
                     observation_errors_loc = observation_errors[responses_to_keep]

src/ert/gui/ertwidgets/analysismodulevariablespanel.py

@@ -1,5 +1,4 @@
 from functools import partial
-
 from qtpy.QtWidgets import (
     QCheckBox,
     QDoubleSpinBox,
@@ -15,6 +14,7 @@
     AnalysisModuleVariablesModel,
 )
 from ert.libres_facade import LibresFacade
+from ert._c_wrappers.analysis import correlation_threshold
 
 
 class AnalysisModuleVariablesPanel(QWidget):
@@ -41,10 +41,16 @@ def __init__(self, analysis_module_name: str, facade: LibresFacade):
                 variable_type = analysis_module_variables_model.getVariableType(
                     variable_name
                 )
+
                 variable_value = analysis_module_variables_model.getVariableValue(
                     self.facade, self._analysis_module_name, variable_name
                 )
 
+                if variable_name == "LOCALIZATION_CORRELATION_THRESHOLD":
+                    variable_value = correlation_threshold(
+                        self.facade.get_ensemble_size(), variable_value
+                    )
+
                 label_name = analysis_module_variables_model.getVariableLabelName(
                     variable_name
                 )