Function compute_variance

datafusion/expr-common/src/statistics.rs:900–938

(
    op: &Operator,
    left: &Distribution,
    right: &Distribution,
)

    note = "Part of the unused Statistics V2 framework; see https://github.com/apache/datafusion/pull/22071"
)]
pub fn compute_variance(
    op: &Operator,
    left: &Distribution,
    right: &Distribution,
) -> Result<ScalarValue> {
    let (left_variance, right_variance) = (left.variance()?, right.variance()?);

    match op {
        // Note the independence assumption below:
        Operator::Plus => return left_variance.add_checked(right_variance),
        // Note the independence assumption below:
        Operator::Minus => return left_variance.add_checked(right_variance),
        // Note the independence assumption below:
        Operator::Multiply => {
            // For more details, along with an explanation of the formula below, see:
            //
            // <https://en.wikipedia.org/wiki/Distribution_of_the_product_of_two_random_variables>
            let (left_mean, right_mean) = (left.mean()?, right.mean()?);
            let left_mean_sq = left_mean.mul_checked(&left_mean)?;
            let right_mean_sq = right_mean.mul_checked(&right_mean)?;
            let left_sos = left_variance.add_checked(&left_mean_sq)?;
            let right_sos = right_variance.add_checked(&right_mean_sq)?;
            let pos = left_mean_sq.mul_checked(right_mean_sq)?;
            return left_sos.mul_checked(right_sos)?.sub_checked(pos);
        }
        // TODO: We can calculate the variance for division when we support reciprocals,
        // or know the distributions of the operands. For details, see:
        //
        // <https://en.wikipedia.org/wiki/Algebra_of_random_variables>
        // <https://stats.stackexchange.com/questions/185683/distribution-of-ratio-between-two-independent-uniform-random-variables>
        //
        // Fall back to an unknown variance value for division:
        Operator::Divide => {}
        // Fall back to an unknown variance value for other cases:
        _ => {}
    }
    let target_type = Distribution::target_type(&[&left_variance, &right_variance])?;
    ScalarValue::try_from(target_type)
}

#[cfg(test)]
mod tests {