feat: add blas/base/zrotg

lib/node_modules/@stdlib/blas/base/zrotg/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.
+
+-->
+
+# zrotg
+
+> Construct a Givens plane rotation.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var zrotg = require( '@stdlib/blas/base/zrotg' );
+```
+
+#### zrotg( za, zb )
+
+Constructs a Givens plane rotation provided two double-precision complex floating-point values `za` and `zb`.
+
+```javascript
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var za = new Complex128( 4.0, 3.0 );
+var zb = new Complex128( 0.0, 0.0 );
+
+var out = zrotg( za, zb );
+// returns <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
+```
+
+The function has the following parameters:
+
+-   **za**: rotational elimination parameter (complex number).
+-   **zb**: rotational elimination parameter (complex number).
+
+The function returns an array with the following elements:
+
+-   **r**: real part of the rotated vector (real number).
+-   **r_imag**: imaginary part of the rotated vector (real number).
+-   **c**: cosine of the rotation angle (real number).
+-   **s**: real part of the sine of the rotation angle (real number).
+-   **s_imag**: imaginary part of the sine of the rotation angle (real number).
+
+#### zrotg.assign( za, zb, out, stride, offset )
+
+Constructs a Givens plane rotation provided two double-precision complex floating-point values `za` and `zb` and assigns results to an output array.
+
+```javascript
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var za = new Complex128( 4.0, 3.0 );
+var zb = new Complex128( 0.0, 0.0 );
+
+var out = new Float64Array( 5 );
+
+var y = zrotg.assign( za, zb, out, 1, 0 );
+// returns <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
+
+var bool = ( y === out );
+// returns true
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `zrotg()` corresponds to the [BLAS][blas] level 1 function [`zrotg`][blas-zrotg].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+```javascript
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var zrotg = require( '@stdlib/blas/base/zrotg' );
+
+var out;
+var i;
+
+function rand() {
+    return new Complex128( discreteUniform( -5, 5 ), discreteUniform( -5, 5 ) );
+}
+
+for ( i = 0; i < 100; i++ ) {
+    out = zrotg( rand(), rand() );
+    console.log( out );
+}
+```
+
+</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
+#include "stdlib/blas/base/zrotg.h"
+```
+
+#### c_zrotg( a, b, \*Out, strideOut )
+
+Constructs a Givens plane rotation provided two double-precision complex floating-point values `a` and `b`.
+
+```c
+#include "stdlib/complex/float64/ctor.h"
+
+double Out[ 5 ];
+const stdlib_complex128_t a = stdlib_complex128( 4.0, 3.0 );
+const stdlib_complex128_t b = stdlib_complex128( 0.0, 0.0 );
+
+c_zrotg( a, b, Out, 1 );
+// Out => [ 4.0, 3.0, 1.0, 0.0, 0.0 ]
+```
+
+The function accepts the following arguments:
+
+-   **a**: `[in] stdlib_complex128_t` rotational elimination parameter.
+-   **b**: `[in] stdlib_complex128_t` rotational elimination parameter.
+-   **Out**: `[out] double*` output array.
+-   **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
+
+```c
+void c_zrotg( const stdlib_complex128_t a, const stdlib_complex128_t b, double *Out, const CBLAS_INT strideOut );
+```
+
+#### c_zrotg_assign( a, b, \*Out, strideOut, offsetOut )
+
+Constructs a Givens plane rotation provided two double-precision complex floating-point values `a` and `b` using alternative indexing semantics.
+
+```c
+#include "stdlib/complex/float64/ctor.h"
+
+double Out[ 5 ];
+const stdlib_complex128_t a = stdlib_complex128( 4.0, 3.0 );
+const stdlib_complex128_t b = stdlib_complex128( 0.0, 0.0 );
+
+c_zrotg_assign( a, b, Out, 1, 0 );
+// Out => [ 4.0, 3.0, 1.0, 0.0, 0.0 ]
+```
+
+The function accepts the following arguments:
+
+-   **a**: `[in] stdlib_complex128_t` rotational elimination parameter.
+-   **b**: `[in] stdlib_complex128_t` rotational elimination parameter.
+-   **Out**: `[out] double*` output array.
+-   **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
+-   **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.
+
+```c
+void c_zrotg_assign( const stdlib_complex128_t a, const stdlib_complex128_t b, double *Out, const CBLAS_INT strideOut, const CBLAS_INT offsetOut );
+```
+
+</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
+#include "stdlib/blas/base/zrotg.h"
+#include "stdlib/complex/float64/ctor.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Specify rotational elimination parameters:
+    const stdlib_complex128_t a = stdlib_complex128( 4.0, 3.0 );
+    const stdlib_complex128_t b = stdlib_complex128( 0.0, 0.0 );
+    int i;
+
+    // Create output array:
+    double Out[ 5 ];
+
+    // Specify stride length:
+    const int strideOut = 1;
+
+    // Apply plane rotation:
+    c_zrotg( a, b, Out, strideOut );
+
+    // Print the result:
+    for ( i = 0; i < 5; i++ ) {
+        printf( "Out[%d] = %lf\n", i, Out[ i ] );
+    }
+
+    // Apply plane rotation using alternative indexing semantics:
+    c_zrotg_assign( a, b, Out, strideOut, 0 );
+
+    // Print the result:
+    for ( i = 0; i < 5; i++ ) {
+        printf( "Out[%d] = %lf\n", i, Out[ i ] );
+    }
+}
+```
+
+</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">
+
+[blas]: http://www.netlib.org/blas
+
+[blas-zrotg]: https://www.netlib.org/lapack/explore-html/d7/dc5/group__rotg_ga97ce56a6808661b36ab62269393ac10e.html
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/base/zrotg/benchmark/benchmark.assign.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 discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var Float64Array = require( '@stdlib/array/float64' );
+var pkg = require( './../package.json' ).name;
+var zrotg = require( './../lib/assign.js' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) { // eslint-disable-line no-unused-vars
+	var za;
+	var zb;
+	var z;
+
+	za = new Complex128( discreteUniform( -5, 5 ), discreteUniform( -5, 5 ) );
+	zb = new Complex128( discreteUniform( -5, 5 ), discreteUniform( -5, 5 ) );
+	z = new Float64Array( 5 );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			zrotg( za, zb, z, 1, 0 );
+			if ( isnan( z[ i%4 ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z[ i%4 ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();