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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) 2026 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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> Construct 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 double-precision complex floating-point values `za` and `zb`.
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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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var zb = new Complex128( 0.0, 0.0 );
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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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The function has the following parameters:
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- **za**: rotational elimination parameter (complex number).
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- **zb**: rotational elimination parameter (complex number).
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The function returns an array with the following elements:
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- **r**: real part of the rotated vector (real number).
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- **r_imag**: imaginary part of the rotated vector (real number).
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- **c**: cosine of the rotation angle (real number).
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- **s**: real part of the sine of the rotation angle (real number).
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- **s_imag**: imaginary part of the sine of the rotation angle (real number).
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#### zrotg.assign( za, zb, out, stride, offset )
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Constructs a Givens plane rotation provided two double-precision complex floating-point values `za` and `zb` and assigns results to an output array.
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```javascript
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var Float64Array = require( '@stdlib/array/float64' );
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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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var out = new Float64Array( 5 );
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var y = zrotg.assign( za, zb, out, 1, 0 );
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// returns <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
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var bool = ( y === out );
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// returns true
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```
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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`][blas-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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```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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#include "stdlib/blas/base/zrotg.h"
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```
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#### c_zrotg( a, b, \*Out, strideOut )
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Constructs a Givens plane rotation provided two double-precision complex floating-point values `a` and `b`.
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```c
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#include "stdlib/complex/float64/ctor.h"
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double Out[ 5 ];
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const stdlib_complex128_t a = stdlib_complex128( 4.0, 3.0 );
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const stdlib_complex128_t b = stdlib_complex128( 0.0, 0.0 );
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c_zrotg( a, b, Out, 1 );
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// Out => [ 4.0, 3.0, 1.0, 0.0, 0.0 ]
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```
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The function accepts the following arguments:
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- **a**: `[in] stdlib_complex128_t` rotational elimination parameter.
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- **b**: `[in] stdlib_complex128_t` rotational elimination parameter.
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- **Out**: `[out] double*` output array.
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- **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
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```c
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void c_zrotg( const stdlib_complex128_t a, const stdlib_complex128_t b, double *Out, const CBLAS_INT strideOut );
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```
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#### c_zrotg_assign( a, b, \*Out, strideOut, offsetOut )
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Constructs a Givens plane rotation provided two double-precision complex floating-point values `a` and `b` using alternative indexing semantics.
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```c
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#include "stdlib/complex/float64/ctor.h"
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double Out[ 5 ];
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const stdlib_complex128_t a = stdlib_complex128( 4.0, 3.0 );
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const stdlib_complex128_t b = stdlib_complex128( 0.0, 0.0 );
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c_zrotg_assign( a, b, Out, 1, 0 );
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// Out => [ 4.0, 3.0, 1.0, 0.0, 0.0 ]
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```
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The function accepts the following arguments:
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- **a**: `[in] stdlib_complex128_t` rotational elimination parameter.
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- **b**: `[in] stdlib_complex128_t` rotational elimination parameter.
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- **Out**: `[out] double*` output array.
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- **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
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- **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.
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```c
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void c_zrotg_assign( const stdlib_complex128_t a, const stdlib_complex128_t b, double *Out, const CBLAS_INT strideOut, const CBLAS_INT offsetOut );
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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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#include "stdlib/blas/base/zrotg.h"
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#include "stdlib/complex/float64/ctor.h"
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#include <stdio.h>
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int main( void ) {
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// Specify rotational elimination parameters:
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const stdlib_complex128_t a = stdlib_complex128( 4.0, 3.0 );
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const stdlib_complex128_t b = stdlib_complex128( 0.0, 0.0 );
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int i;
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// Create output array:
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double Out[ 5 ];
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// Specify stride length:
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const int strideOut = 1;
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// Apply plane rotation:
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c_zrotg( a, b, Out, strideOut );
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// Print the result:
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for ( i = 0; i < 5; i++ ) {
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printf( "Out[%d] = %lf\n", i, Out[ i ] );
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}
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// Apply plane rotation using alternative indexing semantics:
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c_zrotg_assign( a, b, Out, strideOut, 0 );
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// Print the result:
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for ( i = 0; i < 5; i++ ) {
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printf( "Out[%d] = %lf\n", i, Out[ i ] );
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}
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}
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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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[blas-zrotg]: https://www.netlib.org/lapack/explore-html/d7/dc5/group__rotg_ga97ce56a6808661b36ab62269393ac10e.html
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/base/zrotg/benchmark/benchmark.assign.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 Float64Array = require( '@stdlib/array/float64' );
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var pkg = require( './../package.json' ).name;
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var zrotg = require( './../lib/assign.js' );
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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, new Float64Array(5), 1, 0 );
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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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});

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