mathjs/lib/type/complex/Complex.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict';

function _typeof(obj) { if (typeof Symbol === "function" && typeof Symbol.iterator === "symbol") { _typeof = function _typeof(obj) { return typeof obj; }; } else { _typeof = function _typeof(obj) { return obj && typeof Symbol === "function" && obj.constructor === Symbol && obj !== Symbol.prototype ? "symbol" : typeof obj; }; } return _typeof(obj); }

var Complex = require('complex.js');

var format = require('../../utils/number').format;

var isNumber = require('../../utils/number').isNumber;

function factory(type, config, load, typed, math) {
  /**
   * Attach type information
   */
  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) {
    var str = '';
    var im = this.im;
    var re = this.re;
    var strRe = format(this.re, options);
    var strIm = format(this.im, options); // round either re or im when smaller than the configured precision

    var precision = isNumber(options) ? options : options ? options.precision : null;

    if (precision !== null) {
      var 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:
        var arg = arguments[0];

        if (_typeof(arg) === 'object') {
          return Complex(arg);
        }

        throw new TypeError('Input has to be an object with r and phi keys.');

      case 2:
        var r = arguments[0];
        var phi = arguments[1];

        if (isNumber(r)) {
          if (type.isUnit(phi) && phi.hasBase('ANGLE')) {
            // convert unit to a number in radians
            phi = phi.toNumber('rad');
          }

          if (isNumber(phi)) {
            return new Complex({
              r: r,
              phi: 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);
  }; // apply the current epsilon


  Complex.EPSILON = config.epsilon; // listen for changed in the configuration, automatically apply changed epsilon

  math.on('config', function (curr, prev) {
    if (curr.epsilon !== prev.epsilon) {
      Complex.EPSILON = curr.epsilon;
    }
  });
  /**
   * 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;
}

exports.name = 'Complex';
exports.path = 'type';
exports.factory = factory;
exports.math = true; // request access to the math namespace