mathjs/lib/function/arithmetic/log1p.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';

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 BigNumber(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 ArrayMatrix(x) {
      return deepMap(x, log1p);
    },
    'any, any': function anyAny(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 xRe1p = x.re + 1;
    return new type.Complex(Math.log(Math.sqrt(xRe1p * xRe1p + x.im * x.im)), Math.atan2(x.im, xRe1p));
  }

  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;