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feat: add blas/base/drot
#1823
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feat: add blas/base/drot
#1823
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feat: add BLAS Level 1 drot routine
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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"); | ||
you may not use this file except in compliance with the License. | ||
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 | ||
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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--> | ||
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# drot | ||
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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:drot" 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 | ||
var drot = require( '@stdlib/blas/base/drot' ); | ||
``` | ||
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#### drot( N, x, strideX, y, strideY, c, s ) | ||
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Applies a plane rotation. | ||
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```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] ); | ||
var y = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] ); | ||
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drot( x.length, x, 1, y, 1, 0.8, 0.6 ); | ||
// x => <Float64Array>[ ~4.4, ~5.8, 7.2, 8.6, 10.0 ] | ||
// y => <Float64Array>[ ~4.2, 4.4, 4.6, 4.8, 5.0 ] | ||
``` | ||
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The function has the following parameters: | ||
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- **N**: number of indexed elements. | ||
- **x**: first input [`Float64Array`][mdn-float64array]. | ||
- **strideX**: index increment for `x`. | ||
- **y**: second input [`Float64Array`][mdn-float64array]. | ||
- **strideY**: index increment for `y`. | ||
- **c**: cosine of the angle of rotation. | ||
- **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 | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] ); | ||
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drot( 3, x, 2, y, 2, 0.8, 0.6 ); | ||
// x => <Float64Array>[ 5.0, 2.0, 7.8, 4.0, 10.6, 6.0 ] | ||
// y => <Float64Array>[ ~5.0, 8.0, 5.4, 10.0, ~5.8, 12.0 ] | ||
``` | ||
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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 Float64Array = require( '@stdlib/array/float64' ); | ||
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// Initial arrays... | ||
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] ); | ||
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// Create offset views... | ||
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element | ||
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element | ||
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drot( 3, x1, -2, y1, 1, 0.8, 0.6 ); | ||
// x0 => <Float64Array>[ 1.0, ~8.8, 3.0, 9.8, 5.0, 10.8 ] | ||
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 4.4, 6.4, ~8.4 ] | ||
``` | ||
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#### drot.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 | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] ); | ||
var y = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] ); | ||
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drot.ndarray( 4, x, 1, 1, y, 1, 1, 0.8, 0.6 ); | ||
// x => <Float64Array>[ 1.0, ~5.8, 7.2, 8.6, 10.0 ] | ||
// y => <Float64Array>[ 6.0, 4.4, ~4.6, ~4.8, 5.0 ] | ||
``` | ||
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The function has the following additional parameters: | ||
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- **offsetX**: starting index for `x`. | ||
- **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 | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] ); | ||
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drot.ndarray( 3, x, 2, 1, y, 2, 1, 0.8, 0.6 ); | ||
// x => <Float64Array>[ 1.0, 6.4, 3.0, 9.2, 5.0, 12.0 ] | ||
// y => <Float64Array>[ 7.0, 5.2, 9.0, 5.6, 11.0, ~6.0 ] | ||
``` | ||
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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. | ||
- `drot()` corresponds to the [BLAS][blas] level 1 function [`drot`][drot]. | ||
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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/array/discrete-uniform' ); | ||
var drot = require( '@stdlib/blas/base/drot' ); | ||
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var opts = { | ||
'dtype': 'float64' | ||
}; | ||
var x = discreteUniform( 10, 0, 500, opts ); | ||
console.log( x ); | ||
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var y = discreteUniform( x.length, 0, 255, opts ); | ||
console.log( y ); | ||
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// Apply a plane rotation: | ||
drot( x.length, x, 1, y, 1, 0.8, 0.6 ); | ||
console.log( x ); | ||
console.log( y ); | ||
``` | ||
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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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[drot]: https://www.netlib.org/lapack/explore-html/d1/d45/group__rot_gae48ef017306866ac2d5a8c5a52617858.html#gae48ef017306866ac2d5a8c5a5261785 | ||
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array | ||
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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 --> |
103 changes: 103 additions & 0 deletions
103
lib/node_modules/@stdlib/blas/base/drot/benchmark/benchmark.js
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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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'use strict'; | ||
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// MODULES // | ||
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var bench = require( '@stdlib/bench' ); | ||
var uniform = require( '@stdlib/random/array/uniform' ); | ||
var isnan = require( '@stdlib/math/base/assert/is-nan' ); | ||
var pow = require( '@stdlib/math/base/special/pow' ); | ||
var pkg = require( './../package.json' ).name; | ||
var drot = require( './../lib/drot.js' ); | ||
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// VARIABLES // | ||
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var options = { | ||
'dtype': 'float64' | ||
}; | ||
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// FUNCTIONS // | ||
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/** | ||
* Creates a benchmark function. | ||
* | ||
* @private | ||
* @param {PositiveInteger} len - array length | ||
* @returns {Function} benchmark function | ||
*/ | ||
function createBenchmark( len ) { | ||
var x = uniform( len, -100.0, 100.0, options ); | ||
var y = uniform( len, -100.0, 100.0, options ); | ||
return benchmark; | ||
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/** | ||
* Benchmark function. | ||
* | ||
* @private | ||
* @param {Benchmark} b - benchmark instance | ||
*/ | ||
function benchmark( b ) { | ||
var z; | ||
var i; | ||
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b.tic(); | ||
for ( i = 0; i < b.iterations; i++ ) { | ||
z = drot( x.length, x, 1, y, 1, 0.707, 0.707 ); | ||
if ( isnan( z[ i%x.length ] ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
} | ||
b.toc(); | ||
if ( isnan( z[ i%x.length ] ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
b.pass( 'benchmark finished' ); | ||
b.end(); | ||
} | ||
} | ||
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// MAIN // | ||
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/** | ||
* Main execution sequence. | ||
* | ||
* @private | ||
*/ | ||
function main() { | ||
var len; | ||
var min; | ||
var max; | ||
var f; | ||
var i; | ||
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min = 1; // 10^min | ||
max = 6; // 10^max | ||
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for ( i = min; i <= max; i++ ) { | ||
len = pow( 10, i ); | ||
f = createBenchmark( len ); | ||
bench( pkg+':len='+len, f ); | ||
} | ||
} | ||
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main(); |
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