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feat: add blas/base/dsbmv
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d811c8c
feat: add blas/base/dsbmv
ShabiShett07 6e2483c
chore: add complete implementation
ShabiShett07 0a25c0d
chore: update copyright years
stdlib-bot 409d821
chore: add test cases
ShabiShett07 16a9063
chore: add test cases
ShabiShett07 30e624d
chore: update test cases
ShabiShett07 a4a8183
chore: update examples
ShabiShett07 e25f528
chore: update examples
ShabiShett07 5f6910a
chore: update fixtures
ShabiShett07 4fd0fcd
chore: update jsdoc
ShabiShett07 7475eff
chore: update examples
ShabiShett07 55a7239
chore: fix test fixtures
ShabiShett07 56ff685
chore: fix test fixtures
ShabiShett07 87bd6e9
test: update test cases
ShabiShett07 3f6abe6
remove: indentation
ShabiShett07 541a527
bench: update variable declarations
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chore: update example
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chore: update jsdoc
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chore: use alpha and beta symbols
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<!-- | ||
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@license Apache-2.0 | ||
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Copyright (c) 2025 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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# dsbmv | ||
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> Perform the matrix-vector operation `y = alpha*A*x + beta*y`. | ||
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<section class="usage"> | ||
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## Usage | ||
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```javascript | ||
var dsbmv = require( '@stdlib/blas/base/dsbmv' ); | ||
``` | ||
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#### dsbmv( order, uplo, N, K, α, A, x, LDA, sx, β, y, sy ) | ||
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Performs the matrix-vector operation `y = alpha*A*x + beta*y` where `alpha` and `beta` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric band matrix, with `K` super-diagonals. | ||
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```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var A = new Float64Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] ); | ||
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); | ||
var y = new Float64Array( [ 0.0, 0.0, 0.0 ] ); | ||
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dsbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, 1 ); | ||
// y => <Float64Array>[ 10.0, 25.0, 10.0 ] | ||
``` | ||
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The function has the following parameters: | ||
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- **order**: storage layout. | ||
- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied. | ||
- **N**: specifies the order of the matrix `A`. | ||
- **K**: specifies the number of super-diagonals of the matrix `A` | ||
- **α**: scalar constant. | ||
- **A**: packed banded form of a symmetric matrix `A` stored in linear memory as a [`Float64Array`][mdn-float64array]. | ||
- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`) | ||
- **x**: input [`Float64Array`][mdn-float64array]. | ||
- **sx**: stride length for `x`. | ||
- **β**: scalar constant. | ||
- **y**: output [`Float64Array`][mdn-float64array]. | ||
- **sy**: stride length for `y`. | ||
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The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of `y` in reverse order, | ||
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```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var A = new Float64Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] ); | ||
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); | ||
var y = new Float64Array( [ 0.0, 0.0, 0.0 ] ); | ||
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dsbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, -1 ); | ||
// y => <Float64Array>[ 10.0, 25.0, 10.0 ] | ||
``` | ||
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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( [ 0.0, 1.0, 2.0, 3.0 ] ); | ||
var y0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] ); | ||
var A = new Float64Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] ); | ||
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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*1 ); // start at 2nd element | ||
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dsbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x1, 1, 0.0, y1, 1 ); | ||
// y0 => <Float64Array>[ 0.0, 10.0, 25.0, 10.0 ] | ||
``` | ||
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#### dsbmv.ndarray( uplo, N, K, α, A, sa1, sa2, oa, x, sx, ox, β, y, sy, oy ) | ||
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Performs the matrix-vector operation `y = alpha*A*x + beta*y` using alternative indexing semantics where `alpha` and `beta` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric band matrix, with `K` super-diagonals. | ||
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```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var A = new Float64Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] ); | ||
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); | ||
var y = new Float64Array( [ 0.0, 0.0, 0.0 ] ); | ||
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dsbmv.ndarray( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 0, 0.0, y, 1, 0 ); | ||
// y => <Float64Array>[ 10.0, 25.0, 10.0 ] | ||
``` | ||
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The function has the following additional parameters: | ||
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- **oa**: starting index for `A`. | ||
- **sa1**: first dimension stride length for `A`. | ||
- **sa2**: second dimension stride length for `A`. | ||
- **ox**: starting index for `x`. | ||
- **oy**: 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, | ||
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```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var A = new Float64Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] ); | ||
var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); | ||
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] ); | ||
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dsbmv.ndarray( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 1, 0.0, y, 1, 1 ); | ||
// y => <Float64Array>[ 0.0, 10.0, 25.0, 10.0 ] | ||
``` | ||
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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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- `dsbmv()` corresponds to the [BLAS][blas] level 2 function [`dsbmv`][dsbmv]. | ||
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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 dsbmv = require( '@stdlib/blas/base/dsbmv' ); | ||
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var opts = { | ||
'dtype': 'float64' | ||
}; | ||
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var N = 3; | ||
var A = [ 1.0, 2.0, 3.0, 4.0, 5.0, 0.0 ]; | ||
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var x = discreteUniform( N, -10, 10, opts ); | ||
var y = discreteUniform( N, -10, 10, opts ); | ||
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dsbmv( 'row-major', 'upper', N, 1, 1.0, A, 2, x, 1, 1.0, y, 1 ); | ||
console.log( y ); | ||
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dsbmv.ndarray( 'upper', N, 1, 1.0, A, 2, 1, 0, x, 1, 0, 1.0, y, 1, 0 ); | ||
console.log( y ); | ||
``` | ||
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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 | ||
TODO | ||
``` | ||
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#### TODO | ||
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TODO. | ||
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```c | ||
TODO | ||
``` | ||
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TODO | ||
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```c | ||
TODO | ||
``` | ||
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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 | ||
TODO | ||
``` | ||
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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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[dsbmv]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d15/group__double__blas__level2_ga5c7ca036c788c5fd42e04ade0dc92d44.html | ||
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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 --> |
97 changes: 97 additions & 0 deletions
97
lib/node_modules/@stdlib/blas/base/dsbmv/benchmark/benchmark.js
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/** | ||
* @license Apache-2.0 | ||
* | ||
* Copyright (c) 2025 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 floor = require( '@stdlib/math/base/special/floor' ); | ||
var pkg = require( './../package.json' ).name; | ||
var dsbmv = require( './../lib/dsbmv.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} N - array dimension size | ||
* @returns {Function} benchmark function | ||
*/ | ||
function createBenchmark( N ) { | ||
var x = uniform( N, -10.0, 10.0, options ); | ||
var y = uniform( N, -10.0, 10.0, options ); | ||
var A = uniform( N*N, -10.0, 10.0, 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 = dsbmv( 'row-major', 'upper', N, 1.0, 1, A, 2, x, 1, 1.0, y, 1 ); | ||
if ( isnan( z[ i%z.length ] ) ) { | ||
b.fail( 'should not return NaN' ); | ||
} | ||
} | ||
b.toc(); | ||
if ( isnan( z[ i%z.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 N; | ||
var f; | ||
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N = floor( pow( pow( 10, 1 ), 1.0/2.0 ) ); | ||
f = createBenchmark( N ); | ||
bench( pkg+':size='+(N*N), f ); | ||
} | ||
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main(); |
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I suggest adding a comment here illustrating the "original" matrix. E.g.,