Geometric Mean Function - Worked Example

Mathematical Programming with Julia

Julia Workshop

Geometric Mean

This script will calculate the geometric mean of the given data and print the result to the console. If any invalid values are encountered, it will either throw an error or issue a warning as appropriate.

Function

function geometric_mean(data)
    """
    Calculates the geometric mean of a series of numbers. 

    Args:
        data: A vector of numbers.

    Returns:
        The geometric mean of the data.

    Raises:
        DomainError: If any value in the data is less than or equal to zero.
        Warning: If any value in the data is greater than 3.
    """

    # Check for invalid values
    if any(x <= 0 for x in data)
        throw(DomainError(data, "Geometric mean is undefined for non-positive values."))
    end

    if any(x > 3 for x in data)
        @warn("Some values in the data are greater than 3.") 
    end

    # Calculate the geometric mean
    product = prod(data)
    return product^(1/length(data))
end

Explanation:

  1. Function Definition:
    • geometric_mean(data): Defines a function named geometric_mean that takes a single argument, data, which is expected to be a vector of numbers.
  2. Error Handling:
    • if any(x <= 0 for x in data): Checks if any value in the data vector is less than or equal to zero. If so, it throws a DomainError with a descriptive message, as the geometric mean is undefined for non-positive values.
    • if any(x > 3 for x in data): Checks if any value in the data vector is greater than 3. If so, it issues a @warn message to alert the user about the potential outliers.
  3. Calculate Geometric Mean:
    • product = prod(data): Calculates the product of all values in the data vector using the prod() function.
    • return product^(1/length(data)): Calculates the geometric mean by raising the product to the power of 1/n, where n is the number of elements in the data vector.

How to Use:

  1. Prepare your data: Create a vector containing the numbers for which you want to calculate the geometric mean.

  2. Call the function: Call the geometric_mean() function with the data vector as the argument.

    data = [1.5, 2.0, 2.5, 3.0] 
result = geometric_mean(data) 
println("Geometric Mean:", result)