feat: add optimize/base/brentq

lib/node_modules/@stdlib/optimize/base/brentq/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# brentq
+
+> Find a zero of a continuous function using Brent's method.
+
+<section class="intro">
+
+Finds a zero of a continuous function $f$ on the interval $\lbrack a, b \rbrack$ where the sign of $f(a)$ and $f(b)$ must be opposite.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var brentq = require( '@stdlib/optimize/base/brentq' );
+```
+
+#### brentq( f, a, b&#91;, options&#93; )
+
+Finds a zero of a continuous function `f` on the interval `[a, b]`.
+
+```javascript
+function f( x ) {
+    return ( x * x ) - 1;
+}
+
+var root = brentq( f, 0, 2 );
+// returns 1.0
+```
+
+The function accepts the following options:
+
+-   **maxIter**: maximum number of iterations. Default: `100`.
+-   **xtol**: absolute tolerance. Default: `2e-12`.
+-   **rtol**: relative tolerance. Default: `8.88e-16`.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var sin = require( '@stdlib/math/base/special/sin' );
+var brentq = require( '@stdlib/optimize/base/brentq' );
+
+function f( x ) {
+    return sin( x );
+}
+
+var root = brentq( f, 3.0, 3.2 );
+console.log( root );
+// => 3.141592653589793
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/optimize/base/brentq/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var brentq = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var root;
+	var i;
+
+	function f( x ) {
+		return ( x * x ) - 1.0;
+	}
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		root = brentq( f, 0.0, 2.0 );
+		if ( isnan( root ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( root ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/optimize/base/brentq/docs/repl.txt

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+
+{{alias}}( f, a, b[, options] )
+    Finds a zero of a continuous function `f` on the interval `[a, b]`.
+
+    Parameters
+    ----------
+    f: Function
+        Objective function.
+    a: number
+        Lower bound.
+    b: number
+        Upper bound.
+    options: Object (optional)
+        Function options.
+    options.maxIter: number (optional)
+        Maximum number of iterations. Default: 100.
+    options.xtol: number (optional)
+        Absolute tolerance. Default: 2e-12.
+    options.rtol: number (optional)
+        Relative tolerance. Default: 8.88e-16.
+
+    Returns
+    -------
+    x: number
+        Zero.
+
+    Examples
+    --------
+    > function f( x ) { return x*x - 1.0; };
+    > {{alias}}( f, 0.0, 2.0 )
+    1.0
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/optimize/base/brentq/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Interface defining options.
+*/
+interface Options {
+	/**
+	* Maximum number of iterations.
+	*/
+	maxIter?: number;
+
+	/**
+	* Absolute tolerance.
+	*/
+	xtol?: number;
+
+	/**
+	* Relative tolerance.
+	*/
+	rtol?: number;
+}
+
+/**
+* Callback function.
+*
+* @param x - input value
+* @returns function value
+*/
+type Unary = ( x: number ) => number;
+
+/**
+* Finds a zero of a continuous function `f` on the interval `[a, b]`.
+*
+* @param f - objective function
+* @param a - lower bound
+* @param b - upper bound
+* @param options - function options
+* @returns zero
+*
+* @example
+* function f( x ) {
+*     return x * x - 1.0;
+* }
+* var v = brentq( f, 0.0, 2.0 );
+* // returns 1.0
+*/
+declare function brentq( f: Unary, a: number, b: number, options?: Options ): number;
+
+export = brentq;

lib/node_modules/@stdlib/optimize/base/brentq/docs/types/test.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+import brentq = require( './index' );
+
+/**
+* Callback function.
+*
+* @param x - input value
+* @returns result
+*/
+function f( x: number ): number {
+	return x * x - 1.0;
+}
+
+// TESTS //
+
+// The function returns a number...
+{
+	brentq( f, 0.0, 2.0 ); // $ExpectType number
+	brentq( f, 0.0, 2.0, { 'maxIter': 20 } ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided an invalid first argument...
+{
+	brentq( true, 0.0, 2.0 ); // $ExpectError
+	brentq( false, 0.0, 2.0 ); // $ExpectError
+	brentq( 5, 0.0, 2.0 ); // $ExpectError
+	brentq( [], 0.0, 2.0 ); // $ExpectError
+	brentq( {}, 0.0, 2.0 ); // $ExpectError
+	brentq( 'abc', 0.0, 2.0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an invalid second argument...
+{
+	brentq( f, true, 2.0 ); // $ExpectError
+	brentq( f, false, 2.0 ); // $ExpectError
+	brentq( f, [], 2.0 ); // $ExpectError
+	brentq( f, {}, 2.0 ); // $ExpectError
+	brentq( f, 'abc', 2.0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an invalid third argument...
+{
+	brentq( f, 0.0, true ); // $ExpectError
+	brentq( f, 0.0, false ); // $ExpectError
+	brentq( f, 0.0, [] ); // $ExpectError
+	brentq( f, 0.0, {} ); // $ExpectError
+	brentq( f, 0.0, 'abc' ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an invalid options argument...
+{
+	brentq( f, 0.0, 2.0, true ); // $ExpectError
+	brentq( f, 0.0, 2.0, false ); // $ExpectError
+	brentq( f, 0.0, 2.0, 5 ); // $ExpectError
+	brentq( f, 0.0, 2.0, [] ); // $ExpectError
+	brentq( f, 0.0, 2.0, 'abc' ); // $ExpectError
+}

lib/node_modules/@stdlib/optimize/base/brentq/examples/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+var pow = require( '@stdlib/math/base/special/pow' );
+var sin = require( '@stdlib/math/base/special/sin' );
+var brentq = require( './../lib' );
+
+function f( x ) {
+	return pow( x, 3 ) - ( 2.0 * x ) - 5.0;
+}
+
+var root = brentq( f, 2.0, 3.0 );
+console.log( 'f(x) = x^3 - 2x - 5' );
+console.log( 'Root: %d', root );
+console.log( 'f(root): %d', f( root ) );
+
+// Example with options
+function g( x ) {
+	return sin( x );
+}
+
+root = brentq( g, 3.0, 4.0, {
+	'xtol': 1e-4
+});
+console.log( '\nf(x) = sin(x)' );
+console.log( 'Root matching 3.14 on [3, 4] with xtol 1e-4: %d', root );
+console.log( 'f(root): %d', g( root ) );