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Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"},"license":"Apache-2.0","homepage":"https://stdlib.io","keywords":["stdlib","stdmath","mathematics","math","special function","special","function","incomplete gamma","inverse","approximation","scalar","number"],"repository":{"type":"git","url":"git://github.com/stdlib-js/math-base-special-gammaincinv.git"},"description":"Inverse incomplete gamma function.","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# gammaincinv\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> Inverse of [incomplete gamma function][incomplete-gamma-function].\n\n<section class=\"intro\">\n\nComputes the inverse of the lower [incomplete gamma function][incomplete-gamma-function]\n\n<!-- <equation class=\"equation\" label=\"eq:lower_incomplete_gamma\" align=\"center\" raw=\"P( x, a ) = \\frac{\\gamma(a,x)}{\\Gamma(a)} = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a-1} e^{-t} \\; dt\" alt=\"Regularized lower incomplete gamma function.\"> -->\n\n<div class=\"equation\" align=\"center\" data-raw-text=\"P( x, a ) = \\frac{\\gamma(a,x)}{\\Gamma(a)} = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a-1} e^{-t} \\; dt\" data-equation=\"eq:lower_incomplete_gamma\">\n    <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/gammaincinv/docs/img/equation_lower_incomplete_gamma.svg\" alt=\"Regularized lower incomplete gamma function.\">\n    <br>\n</div> -->\n\n<!-- </equation> -->\n\nSpecifically, for given `p` and `a` it finds the `x` such that `p =  P(x, a)`.\n\nThe function can also be used to invert the upper incomplete gamma function, which is defined as follows:\n\n<!-- <equation class=\"equation\" label=\"eq:upper_incomplete_gamma\" align=\"center\" raw=\"Q( x, a ) = \\frac{\\Gamma(a,x)}{\\Gamma(a)} = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a-1} e^{-t} \\; dt\" alt=\"Regularized upper incomplete gamma function.\"> -->\n\n<!-- <div class=\"equation\" align=\"center\" data-raw-text=\"Q( x, a ) = \\frac{\\Gamma(a,x)}{\\Gamma(a)} = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a-1} e^{-t} \\; dt\" data-equation=\"eq:upper_incomplete_gamma\">\n    <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/gammaincinv/docs/img/equation_upper_incomplete_gamma.svg\" alt=\"Regularized upper incomplete gamma function.\">\n    <br>\n</div>\n\n<!-- </equation> -->\n\nAgain, for given `p` and `a` the function returns the `x` which satisfies `p = Q(x, a)`.\n\n</section>\n\n<!-- /.intro -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/math-base-special-gammaincinv\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar gammaincinv = require( '@stdlib/math-base-special-gammaincinv' );\n```\n\n#### gammaincinv( p, s\\[, upper ] )\n\nInverts the regularized incomplete gamma function. Contrary to the more commonly used definition, in this implementation the first argument is the probability `p` and the second argument is the scale factor `a`. By default, the function inverts the _lower_ regularized incomplete gamma function, `P(x,a)`. To invert the _upper_ function instead, i.e. `Q(x,a)`, set the `upper` argument to `true`.\n\n```javascript\nvar y = gammaincinv( 0.5, 2.0 );\n// returns ~1.678\n\ny = gammaincinv( 0.1, 10.0 );\n// returns ~6.221\n\ny = gammaincinv( 0.75, 3.0 );\n// returns ~3.92\n\ny = gammaincinv( 0.75, 3.0, true );\n// returns ~1.727\n```\n\nIf provided `NaN` as any argument, the function returns `NaN`.\n\n```javascript\nvar y = gammaincinv( NaN, 1.0 );\n// returns NaN\n\ny = gammaincinv( 0.5, NaN );\n// returns NaN\n```\n\nIf provided a value outside `[0,1]` for `p`, the function returns `NaN`.\n\n```javascript\nvar y = gammaincinv( 1.2, 1.0 );\n// returns NaN\n\ny = gammaincinv( -0.5, 1.0 );\n// returns NaN\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar uniform = require( '@stdlib/random-array-uniform' );\nvar logEachMap = require( '@stdlib/console-log-each-map' );\nvar gammaincinv = require( '@stdlib/math-base-special-gammaincinv' );\n\nvar opts = {\n    'dtype': 'float64'\n};\nvar p = uniform( 100, 0.0, 1.0, opts );\nvar a = uniform( 100, 0.0, 50.0, opts );\n\nlogEachMap( 'p: %0.4f, \\t a: %0.4f, \\t P^(-1)(p, a): %0.4f', p, a, gammaincinv );\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/gamma`][@stdlib/math/base/special/gamma]</span><span class=\"delimiter\">: </span><span class=\"description\">gamma function.</span>\n-   <span class=\"package-name\">[`@stdlib/math-base/special/gamma1pm1`][@stdlib/math/base/special/gamma1pm1]</span><span class=\"delimiter\">: </span><span class=\"description\">compute gamma(x+1) - 1.</span>\n-   <span class=\"package-name\">[`@stdlib/math-base/special/gammainc`][@stdlib/math/base/special/gammainc]</span><span class=\"delimiter\">: </span><span class=\"description\">incomplete gamma function.</span>\n-   <span class=\"package-name\">[`@stdlib/math-base/special/gammaln`][@stdlib/math/base/special/gammaln]</span><span class=\"delimiter\">: </span><span class=\"description\">natural logarithm of the gamma 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## License\n\nSee [LICENSE][stdlib-license].\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-gammaincinv.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-gammaincinv\n\n[test-image]: https://github.com/stdlib-js/math-base-special-gammaincinv/actions/workflows/test.yml/badge.svg?branch=v0.2.3\n[test-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/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-gammaincinv/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-gammaincinv?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/math-base-special-gammaincinv.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/math-base-special-gammaincinv/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-gammaincinv/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-gammaincinv/main/LICENSE\n\n[incomplete-gamma-function]: https://en.wikipedia.org/wiki/Incomplete_gamma_function\n\n<!-- <related-links> -->\n\n[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma\n\n[@stdlib/math/base/special/gamma1pm1]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma1pm1\n\n[@stdlib/math/base/special/gammainc]: https://www.npmjs.com/package/@stdlib/math-base-special-gammainc\n\n[@stdlib/math/base/special/gammaln]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaln\n\n<!-- </related-links> -->\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}