@stdlib/math-base-special-gammainc
v0.3.1TypeScript
Incomplete gamma function.
51.9K/weekUpdated yesterdayApache-2.0 AND BSL-1.0Unpacked: 249.8 KB
Published by The Stdlib Authors
npm install @stdlib/math-base-special-gammaincWe believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js. The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases. When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there. To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
About stdlib...
gammainc
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Incomplete gamma function][incomplete-gamma-function].
Evaluates the regularized lower [incomplete gamma function][incomplete-gamma-function]:
The function can also be used to evaluate the regularized upper incomplete gamma function, which is defined as follows:
The two functions have the relationship Q(x,a) = 1 - P(x,a).
In addition, this routine can be used to evaluate the _unregularized_ gamma functions. The range of above functions is [0,1], which is not the case for the _unregularized_ versions. The unregularized lower incomplete gamma function is defined as
and the upper unregularized incomplete gamma function is
The relationship between the two functions is Γ(a,x) = γ(a,x) + Γ(a).
Installation
``bash`
npm install @stdlib/math-base-special-gammainc
Usage
`javascript`
var gammainc = require( '@stdlib/math-base-special-gammainc' );
#### gammainc( x, s\[, regularized\[, upper ]] )
By default, evaluates the regularized lower [incomplete gamma function][incomplete-gamma-function] for inputs x and s. The third and fourth parameters of the function can be used to specify whether instead to evaluate the non-regularized and/or upper incomplete gamma functions, respectively.
`javascript
var y = gammainc( 6.0, 2.0 );
// returns ~0.9826
y = gammainc( 1.0, 2.0, true, true );
// returns ~0.7358
y = gammainc( 7.0, 5.0 );
// returns ~0.8270
y = gammainc( 7.0, 5.0, false );
// returns ~19.8482
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = gammainc( NaN, 1.0 );
// returns NaN
y = gammainc( 1.0, NaN );
// returns NaN
`
If provided a negative x, the function returns NaN.
`javascript`
var y = gammainc( -2.0, 2.0 );
// returns NaN
If provided a nonpositive s, the function returns NaN.
`javascript
var y = gammainc( 2.0, -1.0 );
// returns NaN
y = gammainc( 2.0, 0.0 );
// returns NaN
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var gammainc = require( '@stdlib/math-base-special-gammainc' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, 0.0, 10.0, opts );
var s = uniform( 100, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, \t s: %0.4f, \t f(x,s): %0.4f', x, s, gammainc );
`
*
C APIs
$3
`c`
#include "stdlib/math/base/special/gammainc.h"
#### stdlib_base_gammainc( x, a, regularized, upper )
Evaluates the [incomplete gamma function][incomplete-gamma-function] for inputs x and a.
`c
double out = stdlib_base_gammainc( 0.0, 1.0, true, false );
// returns 0.0
out = stdlib_base_gammainc( 6.0, 2.0, true, false );
// returns ~0.9826
`
The function accepts the following arguments:
- x: [in] double input value.[in] double
- a: input value.[in] bool
- regularized: boolean indicating whether to evaluate a regularized incomplete gamma function.[in] bool
- upper: boolean indicating whether to evaluate the upper incomplete gamma function.
`c`
double stdlib_base_gammainc( const double x, const double a, const bool regularized, const bool upper );
$3
`c
#include "stdlib/math/base/special/gammainc.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double x;
double a;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
x = random_uniform( 0.0, 1000.0 );
a = random_uniform( 1.0, 1000.0 );
y = stdlib_base_gammainc( x, a, true, false );
printf( "x: %lf, s: %lf, f(x,s): %lf\n", x, a, y );
}
}
`
*
See Also
- [@stdlib/math-base/special/gamma][@stdlib/math/base/special/gamma]: gamma function.
- [@stdlib/math-base/special/gamma1pm1][@stdlib/math/base/special/gamma1pm1]: compute gamma(x+1) - 1.
- [@stdlib/math-base/special/gammaincinv][@stdlib/math/base/special/gammaincinv]: inverse incomplete gamma function.
- [@stdlib/math-base/special/gammaln][@stdlib/math/base/special/gammaln]: natural logarithm of the gamma function.
*
Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-gammainc.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-gammainc
[test-image]: https://github.com/stdlib-js/math-base-special-gammainc/actions/workflows/test.yml/badge.svg?branch=v0.3.1
[test-url]: https://github.com/stdlib-js/math-base-special-gammainc/actions/workflows/test.yml?query=branch:v0.3.1
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-gammainc/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-gammainc?branch=main
[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-gammainc/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-gammainc/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-gammainc/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-gammainc/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-gammainc/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-gammainc/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-gammainc/blob/main/branches.md
[incomplete-gamma-function]: https://en.wikipedia.org/wiki/Incomplete_gamma_function
[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma
[@stdlib/math/base/special/gamma1pm1]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma1pm1
[@stdlib/math/base/special/gammaincinv]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaincinv
[@stdlib/math/base/special/gammaln]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaln