npm package: @stdlib/blas-base-dspmv
Description: Perform the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix supplied in packed form.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dspmv

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Perform the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors and, `A` is an `N` by `N` symmetric matrix supplied in packed form.

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-base-dspmv
```

</section>

<section class="usage">

## Usage

```javascript
var dspmv = require( '@stdlib/blas-base-dspmv' );
```

#### dspmv( order, uplo, N, α, AP, x, sx, β, y, sy )

Performs the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix supplied in packed form `AP`.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, 1 );
// y => <Float64Array>[ 7.0, 12.0, 15.0 ]
```

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`.
-   **α**: scalar constant.
-   **AP**: packed form of a symmetric matrix `A` stored in linear memory as a [`Float64Array`][mdn-float64array].
-   **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 AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, -1 );
// y => <Float64Array>[ 15.0, 12.0, 7.0 ]
```

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, 1.0 ] );
var y0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
var AP = new Float64Array( [ 1.0, 2.0, 3.0 ] );

// 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

dspmv( 'row-major', 'upper', 2, 1.0, AP, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 0.0, 6.0, 4.0 ]
```

#### dspmv.ndarray( order, uplo, N, α, AP, oa, x, sx, ox, β, y, sy, oy )

Performs the matrix-vector operation `y = α*A*x + β*y` using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix supplied in packed form `AP`.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );
// y => <Float64Array>[ 7.0, 12.0, 15.0 ]
```

The function has the following additional parameters:

-   **oa**: starting index for `AP`.
-   **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 AP = new Float64Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 2, x, 1, 0, 1.0, y, -1, 2 );
// y => <Float64Array>[ 15.0, 12.0, 7.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   `dspmv()` corresponds to the [BLAS][blas] level 2 function [`dspmv`][dspmv].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dspmv = require( '@stdlib/blas-base-dspmv' );

var opts = {
    'dtype': 'float64'
};

var N = 3;
var AP = discreteUniform( N * ( N + 1 ) / 2, -10, 10, opts );

var x = discreteUniform( N, -10, 10, opts );
var y = discreteUniform( N, -10, 10, opts );

dspmv.ndarray( 'row-major', 'upper', N, 1.0, AP, 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 -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/blas-base-dspmv/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-base-dspmv/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-base-dspmv/tree/umd
[umd-readme]: https://github.com/stdlib-js/blas-base-dspmv/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/blas-base-dspmv/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-base-dspmv/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/blas-base-dspmv/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-dspmv/main/LICENSE

[blas]: http://www.netlib.org/blas

[dspmv]: https://www.netlib.org/lapack/explore-html/d0/d4b/group__hpmv_ga739f8dc2316523832bde2b237fcad8a6.html#ga739f8dc2316523832bde2b237fcad8a6

[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>

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