feat: add blas/base/dsbmv

lib/node_modules/@stdlib/blas/base/dsbmv/README.md

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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.
+
+-->
+
+# dsbmv
+
+> Perform 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.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dsbmv = require( '@stdlib/blas/base/dsbmv' );
+```
+
+#### dsbmv( order, uplo, N, K, α, A, x, LDA, sx, β, y, sy )
+
+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.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+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 ] );
+
+dsbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, 1 );
+// y => <Float64Array>[ 10.0, 25.0, 10.0 ]
+```
+
+The function has the following parameters:
+
+-   **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**: index increment for `x`.
+-   **β**: scalar constant.
+-   **y**: output [`Float64Array`][mdn-float64array].
+-   **sy**: index increment for `y`.
+
+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,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+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 ] );
+
+dsbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, -1 );
+// y => <Float64Array>[ 10.0, 25.0, 10.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// 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 ] );
+
+// 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
+
+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 ]
+```
+
+#### dsbmv.ndarray( uplo, N, K, α, A, sa1, sa2, oa, x, sx, ox, β, y, sy, oy )
+
+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.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+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 ] );
+
+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 ]
+```
+
+The function has the following additional parameters:
+
+-   **oa**: starting index for `A`.
+-   **sa1**: first dimension index increment for `A`.
+-   **sa2**: second dimension index increment for `A`.
+-   **ox**: starting index for `x`.
+-   **oy**: starting index for `y`.
+
+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,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+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 ] );
+
+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 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dsbmv()` corresponds to the [BLAS][blas] level 2 function [`dsbmv`][dsbmv].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var dsbmv = require( '@stdlib/blas/base/dsbmv' );
+
+var opts = {
+    'dtype': 'float64'
+};
+
+var N = 3;
+var A = [ 1, 2, 0, 3, 4, 5 ];
+
+var x = discreteUniform( N, -10, 10, opts );
+var y = discreteUniform( N, -10, 10, opts );
+
+dsbmv.ndarray( 'upper', N, 1, 1.0, A, 1, 2, 0, x, 1, 0, 1.0, y, 1, 0 );
+console.log( y );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</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
+
+[dsbmv]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d15/group__double__blas__level2_ga5c7ca036c788c5fd42e04ade0dc92d44.html
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

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.
+*/
+
+'use strict';
+
+// MODULES //
+
+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' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var x = uniform( len, -10.0, 10.0, options );
+	var y = uniform( len, -10.0, 10.0, options );
+	var A = [ 0,
+		9,
+		10,
+		11,
+		12,
+		5,
+		1,
+		2,
+		0 ];
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			z = dsbmv( 'row-major', 'upper', len, 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();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var f;
+
+	len = floor( pow( pow( 10, 1 ), 1.0/2.0 ) );
+	f = createBenchmark( len );
+	bench( pkg+':size='+(len*len), f );
+}
+
+main();