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