Dax Function: ATANH

Category: Mathematical and Trigonometric Functions

The ATANH function in Power BI is a DAX (Data Analysis Expressions) function that calculates the inverse hyperbolic tangent (arctanh) of a given number. The result is a scalar value that represents the hyperbolic angle in radians corresponding to the given value.

Purpose

The ATANH function is used for mathematical and scientific calculations involving hyperbolic functions. It is particularly helpful in domains like physics, engineering, and data modeling where hyperbolic functions are applied.

Type of Calculations

The ATANH function performs the inverse hyperbolic tangent calculation. It takes a number x (where −1 < x < 1) and computes the hyperbolic angle yyy such that:

tanh⁡(y)=x

Practical Use Cases

1. Scientific Applications: Solving equations in physics or engineering involving hyperbolic functions.
2. Data Transformation: Converting scaled data into a hyperbolic angle representation.
3. Signal Processing: Modeling hyperbolic relationships in data patterns.

How Does ATAN  Dax Function Works?

The ATANH function calculates the inverse hyperbolic tangent using the formula:

Where:

• x is the input value.
• ln⁡ represents the natural logarithm.

The input xxx must lie within the range −1< x < 1. If the input is outside this range, the function will return an error.

Mathematical Example

For x = 0.5 :

What Does It Return?

The ATANH function returns a scalar value representing the inverse hyperbolic tangent of the input number in radians.

When Should We Use It?

• When modeling relationships with hyperbolic functions in scientific or mathematical datasets.
• For transforming data in machine learning workflows.
• To compute hyperbolic angles for scaled data in visualization and analysis.

Examples

Basic Usage

Output: 0.5493 radians.

Column Usage

Suppose you have a column [Values] containing numbers between -1 and 1. You can calculate the inverse hyperbolic tangent for each row as:

This calculates the arctangent for each row in the column.

Advanced Usage

Combine with other DAX functions for complex calculations:

This computes the inverse hyperbolic tangent of the average of a column [Scaled Data].

Tips and Tricks

1. 1. Input Range: Ensure the input values are strictly between -1 and 1. Inputs outside this range will result in an error.
   2. Radians Conversion: The result is in radians. If degrees are required, use the DEGREES function to convert.
   3. Combining with Other Functions: Combine with aggregation functions like SUM, AVERAGE, or MAX to apply ATANH to summarized data.

Performance Impact of ATANH DAX Function:

• For large datasets, use SUMMARIZE or similar functions to pre-aggregate data before applying ATANH.
• Validate input ranges to avoid errors during computation.

Related Functions You Might Need

• TANH: Computes the hyperbolic tangent of a number.
• ATAN: Calculates the inverse tangent (arctan) of a number.
• LN: Returns the natural logarithm of a number.
• DEGREES: Converts radians to degrees.

Want to Learn More?
For more information, check out the official Microsoft documentation for ATANH. You can also experiment with this function in your Power BI reports to explore its capabilities.

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