mathjs/lib/function/relational/smallerEq.js

'use strict';

var nearlyEqual = require('../../utils/number').nearlyEqual;
var bigNearlyEqual = require('../../utils/bignumber/nearlyEqual');

function factory (type, config, load, typed) {

  var matrix = load(require('../../type/matrix/function/matrix'));

  var algorithm03 = load(require('../../type/matrix/utils/algorithm03'));
  var algorithm07 = load(require('../../type/matrix/utils/algorithm07'));
  var algorithm12 = load(require('../../type/matrix/utils/algorithm12'));
  var algorithm13 = load(require('../../type/matrix/utils/algorithm13'));
  var algorithm14 = load(require('../../type/matrix/utils/algorithm14'));

  var latex = require('../../utils/latex');

  /**
   * Test whether value x is smaller or equal to y.
   *
   * The function returns true when x is smaller than y or the relative
   * difference between x and y is smaller than the configured epsilon. The
   * function cannot be used to compare values smaller than approximately 2.22e-16.
   *
   * For matrices, the function is evaluated element wise.
   * Strings are compared by their numerical value.
   *
   * Syntax:
   *
   *    math.smallerEq(x, y)
   *
   * Examples:
   *
   *    math.smaller(1 + 2, 3);        // returns false
   *    math.smallerEq(1 + 2, 3);      // returns true
   *
   * See also:
   *
   *    equal, unequal, smaller, larger, largerEq, compare
   *
   * @param  {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} x First value to compare
   * @param  {number | BigNumber | Fraction | boolean | Unit | string | Array | Matrix} y Second value to compare
   * @return {boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false
   */
  var smallerEq = typed('smallerEq', {

    'boolean, boolean': function (x, y) {
      return x <= y;
    },

    'number, number': function (x, y) {
      return x <= y || nearlyEqual(x, y, config.epsilon);
    },

    'BigNumber, BigNumber': function (x, y) {
      return x.lte(y) || bigNearlyEqual(x, y, config.epsilon);
    },

    'Fraction, Fraction': function (x, y) {
      return x.compare(y) !== 1;
    },

    'Complex, Complex': function () {
      throw new TypeError('No ordering relation is defined for complex numbers');
    },

    'Unit, Unit': function (x, y) {
      if (!x.equalBase(y)) {
        throw new Error('Cannot compare units with different base');
      }
      return smallerEq(x.value, y.value);
    },

    'SparseMatrix, SparseMatrix': function(x, y) {
      return algorithm07(x, y, smallerEq);
    },

    'SparseMatrix, DenseMatrix': function(x, y) {
      return algorithm03(y, x, smallerEq, true);
    },

    'DenseMatrix, SparseMatrix': function(x, y) {
      return algorithm03(x, y, smallerEq, false);
    },

    'DenseMatrix, DenseMatrix': function(x, y) {
      return algorithm13(x, y, smallerEq);
    },

    'Array, Array': function (x, y) {
      // use matrix implementation
      return smallerEq(matrix(x), matrix(y)).valueOf();
    },

    'Array, Matrix': function (x, y) {
      // use matrix implementation
      return smallerEq(matrix(x), y);
    },

    'Matrix, Array': function (x, y) {
      // use matrix implementation
      return smallerEq(x, matrix(y));
    },

    'SparseMatrix, any': function (x, y) {
      return algorithm12(x, y, smallerEq, false);
    },

    'DenseMatrix, any': function (x, y) {
      return algorithm14(x, y, smallerEq, false);
    },

    'any, SparseMatrix': function (x, y) {
      return algorithm12(y, x, smallerEq, true);
    },

    'any, DenseMatrix': function (x, y) {
      return algorithm14(y, x, smallerEq, true);
    },

    'Array, any': function (x, y) {
      // use matrix implementation
      return algorithm14(matrix(x), y, smallerEq, false).valueOf();
    },

    'any, Array': function (x, y) {
      // use matrix implementation
      return algorithm14(matrix(y), x, smallerEq, true).valueOf();
    }
  });

  smallerEq.toTex = {
    2: '\\left(${args[0]}' + latex.operators['smallerEq'] + '${args[1]}\\right)'
  };

  return smallerEq;
}

exports.name = 'smallerEq';
exports.factory = factory;