Complex.js

import Complex from 'complex.js'
import { format } from '../../utils/number.js'
import { isNumber, isUnit } from '../../utils/is.js'
import { factory } from '../../utils/factory.js'

const name = 'Complex'
const dependencies = []

export const createComplexClass = /* #__PURE__ */ factory(name, dependencies, () => {
  /**
   * Attach type information
   */
  Object.defineProperty(Complex, 'name', { value: 'Complex' })
  Complex.prototype.constructor = Complex
  Complex.prototype.type = 'Complex'
  Complex.prototype.isComplex = true

  /**
   * Get a JSON representation of the complex number
   * @returns {Object} Returns a JSON object structured as:
   *                   `{"mathjs": "Complex", "re": 2, "im": 3}`
   */
  Complex.prototype.toJSON = function () {
    return {
      mathjs: 'Complex',
      re: this.re,
      im: this.im
    }
  }

  /*
   * Return the value of the complex number in polar notation
   * The angle phi will be set in the interval of [-pi, pi].
   * @return {{r: number, phi: number}} Returns and object with properties r and phi.
   */
  Complex.prototype.toPolar = function () {
    return {
      r: this.abs(),
      phi: this.arg()
    }
  }

  /**
   * Get a string representation of the complex number,
   * with optional formatting options.
   * @param {Object | number | Function} [options]  Formatting options. See
   *                                                lib/utils/number:format for a
   *                                                description of the available
   *                                                options.
   * @return {string} str
   */
  Complex.prototype.format = function (options) {
    let str = ''
    let im = this.im
    let re = this.re
    const strRe = format(this.re, options)
    const strIm = format(this.im, options)

    // round either re or im when smaller than the configured precision
    const precision = isNumber(options) ? options : options ? options.precision : null
    if (precision !== null) {
      const epsilon = Math.pow(10, -precision)
      if (Math.abs(re / im) < epsilon) {
        re = 0
      }
      if (Math.abs(im / re) < epsilon) {
        im = 0
      }
    }

    if (im === 0) {
      // real value
      str = strRe
    } else if (re === 0) {
      // purely complex value
      if (im === 1) {
        str = 'i'
      } else if (im === -1) {
        str = '-i'
      } else {
        str = strIm + 'i'
      }
    } else {
      // complex value
      if (im < 0) {
        if (im === -1) {
          str = strRe + ' - i'
        } else {
          str = strRe + ' - ' + strIm.substring(1) + 'i'
        }
      } else {
        if (im === 1) {
          str = strRe + ' + i'
        } else {
          str = strRe + ' + ' + strIm + 'i'
        }
      }
    }
    return str
  }

  /**
   * Create a complex number from polar coordinates
   *
   * Usage:
   *
   *     Complex.fromPolar(r: number, phi: number) : Complex
   *     Complex.fromPolar({r: number, phi: number}) : Complex
   *
   * @param {*} args...
   * @return {Complex}
   */
  Complex.fromPolar = function (args) {
    switch (arguments.length) {
      case 1:
      {
        const arg = arguments[0]
        if (typeof arg === 'object') {
          return Complex(arg)
        } else {
          throw new TypeError('Input has to be an object with r and phi keys.')
        }
      }
      case 2:
      {
        const r = arguments[0]
        let phi = arguments[1]
        if (isNumber(r)) {
          if (isUnit(phi) && phi.hasBase('ANGLE')) {
            // convert unit to a number in radians
            phi = phi.toNumber('rad')
          }

          if (isNumber(phi)) {
            return new Complex({ r, phi })
          }

          throw new TypeError('Phi is not a number nor an angle unit.')
        } else {
          throw new TypeError('Radius r is not a number.')
        }
      }

      default:
        throw new SyntaxError('Wrong number of arguments in function fromPolar')
    }
  }

  Complex.prototype.valueOf = Complex.prototype.toString

  /**
   * Create a Complex number from a JSON object
   * @param {Object} json  A JSON Object structured as
   *                       {"mathjs": "Complex", "re": 2, "im": 3}
   *                       All properties are optional, default values
   *                       for `re` and `im` are 0.
   * @return {Complex} Returns a new Complex number
   */
  Complex.fromJSON = function (json) {
    return new Complex(json)
  }

  /**
   * Compare two complex numbers, `a` and `b`:
   *
   * - Returns 1 when the real part of `a` is larger than the real part of `b`
   * - Returns -1 when the real part of `a` is smaller than the real part of `b`
   * - Returns 1 when the real parts are equal
   *   and the imaginary part of `a` is larger than the imaginary part of `b`
   * - Returns -1 when the real parts are equal
   *   and the imaginary part of `a` is smaller than the imaginary part of `b`
   * - Returns 0 when both real and imaginary parts are equal.
   *
   * @params {Complex} a
   * @params {Complex} b
   * @returns {number} Returns the comparison result: -1, 0, or 1
   */
  Complex.compare = function (a, b) {
    if (a.re > b.re) { return 1 }
    if (a.re < b.re) { return -1 }

    if (a.im > b.im) { return 1 }
    if (a.im < b.im) { return -1 }

    return 0
  }

  return Complex
}, { isClass: true })