feat: add BLAS Level 1 routine for zdrot

lib/node_modules/@stdlib/blas/base/zdrot/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# zdrot
+
+> Applies a plane rotation on complex double-precision floating-point vectors.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var zdrot = require( '@stdlib/blas/base/zdrot' );
+```
+
+#### zdrot( N, zx, strideX, zy, strideY, c, s )
+
+Applies a plane rotation on complex double-precision floating-point vectors.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var real = require( '@stdlib/complex/real' );
+var imag = require( '@stdlib/complex/imag' );
+
+var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+var zy = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+zdrot( zx.length, zx, 1, zy, 1, 0.8, 0.6 );
+
+var z = zy.get( 0 );
+// returns <Complex128>
+
+var re = real( z );
+// returns ~-0.6
+
+var im = imag( z );
+// returns ~-1.2
+
+z = zx.get( 0 );
+// returns <Complex128>
+
+re = real( z );
+// returns ~0.8
+
+im = imag( z );
+// returns ~1.6
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **zx**: first input [`Complex128Array`][@stdlib/array/complex128].
+-   **strideX**: index increment for `zx`.
+-   **zy**: second input [`Complex128Array`][@stdlib/array/complex128].
+-   **strideY**: index increment for `zy`.
+
+The `N` and stride parameters determine how values from `zx` and `zy` are rotated. For example, to apply a plane rotation to every other element,
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var real = require( '@stdlib/complex/real' );
+var imag = require( '@stdlib/complex/imag' );
+
+var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+var zy = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+zdrot( 2, zx, 2, zy, 2, 0.8, 0.6 );
+
+var z = zy.get( 0 );
+// returns <Complex128>
+
+var re = real( z );
+// returns ~-0.6
+
+var im = imag( z );
+// returns ~-1.2
+
+z = zx.get( 0 );
+// returns <Complex128>
+
+re = real( z );
+// returns ~0.8
+
+im = imag( z );
+// returns ~1.6
+```
+
+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 Complex128Array = require( '@stdlib/array/complex128' );
+var real = require( '@stdlib/complex/real' );
+var imag = require( '@stdlib/complex/imag' );
+
+// Initial arrays...
+var zx0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+var zy0 = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create offset views...
+var zx1 = new Complex128Array( zx0.buffer, zx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var zy1 = new Complex128Array( zy0.buffer, zy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
+
+zdrot( 2, zx1, -2, zy1, 1, 0.8, 0.6 );
+
+var z = zy0.get( 2 );
+// returns <Complex128>
+
+var re = real( z );
+// returns ~-4.2
+
+var im = imag( z );
+// returns ~-4.8
+
+z = zx0.get( 3 );
+// returns <Complex128>
+
+re = real( z );
+// returns ~5.6
+
+im = imag( z );
+// returns ~6.4
+```
+
+#### zdrot.ndarray( N, zx, strideX, offsetX, zy, strideY, offsetY, c, s )
+
+Applies a plane rotation on complex double-precision floating-point vectors using alternative indexing semantics.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var real = require( '@stdlib/complex/real' );
+var imag = require( '@stdlib/complex/imag' );
+
+var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var zy = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+zdrot.ndarray( zx.length, zx, 1, 0, zy, 1, 0, 0.8, 0.6 );
+
+var z = zy.get( 0 );
+// returns <Complex128>
+
+var re = real( z );
+// returns ~-0.6
+
+var im = imag( z );
+// returns ~-1.2
+
+z = zx.get( 0 );
+// returns <Complex128>
+
+re = real( z );
+// returns ~0.8
+
+im = imag( z );
+// returns ~1.6
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `zx`.
+-   **offsetY**: starting index for `zy`.
+
+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, to apply a plane rotation to every other element starting from the second element,
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var real = require( '@stdlib/complex/real' );
+var imag = require( '@stdlib/complex/imag' );
+
+var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+var zy = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+zdrot.ndarray( 2, zx, 2, 1, zy, 2, 1, 0.8, 0.6 );
+
+var z = zy.get( 3 );
+// returns <Complex128>
+
+var re = real( z );
+// returns ~-4.2
+
+var im = imag( z );
+// returns ~-4.8
+
+z = zx.get( 1 );
+// returns <Complex128>
+
+re = real( z );
+// returns ~2.4
+
+im = imag( z );
+// returns ~3.2
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions leave `zx` and `zy` unchanged.
+-   `zdrot()` corresponds to the [BLAS][blas] level 1 function [`zdrot`][zdrot].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var filledarrayBy = require( '@stdlib/array/filled-by' );
+var Complex128 = require( '@stdlib/complex/float64' );
+var zdrot = require( '@stdlib/blas/base/zdrot' );
+
+function rand() {
+    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
+}
+
+var zx = filledarrayBy( 10, 'complex128', rand );
+console.log( zx.get( 0 ).toString() );
+
+var zy = filledarrayBy( 10, 'complex128', rand );
+console.log( zy.get( 0 ).toString() );
+
+// Apply a plane rotation:
+zdrot( zx.length, zx, 1, zy, 1, 0.8, 0.6 );
+console.log( zx.get( zx.length-1 ).toString() );
+console.log( zy.get( zy.length-1 ).toString() );
+```
+
+</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/zdrot.h"
+```
+
+#### c_zdrot( N, \*X, strideX, \*Y, strideY, c, s )
+
+Applies a plane rotation on complex double-precision floating-point vectors.
+
+```c
+double x[] = { 1.0, 2.0, 3.0, 4.0 }; // interleaved real and imaginary components
+double y[] = { 5.0, 6.0, 7.0, 8.0 };
+
+c_zdrot( 2, (void *)x, 1, (void *)Y, 1, 0.8, 0.6 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **zx**: `[inout] void*` first input array.
+-   **strideX**: `[in] CBLAS_INT` index increment for `zx`.
+-   **zy**: `[inout] void*` first input array.
+-   **strideY**: `[in] CBLAS_INT` index increment for `zy`.
+-   **c**: `[in] double` cosine of the angle of rotation.
+-   **s**: `[in] double` sine of the angle of rotation.
+
+```c
+void c_zdrot( const CBLAS_INT N, void *X, const CBLAS_INT strideX, void *Y, const CBLAS_INT strideY, const double c, const double s );
+```
+
+</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/zdrot.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create strided arrays:
+    double zx[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
+    double zy[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+    // Specify the number of elements:
+    const int N = 4;
+
+    // Specify stride lengths:
+    const int strideX = 1;
+    const int strideY = -1;
+
+    // Copy elements:
+    c_zdrot( N, (void *)zx, strideX, (void *)zy, strideY, 0.8, 0.6 );
+
+    // Print the result:
+    for ( int i = 0; i < N; i++ ) {
+        printf( "zx[ %i ] = %lf + %lfj\n", i, zx[ i*2 ], zx[ (i*2)+1 ] );
+        printf( "zy[ %i ] = %lf + %lfj\n", i, zy[ i*2 ], zy[ (i*2)+1 ] );
+    }
+}
+```
+
+</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
+
+[zdrot]: http://www.netlib.org/lapack/explore-html/da/df6/group__complex__blas__level1.html
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
+
+</section>
+
+<!-- /.links -->