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feat: add blas/base/srotm
PR-URL: #2267 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/srotm/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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# srotm
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> Apply a modified Givens plane rotation.
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<section class="usage">
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## Usage
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```javascript
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var srotm = require( '@stdlib/blas/base/srotm' );
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```
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#### srotm( N, x, strideX, y, strideY, param )
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Applies a modified Givens plane rotation.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var y = new Float32Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
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var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
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srotm( 2, x, 2, y, 1, param );
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// x => <Float32Array>[ ~-17.0, 2.0, ~-18.0, 4.0, 5.0 ]
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// y => <Float32Array>[ ~8.0, ~13.0, 8.0, 9.0, 10.0 ]
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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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- **x**: first input [`Float32Array`][mdn-float32array].
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- **strideX**: index increment for `x`.
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- **y**: second input [`Float32Array`][mdn-float32array].
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- **strideY**: index increment for `y`.
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- **param**: parameters for the modified Givens transformation
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The `N` and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a modified Givens plane rotation to every other element,
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
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srotm( 3, x, 2, y, 2, param );
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// x => <Float32Array>[ ~-20.0, 2.0, ~-24.0, 4.0, ~-28.0, 6.0 ]
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// y => <Float32Array>[ ~9.0, 8.0, ~15.0, 10.0, ~21.0, 12.0 ]
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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 Float32Array = require( '@stdlib/array/float32' );
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// Initial arrays...
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var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var y0 = new Float32Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
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var param = new Float32Array( [ 1.0, 0.0, 2.0, 3.0, 0.0 ] );
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// Create offset views...
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var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element
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srotm( 2, x1, 1, y1, 1, param );
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// x0 => <Float32Array>[ 1.0, ~9.0, ~10.0, 4.0, 5.0 ]
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// y0 => <Float32Array>[ 6.0, 7.0, 8.0, ~-2.0, ~-3.0 ]
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```
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#### srotm.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, param )
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Applies a modified Givens plane rotation using alternative indexing semantics.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var y = new Float32Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
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var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
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srotm.ndarray( 2, x, 1, 0, y, 2, 1, param );
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// x => <Float32Array>[ ~-20.0, ~-25.0, 3.0, 4.0, 5.0 ]
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// y => <Float32Array>[ 6.0, ~9.0, 8.0, ~13.0, 10.0 ]
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `x`.
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- **offsetY**: starting index for `y`.
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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 modified Givens plane rotation to every other element starting from the second element,
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
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srotm.ndarray( 3, x, 2, 1, y, 2, 1, param );
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// x => <Float32Array>[ 1.0, ~-22.0, 3.0, ~-26.0, 5.0, ~-30.0 ]
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// y => <Float32Array>[ 7.0, ~12.0, 9.0, ~18.0, 11.0, ~24.0 ]
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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 `x` and `y` unchanged.
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- `srotm()` corresponds to the [BLAS][blas] level 1 function [`srotm`][srotm].
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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/array/discrete-uniform' );
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var srotm = require( '@stdlib/blas/base/srotm' );
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var opts = {
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'dtype': 'float32'
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};
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var x = discreteUniform( 10, 0, 500, opts );
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console.log( x );
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var y = discreteUniform( x.length, 0, 255, opts );
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console.log( y );
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var param = discreteUniform( 5, -5, 5, opts );
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console.log( param );
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// Apply a plane rotation:
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srotm( x.length, x, 1, y, 1, param );
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console.log( x );
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console.log( y );
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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/srotm.h"
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```
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#### c_srotm( N, \*X, strideX, \*Y, strideY, param )
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Applies a modified Givens plane rotation.
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```c
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float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f };
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float y[] = { 6.0f, 7.0f, 8.0f, 9.0f, 10.0f };
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const float param[5] = { 0.0f, 0.0f, 2.0f, -3.0f, 0.0f };
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c_srotm( 5, x, 1, y, 1, param );
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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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- **X**: `[inout] float*` first input array.
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- **strideX**: `[in] CBLAS_INT` index increment for `X`.
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- **Y**: `[inout] float*` second input array.
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- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
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- **param**: `[in] float` parameters for the modified Givens transformation.
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```c
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void c_srotm( const CBLAS_INT N, float *X, const CBLAS_INT strideX, float *Y, const CBLAS_INT strideY, const float *param );
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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/srotm.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 };
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float y[] = { 6.0f, 7.0f, 8.0f, 9.0f, 10.0f };
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// Specify the number of elements:
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const int N = 5;
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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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// Specify parameters for the modified Givens transformation:
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const float param[5] = { 0.0f, 0.0f, 2.0f, -3.0f, 0.0f };
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// Apply plane rotation:
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c_srotm( N, x, strideX, y, strideY, param );
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// Print the result:
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for ( int i = 0; i < 5; i++ ) {
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printf( "x[ %i ] = %f, y[ %i ] = %f\n", i, x[ i ], i, y[ i ] );
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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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[srotm]: https://www.netlib.org/lapack/explore-html/d1/d45/group__rot_gae48ef017306866ac2d5a8c5a52617858.html#gae48ef017306866ac2d5a8c5a5261785
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[mdn-float32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

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