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@stdlib/math-base-special-gammainc
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We 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.
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Evaluates the regularized lower 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)
.
npm install @stdlib/math-base-special-gammainc
var gammainc = require( '@stdlib/math-base-special-gammainc' );
By default, evaluates the regularized lower 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.
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
.
var y = gammainc( NaN, 1.0 );
// returns NaN
y = gammainc( 1.0, NaN );
// returns NaN
If provided a negative x
, the function returns NaN
.
var y = gammainc( -2.0, 2.0 );
// returns NaN
If provided a nonpositive s
, the function returns NaN
.
var y = gammainc( 2.0, -1.0 );
// returns NaN
y = gammainc( 2.0, 0.0 );
// returns NaN
var randu = require( '@stdlib/random-base-randu' );
var gammainc = require( '@stdlib/math-base-special-gammainc' );
var i;
var x;
var s;
for ( i = 0; i < 100; i++ ) {
x = randu() * 10.0;
s = randu() * 10.0;
console.log( 'x: %d, \t s: %d, \t f(x,s): %d', x.toFixed( 4 ), s.toFixed( 4 ), gammainc( x, s ).toFixed( 4 ) );
}
@stdlib/math-base/special/gamma
: gamma function.@stdlib/math-base/special/gamma1pm1
: compute gamma(x+1) - 1.@stdlib/math-base/special/gammaincinv
: inverse incomplete gamma function.@stdlib/math-base/special/gammaln
: natural logarithm of the gamma function.This package is part of 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, see the main project repository.
Copyright © 2016-2024. The Stdlib Authors.
FAQs
Incomplete gamma function.
The npm package @stdlib/math-base-special-gammainc receives a total of 42,048 weekly downloads. As such, @stdlib/math-base-special-gammainc popularity was classified as popular.
We found that @stdlib/math-base-special-gammainc demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 4 open source maintainers collaborating on the project.
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