mathjs: A JavaScript repository from robz

http://mathjs.org

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with real and complex numbers, units, and matrices. Powerful and easy to use.

Features

Supports numbers, complex numbers, units, strings, arrays, and matrices.
Is compatible with JavaScript's built-in Math library.
Contains a flexible expression parser.
Supports chained operations.
Comes with a large set of built-in functions and constants.
Has no dependencies. Runs on any JavaScript engine.
Can be used as a command line application as well.
Is easily extensible.

Install

Math.js can be installed using npm, bower, or by just downloading the library.

WARNING: math.js is in early stage and the API is not yet stabilized. Please be careful when upgrading to a newer version. An overview of the changes is available here.

npm

Math.js can be installed using npm:

npm install mathjs

Note: when installed globally (using the -g option), math.js is available as a command line application mathjs, see section command line interface.

bower

Or using bower:

bower install mathjs

download

Or by downloading the latest version from mathjs.org:

math.js (Development version)
math.min.js (Production version)

Load

Node.js

Load math.js in node.js:

var math = require('mathjs');

math.sqrt(-4); // 2i

Browser

Math.js can be loaded as a regular javascript file in the browser:

<!DOCTYPE HTML>
<html>
<head>
    <script src="math.js" type="text/javascript"></script>
</head>
<body>
    <script type="text/javascript">
        math.sqrt(-4); // 2i
    </script>
</body>
</html>

Require.js

Load math.js in the browser using require.js:

require.config({
    paths: {
        mathjs: 'path/to/mathjs',
    }
});
require(['mathjs'], function (math) {
    math.sqrt(-4); // 2i
});

Use

Math.js can be used similar to JavaScript's built-in Math library. Besides that, math.js can evaluate expressions (see Expressions) and supports chained operations (see Chained operations).

The example code below shows how to use math.js. More examples can be found in the examples directory.

// load math.js
var math = require('mathjs');

// functions and constants
math.round(math.e, 3);            // 2.718
math.atan2(3, -3) / math.pi;      // 0.75
math.log(1000, 10);               // 3
math.sqrt(-4);                    // 2i
math.pow([[-1, 2], [3, 1]], 2);   // [[7, 0], [0, 7]]

// expressions
math.eval('12 / (2.3 + 0.7)');    // 4
math.eval('5.08 cm in inch');     // 2 inch
math.eval('sin(45 deg) ^ 2');     // 0.5
math.eval('9 / 3 + 2i');          // 3 + 2i
math.eval('det([-1, 2; 3, 1])');  // -7

// chained operations
math.select(3)
    .add(4)
    .multiply(2)
    .done(); // 14

Expressions

Math.js contains a flexible and easy to use expression parser. The parser supports all data types, methods and constants available in math.js. Expressions can be evaluated in various ways:

Using the function math.eval(expr [,scope]).
Using the function math.parse(expr [,scope]).
By creating a parser, math.parser(), which contains functions eval, parse, and keeps a scope with assigned variables in memory.

Eval

Math.js comes with a function math.eval to evaluate expressions. Syntax:

math.eval(expr)
math.eval(expr, scope)
math.eval([expr1, expr2, expr3, ...])
math.eval([expr1, expr2, expr3, ...], scope)

Function eval accepts a single expression or an array with expressions as first argument, and has an optional second argument containing a scope with variables and functions. The scope is a regular JavaScript Object. The scope will be used to resolve symbols, and to write assigned variables or function.

The following code demonstrates how to evaluate expressions.

// load math.js
var math = require('mathjs');

// evaluate expressions
math.eval('sqrt(3^2 + 4^2)');           // 5
math.eval('sqrt(-4)');                  // 2i
math.eval('2 inch in cm');              // 5.08 cm
math.eval('cos(45 deg)');               // 0.7071067811865476

// provide a scope
var scope = {
    a: 3,
    b: 4
};
math.eval('a * b', scope);              // 12
math.eval('c = 2.3 + 4.5', scope);      // 6.8
scope.c;                                // 6.8

Parse

Math.js contains a function math.parse to parse expressions into a node tree. The syntax is similar to math.eval:

math.parse(expr)
math.parse(expr, scope)
math.parse([expr1, expr2, expr3, ...])
math.parse([expr1, expr2, expr3, ...], scope)

Function parse accepts a single expression or an array with expressions as first argument, and has an optional second argument containing a scope with variables and functions. The scope is a regular JavaScript Object. The scope will be used to resolve symbols, and to write assigned variables or function. Variables are linked dynamically to the provided scope.

Example usage:

// load math.js
var math = require('mathjs');

// parse an expression into a node, and evaluate the node
var node1 = math.parse('sqrt(3^2 + 4^2)');
node1.eval(); // 5

// provide a scope
var scope = {
    x: 3,
    a: 2
};
var node2 = math.parse('x^a', scope);
node2.eval(); // 9

// change a value in the scope and re-evaluate the node
scope.a = 3;
node2.eval(); // 27

Parser

In addition to the static functions math.eval and math.parse, math.js contains a parser with functions eval and parse, which automatically keeps a scope with assigned variables in memory. The parser also contains some convenience methods to get, set, and remove variables from memory.

A parser can be created by:

var parser = math.parser();

The parser contains the following methods:

clear() Completely clear the parsers scope.
eval(expr) Evaluate an expression.
get(name) Retrieve a variable or function from the parsers scope.
parse(expr) Parse an expression into a node tree.
remove(name) Remove a variable or function from the parsers scope.
set(name, value) Set a variable or function in the parsers scope. A node can be evaluated as node.eval().

The following code shows how to create and use a parser.

// load math.js
var math = require('mathjs');

// create a parser
var parser = math.parser();

// evaluate expressions
parser.eval('sqrt(3^2 + 4^2)');         // 5
parser.eval('sqrt(-4)');                // 2i
parser.eval('2 inch in cm');            // 5.08 cm
parser.eval('cos(45 deg)');             // 0.7071067811865476

// define variables and functions
parser.eval('x = 7 / 2');               // 3.5
parser.eval('x + 3');                   // 6.5
parser.eval('function f(x, y) = x^y');  // f(x, y)
parser.eval('f(2, 3)');                 // 8

// get and set variables and functions
var x = parser.get('x');                // x = 7
var f = parser.get('f');                // f = function
var g = f(3, 3);                        // g = 27
parser.set('h', 500);
parser.eval('h / 2');                   // 250
parser.set('hello', function (name) {
    return 'hello, ' + name + '!';
});
parser.eval('hello("user")');           // "hello, user!"

// clear defined functions and variables
parser.clear();

Chained operations

Math.js supports chaining operations by wrapping a value into a Selector. A selector can be created with the function math.select(value). All methods available in the math namespace can be executed via the selector. The methods will be executed with the selectors value as first argument, followed by extra arguments provided by the function call itself.

math.select(3)
    .add(4)
    .subtract(2)
    .done(); // 5

math.select( [[1, 2], [3, 4]] )
    .subset(math.index(0, 0), 8)
    .multiply(3)
    .done(); // [[24, 6], [9, 12]]

The Selector has a number of special functions:

done() Finalize the chained operation and return the selectors value.
valueOf() The same as done(), returns the selectors value.
toString() Executes math.format(value) onto the selectors value, returning a string representation of the value.

Data types

Math.js supports both native data types like Number, String, and Array, as well as advanced data types like Complex and Unit.

Number

The built-in type Number can be used in all methods.

math.subtract(7.1, 2.3);        // 4.8
math.round(math.pi, 3);         // 3.142
math.sqrt(new Number(4.41e2));  // 21

String

The built-in type String can be used in applicable methods.

math.add('hello ', 'world');    // 'hello world'
math.max('A', 'D', 'C');        // 'D'

Complex

Math.js supports complex numbers. Most methods can be executed with complex numbers as arguments.

var a = math.complex(2, 3);     // 2 + 3i
a.re;                           // 2
a.im;                           // 3
var b = math.complex('4 - 2i'); // 4 - 2i
math.add(a, b);                 // 6 + i
math.sqrt(-4);                  // 2i

Unit

Math.js supports units. Basic operations add, subtract, multiply, and divide can be performed on units. Trigonometric methods like sin support units with an angle as argument. Units can be converted from one to another using function in, an the value of a unit can be retrieved using toNumber.

var a = math.unit(55, 'cm');    // 550 mm
var b = math.unit('0.1m');      // 100 mm
math.add(a, b);                 // 0.65 m
b.in('cm');                     // 10 cm  Alternatively: math.in(b, 'cm')
b.toNumber('cm');               // 10

math.eval('2 inch in cm');      // 5.08 cm
math.eval('cos(45 deg)');       // 0.7071067811865476

Array and Matrix

Math.js supports n-dimensional arrays and matrices. Both regular JavaScript Array and the math.js Matrix can be used interchangeably in all math.js functions.

A Matrix is an object wrapped around a regular JavaScript Array, providing utility methods for easy matrix manipulation such as subset, size, resize, clone, and more.

Matrix indexes in math.js are zero-based, like most programming languages including JavaScript itself. The lower-bound of a range is included, the upper-bound is excluded. Note that mathematical applications like Matlab and Octave work differently, as they use one-based indexes and include the upper-bound of a range.

var matrix = math.matrix([1, 4, 9, 16, 25]);    // Matrix, [1, 4, 9, 16, 25]
math.sqrt(matrix);                              // Matrix, [1, 2, 3, 4, 5]

var array = [1, 2, 3, 4, 5];
math.factorial(array);                          // Array,  [1, 2, 6, 24, 120]

var a = [[1, 2], [3, 4]];                       // Array,  [[1, 2], [3, 4]]
var b = math.matrix([[5, 6], [1, 1]]);          // Matrix, [[5, 6], [1, 1]]
b.subset(math.index(1, [0, 2]), [[7, 8]]);      // Matrix, [[5, 6], [7, 8]]
var c = math.multiply(a, b);                    // Matrix, [[19, 22], [43, 50]]
var d = c.subset(math.index(1, 0));             // 43

Matrices are supported by the parser. IMPORTANT: matrix indexes and ranges work different from the indexes in JavaScript: They are one-based with an included upper-bound, similar to most math applications.

parser = math.parser();

parser.eval('a = [1, 2; 3, 4]');                // Matrix, [[1, 2], [3, 4]]
parser.eval('b = zeros(2, 2)');                 // Matrix, [[0, 0], [0, 0]]
parser.eval('b(1, 1:2) = [5, 6]');              // Matrix, [[5, 6], [0, 0]]
parser.eval('b(2, :) = [7, 8]');                // Matrix, [[5, 6], [7, 8]]
parser.eval('c = a * b');                       // Matrix, [[19, 22], [43, 50]]
parser.eval('d = c(2, 1)');                     // 43
parser.eval('e = c(2, 1:end)');                 // Matrix, [[43, 50]]

Constants

Math.js has the following built-in constants.

math.E, math.e
math.I, math.i
math.Infinity
math.LN2
math.LN10
math.LOG2E
math.LOG10E
math.NaN
math.PI, math.pi
math.SQRT1_2
math.SQRT2

Operators

The following operators are available in the expression parser of math.js.

x + y (add)
x - y (subtract)
x * y (multiply)
x .* y (element-wise multiply)
x / y (divide)
x ./ y (element-wise divide)
x % y (mod)
x ^ y (power)
x ^ y (element-wise power)
-y (unary minus)
y' (transpose)
y! (factorial)
x = y (assignment)
x : y (range)
x in y (unit conversion)
x == y (equal)
x != y (unequal)
x < y (smaller)
x > y (larger)
x <= y (smallereq)
x >= y (largereq)

Methods

Math.js contains the following methods. The methods support all available data types (Number, Complex, Unit, String, and Array) where applicable.

Arithmetic

math.abs(x)
math.add(x, y)
math.ceil(x)
math.cube(x)
math.divide(x, y)
math.edivide(x, y)
math.emultiply(x, y)
math.epow(x, y)
math.equal(x)
math.exp(x)
math.fix(x)
math.floor(x)
math.gcd(a, b, c, ...)
math.larger(x, y)
math.largereq(x, y)
math.lcm(a, b, c, ...)
math.log(x [, base])
math.log10(x)
math.mod(x, y)
math.multiply(x, y)
math.pow(x, y)
math.round(x [, n])
math.sign()
math.smaller(x, y)
math.smallereq(x, y)
math.subtract(x, y)
math.sqrt(x)
math.square(x)
math.unary(x)
math.unequal(x)
math.xgcd(a, b)

Complex

math.re(x)
math.im(x)
math.arg(x)
math.conj(x)

Construction

math.boolean(x)
math.complex(re, im)
math.index(a, b, c, ...)
math.matrix(x)
math.number(x)
math.parser()
math.string(x)
math.unit(x)

Expression

math.eval(expr [, scope])
math.help(text)
math.parse(expr [, scope])

Matrix

math.concat(a, b, c, ... [, dim])
math.det(x)
math.diag(x)
math.eye(m, n, p, ...)
math.inv(x)
math.ones(m, n, p, ...)
math.range(start, end [, step])
math.size(x)
math.squeeze(x)
math.subset(x, index [, replacement])
math.transpose(x)
math.zeros(m, n, p, ...)

Probability

math.factorial(x)
math.random([min, max])
math.randomInt([min, max])
math.pickRandom([min, max])
math.distribution(name)

Statistics

math.max(a, b, c, ...)
math.min(a, b, c, ...)

Trigonometry

math.acos(x)
math.asin(x)
math.atan(x)
math.atan2(y, x)
math.cos(x)
math.cot(x)
math.csc(x)
math.sec(x)
math.sin(x)
math.tan(x)

Units

math.in(x, unit)

Utils

math.clone(x)
math.forEach(x, callback)
math.format([template, ] values)
math.import(filename | object, override)
math.map(x, callback)
math.select([x])
math.typeof(x)

Extend

The library can easily be extended with functions and variables using the import function. The function import accepts a filename or an object with functions and variables.

var math = require('mathjs');

// define new functions and variables
math.import({
    myvalue: 42,
    hello: function (name) {
        return 'hello, ' + name + '!';
    }
});

// defined methods can be used in both JavaScript as well as the parser
math.myvalue * 2;               // 84
math.hello('user');             // 'hello, user!'

var parser = math.parser();
parser.eval('myvalue + 10');    // 52
parser.eval('hello("user")');   // 'hello, user!'

External libraries like numbers.js and numeric.js can be imported as well. The libraries must be installed using npm:

npm install numbers
npm install numeric

The libraries can be easily imported into math.js using import. By default, existing functions will not be overwritten, and math.js will create a wrapper function around the imported functions which converts data types like Matrix to primitive types like Array.

var math = require('mathjs');

// import the numbers.js and numeric.js libraries into math.js
math.import('numbers');
math.import('numeric');

// use functions from numbers.js
math.fibonacci(7);                          // 13
math.eval('fibonacci(7)');                  // 13

// use functions from numeric.js
math.eval('eig([1, 2; 4, 3])').lambda.x;    // [5, -1]

Command Line Interface (CLI)

When math.js is installed globally using npm, its expression parser can be used from the command line. To install math.js globally:

npm install -g mathjs

Normally, a global installation must be run with admin rights (precede the command with sudo). After installation, the application mathjs is available:

$ mathjs
> 12 / (2.3 + 0.7)
4
> 5.08 cm in inch
2 inch
> sin(45 deg) ^ 2
0.5
> 9 / 3 + 2i
3 + 2i
> det([-1, 2; 3, 1])
-7

The command line interface can be used open a prompt, to execute a script, or to pipe input and output streams:

$ mathjs                                 # Open a command prompt
$ mathjs script.txt                      # Run a script file, output to console
$ mathjs script.txt > results.txt        # Run a script file, output to file
$ cat script.txt | mathjs                # Run input stream, output to console
$ cat script.txt | mathjs > results.txt  # Run input stream, output to file

Build

First clone the project from github:

git clone git://github.com/josdejong/mathjs.git

The project uses jake as build tool. To be able to run jake from the command line, jake must be installed globally:

sudo npm install -g jake

Then, the project can be build by executing jake in the root of the project:

cd mathjs
jake

This will build the library math.js and math.min.js from the source files and execute tests.

Test

To execute tests for the library, run:

npm test

Contribute

We can't do this alone. Contributions to the math.js library are very welcome! You can contribute in different ways: spread the word, report bugs, come up with ideas and suggestions, and contribute to the code.

There are a few preferences regarding code contributions:

Math.js follows the node.js code style as described here.
Send pull requests to the develop branch, not the master branch.
Only commit changes done in the source files under lib, not to the builds, which are under dist. builds math.js and math.min.js.

Thanks!

Roadmap

Version 1.0:

An expression parser.
A basic set of functions and constants.
Data types Number, Complex, Matrix, Unit, String.
Examples and documentation.
Extensive testing.

Version 2.0:

A basic set of functions covering all common mathematical areas.
Functions and data types for numeral systems: Bin, Oct, Hex, Dec.
Arbitrary precision calculations with a BigNumber data type.
Support for derived units (like km/h, kg*m/s2, etc).

License

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

robz/mathjs

Features

Install

npm

bower

download

Load

Node.js

Browser

Require.js

Use

Expressions

Eval

Parse

Parser

Chained operations

Data types

Number

String

Complex

Unit

Array and Matrix

Constants

Operators

Methods

Arithmetic

Complex

Construction

Expression

Matrix

Probability

Statistics

Trigonometry

Units

Utils

Extend

Command Line Interface (CLI)

Build

Test

Contribute

Roadmap

License