feat: add lapack/base/dlartg

lib/node_modules/@stdlib/lapack/base/dlartg/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# dlartg
+
+> LAPACK routine to construct a Givens rotation of a two-dimensional vector that zeros out the second component.
+
+<section class="intro">
+
+This routine constructs a Givens rotation for a two-dimensional vector such that the following equation is satisfied:
+
+
+<!-- <equation class="equation" label="eq:givens_rotation" align="center" raw="\begin{bmatrix} C & S \\ -S & C \end{bmatrix} \begin{bmatrix} F \\ G \end{bmatrix} = \begin{bmatrix} R \\ 0 \end{bmatrix}
+" alt="Equation for Givens rotation."> -->
+
+```math
+\begin{bmatrix} C & S \\ -S & C \end{bmatrix} \begin{bmatrix} F \\ G \end{bmatrix} = \begin{bmatrix} R \\ 0 \end{bmatrix}
+```
+
+<!-- </equation> -->
+
+where `C` represents the cosine of the rotation `S` represents the sine of the rotation and `R` represents the length of the vector after rotation.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlartg = require( '@stdlib/lapack/base/dlartg' );
+```
+
+#### dlartg( F, G, C, S, R )
+
+Constructs a Givens rotation of a two-dimensional vector that zeros out the second component. For a two-dimensional vector `( F, G )` it computes the sine `S`, cosine `C` and the resultant `R`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var F = new Float64Array( [ 3.0 ] );
+var G = new Float64Array( [ 4.0 ] );
+var C = new Float64Array( 1 );
+var S = new Float64Array( 1 );
+var R = new Float64Array( 1 );
+
+dlartg( F, G, C, S, R );
+// R => <Float64Array>[ 5.0 ]
+// C => <Float64Array>[ 0.6 ]
+// S => <Float64Array>[ 0.8 ]
+```
+
+The function has the following parameters:
+
+-   **F**: [`Float64Array`][mdn-float64array] containing a single element representing the first component of the vector to be rotated.
+-   **G**: [`Float64Array`][mdn-float64array] containing a single element representing the second component of the vector to be rotated
+-   **C**: [`Float64Array`][mdn-float64array] containing a single element which is overwritten by the cosine of the rotation.
+-   **S**: [`Float64Array`][mdn-float64array] containing a single element which is overwritten by the sine of the rotation.
+-   **R**: [`Float64Array`][mdn-float64array] containing a single element which is overwritten by the length of the rotated vector.
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var F0 = new Float64Array( [ 0.0, 3.0 ] );
+var G0 = new Float64Array( [ 0.0, 4.0 ] );
+var C0 = new Float64Array( [ 0.0, 0.0 ] );
+var S0 = new Float64Array( [ 0.0, 0.0 ] );
+var R0 = new Float64Array( [ 0.0, 0.0 ] );
+
+// Create offset views...
+var F1 = new Float64Array( F0.buffer, F0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var G1 = new Float64Array( G0.buffer, G0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var C1 = new Float64Array( C0.buffer, C0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var S1 = new Float64Array( S0.buffer, S0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var R1 = new Float64Array( R0.buffer, R0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlartg( F1, G1, C1, S1, R1 );
+// R0 => <Float64Array>[ 0.0, 5.0 ]
+// C0 => <Float64Array>[ 0.0, 0.6 ]
+// S0 => <Float64Array>[ 0.0, 0.8 ]
+```
+
+#### dlartg.ndarray( F, offsetF, G, offsetG, C, offsetC, S, offsetS, R, offsetR )
+
+Constructs a Givens rotation of a two-dimensional vector that zeros out the second component, using alternative indexing semantics. For a two-dimensional vector `( F, G )` it computes the sine `S`, cosine `C` and the resultant `R`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var F = new Float64Array( [ 3.0 ] );
+var G = new Float64Array( [ 4.0 ] );
+var C = new Float64Array( 1 );
+var S = new Float64Array( 1 );
+var R = new Float64Array( 1 );
+
+dlartg.ndarray( F, 0, G, 0, C, 0, S, 0, R, 0 );
+// R => <Float64Array>[ 5.0 ]
+// C => <Float64Array>[ 0.6 ]
+// S => <Float64Array>[ 0.8 ]
+```
+
+The function has the following parameters:
+
+-   **F**: [`Float64Array`][mdn-float64array] containing a single element representing the first component of the vector to be rotated.
+-   **offsetF**: index of the element in `F`.
+-   **G**: [`Float64Array`][mdn-float64array] containing a single element representing the second component of the vector to be rotated.
+-   **offsetG**: index of the element in `G`.
+-   **C**: [`Float64Array`][mdn-float64array] containing a single element which is overwritten by the cosine of the rotation.
+-   **offsetC**: index of the element in `C`.
+-   **S**: [`Float64Array`][mdn-float64array] containing a single element which is overwritten by the sine of the rotation.
+-   **offsetS**: index of the element in `S`.
+-   **R**: [`Float64Array`][mdn-float64array] containing a single element which is overwritten by the length of the rotated vector.
+-   **offsetR**: index of the element in `R`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var F = new Float64Array( [ 0.0, 3.0 ] );
+var G = new Float64Array( [ 0.0, 4.0 ] );
+var C = new Float64Array( 2 );
+var S = new Float64Array( 2 );
+var R = new Float64Array( 2 );
+
+dlartg.ndarray( F, 1, G, 1, C, 1, S, 1, R, 1 );
+// R => <Float64Array>[ 0.0, 5.0 ]
+// C => <Float64Array>[ 0.0, 0.6 ]
+// S => <Float64Array>[ 0.0, 0.8 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlartg()` corresponds to the [LAPACK][LAPACK] function [`dlartg`][lapack-dlartg].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var dlartg = require( '@stdlib/lapack/base/dlartg' );
+
+var F = uniform( 1, -10.0, 10.0 );
+var G = uniform( 1, -10.0, 10.0 );
+var C = new Float64Array( 1 );
+var S = new Float64Array( 1 );
+var R = new Float64Array( 1 );
+
+dlartg( F, G, C, S, R );
+
+console.log( C );
+console.log( S );
+console.log( R );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dlartg]: https://netlib.org/lapack/explore-html/da/dd3/group__lartg_ga86f8f877eaea0386cdc2c3c175d9ea88.html#ga86f8f877eaea0386cdc2c3c175d9ea88
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dlartg/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var dlartg = require( './../lib/dlartg.js' );
+
+
+// VARIABLES //
+
+var opts = {
+	'dtype': 'float64'
+};
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var C;
+	var S;
+	var R;
+	var F;
+	var G;
+	var i;
+
+	F = discreteUniform( 1, -50, 50, opts );
+	G = discreteUniform( 1, -50, 50, opts );
+	C = new Float64Array( 1 );
+	S = new Float64Array( 1 );
+	R = new Float64Array( 1 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		dlartg( F, G, C, S, R );
+		if ( isnan( C[ 0 ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( S[ 0 ] ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});