Some basic but difficult to implement mathmatical functions
Note: for distribution functions please see
npm install mathfn
var mathfn = ;console; // 0.0
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.
p = erf(x)- The error function
This function is implemented using the "Abramowitz & Stegun" approximation
its theortical accuracy is
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
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
p = gamma(x)The gamma function
This acutally contains 3 diffrent approximations of
gamma(x) which one is
automatically determined by the
p = logGamma(x)The logarithmic gamma function
For values less than
12 the result is calculated using
any other case a specific approximation is used.
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
y = log1p(x)- Calculates
y = ln(1 + x)
x is a very small number computers calculates
ln(1 + x) as
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,
ln(x!) instead can in some cases solve this problem.
All functions are tested by comparing with a mathematical reference either MatLab, Maple or R.
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/
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.