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Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"},"license":"Apache-2.0 AND BSL-1.0","homepage":"https://stdlib.io","keywords":["stdlib","stdmath","mathematics","math","special function","special","function","beta","incomplete beta","approximation","scalar","number","derivative","kernel"],"repository":{"type":"git","url":"git://github.com/stdlib-js/math-base-special-kernel-betainc.git"},"description":"Incomplete beta function and its first derivative.","contributors":[{"name":"The Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"}],"maintainers":[{"name":"stdlib-bot","email":"kgryte+stdlibbot@gmail.com"},{"name":"kgryte","email":"kgryte@gmail.com"},{"name":"planeshifter","email":"pgb@andrew.cmu.edu"},{"name":"rreusser","email":"rsreusser@gmail.com"}],"readme":"<!--\n\n@license Apache-2.0\n\nCopyright (c) 2018 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>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.</p>\n  <p>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.</p>\n  <p>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.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# Kernel Betainc\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> [Incomplete beta function][incomplete-beta-function] and its first derivative.\n\n<section class=\"intro\">\n\n</section>\n\n<!-- /.intro -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/math-base-special-kernel-betainc\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar kernelBetainc = require( '@stdlib/math-base-special-kernel-betainc' );\n```\n\n#### kernelBetainc( x, a, b, regularized, upper )\n\nEvaluates the [incomplete beta function][incomplete-beta-function] and its first derivative for parameters `x`, `a > 0` and `b > 0`. The `regularized` and `upper` boolean parameters are used to specify whether to evaluate the regularized or non-regularized and the upper or lower incomplete beta functions, respectively.\n\n```javascript\nvar out = kernelBetainc( 0.8, 1.0, 0.3, false, false );\n// returns [ ~1.277, ~0.926 ]\n\nout = kernelBetainc( 0.2, 1.0, 2.0, true, false );\n// returns [ 0.36, 1.6 ]\n\nout = kernelBetainc( 0.2, 1.0, 2.0, true, true );\n// returns [ 0.64, 1.6 ]\n```\n\nIf provided `NaN` for `x`, `a`, or `b`, the function returns `[ NaN, NaN ]`.\n\n```javascript\nvar out = kernelBetainc( NaN, 1.0, 1.0, true, true );\n// returns [ NaN, NaN ]\n\nout = kernelBetainc( 0.8, NaN, 1.0, true, true );\n// returns [ NaN, NaN ]\n\nout = kernelBetainc( 0.8, 1.0, NaN, true, true );\n// returns [ NaN, NaN ]\n```\n\nIf `x` is outside the interval `[0,1]`, the function returns `[ NaN, NaN ]`.\n\n```javascript\nvar out = kernelBetainc( 1.5, 1.0, 1.0, true, true );\n// returns [ NaN, NaN ]\n\nout = kernelBetainc( -0.5, 1.0, 1.0, true, true );\n// returns [ NaN, NaN ]\n```\n\nIf `a` or `b` is negative, the function returns `[ NaN, NaN ]`.\n\n```javascript\nvar out = kernelBetainc( 0.5, -2.0, 2.0, true, true );\n// returns [ NaN, NaN ]\n\nout = kernelBetainc( 0.5, 2.0, -2.0, true, true );\n// returns [ NaN, NaN ]\n```\n\n#### kernelBetainc.assign( x, a, b, regularized, upper, out, stride, offset )\n\nEvaluates the [incomplete beta function][incomplete-beta-function] and its first derivative for parameters `x`, `a > 0` and `b > 0` and assigns results to a provided output array.\n\n```javascript\nvar Float64Array = require( '@stdlib/array-float64' );\n\nvar out = new Float64Array( 2 );\nvar v = kernelBetainc.assign( 0.2, 1.0, 2.0, true, true, out, 1, 0 );\n// returns <Float64Array>[ 0.64, 1.6 ]\n\nvar bool = ( v === out );\n// returns true\n```\n\nThe `offset` parameter specifies the index of the first output array element, and the `stride` parameter specifies the stride length between consecutive output array elements.\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar randu = require( '@stdlib/random-base-randu' );\nvar kernelBetainc = require( '@stdlib/math-base-special-kernel-betainc' );\n\nvar out;\nvar i;\nvar x;\nvar a;\nvar b;\n\nout = [ 0.0, 0.0 ];\nfor ( i = 0; i < 100; i++ ) {\n    x = randu();\n    a = randu() * 10.0;\n    b = randu() * 10.0;\n    kernelBetainc.assign( x, a, b, true, false, out, 1, 0 );\n    console.log( 'x: %d, \\t a: %d, \\t b: %d, \\t f(x,a,b): %d, \\t f^1(x,a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) );\n}\n```\n\n</section>\n\n<!-- /.examples -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n* * *\n\n## See Also\n\n-   <span class=\"package-name\">[`@stdlib/math-base/special/betainc`][@stdlib/math/base/special/betainc]</span><span class=\"delimiter\">: </span><span class=\"description\">incomplete beta function.</span>\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\n\n* * *\n\n## Notice\n\nThis 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.\n\nFor 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].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## Copyright\n\nCopyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-kernel-betainc.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-kernel-betainc\n\n[test-image]: https://github.com/stdlib-js/math-base-special-kernel-betainc/actions/workflows/test.yml/badge.svg?branch=v0.2.3\n[test-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/actions/workflows/test.yml?query=branch:v0.2.3\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-kernel-betainc/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-kernel-betainc?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/math-base-special-kernel-betainc.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/math-base-special-kernel-betainc/main\n\n-->\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-base-special-kernel-betainc/blob/main/branches.md\n\n[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function\n\n<!-- <related-links> -->\n\n[@stdlib/math/base/special/betainc]: https://www.npmjs.com/package/@stdlib/math-base-special-betainc\n\n<!-- </related-links> -->\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}