npm package: @stdlib/blas-base-dsymv
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.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dsymv

[![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.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### dsymv( order, uplo, N, α, A, LDA, 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.

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

var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0 ] );

dsymv( 'row-major', 'lower', 3, 1.0, A, 3, x, 1, 0.0, y, 1 );
// y => <Float64Array>[ 1.0, 2.0, 3.0 ]
```

The function has the following parameters:

-   **order**: storage layout.
-   **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced.
-   **N**: number of elements along each dimension of `A`.
-   **α**: scalar constant.
-   **A**: input matrix 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 `x` in reverse order,

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

var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsymv( 'row-major', 'upper', 3, 2.0, A, 3, x, -1, 1.0, y, 1 );
// y => <Float64Array>[ 7.0, 10.0, 9.0 ]
```

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

dsymv( 'row-major', 'upper', 3, 1.0, A, 3, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ]
```

#### dsymv.ndarray( order, uplo, N, α, A, LDA, 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.

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

var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsymv.ndarray( 'row-major', 'upper', 3, 2.0, A, 3, x, -1, 2, 1.0, y, 1, 0 );
// y => <Float64Array>[ 7.0, 10.0, 9.0 ]
```

The function has the following additional parameters:

-   **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, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dsymv.ndarray( 'row-major', 'lower', 3, 1.0, A, 3, x, -1, 2, 1.0, y, -1, 2 );
// y => <Float64Array>[ 4.0, 3.0, 2.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

var N = 3;
var A = ones( N*N, opts.dtype );

var x = discreteUniform( N, 0, 255, opts );
var y = discreteUniform( N, 0, 255, opts );

dsymv.ndarray( 'row-major', 'upper', N, 1.0, A, N, x, 1, 0, 1.0, y, 1, 0 );
console.log( y );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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

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

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

[dsymv]: https://www.netlib.org/lapack/explore-html/db/d17/group__hemv_ga0b20bcf6e94079dce2f3d035798e9738.html#ga0b20bcf6e94079dce2f3d035798e9738

[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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