Python's statistics.correlation in TypeScript

✓ Verified: Python 3.12

Rosetta Stone: python/prod

How to use

Install via yarn add locutus and import: import { correlation } from 'locutus/python/statistics/correlation'.

Or with CommonJS: const { correlation } = require('locutus/python/statistics/correlation')

Use a bundler that supports tree-shaking so you only ship the functions you actually use. Vite, webpack, Rollup, and Parcel all handle this. For server-side use this is less of a concern.

Examples

These examples are extracted from test cases that automatically verify our functions against their native counterparts.

#	code	expected result
1	`correlation([1, 2, 3], [1, 5, 7])`	`0.9819805060619659`
2	`correlation([1, 2, 3], [7, 5, 3])`	`-1`
3	`correlation([1, 2, 3], [3, 2, 1], 'ranked')`	`-1`

Notes

Returns Pearson correlation by default and supports Python’s ranked mode for Spearman correlation.

Dependencies

This function uses the following Locutus functions:

_statistics (python/_helpers)

Here's what our current TypeScript equivalent to Python's statistics.correlation looks like.

import { assertStatisticsArray, sumProducts, toStatisticNumber } from '../_helpers/_statistics.ts'

export function correlation(x: unknown, y: unknown, method: 'linear' | 'ranked' = 'linear'): number {
  //      discuss at: https://locutus.io/python/statistics/correlation/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns Pearson correlation by default and supports Python's ranked mode for Spearman correlation.
  //       example 1: correlation([1, 2, 3], [1, 5, 7])
  //       returns 1: 0.9819805060619659
  //       example 2: correlation([1, 2, 3], [7, 5, 3])
  //       returns 2: -1
  //       example 3: correlation([1, 2, 3], [3, 2, 1], 'ranked')
  //       returns 3: -1

  const left = assertStatisticsArray(x, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))
  const right = assertStatisticsArray(y, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))

  const n = left.length
  if (right.length !== n) {
    throw new Error('correlation requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('correlation requires at least two data points')
  }
  if (method !== 'linear' && method !== 'ranked') {
    throw new TypeError(`Unknown method: '${String(method)}'`)
  }

  const xValues = method === 'ranked' ? rankValues(left) : centerValues(left)
  const yValues = method === 'ranked' ? rankValues(right) : centerValues(right)

  const sxy = sumProducts(xValues, yValues)
  const sxx = sumProducts(xValues, xValues)
  const syy = sumProducts(yValues, yValues)
  const denominator = Math.sqrt(sxx * syy)
  if (denominator === 0) {
    throw new Error('at least one of the inputs is constant')
  }

  return sxy / denominator
}

function centerValues(values: number[]): number[] {
  const mean = values.reduce((sum, value) => sum + value, 0) / values.length
  return values.map((value) => value - mean)
}

function rankValues(values: number[]): number[] {
  const n = values.length
  const start = (n - 1) / -2
  const indexed = values.map((value, index) => ({ value, index })).sort((a, b) => a.value - b.value)
  const ranks = new Array<number>(n)

  let position = 0
  while (position < indexed.length) {
    let end = position + 1
    while (end < indexed.length && indexed[end]?.value === indexed[position]?.value) {
      end += 1
    }
    const averageRank = start + (position + end - 1) / 2
    for (let cursor = position; cursor < end; cursor += 1) {
      const entry = indexed[cursor]
      if (entry) {
        ranks[entry.index] = averageRank
      }
    }
    position = end
  }

  return ranks
}

import { assertStatisticsArray, sumProducts, toStatisticNumber } from '../_helpers/_statistics.ts'

export function correlation(x, y, method = 'linear') {
  //      discuss at: https://locutus.io/python/statistics/correlation/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns Pearson correlation by default and supports Python's ranked mode for Spearman correlation.
  //       example 1: correlation([1, 2, 3], [1, 5, 7])
  //       returns 1: 0.9819805060619659
  //       example 2: correlation([1, 2, 3], [7, 5, 3])
  //       returns 2: -1
  //       example 3: correlation([1, 2, 3], [3, 2, 1], 'ranked')
  //       returns 3: -1

  const left = assertStatisticsArray(x, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))
  const right = assertStatisticsArray(y, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))

  const n = left.length
  if (right.length !== n) {
    throw new Error('correlation requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('correlation requires at least two data points')
  }
  if (method !== 'linear' && method !== 'ranked') {
    throw new TypeError(`Unknown method: '${String(method)}'`)
  }

  const xValues = method === 'ranked' ? rankValues(left) : centerValues(left)
  const yValues = method === 'ranked' ? rankValues(right) : centerValues(right)

  const sxy = sumProducts(xValues, yValues)
  const sxx = sumProducts(xValues, xValues)
  const syy = sumProducts(yValues, yValues)
  const denominator = Math.sqrt(sxx * syy)
  if (denominator === 0) {
    throw new Error('at least one of the inputs is constant')
  }

  return sxy / denominator
}

function centerValues(values) {
  const mean = values.reduce((sum, value) => sum + value, 0) / values.length
  return values.map((value) => value - mean)
}

function rankValues(values) {
  const n = values.length
  const start = (n - 1) / -2
  const indexed = values.map((value, index) => ({ value, index })).sort((a, b) => a.value - b.value)
  const ranks = new Array(n)

  let position = 0
  while (position < indexed.length) {
    let end = position + 1
    while (end < indexed.length && indexed[end]?.value === indexed[position]?.value) {
      end += 1
    }
    const averageRank = start + (position + end - 1) / 2
    for (let cursor = position; cursor < end; cursor += 1) {
      const entry = indexed[cursor]
      if (entry) {
        ranks[entry.index] = averageRank
      }
    }
    position = end
  }

  return ranks
}

// python/_helpers/_statistics (Locutus helper dependency)
function assertStatisticsArray(data: unknown, functionName: string): unknown[] {
  if (!Array.isArray(data)) {
    throw new TypeError(`${functionName}() data must be an array`)
  }

  return data
}

function toStatisticNumber(value: unknown, functionName: string): number {
  if (typeof value === 'number') {
    return value
  }

  if (typeof value === 'boolean') {
    return value ? 1 : 0
  }

  if (typeof value === 'bigint') {
    const numericValue = Number(value)
    if (!Number.isSafeInteger(numericValue)) {
      throw new RangeError(`${functionName}() bigint values must fit within JS safe integers`)
    }

    return numericValue
  }

  throw new TypeError(`${functionName}() data must contain only real numbers`)
}

function sumProducts(left: number[], right: number[]): number {
  let total = 0
  for (let index = 0; index < left.length; index += 1) {
    total += (left[index] ?? 0) * (right[index] ?? 0)
  }
  return total
}

// python/statistics/correlation (target function module)
function correlation(x: unknown, y: unknown, method: 'linear' | 'ranked' = 'linear'): number {
  //      discuss at: https://locutus.io/python/statistics/correlation/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns Pearson correlation by default and supports Python's ranked mode for Spearman correlation.
  //       example 1: correlation([1, 2, 3], [1, 5, 7])
  //       returns 1: 0.9819805060619659
  //       example 2: correlation([1, 2, 3], [7, 5, 3])
  //       returns 2: -1
  //       example 3: correlation([1, 2, 3], [3, 2, 1], 'ranked')
  //       returns 3: -1

  const left = assertStatisticsArray(x, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))
  const right = assertStatisticsArray(y, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))

  const n = left.length
  if (right.length !== n) {
    throw new Error('correlation requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('correlation requires at least two data points')
  }
  if (method !== 'linear' && method !== 'ranked') {
    throw new TypeError(`Unknown method: '${String(method)}'`)
  }

  const xValues = method === 'ranked' ? rankValues(left) : centerValues(left)
  const yValues = method === 'ranked' ? rankValues(right) : centerValues(right)

  const sxy = sumProducts(xValues, yValues)
  const sxx = sumProducts(xValues, xValues)
  const syy = sumProducts(yValues, yValues)
  const denominator = Math.sqrt(sxx * syy)
  if (denominator === 0) {
    throw new Error('at least one of the inputs is constant')
  }

  return sxy / denominator
}

function centerValues(values: number[]): number[] {
  const mean = values.reduce((sum, value) => sum + value, 0) / values.length
  return values.map((value) => value - mean)
}

function rankValues(values: number[]): number[] {
  const n = values.length
  const start = (n - 1) / -2
  const indexed = values.map((value, index) => ({ value, index })).sort((a, b) => a.value - b.value)
  const ranks = new Array<number>(n)

  let position = 0
  while (position < indexed.length) {
    let end = position + 1
    while (end < indexed.length && indexed[end]?.value === indexed[position]?.value) {
      end += 1
    }
    const averageRank = start + (position + end - 1) / 2
    for (let cursor = position; cursor < end; cursor += 1) {
      const entry = indexed[cursor]
      if (entry) {
        ranks[entry.index] = averageRank
      }
    }
    position = end
  }

  return ranks
}

// python/_helpers/_statistics (Locutus helper dependency)
function assertStatisticsArray(data, functionName) {
  if (!Array.isArray(data)) {
    throw new TypeError(`${functionName}() data must be an array`)
  }

  return data
}

function toStatisticNumber(value, functionName) {
  if (typeof value === 'number') {
    return value
  }

  if (typeof value === 'boolean') {
    return value ? 1 : 0
  }

  if (typeof value === 'bigint') {
    const numericValue = Number(value)
    if (!Number.isSafeInteger(numericValue)) {
      throw new RangeError(`${functionName}() bigint values must fit within JS safe integers`)
    }

    return numericValue
  }

  throw new TypeError(`${functionName}() data must contain only real numbers`)
}

function sumProducts(left, right) {
  let total = 0
  for (let index = 0; index < left.length; index += 1) {
    total += (left[index] ?? 0) * (right[index] ?? 0)
  }
  return total
}

// python/statistics/correlation (target function module)
function correlation(x, y, method = 'linear') {
  //      discuss at: https://locutus.io/python/statistics/correlation/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns Pearson correlation by default and supports Python's ranked mode for Spearman correlation.
  //       example 1: correlation([1, 2, 3], [1, 5, 7])
  //       returns 1: 0.9819805060619659
  //       example 2: correlation([1, 2, 3], [7, 5, 3])
  //       returns 2: -1
  //       example 3: correlation([1, 2, 3], [3, 2, 1], 'ranked')
  //       returns 3: -1

  const left = assertStatisticsArray(x, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))
  const right = assertStatisticsArray(y, 'correlation').map((value) => toStatisticNumber(value, 'correlation'))

  const n = left.length
  if (right.length !== n) {
    throw new Error('correlation requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('correlation requires at least two data points')
  }
  if (method !== 'linear' && method !== 'ranked') {
    throw new TypeError(`Unknown method: '${String(method)}'`)
  }

  const xValues = method === 'ranked' ? rankValues(left) : centerValues(left)
  const yValues = method === 'ranked' ? rankValues(right) : centerValues(right)

  const sxy = sumProducts(xValues, yValues)
  const sxx = sumProducts(xValues, xValues)
  const syy = sumProducts(yValues, yValues)
  const denominator = Math.sqrt(sxx * syy)
  if (denominator === 0) {
    throw new Error('at least one of the inputs is constant')
  }

  return sxy / denominator
}

function centerValues(values) {
  const mean = values.reduce((sum, value) => sum + value, 0) / values.length
  return values.map((value) => value - mean)
}

function rankValues(values) {
  const n = values.length
  const start = (n - 1) / -2
  const indexed = values.map((value, index) => ({ value, index })).sort((a, b) => a.value - b.value)
  const ranks = new Array(n)

  let position = 0
  while (position < indexed.length) {
    let end = position + 1
    while (end < indexed.length && indexed[end]?.value === indexed[position]?.value) {
      end += 1
    }
    const averageRank = start + (position + end - 1) / 2
    for (let cursor = position; cursor < end; cursor += 1) {
      const entry = indexed[cursor]
      if (entry) {
        ranks[entry.index] = averageRank
      }
    }
    position = end
  }

  return ranks
}

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