datafusion_functions_aggregate/
covariance.rs

// Licensed to the Apache Software Foundation (ASF) under one
// or more contributor license agreements.  See the NOTICE file
// distributed with this work for additional information
// regarding copyright ownership.  The ASF licenses this file
// to you under the Apache License, Version 2.0 (the
// "License"); you may not use this file except in compliance
// with the License.  You may obtain a copy of the License at
//
//   http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the License is distributed on an
// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.  See the License for the
// specific language governing permissions and limitations
// under the License.

//! [`CovarianceSample`]: covariance sample aggregations.

use std::fmt::Debug;
use std::mem::size_of_val;
use std::sync::OnceLock;

use arrow::{
    array::{ArrayRef, Float64Array, UInt64Array},
    compute::kernels::cast,
    datatypes::{DataType, Field},
};

use datafusion_common::{
    downcast_value, plan_err, unwrap_or_internal_err, DataFusionError, Result,
    ScalarValue,
};
use datafusion_expr::aggregate_doc_sections::DOC_SECTION_STATISTICAL;
use datafusion_expr::{
    function::{AccumulatorArgs, StateFieldsArgs},
    type_coercion::aggregates::NUMERICS,
    utils::format_state_name,
    Accumulator, AggregateUDFImpl, Documentation, Signature, Volatility,
};
use datafusion_functions_aggregate_common::stats::StatsType;

make_udaf_expr_and_func!(
    CovarianceSample,
    covar_samp,
    y x,
    "Computes the sample covariance.",
    covar_samp_udaf
);

make_udaf_expr_and_func!(
    CovariancePopulation,
    covar_pop,
    y x,
    "Computes the population covariance.",
    covar_pop_udaf
);

pub struct CovarianceSample {
    signature: Signature,
    aliases: Vec<String>,
}

impl Debug for CovarianceSample {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        f.debug_struct("CovarianceSample")
            .field("name", &self.name())
            .field("signature", &self.signature)
            .finish()
    }
}

impl Default for CovarianceSample {
    fn default() -> Self {
        Self::new()
    }
}

impl CovarianceSample {
    pub fn new() -> Self {
        Self {
            aliases: vec![String::from("covar")],
            signature: Signature::uniform(2, NUMERICS.to_vec(), Volatility::Immutable),
        }
    }
}

impl AggregateUDFImpl for CovarianceSample {
    fn as_any(&self) -> &dyn std::any::Any {
        self
    }

    fn name(&self) -> &str {
        "covar_samp"
    }

    fn signature(&self) -> &Signature {
        &self.signature
    }

    fn return_type(&self, arg_types: &[DataType]) -> Result<DataType> {
        if !arg_types[0].is_numeric() {
            return plan_err!("Covariance requires numeric input types");
        }

        Ok(DataType::Float64)
    }

    fn state_fields(&self, args: StateFieldsArgs) -> Result<Vec<Field>> {
        let name = args.name;
        Ok(vec![
            Field::new(format_state_name(name, "count"), DataType::UInt64, true),
            Field::new(format_state_name(name, "mean1"), DataType::Float64, true),
            Field::new(format_state_name(name, "mean2"), DataType::Float64, true),
            Field::new(
                format_state_name(name, "algo_const"),
                DataType::Float64,
                true,
            ),
        ])
    }

    fn accumulator(&self, _acc_args: AccumulatorArgs) -> Result<Box<dyn Accumulator>> {
        Ok(Box::new(CovarianceAccumulator::try_new(StatsType::Sample)?))
    }

    fn aliases(&self) -> &[String] {
        &self.aliases
    }

    fn documentation(&self) -> Option<&Documentation> {
        Some(get_covar_samp_doc())
    }
}

static DOCUMENTATION: OnceLock<Documentation> = OnceLock::new();

fn get_covar_samp_doc() -> &'static Documentation {
    DOCUMENTATION.get_or_init(|| {
        Documentation::builder()
            .with_doc_section(DOC_SECTION_STATISTICAL)
            .with_description("Returns the sample covariance of a set of number pairs.")
            .with_syntax_example("covar_samp(expression1, expression2)")
            .with_sql_example(
                r#"```sql
> SELECT covar_samp(column1, column2) FROM table_name;
+-----------------------------------+
| covar_samp(column1, column2)      |
+-----------------------------------+
| 8.25                              |
+-----------------------------------+
```"#,
            )
            .with_standard_argument("expression1", Some("First"))
            .with_standard_argument("expression2", Some("Second"))
            .build()
            .unwrap()
    })
}

pub struct CovariancePopulation {
    signature: Signature,
}

impl Debug for CovariancePopulation {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        f.debug_struct("CovariancePopulation")
            .field("name", &self.name())
            .field("signature", &self.signature)
            .finish()
    }
}

impl Default for CovariancePopulation {
    fn default() -> Self {
        Self::new()
    }
}

impl CovariancePopulation {
    pub fn new() -> Self {
        Self {
            signature: Signature::uniform(2, NUMERICS.to_vec(), Volatility::Immutable),
        }
    }
}

impl AggregateUDFImpl for CovariancePopulation {
    fn as_any(&self) -> &dyn std::any::Any {
        self
    }

    fn name(&self) -> &str {
        "covar_pop"
    }

    fn signature(&self) -> &Signature {
        &self.signature
    }

    fn return_type(&self, arg_types: &[DataType]) -> Result<DataType> {
        if !arg_types[0].is_numeric() {
            return plan_err!("Covariance requires numeric input types");
        }

        Ok(DataType::Float64)
    }

    fn state_fields(&self, args: StateFieldsArgs) -> Result<Vec<Field>> {
        let name = args.name;
        Ok(vec![
            Field::new(format_state_name(name, "count"), DataType::UInt64, true),
            Field::new(format_state_name(name, "mean1"), DataType::Float64, true),
            Field::new(format_state_name(name, "mean2"), DataType::Float64, true),
            Field::new(
                format_state_name(name, "algo_const"),
                DataType::Float64,
                true,
            ),
        ])
    }

    fn accumulator(&self, _acc_args: AccumulatorArgs) -> Result<Box<dyn Accumulator>> {
        Ok(Box::new(CovarianceAccumulator::try_new(
            StatsType::Population,
        )?))
    }

    fn documentation(&self) -> Option<&Documentation> {
        Some(get_covar_pop_doc())
    }
}

fn get_covar_pop_doc() -> &'static Documentation {
    DOCUMENTATION.get_or_init(|| {
        Documentation::builder()
            .with_doc_section(DOC_SECTION_STATISTICAL)
            .with_description(
                "Returns the population covariance of a set of number pairs.",
            )
            .with_syntax_example("covar_pop(expression1, expression2)")
            .with_sql_example(
                r#"```sql
> SELECT covar_pop(column1, column2) FROM table_name;
+-----------------------------------+
| covar_pop(column1, column2)       |
+-----------------------------------+
| 7.63                              |
+-----------------------------------+
```"#,
            )
            .with_standard_argument("expression1", Some("First"))
            .with_standard_argument("expression2", Some("Second"))
            .build()
            .unwrap()
    })
}

/// An accumulator to compute covariance
/// The algorithm used is an online implementation and numerically stable. It is derived from the following paper
/// for calculating variance:
/// Welford, B. P. (1962). "Note on a method for calculating corrected sums of squares and products".
/// Technometrics. 4 (3): 419–420. doi:10.2307/1266577. JSTOR 1266577.
///
/// The algorithm has been analyzed here:
/// Ling, Robert F. (1974). "Comparison of Several Algorithms for Computing Sample Means and Variances".
/// Journal of the American Statistical Association. 69 (348): 859–866. doi:10.2307/2286154. JSTOR 2286154.
///
/// Though it is not covered in the original paper but is based on the same idea, as a result the algorithm is online,
/// parallelizable and numerically stable.

#[derive(Debug)]
pub struct CovarianceAccumulator {
    algo_const: f64,
    mean1: f64,
    mean2: f64,
    count: u64,
    stats_type: StatsType,
}

impl CovarianceAccumulator {
    /// Creates a new `CovarianceAccumulator`
    pub fn try_new(s_type: StatsType) -> Result<Self> {
        Ok(Self {
            algo_const: 0_f64,
            mean1: 0_f64,
            mean2: 0_f64,
            count: 0_u64,
            stats_type: s_type,
        })
    }

    pub fn get_count(&self) -> u64 {
        self.count
    }

    pub fn get_mean1(&self) -> f64 {
        self.mean1
    }

    pub fn get_mean2(&self) -> f64 {
        self.mean2
    }

    pub fn get_algo_const(&self) -> f64 {
        self.algo_const
    }
}

impl Accumulator for CovarianceAccumulator {
    fn state(&mut self) -> Result<Vec<ScalarValue>> {
        Ok(vec![
            ScalarValue::from(self.count),
            ScalarValue::from(self.mean1),
            ScalarValue::from(self.mean2),
            ScalarValue::from(self.algo_const),
        ])
    }

    fn update_batch(&mut self, values: &[ArrayRef]) -> Result<()> {
        let values1 = &cast(&values[0], &DataType::Float64)?;
        let values2 = &cast(&values[1], &DataType::Float64)?;

        let mut arr1 = downcast_value!(values1, Float64Array).iter().flatten();
        let mut arr2 = downcast_value!(values2, Float64Array).iter().flatten();

        for i in 0..values1.len() {
            let value1 = if values1.is_valid(i) {
                arr1.next()
            } else {
                None
            };
            let value2 = if values2.is_valid(i) {
                arr2.next()
            } else {
                None
            };

            if value1.is_none() || value2.is_none() {
                continue;
            }

            let value1 = unwrap_or_internal_err!(value1);
            let value2 = unwrap_or_internal_err!(value2);
            let new_count = self.count + 1;
            let delta1 = value1 - self.mean1;
            let new_mean1 = delta1 / new_count as f64 + self.mean1;
            let delta2 = value2 - self.mean2;
            let new_mean2 = delta2 / new_count as f64 + self.mean2;
            let new_c = delta1 * (value2 - new_mean2) + self.algo_const;

            self.count += 1;
            self.mean1 = new_mean1;
            self.mean2 = new_mean2;
            self.algo_const = new_c;
        }

        Ok(())
    }

    fn retract_batch(&mut self, values: &[ArrayRef]) -> Result<()> {
        let values1 = &cast(&values[0], &DataType::Float64)?;
        let values2 = &cast(&values[1], &DataType::Float64)?;
        let mut arr1 = downcast_value!(values1, Float64Array).iter().flatten();
        let mut arr2 = downcast_value!(values2, Float64Array).iter().flatten();

        for i in 0..values1.len() {
            let value1 = if values1.is_valid(i) {
                arr1.next()
            } else {
                None
            };
            let value2 = if values2.is_valid(i) {
                arr2.next()
            } else {
                None
            };

            if value1.is_none() || value2.is_none() {
                continue;
            }

            let value1 = unwrap_or_internal_err!(value1);
            let value2 = unwrap_or_internal_err!(value2);

            let new_count = self.count - 1;
            let delta1 = self.mean1 - value1;
            let new_mean1 = delta1 / new_count as f64 + self.mean1;
            let delta2 = self.mean2 - value2;
            let new_mean2 = delta2 / new_count as f64 + self.mean2;
            let new_c = self.algo_const - delta1 * (new_mean2 - value2);

            self.count -= 1;
            self.mean1 = new_mean1;
            self.mean2 = new_mean2;
            self.algo_const = new_c;
        }

        Ok(())
    }

    fn merge_batch(&mut self, states: &[ArrayRef]) -> Result<()> {
        let counts = downcast_value!(states[0], UInt64Array);
        let means1 = downcast_value!(states[1], Float64Array);
        let means2 = downcast_value!(states[2], Float64Array);
        let cs = downcast_value!(states[3], Float64Array);

        for i in 0..counts.len() {
            let c = counts.value(i);
            if c == 0_u64 {
                continue;
            }
            let new_count = self.count + c;
            let new_mean1 = self.mean1 * self.count as f64 / new_count as f64
                + means1.value(i) * c as f64 / new_count as f64;
            let new_mean2 = self.mean2 * self.count as f64 / new_count as f64
                + means2.value(i) * c as f64 / new_count as f64;
            let delta1 = self.mean1 - means1.value(i);
            let delta2 = self.mean2 - means2.value(i);
            let new_c = self.algo_const
                + cs.value(i)
                + delta1 * delta2 * self.count as f64 * c as f64 / new_count as f64;

            self.count = new_count;
            self.mean1 = new_mean1;
            self.mean2 = new_mean2;
            self.algo_const = new_c;
        }
        Ok(())
    }

    fn evaluate(&mut self) -> Result<ScalarValue> {
        let count = match self.stats_type {
            StatsType::Population => self.count,
            StatsType::Sample => {
                if self.count > 0 {
                    self.count - 1
                } else {
                    self.count
                }
            }
        };

        if count == 0 {
            Ok(ScalarValue::Float64(None))
        } else {
            Ok(ScalarValue::Float64(Some(self.algo_const / count as f64)))
        }
    }

    fn size(&self) -> usize {
        size_of_val(self)
    }
}
datafusion_functions_aggregate/covariance.rs

datafusion_functions_aggregate/
covariance.rs
