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feat: add lapack/base/crot
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‎lib/node_modules/@stdlib/lapack/base/crot/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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# crot
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> Apply a plane rotation with real cosine and complex sine to a pair of single-precision complex floating-point vectors.
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<section class="usage">
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## Usage
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```javascript
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var crot = require( '@stdlib/lapack/base/crot' );
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```
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#### crot( N, cx, strideCX, cy, strideCY, c, s )
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Applies a plane rotation with real cosine and complex sine.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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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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var s = new Complex64( 0.0, 0.75 );
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crot( cx.length, cx, 1, cy, 1, 1.25, s );
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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 ~-1.5
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var im = imagf( z );
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// returns ~0.75
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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 ~1.25
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im = imagf( z );
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// returns ~2.5
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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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- **strideCX**: stride length for `cx`.
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- **cy**: second input [`Complex64Array`][@stdlib/array/complex64].
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- **strideCY**: stride length 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 Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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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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var s = new Complex64( 0.0, 0.75 );
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crot( 2, cx, 2, cy, 2, 1.25, s );
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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 ~-1.5
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var im = imagf( z );
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// returns ~0.75
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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 ~1.25
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im = imagf( z );
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// returns ~2.5
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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 Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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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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var s = new Complex64( 0.0, 0.75 );
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crot( 2, cx1, -2, cy1, 1, 1.25, s );
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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 ~-6
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var im = imagf( z );
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// returns ~5.25
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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 ~8.75
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im = imagf( z );
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// returns ~10
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```
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#### crot.ndarray( N, cx, strideCX, offsetCX, cy, strideCY, offsetCY, c, s )
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Applies a plane rotation with real cosine and complex sine using alternative indexing semantics.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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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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var s = new Complex64( 0.0, 0.75 );
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crot.ndarray( cx.length, cx, 1, 0, cy, 1, 0, 1.25, s );
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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 ~-1.5
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var im = imagf( z );
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// returns ~0.75
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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 ~1.25
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im = imagf( z );
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// returns ~2.5
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```
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The function has the following additional parameters:
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- **offsetCX**: starting index for `cx`.
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- **offsetCY**: 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 Complex64 = require( '@stdlib/complex/float32/ctor' );
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var realf = require( '@stdlib/complex/float32/real' );
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var imagf = require( '@stdlib/complex/float32/imag' );
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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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var s = new Complex64( 0.0, 0.75 );
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crot.ndarray( 2, cx, 2, 1, cy, 2, 1, 1.25, s );
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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 ~-6.0
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var im = imagf( z );
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// returns ~5.25
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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 ~3.75
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im = imagf( z );
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// returns ~5.0
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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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- `crot()` corresponds to the [LAPACK][lapack] routine [`crot`][crot].
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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 zcopy = require( '@stdlib/blas/base/zcopy' );
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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 crot = require( '@stdlib/lapack/base/crot' );
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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 = zcopy( 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 = zcopy( cy.length, cy, 1, zeros( cy.length, 'complex64' ), 1 );
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var s = new Complex64( 0.0, 0.75 );
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// Apply a plane rotation:
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crot( cx.length, cx, 1, cy, 1, 1.25, s );
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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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<!-- 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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[lapack]: http://www.netlib.org/lapack
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[crot]: https://netlib.org/lapack/explore-html/d1/d45/group__rot_ga25544801d45dcabdec7b24d863ebea9c.html#ga25544801d45dcabdec7b24d863ebea9c
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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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