mathjs/lib/function/arithmetic/log.js

'use strict';

function factory (type, config, load, typed) {
  var collection = load(require('../../type/matrix/collection'));
  var divideScalar = load(require('./divideScalar'));

  /**
   * Calculate the logarithm of a value.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.log(x)
   *    math.log(x, base)
   *
   * Examples:
   *
   *    math.log(3.5);                  // returns 1.252762968495368
   *    math.exp(math.log(2.4));        // returns 2.4
   *
   *    math.pow(10, 4);                // returns 10000
   *    math.log(10000, 10);            // returns 4
   *    math.log(10000) / math.log(10); // returns 4
   *
   *    math.log(1024, 2);              // returns 10
   *    math.pow(2, 10);                // returns 1024
   *
   * See also:
   *
   *    exp, log10
   *
   * @param {number | BigNumber | Complex | Array | Matrix} x
   *            Value for which to calculate the logarithm.
   * @param {number | BigNumber | Complex} [base=e]
   *            Optional base for the logarithm. If not provided, the natural
   *            logarithm of `x` is calculated.
   * @return {number | BigNumber | Complex | Array | Matrix}
   *            Returns the logarithm of `x`
   */
  var log = typed('log', {
    'number': _logNumber,

    'Complex': _logComplex,

    'BigNumber': function (x) {
      if (!x.isNegative() || config.predictable) {
        return x.ln();
      }
      else {
        // downgrade to number, return Complex valued result
        return _logComplex(new type.Complex(x.toNumber(), 0));
      }
    },

    'Array | Matrix': function (x) {
      return collection.deepMap(x, log);
    },

    'any, any': function (x, base) {
      // calculate logarithm for a specified base, log(x, base)
      return divideScalar(log(x), log(base));
    }
  });

  /**
   * Calculate the natural logarithm of a number
   * @param {number} x
   * @returns {number | Complex}
   * @private
   */
  function _logNumber(x) {
    if (x >= 0 || config.predictable) {
      return Math.log(x);
    }
    else {
      // negative value -> complex value computation
      return log(new type.Complex(x, 0));
    }
  }

  /**
   * Calculate the natural logarithm of a complex number
   * @param {Complex} x
   * @returns {Complex}
   * @private
   */
  function _logComplex(x) {
    return new type.Complex (
        Math.log(Math.sqrt(x.re * x.re + x.im * x.im)),
        Math.atan2(x.im, x.re)
    );
  }

  return log;
}

exports.name = 'log';
exports.factory = factory;