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data-explorer/kusto/functions-library/entropy-fl.md

@@ -0,0 +1,117 @@
+---
+title:  entropy_fl()
+description:  This article describes entropy_fl() user-defined function.
+ms.reviewer: adieldar
+ms.topic: reference
+ms.date: 09/10/2025
+monikerRange: "microsoft-fabric || azure-data-explorer || azure-monitor || microsoft-sentinel"
+---
+# entropy_fl()
+
+>[!INCLUDE [applies](../includes/applies-to-version/applies.md)] [!INCLUDE [fabric](../includes/applies-to-version/fabric.md)] [!INCLUDE [azure-data-explorer](../includes/applies-to-version/azure-data-explorer.md)] [!INCLUDE [monitor](../includes/applies-to-version/monitor.md)] [!INCLUDE [sentinel](../includes/applies-to-version/sentinel.md)]
+
+The function `entropy_fl()` is a [user-defined function (UDF)](../query/functions/user-defined-functions.md) that calculates the [Shannon Entropy](https://en.wikipedia.org/wiki/Entropy_(information_theory)) of multiple probability vectors.
+
+## Syntax
+
+`T | invoke entropy_fl(`*val_col*`)`
+
+[!INCLUDE [syntax-conventions-note](../includes/syntax-conventions-note.md)]
+
+## Parameters
+
+| Name | Type | Required | Description |
+|--|--|--|--|
+| *val_col* | `string` |  :heavy_check_mark: | The name of the column containing the probability vectors.|
+
+## Function definition
+
+You can define the function by either embedding its code as a query-defined function, or creating it as a stored function in your database, as follows:
+
+### [Query-defined](#tab/query-defined)
+
+Define the function using the following [let statement](../query/let-statement.md). No permissions are required.
+
+> [!IMPORTANT]
+> A [let statement](../query/let-statement.md) can't run on its own. It must be followed by a [tabular expression statement](../query/tabular-expression-statements.md). To run a working example of `time_weighted_avg_fl()`, see [Example](#example).
+
+```kusto
+let entropy_fl=(tbl:(*), val_col:string)
+{
+	tbl
+    | extend _vals = column_ifexists(val_col, dynamic(null))
+    | mv-apply pa=_vals to typeof(real) on 
+    (summarize H=sum(-pa*log2(pa)))
+    | project-away _vals
+};
+// Write your query to use the function here.
+```
+
+### [Stored](#tab/stored)
+
+Define the stored function once using the following [`.create function`](../management/create-function.md). [Database User permissions](../access-control/role-based-access-control.md) are required.
+
+> [!IMPORTANT]
+> You must run this code to create the function before you can use the function as shown in the [Example](#example).
+
+```kusto
+.create-or-alter function with (folder = "Packages\\Stats", docstring = "Shannon entropy")
+entropy_fl(tbl:(*), val_col:string)
+{
+	tbl
+    | extend _vals = column_ifexists(val_col, dynamic(null))
+    | mv-apply pa=_vals to typeof(real) on 
+    (summarize H=sum(-pa*log2(pa)))
+    | project-away _vals
+}
+```
+
+---
+
+## Example
+
+The following example uses the [invoke operator](../query/invoke-operator.md) to run the function.
+
+### [Query-defined](#tab/query-defined)
+
+To use a query-defined function, invoke it after the embedded function definition.
+
+```kusto
+let entropy_fl=(tbl:(*), val_col:string)
+{
+	tbl
+    | extend _vals = column_ifexists(val_col, dynamic(null))
+    | mv-apply pa=_vals to typeof(real) on 
+    (summarize H=sum(-pa*log2(pa)))
+    | project-away _vals
+};
+let probs = datatable(p:dynamic) [
+    dynamic([0.2, 0.4, 0.3, 0.1]),
+    dynamic([0.5, 0.5])
+];
+probs
+| invoke entropy_fl('p')
+```
+
+### [Stored](#tab/stored)
+
+> [!IMPORTANT]
+> For this example to run successfully, you must first run the [Function definition](#function-definition) code to store the function.
+
+```kusto
+let probs = datatable(p:dynamic) [
+    dynamic([0.2, 0.4, 0.3, 0.1]),
+    dynamic([0.5, 0.5])
+];
+probs
+| invoke entropy_fl('p')
+```
+
+---
+
+**Output**
+
+| p | H |
+|---|---|
+[0.2, 0.4, 0.3, 0.1] | 1.84643934467102 |
+[0.5, 0.5] | 1 |

data-explorer/kusto/functions-library/functions-library.md

@@ -101,6 +101,7 @@ The following section contains common [PromQL](https://prometheus.io/docs/promet
 | [bartlett_test_fl()](bartlett-test-fl.md) | Perform the Bartlett test. |
 | [binomial_test_fl()](binomial-test-fl.md) | Perform the binomial test. |
 | [comb_fl()](comb-fl.md) | Calculate *C(n, k)*, the number of combinations for selection of k items out of n. |
+| [entropy_fl()](entropy-fl.md) | Calculate Shannon Entropy of multiple probability vectors. |
 | [factorial_fl()](factorial-fl.md) | Calculate *n!*, the factorial of n. |
 | [ks_test_fl()](ks-test-fl.md) | Perform a Kolmogorov Smirnov test. |
 | [levene_test_fl()](levene-test-fl.md) | Perform a Levene test. |

data-explorer/kusto/functions-library/toc.yml

@@ -26,6 +26,9 @@ items:
 - name: detect_anomalous_spike_fl()
   displayName: functions library, security, cybersecurity, anomaly detection, spike, cyber, detect anomalous spike
   href: detect-anomalous-spike-fl.md
+- name: entropy_fl()
+  displayName: functions library, information theory, Shannon entropy
+  href: entropy-fl.md
 - name: factorial_fl()
   displayName: functions library, statistics
   href: factorial-fl.md