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feat: add blas/base/zrotg
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‎lib/node_modules/@stdlib/blas/base/zrotg/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 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.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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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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# zrotg
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> Constructs a Givens plane rotation.
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<section class="usage">
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## Usage
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```javascript
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var zrotg = require( '@stdlib/blas/base/zrotg' );
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```
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#### zrotg( za, zb )
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Constructs a Givens plane rotation provided two single-precision floating-point values `a` and `b`.
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```javascript
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var za = new Complex128( 4.0, 3.0 );
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// returns <Complex128>
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var zb = new Complex128( 0.0, 0.0 );
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// returns <Complex128>
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var out = zrotg( za, zb );
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// out => <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
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```
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The function has the following parameters:
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- **za**: rotational elimination parameter.
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- **za**: rotational elimination parameter.
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- `zrotg()` corresponds to the [BLAS][blas] level 1 function [`zrotg`][zrotg].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var zrotg = require( '@stdlib/blas/base/zrotg' );
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var out;
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var i;
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function rand() {
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return new Complex128( discreteUniform( -5, 5 ), discreteUniform( -5, 5 ) );
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}
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for ( i = 0; i < 100; i++ ) {
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out = zrotg( rand(), rand() );
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console.log( out );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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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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</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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<section class="links">
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[blas]: http://www.netlib.org/blas
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[zrotg]: https://www.netlib.org/lapack/explore-html/d7/dc5/group__rotg_ga97ce56a6808661b36ab62269393ac10e.html
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/base/zrotg/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 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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// MODULES //
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var bench = require( '@stdlib/bench' );
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var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var pkg = require( './../package.json' ).name;
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var zrotg = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var za;
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var zb;
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var z;
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var i;
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za = new Complex128( discreteUniform( -5, 5 ), discreteUniform( -5, 5 ) );
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zb = new Complex128( discreteUniform( -5, 5 ), discreteUniform( -5, 5 ) );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = zrotg( za, zb );
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if ( isnan( z[ i%4 ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( z[ i%4 ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/blas/base/zrotg/docs/repl.txt‎

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{{alias}}( za, zb )
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Constructs a Givens plane rotation from two double-precision complex
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floating-point numbers.
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Parameters
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----------
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za: Complex128
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Rotational elimination parameter.
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zb: Complex128
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Rotational elimination parameter.
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Returns
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-------
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out: Float64Array
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Computed values.
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Examples
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--------
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// Standard usage:
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> var za = new {{alias:@stdlib/complex/float64/ctor}}( 4.0, 3.0 );
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> var zb = new {{alias:@stdlib/complex/float64/ctor}}( 0.0, 0.0 );
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> var out = {{alias}}( za, zb )
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out => <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
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See Also
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--------

‎lib/node_modules/@stdlib/blas/base/zrotg/docs/types/index.d.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2025 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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// TypeScript Version: 4.1
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/// <reference types="@stdlib/types"/>
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import { Complex128 } from '@stdlib/types/complex';
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/**
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* Constructs a Givens plane rotation.
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*
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* @param za - rotational elimination parameter
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* @param zb - rotational elimination parameter
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* @returns output array
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*
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* @example
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* var Complex128 = require( '@stdlib/complex/float64/ctor' );
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*
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* var za = new Complex128( 4.0, 3.0 );
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* var zb = new Complex128( 0.0, 0.0 );
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*
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* var out = zrotg( za, zb );
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* // returns <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
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*
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* @example
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* var za = new Complex128( 1.0, 2.0 );
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* var zb = new Complex128( 3.0, 4.0 );
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*
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* var out = zrotg( za, zb );
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* // returns <Float64Array>[ ~1.732, ~5.1961, ~0.5773, ~0.8082, ~0.1154 ]
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*/
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declare function zrotg( za: Complex128, zb: Complex128 ): Float64Array;
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// EXPORTS //
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export = zrotg;

‎lib/node_modules/@stdlib/blas/base/zrotg/docs/types/test.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2025 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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import Complex128 = require( '@stdlib/complex/float64/ctor' );
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import zrotg = require( './index' );
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// TESTS //
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// The function returns a Float64Array...
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{
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const za = new Complex128( 1.0, 1.0 );
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const zb = new Complex128( 2.0, 2.0 );
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zrotg( za, zb ); // $ExpectType Float64Array
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}
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// The compiler throws an error if the function is provided an argument which is not a number...
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{
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const za = new Complex128( 1.0, 1.0 );
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const zb = new Complex128( 2.0, 2.0 );
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zrotg( true, zb ); // $ExpectError
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zrotg( false, zb ); // $ExpectError
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zrotg( null, zb ); // $ExpectError
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zrotg( undefined, zb ); // $ExpectError
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zrotg( '5', zb ); // $ExpectError
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zrotg( [], zb ); // $ExpectError
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zrotg( {}, zb ); // $ExpectError
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zrotg( za, true ); // $ExpectError
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zrotg( za, false ); // $ExpectError
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zrotg( za, null ); // $ExpectError
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zrotg( za, undefined ); // $ExpectError
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zrotg( za, '5' ); // $ExpectError
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zrotg( za, [] ); // $ExpectError
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zrotg( za, {} ); // $ExpectError
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}
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// The compiler throws an error if the function is provided an unsupported number of arguments...
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{
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const za = new Complex128( 1.0, 1.0 );
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const zb = new Complex128( 2.0, 2.0 );
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zrotg(); // $ExpectError
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zrotg( za ); // $ExpectError
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zrotg( za, zb, 3.0 ); // $ExpectError
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}

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