mathjs/test/unit-tests/function/trigonometry/atan2.test.js

// test atan2
import assert from 'assert'

import math from '../../../../src/defaultInstance.js'
import approx from '../../../../tools/approx.js'
const pi = math.pi
const complex = math.complex
const matrix = math.matrix
const sparse = math.sparse
const unit = math.unit
const divide = math.divide
const atan2 = math.atan2
const bigmath = math.create({ precision: 20 })
const Big = bigmath.bignumber
const atan2Big = bigmath.atan2

describe('atan2', function () {
  it('should calculate atan2 correctly', function () {
    assert.strictEqual(atan2(0, 0) / pi, 0)
    assert.strictEqual(atan2(0, 1) / pi, 0)
    assert.strictEqual(atan2(1, 1) / pi, 0.25)
    assert.strictEqual(atan2(1, 0) / pi, 0.5)
    assert.strictEqual(atan2(1, -1) / pi, 0.75)
    assert.strictEqual(atan2(0, -1) / pi, 1)
    assert.strictEqual(atan2(-1, -1) / pi, -0.75)
    assert.strictEqual(atan2(-1, 0) / pi, -0.5)
    assert.strictEqual(atan2(-1, 1) / pi, -0.25)
  })

  it('should calculate atan2 for booleans', function () {
    assert.strictEqual(atan2(true, true), 0.25 * pi)
    assert.strictEqual(atan2(true, false), 0.5 * pi)
    assert.strictEqual(atan2(false, true), 0)
    assert.strictEqual(atan2(false, false), 0)
  })

  it('should calculate atan2 with mixed numbers and booleans', function () {
    assert.strictEqual(atan2(1, true), 0.25 * pi)
    assert.strictEqual(atan2(1, false), 0.5 * pi)
    assert.strictEqual(atan2(true, 1), 0.25 * pi)
    assert.strictEqual(atan2(false, 1), 0)
  })

  it('should return the arctan of for bignumbers', function () {
    assert.deepStrictEqual(atan2Big(Big(0), Big(0)), Big(0))
    assert.deepStrictEqual(atan2Big(Big(0), Big(1)), Big(0))
    assert.deepStrictEqual(atan2Big(Big(1), Big(1)), Big('0.78539816339744830962'))
    assert.deepStrictEqual(atan2Big(Big(1), Big(0)), Big('1.5707963267948966192'))
    assert.deepStrictEqual(atan2Big(Big(1), Big(-1)), Big('2.3561944901923449288'))
    assert.deepStrictEqual(atan2Big(Big(0), Big(-1)), Big('3.1415926535897932385'))
    assert.deepStrictEqual(atan2Big(Big(-1), Big(-1)), Big('-2.3561944901923449288'))
    assert.deepStrictEqual(atan2Big(Big(-1), Big(0)), Big('-1.5707963267948966192'))
    assert.deepStrictEqual(atan2Big(Big(-1), Big(1)), Big('-0.78539816339744830962'))
  })

  it('should return the arctan of for mixed numbers and bignumbers', function () {
    assert.deepStrictEqual(atan2Big(1, Big(1)), Big('0.78539816339744830962'))
    assert.deepStrictEqual(atan2Big(Big(1), 1), Big('0.78539816339744830962'))
  })

  it('should return the arctan of for mixed bignumbers and booleans', function () {
    assert.deepStrictEqual(atan2Big(Big(1), true), Big('0.78539816339744830962'))
    assert.deepStrictEqual(atan2Big(Big(1), false), Big('1.5707963267948966192'))
    assert.deepStrictEqual(atan2Big(true, Big(1)), Big('0.78539816339744830962'))
    assert.deepStrictEqual(atan2Big(false, Big(1)), Big(0))
  })

  it('should throw an error if called with a complex', function () {
    assert.throws(function () { atan2(complex('2+3i'), complex('1-2i')) })
  })

  it('should throw an error if called with a string', function () {
    assert.throws(function () { atan2('string', 1) })
  })

  it('should throw an error if called with a unit', function () {
    assert.throws(function () { atan2(unit('5cm'), 1) })
  })

  describe('Array', function () {
    it('should calculate atan2 array - scalar', function () {
      assert.deepStrictEqual(divide(atan2(1, [1, -1, 0]), pi), [0.25, 0.75, 0.5])
      assert.deepStrictEqual(divide(atan2([1, -1, 0], 1), pi), [0.25, -0.25, 0])
    })

    it('should calculate atan2 array - array', function () {
      assert.deepStrictEqual(divide(atan2([[1, -1, 0], [1, -1, 0]], [[-1, 0, 1], [1, 1, 1]]), pi), [[0.75, -0.5, 0], [0.25, -0.25, 0]])
    })

    it('should calculate atan2 array - dense matrix', function () {
      assert.deepStrictEqual(divide(atan2([[1, -1, 0], [1, -1, 0]], matrix([[-1, 0, 1], [1, 1, 1]])), pi), matrix([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })

    it('should calculate atan2 array - sparse matrix', function () {
      assert.deepStrictEqual(divide(atan2([[1, -1, 0], [1, -1, 0]], sparse([[-1, 0, 1], [1, 1, 1]])), pi), matrix([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })
  })

  describe('DenseMatrix', function () {
    it('should calculate atan2 dense matrix - scalar', function () {
      assert.deepStrictEqual(divide(atan2(1, matrix([1, -1, 0])), pi), matrix([0.25, 0.75, 0.5]))
      assert.deepStrictEqual(divide(atan2(matrix([1, -1, 0]), 1), pi), matrix([0.25, -0.25, 0]))
    })

    it('should calculate atan2 dense matrix - array', function () {
      assert.deepStrictEqual(divide(atan2(matrix([[1, -1, 0], [1, -1, 0]]), [[-1, 0, 1], [1, 1, 1]]), pi), matrix([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })

    it('should calculate atan2 dense matrix - dense matrix', function () {
      assert.deepStrictEqual(divide(atan2(matrix([[1, -1, 0], [1, -1, 0]]), matrix([[-1, 0, 1], [1, 1, 1]])), pi), matrix([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })

    it('should calculate atan2 dense matrix - sparse matrix', function () {
      assert.deepStrictEqual(divide(atan2(matrix([[1, -1, 0], [1, -1, 0]]), sparse([[-1, 0, 1], [1, 1, 1]])), pi), matrix([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })
  })

  describe('SparseMatrix', function () {
    it('should calculate atan2 sparse matrix - scalar', function () {
      assert.deepStrictEqual(divide(atan2(1, sparse([[1, -1], [0, 1]])), pi), matrix([[0.25, 0.75], [0.5, 0.25]]))
      assert.deepStrictEqual(divide(atan2(sparse([[1, -1], [0, 1]]), 1), pi), sparse([[0.25, -0.25], [0, 0.25]]))
    })

    it('should calculate atan2 sparse matrix - array', function () {
      assert.deepStrictEqual(divide(atan2(sparse([[1, -1, 0], [1, -1, 0]]), [[-1, 0, 1], [1, 1, 1]]), pi), sparse([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })

    it('should calculate atan2 sparse matrix - dense matrix', function () {
      assert.deepStrictEqual(divide(atan2(sparse([[1, -1, 0], [1, -1, 0]]), matrix([[-1, 0, 1], [1, 1, 1]])), pi), sparse([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })

    it('should calculate atan2 sparse matrix - sparse matrix', function () {
      assert.deepStrictEqual(divide(atan2(sparse([[1, -1, 0], [1, -1, 0]]), sparse([[-1, 0, 1], [1, 1, 1]])), pi), sparse([[0.75, -0.5, 0], [0.25, -0.25, 0]]))
    })
  })

  it('should calculate the atan2 element-wise for arrays and matrices', function () {
    // array, matrix, range
    approx.deepEqual(divide(atan2([1, 0, -1], [1, 0, -1]), pi), [0.25, 0, -0.75])
    approx.deepEqual(divide(atan2(
      matrix([1, 0, -1]),
      matrix([1, 0, -1])), pi),
    matrix([0.25, 0, -0.75]))
    assert.strictEqual(atan2(0, 2) / pi, 0)
    assert.strictEqual(atan2(0, -2) / pi, 1)
  })

  it('should throw an error in case of invalid number of arguments', function () {
    assert.throws(function () { atan2(1) }, /TypeError: Too few arguments/)
    assert.throws(function () { atan2(1, 2, 3) }, /TypeError: Too many arguments/)
  })

  it('should throw an error in case of invalid type of arguments', function () {
    assert.throws(function () { atan2(null) }, /TypeError: Unexpected type of argument/)
  })

  it('should LaTeX atan2', function () {
    const expression = math.parse('atan2(1,1)')
    assert.strictEqual(expression.toTex(), '\\mathrm{atan2}\\left(1,1\\right)')
  })
})