mathjs/lib/function/trigonometry/csch.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');

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

function factory(type, config, load, typed) {
  /**
   * Calculate the hyperbolic cosecant of a value,
   * defined as `csch(x) = 1 / sinh(x)`.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.csch(x)
   *
   * Examples:
   *
   *    // csch(x) = 1/ sinh(x)
   *    math.csch(0.5)       // returns 1.9190347513349437
   *    1 / math.sinh(0.5)   // returns 1.9190347513349437
   *
   * See also:
   *
   *    sinh, sech, coth
   *
   * @param {number | Complex | Unit | Array | Matrix} x  Function input
   * @return {number | Complex | Array | Matrix} Hyperbolic cosecant of x
   */
  var csch = typed('csch', {
    'number': _csch,
    'Complex': function Complex(x) {
      return x.csch();
    },
    'BigNumber': function BigNumber(x) {
      return new type.BigNumber(1).div(x.sinh());
    },
    'Unit': function Unit(x) {
      if (!x.hasBase(type.Unit.BASE_UNITS.ANGLE)) {
        throw new TypeError('Unit in function csch is no angle');
      }

      return csch(x.value);
    },
    'Array | Matrix': function ArrayMatrix(x) {
      return deepMap(x, csch);
    }
  });
  csch.toTex = {
    1: "\\mathrm{csch}\\left(${args[0]}\\right)"
  };
  return csch;
}
/**
 * Calculate the hyperbolic cosecant of a number
 * @param {number} x
 * @returns {number}
 * @private
 */


function _csch(x) {
  // consider values close to zero (+/-)
  if (x === 0) {
    return Number.POSITIVE_INFINITY;
  } else {
    return Math.abs(2 / (Math.exp(x) - Math.exp(-x))) * sign(x);
  }
}

exports.name = 'csch';
exports.factory = factory;