Skip to content

Latest commit

 

History

History
245 lines (145 loc) · 8.22 KB

README.md

File metadata and controls

245 lines (145 loc) · 8.22 KB
Raw
About stdlib...

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.

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!

ellipe

NPM version Build Status Coverage Status

Compute the complete elliptic integral of the second kind.

The complete elliptic integral of the second kind is defined as

$$E(m)=\int_0^{\pi/2} \sqrt{1 - m (\sin\theta)^2} d\theta$$

where the parameter m is related to the modulus k by m = k^2.

Usage

import ellipe from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-ellipe@deno/mod.js';

ellipe( m )

Computes the complete elliptic integral of the second kind.

var v = ellipe( 0.5 );
// returns ~1.351

v = ellipe( -1.0 );
// returns ~1.910

v = ellipe( 2.0 );
// returns NaN

v = ellipe( Infinity );
// returns NaN

v = ellipe( -Infinity );
// returns NaN

v = ellipe( NaN );
// returns NaN

Notes

  • This function is valid for -∞ < m <= 1.

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import ellipe from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-ellipe@deno/mod.js';

var m;
var i;

for ( i = 0; i < 100; i++ ) {
    m = -1.0 + ( randu() * 2.0 );
    console.log( 'ellipe(%d) = %d', m, ellipe( m ) );
}

References

  • Fukushima, Toshio. 2009. "Fast computation of complete elliptic integrals and Jacobian elliptic functions." Celestial Mechanics and Dynamical Astronomy 105 (4): 305. doi:10.1007/s10569-009-9228-z.
  • Fukushima, Toshio. 2015. "Precise and fast computation of complete elliptic integrals by piecewise minimax rational function approximation." Journal of Computational and Applied Mathematics 282 (July): 71–76. doi:10.1016/j.cam.2014.12.038.

See Also

Notice

This package is part of stdlib, a standard library 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.

Community

Chat

Copyright

Copyright © 2016-2024. The Stdlib Authors.