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feat: add blas/base/grot
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‎lib/node_modules/@stdlib/blas/base/grot/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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# grot
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> Apply a plane rotation.
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<section class="intro">
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This BLAS level 1 routine applies a real plane rotation to real double-precision floating-point vectors. The plane rotation is applied to `N` points, where the points to be rotated are contained in vectors `x` and `y` and where the cosine and sine of the angle of rotation are `c` and `s`, respectively. The operation is as follows:
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<!-- <equation class="equation" label="eq:grot" align="center" raw="\begin{bmatrix}x_i \\ y_i\end{bmatrix} = \begin{bmatrix} c & s \\ -s & c\end{bmatrix}\begin{bmatrix} x_i \\ y_i \end{bmatrix}" alt="Plane rotation"> -->
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<!-- </equation> -->
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where `x_i` and `y_i` are the individual elements on which the rotation is applied.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var grot = require( '@stdlib/blas/base/grot' );
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```
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#### grot( N, x, strideX, y, strideY, c, s )
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Applies a plane rotation.
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
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var y = [ 6.0, 7.0, 8.0, 9.0, 10.0 ];
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grot( x.length, x, 1, y, 1, 0.8, 0.6 );
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// x => [ ~4.4, ~5.8, 7.2, 8.6, 10.0 ]
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// y => [ ~4.2, 4.4, 4.6, 4.8, 5.0 ]
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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 array.
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- **strideX**: index increment for `x`.
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- **y**: second input array.
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- **strideY**: index increment for `y`.
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- **c**: cosine of the angle of rotation.
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- **s**: sine of the angle of rotation.
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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 plane rotation to every other element,
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
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var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];
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grot( 3, x, 2, y, 2, 0.8, 0.6 );
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// x => [ 5.0, 2.0, 7.8, 4.0, 10.6, 6.0 ]
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// y => [ ~5.0, 8.0, 5.4, 10.0, ~5.8, 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 Float64Array = require( '@stdlib/array/float64' );
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// Initial arrays...
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var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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// Create offset views...
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element
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grot( 3, x1, -2, y1, 1, 0.8, 0.6 );
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// x0 => <Float64Array>[ 1.0, ~8.8, 3.0, 9.8, 5.0, 10.8 ]
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// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 4.4, 6.4, ~8.4 ]
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```
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#### grot.ndarray( N, x, strideX, offsetX, y, 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 x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
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var y = [ 6.0, 7.0, 8.0, 9.0, 10.0 ];
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grot.ndarray( 4, x, 1, 1, y, 1, 1, 0.8, 0.6 );
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// x => [ 1.0, ~5.8, 7.2, 8.6, 10.0 ]
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// y => [ 6.0, 4.4, ~4.6, ~4.8, 5.0 ]
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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 plane rotation to every other element starting from the second element,
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```javascript
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var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
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var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];
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grot.ndarray( 3, x, 2, 1, y, 2, 1, 0.8, 0.6 );
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// x => [ 1.0, 6.4, 3.0, 9.2, 5.0, 12.0 ]
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// y => [ 7.0, 5.2, 9.0, 5.6, 11.0, ~6.0 ]
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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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- `grot()` corresponds to the [BLAS][blas] level 1 function [`grot`][grot].
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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 grot = require( '@stdlib/blas/base/grot' );
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var opts = {
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'dtype': 'generic'
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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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// Apply a plane rotation:
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grot( x.length, x, 1, y, 1, 0.8, 0.6 );
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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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<!-- 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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[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 -->

‎lib/node_modules/@stdlib/blas/base/grot/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var pkg = require( './../package.json' ).name;
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var grot = require( './../lib' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var x = uniform( len, -100.0, 100.0, options );
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var y = uniform( len, -100.0, 100.0, options );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var z;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = grot( x.length, x, 1, y, 1, 0.707, 0.707 );
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if ( isnan( z[ i%x.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( z[ i%x.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

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