mathjs/test/unit-tests/function/arithmetic/dotPow.test.js

// test exp
import assert from 'assert'

import approx from '../../../../tools/approx.js'
import math from '../../../../src/defaultInstance.js'
const complex = math.complex
const matrix = math.matrix
const sparse = math.sparse
const unit = math.unit
const dotPow = math.dotPow

describe('dotPow', function () {
  it('should elevate a number to the given power', function () {
    approx.deepEqual(dotPow(2, 3), 8)
    approx.deepEqual(dotPow(2, 4), 16)
    approx.deepEqual(dotPow(-2, 2), 4)
    approx.deepEqual(dotPow(3, 3), 27)
    approx.deepEqual(dotPow(3, -2), 0.111111111111111)
    approx.deepEqual(dotPow(-3, -2), 0.111111111111111)
    approx.deepEqual(dotPow(3, -3), 0.0370370370370370)
    approx.deepEqual(dotPow(-3, -3), -0.0370370370370370)
    approx.deepEqual(dotPow(2, 1.5), 2.82842712474619)
    approx.deepEqual(dotPow(-2, 1.5), complex(0, -2.82842712474619))
  })

  it('should elevate booleans to the given power', function () {
    assert.strictEqual(dotPow(true, true), 1)
    assert.strictEqual(dotPow(true, false), 1)
    assert.strictEqual(dotPow(false, true), 0)
    assert.strictEqual(dotPow(false, false), 1)
  })

  it('should exponentiate mixed numbers and booleans', function () {
    assert.strictEqual(dotPow(2, true), 2)
    assert.strictEqual(dotPow(2, false), 1)
    assert.strictEqual(dotPow(true, 2), 1)
    assert.strictEqual(dotPow(false, 2), 0)
  })

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

  it('should elevate a complex number to the given power', function () {
    approx.deepEqual(dotPow(complex(-1, -1), complex(-1, -1)), complex('-0.0284750589322119 +  0.0606697332231795i'))
    approx.deepEqual(dotPow(complex(-1, -1), complex(-1, 1)), complex('-6.7536199239765713 +  3.1697803027015614i'))
    approx.deepEqual(dotPow(complex(-1, -1), complex(0, -1)), complex('0.0891447921553914 - 0.0321946742909677i'))
    approx.deepEqual(dotPow(complex(-1, -1), complex(0, 1)), complex('9.92340022667813 + 3.58383962127501i'))
    approx.deepEqual(dotPow(complex(-1, -1), complex(1, -1)), complex('-0.1213394664463591 -  0.0569501178644237i'))
    approx.deepEqual(dotPow(complex(-1, -1), complex(1, 1)), complex('-6.3395606054031211 - 13.5072398479531426i'))
    approx.deepEqual(dotPow(complex(-1, 1), complex(-1, -1)), complex('-6.7536199239765713 -  3.1697803027015614i'))
    approx.deepEqual(dotPow(complex(-1, 1), complex(-1, 1)), complex('-0.0284750589322119 -  0.0606697332231795i'))
    approx.deepEqual(dotPow(complex(-1, 1), complex(0, -1)), complex('9.92340022667813 - 3.58383962127501i'))
    approx.deepEqual(dotPow(complex(-1, 1), complex(0, 1)), complex('0.0891447921553914 + 0.0321946742909677i'))
    approx.deepEqual(dotPow(complex(-1, 1), complex(1, -1)), complex('-6.3395606054031211 + 13.5072398479531426i'))
    approx.deepEqual(dotPow(complex(-1, 1), complex(1, 1)), complex('-0.1213394664463591 +  0.0569501178644237i'))

    approx.deepEqual(dotPow(complex(0, -1), complex(-1, -1)), complex('0.000000000000000 + 0.207879576350762i'))
    approx.deepEqual(dotPow(complex(0, -1), complex(-1, 1)), complex('0.000000000000000 + 4.810477380965351i'))
    approx.deepEqual(dotPow(complex(0, -1), complex(1, -1)), complex('0.000000000000000 - 0.207879576350762i'))
    approx.deepEqual(dotPow(complex(0, -1), complex(1, 1)), complex('0.000000000000000 - 4.810477380965351i'))
    approx.deepEqual(dotPow(complex(0, 1), complex(-1, -1)), complex('0.000000000000000 - 4.810477380965351i'))
    approx.deepEqual(dotPow(complex(0, 1), complex(-1, 1)), complex('0.000000000000000 - 0.207879576350762i'))
    approx.deepEqual(dotPow(complex(0, 1), complex(1, -1)), complex('0.000000000000000 + 4.810477380965351i'))
    approx.deepEqual(dotPow(complex(0, 1), complex(1, 1)), complex('0.000000000000000 + 0.207879576350762i'))

    approx.deepEqual(dotPow(complex(1, -1), complex(-1, -1)), complex('0.2918503793793073 +  0.1369786269150605i'))
    approx.deepEqual(dotPow(complex(1, -1), complex(-1, 1)), complex('0.6589325864505904 +  1.4039396486303144i'))
    approx.deepEqual(dotPow(complex(1, -1), complex(0, -1)), complex('0.428829006294368 - 0.154871752464247i'))
    approx.deepEqual(dotPow(complex(1, -1), complex(0, 1)), complex('2.062872235080905 + 0.745007062179724i'))
    approx.deepEqual(dotPow(complex(1, -1), complex(1, -1)), complex('0.2739572538301211 -  0.5837007587586147i'))
    approx.deepEqual(dotPow(complex(1, -1), complex(1, 1)), complex('2.8078792972606288 -  1.3178651729011805i'))
    approx.deepEqual(dotPow(complex(1, 1), complex(-1, -1)), complex('0.6589325864505904 -  1.4039396486303144i'))
    approx.deepEqual(dotPow(complex(1, 1), complex(-1, 1)), complex('0.2918503793793073 -  0.1369786269150605i'))
    approx.deepEqual(dotPow(complex(1, 1), complex(0, -1)), complex('2.062872235080905 - 0.745007062179724i'))
    approx.deepEqual(dotPow(complex(1, 1), complex(0, 1)), complex('0.428829006294368 + 0.154871752464247i'))
    approx.deepEqual(dotPow(complex(1, 1), complex(1, -1)), complex('2.8078792972606288 +  1.3178651729011805i'))
    approx.deepEqual(dotPow(complex(1, 1), complex(1, 1)), complex('0.2739572538301211 +  0.5837007587586147i'))
  })

  it('should throw an error with units', function () {
    assert.throws(function () { dotPow(unit('5cm')) })
  })

  it('should throw an error with strings', function () {
    assert.throws(function () { dotPow('text') })
  })

  describe('Array', function () {
    it('should elevate array .^ scalar', function () {
      approx.deepEqual(dotPow([[1, 2], [0, 4]], 2), [[1, 4], [0, 16]])
      approx.deepEqual(dotPow([[1, 2], [0, 4]], 2.5), [[1, 5.65685424949238], [0, 32]])
      approx.deepEqual(dotPow([[1, 2, 3], [4, 5, 0]], 2), [[1, 4, 9], [16, 25, 0]])
    })

    it('should elevate scalar .^ array', function () {
      approx.deepEqual(dotPow(2, [[1, 2], [0, 4]]), [[2, 4], [1, 16]])
      approx.deepEqual(dotPow(2.5, [[1, 2], [0, 4]]), [[2.5, 6.25], [1, 39.0625]])
      approx.deepEqual(dotPow(2, [[1, 2, 3], [4, 5, 0]]), [[2, 4, 8], [16, 32, 1]])
    })

    it('should elevate array .^ array', function () {
      approx.deepEqual(dotPow([[1, 2, 0], [0, 1, 4]], [[2, 1, 0], [4, 1, 0]]), [[1, 2, 1], [0, 1, 1]])
    })

    it('should elevate array .^ dense matrix', function () {
      approx.deepEqual(dotPow([[1, 2, 0], [0, 1, 4]], matrix([[2, 1, 0], [4, 1, 0]])), matrix([[1, 2, 1], [0, 1, 1]]))
    })

    it('should elevate array .^ sparse matrix', function () {
      approx.deepEqual(dotPow([[1, 2, 0], [0, 1, 4]], sparse([[2, 1, 0], [4, 1, 0]])), matrix([[1, 2, 1], [0, 1, 1]]))
    })
  })

  describe('DenseMatrix', function () {
    it('should elevate dense matrix .^ scalar', function () {
      approx.deepEqual(dotPow(matrix([[1, 2], [0, 4]]), 2), matrix([[1, 4], [0, 16]]))
      approx.deepEqual(dotPow(matrix([[1, 2], [0, 4]]), 2.5), matrix([[1, 5.65685424949238], [0, 32]]))
      approx.deepEqual(dotPow(matrix([[1, 2, 3], [4, 5, 0]]), 2), matrix([[1, 4, 9], [16, 25, 0]]))
    })

    it('should elevate scaler .^ dense matrix', function () {
      approx.deepEqual(dotPow(2, matrix([[1, 2], [0, 4]])), matrix([[2, 4], [1, 16]]))
      approx.deepEqual(dotPow(2.5, matrix([[1, 2], [0, 4]])), matrix([[2.5, 6.25], [1, 39.0625]]))
      approx.deepEqual(dotPow(2, matrix([[1, 2, 3], [4, 5, 0]])), matrix([[2, 4, 8], [16, 32, 1]]))
    })

    it('should elevate dense matrix .^ array', function () {
      approx.deepEqual(dotPow(matrix([[1, 2, 0], [0, 1, 4]]), [[2, 1, 0], [4, 1, 0]]), matrix([[1, 2, 1], [0, 1, 1]]))
    })

    it('should elevate dense matrix .^ dense matrix', function () {
      approx.deepEqual(dotPow(matrix([[1, 2, 0], [0, 1, 4]]), matrix([[2, 1, 0], [4, 1, 0]])), matrix([[1, 2, 1], [0, 1, 1]]))
    })

    it('should elevate dense matrix .^ sparse matrix', function () {
      approx.deepEqual(dotPow(matrix([[1, 2, 0], [0, 1, 4]]), sparse([[2, 1, 0], [4, 1, 0]])), matrix([[1, 2, 1], [0, 1, 1]]))
    })
  })

  describe('SparseMatrix', function () {
    it('should elevate sparse matrix .^ scalar', function () {
      approx.deepEqual(dotPow(sparse([[1, 2], [0, 4]]), 2), sparse([[1, 4], [0, 16]]))
      approx.deepEqual(dotPow(sparse([[1, 2], [0, 4]]), 2.5), sparse([[1, 5.65685424949238], [0, 32]]))
      approx.deepEqual(dotPow(sparse([[1, 2, 3], [4, 5, 0]]), 2), sparse([[1, 4, 9], [16, 25, 0]]))
    })

    it('should elevate scalar .^ sparse matrix', function () {
      approx.deepEqual(dotPow(2, sparse([[1, 2], [0, 4]])), matrix([[2, 4], [1, 16]]))
      approx.deepEqual(dotPow(2.5, sparse([[1, 2], [0, 4]])), matrix([[2.5, 6.25], [1, 39.0625]]))
      approx.deepEqual(dotPow(2, sparse([[1, 2, 3], [4, 5, 0]])), matrix([[2, 4, 8], [16, 32, 1]]))
    })

    it('should elevate sparse matrix .^ array', function () {
      approx.deepEqual(dotPow(sparse([[1, 2, 0], [0, 1, 4]]), [[2, 1, 0], [4, 1, 0]]), matrix([[1, 2, 1], [0, 1, 1]]))
    })

    it('should elevate sparse matrix .^ dense matrix', function () {
      approx.deepEqual(dotPow(sparse([[1, 2, 0], [0, 1, 4]]), matrix([[2, 1, 0], [4, 1, 0]])), matrix([[1, 2, 1], [0, 1, 1]]))
    })

    it('should elevate sparse matrix .^ sparse matrix', function () {
      approx.deepEqual(dotPow(sparse([[1, 2, 0], [0, 1, 4]]), sparse([[2, 1, 0], [4, 1, 0]])), matrix([[1, 2, 1], [0, 1, 1]]))
    })
  })

  it('should LaTeX dotPow', function () {
    const expression = math.parse('dotPow([1,2],[3,4])')
    assert.strictEqual(expression.toTex(), '\\left(\\begin{bmatrix}1\\\\2\\\\\\end{bmatrix}.^\\wedge\\begin{bmatrix}3\\\\4\\\\\\end{bmatrix}\\right)')
  })
})