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feat: add blas/base/csrot
PR-URL: #2256 Ref: #2039 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com>
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‎lib/node_modules/@stdlib/blas/base/csrot/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 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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# csrot
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> Applies a plane rotation.
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<section class="usage">
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## Usage
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```javascript
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var csrot = require( '@stdlib/blas/base/csrot' );
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```
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#### csrot( N, cx, strideX, cy, strideY, c, s )
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Applies a plane rotation.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var realf = require( '@stdlib/complex/realf' );
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var imagf = require( '@stdlib/complex/imagf' );
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var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 );
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var z = cy.get( 0 );
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// returns <Complex64>
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var re = realf( z );
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// returns ~-0.6
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var im = imagf( z );
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// returns ~-1.2
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z = cx.get( 0 );
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// returns <Complex64>
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re = realf( z );
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// returns ~0.8
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im = imagf( z );
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// returns ~1.6
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **cx**: first input [`Complex64Array`][@stdlib/array/complex64].
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- **strideX**: index increment for `cx`.
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- **cy**: second input [`Complex64Array`][@stdlib/array/complex64].
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- **strideY**: index increment for `cy`.
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The `N` and stride parameters determine how values from `cx` and `cy` are accessed at runtime. For example, to apply a plane rotation to every other element,
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var realf = require( '@stdlib/complex/realf' );
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var imagf = require( '@stdlib/complex/imagf' );
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var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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csrot( 2, cx, 2, cy, 2, 0.8, 0.6 );
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var z = cy.get( 0 );
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// returns <Complex64>
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var re = realf( z );
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// returns ~-0.6
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var im = imagf( z );
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// returns ~-1.2
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z = cx.get( 0 );
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// returns <Complex64>
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re = realf( z );
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// returns ~0.8
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im = imagf( z );
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// returns ~1.6
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```
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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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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var realf = require( '@stdlib/complex/realf' );
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var imagf = require( '@stdlib/complex/imagf' );
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// Initial arrays...
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var cx0 = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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var cy0 = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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// Create offset views...
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var cx1 = new Complex64Array( cx0.buffer, cx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var cy1 = new Complex64Array( cy0.buffer, cy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
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csrot( 2, cx1, -2, cy1, 1, 0.8, 0.6 );
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var z = cy0.get( 2 );
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// returns <Complex64>
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var re = realf( z );
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// returns ~-4.2
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var im = imagf( z );
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// returns ~-4.8
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z = cx0.get( 3 );
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// returns <Complex64>
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re = realf( z );
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// returns ~5.6
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im = imagf( z );
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// returns ~6.4
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```
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#### csrot.ndarray( N, cx, strideX, offsetX, cy, strideY, offsetY, c, s )
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Applies a plane rotation using alternative indexing semantics.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var realf = require( '@stdlib/complex/realf' );
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var imagf = require( '@stdlib/complex/imagf' );
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var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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csrot.ndarray( cx.length, cx, 1, 0, cy, 1, 0, 0.8, 0.6 );
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var z = cy.get( 0 );
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// returns <Complex64>
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var re = realf( z );
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// returns ~-0.6
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var im = imagf( z );
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// returns ~-1.2
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z = cx.get( 0 );
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// returns <Complex64>
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re = realf( z );
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// returns ~0.8
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im = imagf( z );
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// returns ~1.6
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `cx`.
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- **offsetY**: starting index for `cy`.
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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,
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var realf = require( '@stdlib/complex/realf' );
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var imagf = require( '@stdlib/complex/imagf' );
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var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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csrot.ndarray( 2, cx, 2, 1, cy, 2, 1, 0.8, 0.6 );
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var z = cy.get( 3 );
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// returns <Complex64>
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var re = realf( z );
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// returns ~-4.2
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var im = imagf( z );
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// returns ~-4.8
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z = cx.get( 1 );
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// returns <Complex64>
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re = realf( z );
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// returns ~2.4
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im = imagf( z );
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// returns ~3.2
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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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- If `N <= 0`, both functions leave `cx` and `cy` unchanged.
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- `csrot()` corresponds to the [BLAS][blas] level 1 function [`csrot`][csrot].
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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 filledarrayBy = require( '@stdlib/array/filled-by' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var ccopy = require( '@stdlib/blas/base/ccopy' );
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var zeros = require( '@stdlib/array/zeros' );
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var logEach = require( '@stdlib/console/log-each' );
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var csrot = require( '@stdlib/blas/base/csrot' );
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function rand() {
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return new Complex64( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
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}
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// Generate random input arrays:
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var cx = filledarrayBy( 10, 'complex64', rand );
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var cxc = ccopy( cx.length, cx, 1, zeros( cx.length, 'complex64' ), 1 );
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var cy = filledarrayBy( 10, 'complex64', rand );
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var cyc = ccopy( cy.length, cy, 1, zeros( cy.length, 'complex64' ), 1 );
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// Apply a plane rotation:
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csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 );
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// Print the results:
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logEach( '(%s,%s) => (%s,%s)', cxc, cyc, cx, cy );
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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/csrot.h"
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```
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#### c_csrot( N, \*X, strideX, \*Y, strideY, c, s )
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Applies a plane rotation.
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```c
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float x[] = { 1.0f, 2.0f, 3.0f, 4.0f }; // interleaved real and imaginary components
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float y[] = { 5.0f, 6.0f, 7.0f, 8.0f };
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c_csrot( 2, (void *)x, 1, (void *)Y, 1, 0.8, 0.6 );
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **CX**: `[inout] void*` first input array.
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- **strideX**: `[in] CBLAS_INT` index increment for `CX`.
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- **CY**: `[inout] void*` second input array.
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- **strideY**: `[in] CBLAS_INT` index increment for `CY`.
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- **c**: `[in] float` cosine of the angle of rotation.
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- **s**: `[in] float` sine of the angle of rotation.
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```c
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void c_csrot( const CBLAS_INT N, void *CX, const CBLAS_INT strideX, void *CY, const CBLAS_INT strideY, const float c, const float s );
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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/csrot.h"
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#include <stdio.h>
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int main( void ) {
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// Create strided arrays:
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float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
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float y[] = { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f };
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// Specify the number of elements:
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const int N = 4;
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// Specify stride lengths:
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const int strideX = 1;
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const int strideY = -1;
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// Copy elements:
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c_csrot( N, (void *)x, strideX, (void *)y, strideY, 0.8f, 0.6f );
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// Print the result:
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for ( int i = 0; i < N; i++ ) {
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printf( "x[ %i ] = %f + %fj\n", i, x[ i*2 ], x[ (i*2)+1 ] );
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printf( "y[ %i ] = %f + %fj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
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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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[csrot]: http://www.netlib.org/lapack/explore-html/da/df6/group__complex__blas__level1.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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[@stdlib/array/complex64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex64
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</section>
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<!-- /.links -->

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