yanatan16 / mathfn

Some basic but difficult to implement mathmatical functions

mathfn

Some basic but difficult to implement mathmatical functions
Note: for distribution functions please see distributions

Installation

npm install mathfn

Example

var mathfn = require('mathfn');

console.log(mathfn.erf(0)); // 0.0

Documentation

mathfn is a slowly growing collection of some difficult mathmatical functions there should be included in Math. but isn't. This is a list of the currently implemented functions and a few details.

Error functions

p = erf(x) - The error function

This function is implemented using the "Abramowitz & Stegun" approximation its theortical accuracy is 1.5 * 10^-7. However the limitations of JavaScript might result in a lower accuracy.

p = erfc(x) The complementary error function

Unlike most implementation of erfc(x), this is not calculated using 1 - erf(x), but is an acutall approximation of erfc(x).

p = invErf(p) The inverse error function

This is calculated using inverf(p) = -inverfc(p + 1), if you known of specific approximation please file an issue or pull request.

p = invErfc(p) The inverse complementary error function

This uses a very common approximation of inverfc(p), see source code for more details.

Gamma functions

p = gamma(x) The gamma function

This acutally contains 3 diffrent approximations of gamma(x) which one is automatically determined by the x value.

p = logGamma(x) The logarithmic gamma function

For values less than 12 the result is calculated using log(gamma(x)), in any other case a specific approximation is used.

Beta functions

These are taken from the jstat library and modified to fit intro the API pattern used in this module. Futhermore they also take advanges of the special log1p function implemented in this module.

p = beta(x, y) - The beta function

p = logBeta(x, y) - The logarithmic beta function

p = incBeta(x, a, b) - The incomplete beta function

p = invIncBeta(p, a, b) - The inverse incomplete beta function

Logarithmic functions

y = log1p(x) - Calculates y = ln(1 + x)

When x is a very small number computers calculates ln(1 + x) as ln(1) which is zero and then every thing is lost. This is a specific approximation of ln(1 + x) and should be used only in case of small values.

y = logFactorial(x) - Calculates y = ln(x!)

x! can quickly get very big, and exceed the limitation of the float value, approimating ln(x!) instead can in some cases solve this problem.

Testing

All functions are tested by comparing with a mathematical reference either MatLab, Maple or R.

Thanks

A special thank to John D. Cook, who writes a very good blog about some of these functions, and maintains a stand alone implementation catalog. See also this article about regarding floating point errors in some mathematical function: http://www.johndcook.com/blog/2010/06/07/math-library-functions-that-seem-unnecessary/

License

The software is license under "MIT"

Copyright (c) 2013 Andreas Madsen

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.