Introduction to MongoDB $atanh Operator

The $atanh operator is a mathematical operator in MongoDB used to calculate the inverse hyperbolic tangent function value of a number. The value returned is a number between -1 and 1.

Syntax

The syntax of the $atanh operator is as follows:

{ $atanh: <expression> }

Here, <expression> represents the numeric expression for which to compute the inverse hyperbolic tangent function value.

Use Cases

The $atanh operator is typically used for handling data with nonlinear relationships. For example, in machine learning, the $atanh operator is often used to scale or transform data to make it more suitable for specific algorithms or models.

Examples

Suppose we have a collection storing information about students’ heights and weights, and we want to calculate the body mass index (BMI) of each student. We can use the $atanh operator to scale the height and weight data before performing the calculation.

Assuming the following documents are in the collection:

{
  "_id": 1,
  "name": "Alice",
  "height": 1.65,
  "weight": 60
},
{
  "_id": 2,
  "name": "Bob",
  "height": 1.80,
  "weight": 80
}

We can calculate the BMI of each student using the following aggregation pipeline:

db.students.aggregate([
  {
    $project: {
      name: 1,
      bmi: {
        $multiply: [
          "$weight",
          {
            $pow: [
              {
                $atanh: {
                  $divide: [
                    "$height",
                    {
                      $multiply: ["$height", "$height"]
                    }
                  ]
                }
              },
              2
            ]
          }
        ]
      }
    }
  }
])

In the above aggregation pipeline, we first use the $project stage to compute the $atanh value for each student. We then use the $multiply operator to multiply the student’s weight and $atanh value, and then multiply the result by 10000 to obtain the BMI value for each student.

Conclusion

The $atanh operator can be used to scale or transform data to make it more suitable for specific algorithms or models. Using the $atanh operator can scale data to a range between -1 and 1, making it better suited for a wide range of algorithmic and model requirements.