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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. | ||
--> | ||
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# csrot | ||
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> Applies a plane rotation. | ||
<section class="usage"> | ||
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## Usage | ||
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```javascript | ||
var csrot = require( '@stdlib/blas/base/csrot' ); | ||
``` | ||
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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 | ||
var Complex64Array = require( '@stdlib/array/complex64' ); | ||
var realf = require( '@stdlib/complex/realf' ); | ||
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 ] ); | ||
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 ); | ||
// returns <Complex64> | ||
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var re = realf( z ); | ||
// returns ~-0.6 | ||
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var im = imagf( z ); | ||
// returns ~-1.2 | ||
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z = cx.get( 0 ); | ||
// returns <Complex64> | ||
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re = realf( z ); | ||
// returns ~0.8 | ||
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im = imagf( z ); | ||
// returns ~1.6 | ||
``` | ||
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The function has the following parameters: | ||
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- **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`. | ||
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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 | ||
var Complex64Array = require( '@stdlib/array/complex64' ); | ||
var realf = require( '@stdlib/complex/realf' ); | ||
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 ] ); | ||
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 ); | ||
// returns <Complex64> | ||
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var re = realf( z ); | ||
// returns ~-0.6 | ||
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var im = imagf( z ); | ||
// returns ~-1.2 | ||
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z = cx.get( 0 ); | ||
// returns <Complex64> | ||
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re = realf( z ); | ||
// returns ~0.8 | ||
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im = imagf( z ); | ||
// returns ~1.6 | ||
``` | ||
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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 | ||
var Complex64Array = require( '@stdlib/array/complex64' ); | ||
var realf = require( '@stdlib/complex/realf' ); | ||
var imagf = require( '@stdlib/complex/imagf' ); | ||
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// 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 ] ); | ||
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// 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 | ||
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csrot( 2, cx1, -2, cy1, 1, 0.8, 0.6 ); | ||
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var z = cy0.get( 2 ); | ||
// returns <Complex64> | ||
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var re = realf( z ); | ||
// returns ~-4.2 | ||
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var im = imagf( z ); | ||
// returns ~-4.8 | ||
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z = cx0.get( 3 ); | ||
// returns <Complex64> | ||
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re = realf( z ); | ||
// returns ~5.6 | ||
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im = imagf( z ); | ||
// returns ~6.4 | ||
``` | ||
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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 | ||
var Complex64Array = require( '@stdlib/array/complex64' ); | ||
var realf = require( '@stdlib/complex/realf' ); | ||
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 ] ); | ||
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 ); | ||
// returns <Complex64> | ||
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var re = realf( z ); | ||
// returns ~-0.6 | ||
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var im = imagf( z ); | ||
// returns ~-1.2 | ||
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z = cx.get( 0 ); | ||
// returns <Complex64> | ||
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re = realf( z ); | ||
// returns ~0.8 | ||
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im = imagf( z ); | ||
// returns ~1.6 | ||
``` | ||
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The function has the following additional parameters: | ||
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- **offsetX**: starting index for `cx`. | ||
- **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 | ||
var Complex64Array = require( '@stdlib/array/complex64' ); | ||
var realf = require( '@stdlib/complex/realf' ); | ||
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 ] ); | ||
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 ); | ||
// returns <Complex64> | ||
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var re = realf( z ); | ||
// returns ~-4.2 | ||
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var im = imagf( z ); | ||
// returns ~-4.8 | ||
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z = cx.get( 1 ); | ||
// returns <Complex64> | ||
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re = realf( z ); | ||
// returns ~2.4 | ||
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im = imagf( z ); | ||
// returns ~3.2 | ||
``` | ||
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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. | ||
- `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 | ||
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' ); | ||
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function rand() { | ||
return new Complex64( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) ); | ||
} | ||
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// Generate random input arrays: | ||
var cx = filledarrayBy( 10, 'complex64', rand ); | ||
var cxc = ccopy( cx.length, cx, 1, zeros( cx.length, 'complex64' ), 1 ); | ||
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var cy = filledarrayBy( 10, 'complex64', rand ); | ||
var cyc = ccopy( cy.length, cy, 1, zeros( cy.length, 'complex64' ), 1 ); | ||
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// Apply a plane rotation: | ||
csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 ); | ||
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// Print the results: | ||
logEach( '(%s,%s) => (%s,%s)', cxc, cyc, cx, cy ); | ||
``` | ||
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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 | ||
#include "stdlib/blas/base/csrot.h" | ||
``` | ||
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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 | ||
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 }; | ||
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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 ); | ||
``` | ||
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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 | ||
#include "stdlib/blas/base/csrot.h" | ||
#include <stdio.h> | ||
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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 }; | ||
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// Specify the number of elements: | ||
const int N = 4; | ||
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// Specify stride lengths: | ||
const int strideX = 1; | ||
const int strideY = -1; | ||
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// Copy elements: | ||
c_csrot( N, (void *)x, strideX, (void *)y, strideY, 0.8f, 0.6f ); | ||
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// 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 --> |
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