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feat: add blas/base/ssbmv
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‎lib/node_modules/@stdlib/blas/base/ssbmv/README.md‎

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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");
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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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# ssbmv
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> 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.
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<section class="usage">
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## Usage
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```javascript
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var ssbmv = require( '@stdlib/blas/base/ssbmv' );
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```
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#### ssbmv( 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
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 1.0, 2.0, 0.0, 4.0, 3.0, 5.0 ] );
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var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
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ssbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, 1 );
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// y => <Float32Array>[ 2.0, 17.0, 21.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied.
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- **N**: specifies the order of the matrix `A`.
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- **K**: specifies the number of super-diagonals of the matrix `A`
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- **α**: scalar constant.
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- **A**: packed banded form of a symmetric matrix `A` stored in linear memory as a [`Float32Array`][mdn-float32array].
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
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- **x**: input [`Float32Array`][mdn-float32array].
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- **sx**: index increment for `x`.
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- **β**: scalar constant.
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- **y**: output [`Float32Array`][mdn-float32array].
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- **sy**: index increment 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
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 1.0, 2.0, 0.0, 4.0, 3.0, 5.0 ] );
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var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
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ssbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, -1 );
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// y => <Float32Array>[ 21.0, 17.0, 2.0 ]
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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( [ 0.0, 1.0, 2.0, 3.0 ] );
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var y0 = new Float32Array( [ 0.0, 0.0, 0.0, 0.0 ] );
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var A = new Float32Array( [ 1.0, 2.0, 0.0, 4.0, 3.0, 5.0 ] );
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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*1 ); // start at 2nd element
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ssbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x1, 1, 0.0, y1, 1 );
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// y0 => <Float32Array>[ 0.0, 2.0, 17.0, 21.0 ]
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```
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#### ssbmv.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
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 1.0, 2.0, 0.0, 4.0, 3.0, 5.0 ] );
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var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
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ssbmv.ndarray( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 0, 0.0, y, 1, 0 );
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// y => <Float32Array>[ 2.0, 17.0, 21.0 ]
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```
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The function has the following additional parameters:
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- **oa**: starting index for `A`.
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- **sa1**: first dimension index increment for `A`.
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- **sa2**: second dimension index increment for `A`.
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- **ox**: starting index for `x`.
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- **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
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 1.0, 2.0, 0.0, 4.0, 3.0, 5.0 ] );
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var x = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0, 0.0 ] );
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ssbmv.ndarray( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 1, 0.0, y, 1, 1 );
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// y => <Float32Array>[ 0.0, 2.0, 17.0, 21.0 ]
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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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- `ssbmv()` corresponds to the [BLAS][blas] level 2 function [`ssbmv`][ssbmv].
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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 ssbmv = require( '@stdlib/blas/base/ssbmv' );
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var opts = {
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'dtype': 'float32'
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};
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var N = 3;
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var A = [ 1, 2, 0, 3, 4, 5 ];
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var x = discreteUniform( N, -10, 10, opts );
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var y = discreteUniform( N, -10, 10, opts );
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ssbmv.ndarray( 'upper', N, 1, 1.0, A, 1, 2, 0, x, 1, 0, 1.0, y, 1, 0 );
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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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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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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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TODO
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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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[ssbmv]: https://www.netlib.org/lapack/explore-html/da/dd4/group__hbmv_ga88a3a066357e907495d20d2b75a6f2ea.html
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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 -->

‎lib/node_modules/@stdlib/blas/base/ssbmv/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) 2025 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 isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var pkg = require( './../package.json' ).name;
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var ssbmv = require( './../lib/ssbmv.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float32'
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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, -10.0, 10.0, options );
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var y = uniform( len, -10.0, 10.0, options );
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var A = [ 0,
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9,
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10,
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11,
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12,
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5,
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1,
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2,
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0 ];
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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 = ssbmv( 'row-major', 'upper', len, 1.0, 1, A, 2, x, 1, 1.0, y, 1 );
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if ( isnanf( z[ i%z.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 ( isnanf( z[ i%z.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 f;
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len = floor( pow( pow( 10, 1 ), 1.0/2.0 ) );
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f = createBenchmark( len );
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bench( pkg+':size='+(len*len), f );
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}
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main();

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