series_atan

This page explains how to use the series_atan function in APL.

The series_atan function computes the arc tangent (inverse tangent) for each element in a numeric array (also known as a series). You use it to transform a dynamic array of numbers into their corresponding arc tangent values, expressed in radians. This is useful when you work with time series or array data and want to normalize, analyze, or transform it using trigonometric operations.

You often use series_atan in scenarios where you want to transform numeric measurements into angular values for further statistical analysis, pattern recognition, or anomaly detection.

For users of other query languages

If you come from other query languages, this section explains how to adjust your existing queries to achieve the same results in APL.

Splunk SPL users

In Splunk SPL, you typically use eval atan(x) to calculate the arc tangent of a scalar value, but SPL doesn’t provide a built-in function for applying atan across arrays or time series directly. In APL, series_atan applies the operation element-wise to arrays, making it easier to work with dynamic and time series data.

Splunk example

... | eval angle=atan(value)

ANSI SQL users

In ANSI SQL, you use ATAN(x) for scalar values. To work with arrays, you typically need to unnest the array, apply ATAN to each element, and then aggregate the results back. APL simplifies this with series_atan, which applies the arc tangent function element-wise to the entire array.

SQL example

SELECT ATAN(value)
FROM numbers;

Usage

Syntax

series_atan(array)

Parameters

Parameter	Type	Description
array	dynamic	A dynamic array of numeric values.

Returns

A dynamic array with the arc tangent of each input element. The results are in radians.

Use case examples

Log analysis

You want to analyze request durations by converting them into angular values for specialized statistical transformations.

Query

['sample-http-logs']
| summarize durations = make_list(req_duration_ms)
| extend atan_durations = series_atan(durations)

Run in Playground

Output

durations	atan_durations
[10, 200, 5000]	[1.4711, 1.5658, 1.5706]

The query aggregates request durations, then transforms them into their arc tangent equivalents for normalized comparison.

List of related functions

• series_asin: Applies the arc sine function element-wise to array values. Use this when you need the inverse sine instead of the inverse cosine.
• series_acos: Returns the arc cosine of each element in an array. Use when you need to invert cosine transformations instead of sine.