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feat: implement betaincinv function
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‎lib/node_modules/@stdlib/math/base/special/betaincinv/Makefile

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# Makefile for betaincinv module
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# Default target
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all: build
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# Build the native module
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build:
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node-gyp configure
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node-gyp build
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# Run tests
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test:
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node test/test.js
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# Run tests with coverage
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test-cov:
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nyc node test/test.js
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# Run examples
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examples:
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node examples/index.js
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# Run benchmarks
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benchmark:
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node benchmark/index.js
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# Clean build artifacts
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clean:
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node-gyp clean
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rm -rf build/
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rm -rf coverage/
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.PHONY: all build test test-cov examples benchmark clean

‎lib/node_modules/@stdlib/math/base/special/betaincinv/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
@@ -15,15 +14,16 @@ distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
2018

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# betaincinv
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> Inverse of the [incomplete beta function][incomplete-beta-function].
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> Inverse incomplete beta function.
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<section class="intro">
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The [inverse incomplete beta function][inverse-incomplete-beta] is the inverse of the [incomplete beta function][incomplete-beta]. It is used in various statistical applications, including hypothesis testing and confidence interval calculations.
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</section>
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<!-- /.intro -->
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var betaincinv = require( '@stdlib/math/base/special/betaincinv' );
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```
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#### betaincinv( p, a, b\[, upper] )
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#### betaincinv( p, a, b )
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Inverts the regularized [incomplete beta function][incomplete-beta-function]. Contrary to the more commonly used definition, in this implementation the first parameter is the probability `p` and the second and third parameter are `a` and `b`. By default, the function inverts the _lower_ regularized [incomplete beta function][incomplete-beta-function]. To invert the _upper_ function instead, set the `upper` argument to `true`.
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Evaluates the inverse of the incomplete beta function:
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```javascript
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var y = betaincinv( 0.2, 3.0, 3.0 );
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var y = betaincinv( 0.5, 1.0, 1.0 );
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// returns 0.5
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y = betaincinv( 0.2, 3.0, 3.0 );
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// returns ~0.327
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y = betaincinv( 0.4, 3.0, 3.0 );
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// returns ~0.446
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y = betaincinv( 0.4, 3.0, 3.0, true );
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// returns ~0.554
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y = betaincinv( 0.4, 1.0, 6.0 );
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// returns ~0.082
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y = betaincinv( 0.8, 1.0, 6.0 );
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// returns ~0.235
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```
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If provided `NaN` as any argument, the function returns `NaN`.
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```javascript
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var y = betaincinv( NaN, 1.0, 1.0 );
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// returns NaN
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y = betaincinv( 0.5, NaN, 1.0 );
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// returns NaN
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y = betaincinv( 0.5, 1.0, NaN );
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// returns NaN
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```
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If provided a value outside `[0,1]` for `p`, the function returns `NaN`.
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```javascript
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var y = betaincinv( 1.2, 1.0, 1.0 );
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// returns NaN
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y = betaincinv( -0.5, 1.0, 1.0 );
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// returns NaN
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```
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If provided a nonpositive `a`, the function returns `NaN`.
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```javascript
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var y = betaincinv( 0.5, -2.0, 2.0 );
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// returns NaN
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y = betaincinv( 0.5, 0.0, 2.0 );
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// returns NaN
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```
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The function accepts the following parameters:
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If provided a nonpositive `b`, the function returns `NaN`.
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- **p**: probability value (input value for the incomplete beta function).
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- **a**: first shape parameter (must be positive).
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- **b**: second shape parameter (must be positive).
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```javascript
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var y = betaincinv( 0.5, 2.0, -2.0 );
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// returns NaN
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The function returns `NaN` if any of the following conditions are met:
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y = betaincinv( 0.5, 2.0, 0.0 );
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// returns NaN
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```
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- `p` is outside the interval `[0,1]`
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- `a` is not positive
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- `b` is not positive
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</section>
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var uniform = require( '@stdlib/random/array/uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var betaincinv = require( '@stdlib/math/base/special/betaincinv' );
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var opts = {
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'dtype': 'float64'
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};
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var p = uniform( 100, 0.0, 1.0, opts );
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var a = uniform( 100, 0.0, 10.0, opts );
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var b = uniform( 100, 0.0, 10.0, opts );
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logEachMap( 'p: %0.4f, \t a: %0.4f, \t b: %0.4f, \t f(p,a,b): %0.4f', p, a, b, betaincinv );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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var y = betaincinv( 0.5, 1.0, 1.0 );
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console.log( y );
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// => 0.5
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* * *
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y = betaincinv( 0.2, 3.0, 3.0 );
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console.log( y );
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// => ~0.327
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## See Also
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y = betaincinv( 0.4, 3.0, 3.0 );
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console.log( y );
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// => ~0.446
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- <span class="package-name">[`@stdlib/math/base/special/beta`][@stdlib/math/base/special/beta]</span><span class="delimiter">: </span><span class="description">beta function.</span>
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- <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>
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- <span class="package-name">[`@stdlib/math/base/special/betaln`][@stdlib/math/base/special/betaln]</span><span class="delimiter">: </span><span class="description">natural logarithm of the beta function.</span>
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y = betaincinv( 0.4, 1.0, 6.0 );
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console.log( y );
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// => ~0.082
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```
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<!-- /.examples -->
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<section class="links">
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[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function
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<!-- <related-links> -->
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[@stdlib/math/base/special/beta]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/beta
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[@stdlib/math/base/special/betainc]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/betainc
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[@stdlib/math/base/special/betaln]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/betaln
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<!-- </related-links> -->
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[incomplete-beta]: https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function
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[inverse-incomplete-beta]: https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function
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</section>
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‎lib/node_modules/@stdlib/math/base/special/betaincinv/benchmark/index.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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var randu = require( '@stdlib/random/base/randu' );
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var betaincinv = require( './../lib' );
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var p;
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var a;
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var b;
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var i;
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console.log( 'Running benchmarks...\n' );
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// Benchmark 1: Basic usage
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console.log( 'Benchmark 1: Basic usage' );
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console.time( 'betaincinv' );
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for ( i = 0; i < 1e6; i++ ) {
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p = randu();
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a = randu() * 10.0 + 1.0;
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b = randu() * 10.0 + 1.0;
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betaincinv( p, a, b );
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}
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console.timeEnd( 'betaincinv' );
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// Benchmark 2: Edge cases
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console.log( '\nBenchmark 2: Edge cases' );
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console.time( 'betaincinv (edge cases)' );
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for ( i = 0; i < 1e6; i++ ) {
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p = (i % 2 === 0) ? 0.0 : 1.0;
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a = 1.0;
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b = 1.0;
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betaincinv( p, a, b );
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}
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console.timeEnd( 'betaincinv (edge cases)' );
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// Benchmark 3: Invalid inputs
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console.log( '\nBenchmark 3: Invalid inputs' );
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console.time( 'betaincinv (invalid inputs)' );
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for ( i = 0; i < 1e6; i++ ) {
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p = (i % 2 === 0) ? -0.5 : 1.5;
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a = 1.0;
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b = 1.0;
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betaincinv( p, a, b );
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}
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console.timeEnd( 'betaincinv (invalid inputs)' );

‎lib/node_modules/@stdlib/math/base/special/betaincinv/binding.gyp

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{
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"targets": [
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{
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"target_name": "betaincinv",
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"sources": [
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"src/betaincinv.c"
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],
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"include_dirs": [
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"<!@(node -p \"require('node-addon-api').include\")"
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],
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"dependencies": [
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"<!(node -p \"require('node-addon-api').gyp\")"
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],
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"cflags!": [
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"-fno-exceptions"
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],
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"cflags_cc!": [
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"-fno-exceptions"
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],
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"xcode_settings": {
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"GCC_ENABLE_CPP_EXCEPTIONS": "YES",
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"CLANG_CXX_LIBRARY": "libc++",
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"MACOSX_DEPLOYMENT_TARGET": "10.7"
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},
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"msvs_settings": {
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"VCCLCompilerTool": {
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"ExceptionHandling": 1
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}
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},
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"defines": [
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"NAPI_DISABLE_CPP_EXCEPTIONS"
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],
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"conditions": [
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['OS=="win"', {
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"defines": [
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"NOMINMAX"
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]
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}]
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]
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}
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]
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}

‎lib/node_modules/@stdlib/math/base/special/betaincinv/examples/index.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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'use strict';
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var uniform = require( '@stdlib/random/array/uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var betaincinv = require( './../lib' );
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var opts = {
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'dtype': 'float64'
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};
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var p = uniform( 100, 0.0, 1.0, opts );
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var a = uniform( 100, 0.0, 10.0, opts );
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var b = uniform( 100, 0.0, 10.0, opts );
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// Example 1: Basic usage
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console.log( '\nExample 1: Basic usage' );
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console.log( 'betaincinv(0.5, 1.0, 1.0) =', betaincinv( 0.5, 1.0, 1.0 ) );
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console.log( 'betaincinv(0.2, 3.0, 3.0) =', betaincinv( 0.2, 3.0, 3.0 ) );
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console.log( 'betaincinv(0.4, 3.0, 3.0) =', betaincinv( 0.4, 3.0, 3.0 ) );
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console.log( 'betaincinv(0.4, 1.0, 6.0) =', betaincinv( 0.4, 1.0, 6.0 ) );
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logEachMap( 'p: %0.4f, \t a: %0.4f, \t b: %0.4f, \t f(p,a,b): %0.4f', p, a, b, betaincinv );
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// Example 2: Edge cases
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console.log( '\nExample 2: Edge cases' );
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console.log( 'betaincinv(0.0, 1.0, 1.0) =', betaincinv( 0.0, 1.0, 1.0 ) );
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console.log( 'betaincinv(1.0, 1.0, 1.0) =', betaincinv( 1.0, 1.0, 1.0 ) );
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// Example 3: Invalid inputs
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console.log( '\nExample 3: Invalid inputs' );
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console.log( 'betaincinv(-0.5, 1.0, 1.0) =', betaincinv( -0.5, 1.0, 1.0 ) );
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console.log( 'betaincinv(1.5, 1.0, 1.0) =', betaincinv( 1.5, 1.0, 1.0 ) );
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console.log( 'betaincinv(0.5, 0.0, 1.0) =', betaincinv( 0.5, 0.0, 1.0 ) );
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console.log( 'betaincinv(0.5, 1.0, -1.0) =', betaincinv( 0.5, 1.0, -1.0 ) );

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