mathjs/lib/function/arithmetic/log1p.js

'use strict';

var deepMap = require('../../utils/collection/deepMap');

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

  /**
   * Calculate the logarithm of a `value+1`.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.log1p(x)
   *    math.log1p(x, base)
   *
   * Examples:
   *
   *    math.log1p(2.5);                 // returns 1.252762968495368
   *    math.exp(math.log1p(1.4));       // returns 2.4
   *
   *    math.pow(10, 4);                 // returns 10000
   *    math.log1p(9999, 10);            // returns 4
   *    math.log1p(9999) / math.log(10); // returns 4
   *
   * See also:
   *
   *    exp, log, log2, log10
   *
   * @param {number | BigNumber | Complex | Array | Matrix} x
   *            Value for which to calculate the logarithm of `x+1`.
   * @param {number | BigNumber | Complex} [base=e]
   *            Optional base for the logarithm. If not provided, the natural
   *            logarithm of `x+1` is calculated.
   * @return {number | BigNumber | Complex | Array | Matrix}
   *            Returns the logarithm of `x+1`
   */
  var log1p = typed('log1p', {
    'number': _log1pNumber,

    'Complex': _log1pComplex,

    'BigNumber': function (x) {
      var y = x.plus(1);
      if (!y.isNegative() || config.predictable) {
        return y.ln();
      }
      else {
        // downgrade to number, return Complex valued result
        return _log1pComplex(new type.Complex(x.toNumber(), 0));
      }
    },

    'Array | Matrix': function (x) {
      return deepMap(x, log1p);
    },

    'any, any': function (x, base) {
      // calculate logarithm for a specified base, log1p(x, base)
      return divideScalar(log1p(x), log(base));
    }
  });

  /**
   * Calculate the natural logarithm of a `number+1`
   * @param {number} x
   * @returns {number | Complex}
   * @private
   */
  function _log1pNumber(x) {
    if (x >= -1 || config.predictable) {
      return (Math.log1p) ? Math.log1p(x) : Math.log(x+1);
    }
    else {
      // negative value -> complex value computation
      return _log1pComplex(new type.Complex(x, 0));
    }
  }

  /**
   * Calculate the natural logarithm of a complex number + 1
   * @param {Complex} x
   * @returns {Complex}
   * @private
   */
  function _log1pComplex(x) {
    var x_re1p = x.re + 1;
    return new type.Complex (
        Math.log(Math.sqrt(x_re1p * x_re1p + x.im * x.im)),
        Math.atan2(x.im, x_re1p)
    );
  }

  log1p.toTex = {
    1: '\\ln\\left(${args[0]}+1\\right)',
    2: '\\log_{${args[1]}}\\left(${args[0]}+1\\right)'
  };

  return log1p;
}

exports.name = 'log1p';
exports.factory = factory;