mathjs/src/function/trigonometry/atan2.js

'use strict'

function factory (type, config, load, typed) {
  const matrix = load(require('../../type/matrix/function/matrix'))

  const algorithm02 = load(require('../../type/matrix/utils/algorithm02'))
  const algorithm03 = load(require('../../type/matrix/utils/algorithm03'))
  const algorithm09 = load(require('../../type/matrix/utils/algorithm09'))
  const algorithm11 = load(require('../../type/matrix/utils/algorithm11'))
  const algorithm12 = load(require('../../type/matrix/utils/algorithm12'))
  const algorithm13 = load(require('../../type/matrix/utils/algorithm13'))
  const algorithm14 = load(require('../../type/matrix/utils/algorithm14'))

  /**
   * Calculate the inverse tangent function with two arguments, y/x.
   * By providing two arguments, the right quadrant of the computed angle can be
   * determined.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.atan2(y, x)
   *
   * Examples:
   *
   *    math.atan2(2, 2) / math.pi       // returns number 0.25
   *
   *    const angle = math.unit(60, 'deg') // returns Unit 60 deg
   *    const x = math.cos(angle)
   *    const y = math.sin(angle)
   *
   *    math.atan(2)             // returns Complex 1.5707963267948966 -1.3169578969248166 i
   *
   * See also:
   *
   *    tan, atan, sin, cos
   *
   * @param {number | Array | Matrix} y  Second dimension
   * @param {number | Array | Matrix} x  First dimension
   * @return {number | Array | Matrix} Four-quadrant inverse tangent
   */
  const atan2 = typed('atan2', {

    'number, number': Math.atan2,

    // Complex numbers doesn't seem to have a reasonable implementation of
    // atan2(). Even Matlab removed the support, after they only calculated
    // the atan only on base of the real part of the numbers and ignored the imaginary.

    'BigNumber, BigNumber': function (y, x) {
      return type.BigNumber.atan2(y, x)
    },

    'SparseMatrix, SparseMatrix': function (x, y) {
      return algorithm09(x, y, atan2, false)
    },

    'SparseMatrix, DenseMatrix': function (x, y) {
      // mind the order of y and x!
      return algorithm02(y, x, atan2, true)
    },

    'DenseMatrix, SparseMatrix': function (x, y) {
      return algorithm03(x, y, atan2, false)
    },

    'DenseMatrix, DenseMatrix': function (x, y) {
      return algorithm13(x, y, atan2)
    },

    'Array, Array': function (x, y) {
      return atan2(matrix(x), matrix(y)).valueOf()
    },

    'Array, Matrix': function (x, y) {
      return atan2(matrix(x), y)
    },

    'Matrix, Array': function (x, y) {
      return atan2(x, matrix(y))
    },

    'SparseMatrix, number | BigNumber': function (x, y) {
      return algorithm11(x, y, atan2, false)
    },

    'DenseMatrix, number | BigNumber': function (x, y) {
      return algorithm14(x, y, atan2, false)
    },

    'number | BigNumber, SparseMatrix': function (x, y) {
      // mind the order of y and x
      return algorithm12(y, x, atan2, true)
    },

    'number | BigNumber, DenseMatrix': function (x, y) {
      // mind the order of y and x
      return algorithm14(y, x, atan2, true)
    },

    'Array, number | BigNumber': function (x, y) {
      return algorithm14(matrix(x), y, atan2, false).valueOf()
    },

    'number | BigNumber, Array': function (x, y) {
      return algorithm14(matrix(y), x, atan2, true).valueOf()
    }
  })

  atan2.toTex = { 2: `\\mathrm{atan2}\\left(\${args}\\right)` }

  return atan2
}

exports.name = 'atan2'
exports.factory = factory