npm package: @stdlib/blas-base-ggemv
Description: Perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`.
Author: The Stdlib Authors
Latest version: 0.1.1

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# ggemv

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> Perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### ggemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )

Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` matrix.

```javascript
var A = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var x = [ 1.0, 1.0, 1.0 ];
var y = [ 1.0, 1.0 ];

ggemv( 'row-major', 'no-transpose', 2, 3, 1.0, A, 3, x, 1, 1.0, y, 1 );
// y => [ 7.0, 16.0 ]
```

The function has the following parameters:

-   **order**: storage layout.
-   **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
-   **M**: number of rows in the matrix `A`.
-   **N**: number of columns in the matrix `A`.
-   **α**: scalar constant.
-   **A**: input matrix stored in linear memory.
-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
-   **x**: first input vector.
-   **sx**: stride length for `x`.
-   **β**: scalar constant.
-   **y**: second input vector.
-   **sy**: stride length for `y`.

The stride parameters determine how operations are performed. For example, to iterate over every other element in `x` and `y`,

```javascript
var A = [ 1.0, 2.0, 3.0, 4.0 ];
var x = [ 1.0, 0.0, 1.0, 0.0 ];
var y = [ 1.0, 0.0, 1.0, 0.0 ];

ggemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x, 2, 1.0, y, 2 );
// y => [ 4.0, 0.0, 8.0, 0.0 ]
```

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 A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );

// 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

ggemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 0.0, 8.0, 4.0 ]
```

#### ggemv.ndarray( trans, M, N, α, A, sa1, sa2, oa, x, sx, ox, β, y, sy, oy )

Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`, using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` matrix.

```javascript
var A = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var x = [ 1.0, 1.0, 1.0 ];
var y = [ 1.0, 1.0 ];

ggemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
// y => [ 7.0, 16.0 ]
```

The function has the following additional parameters:

-   **sa1**: stride of the first dimension of `A`.
-   **sa2**: stride of the second dimension of `A`.
-   **oa**: starting index 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 = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var x = [ 0.0, 1.0, 2.0, 3.0 ];
var y = [ 7.0, 8.0, 9.0, 10.0 ];

ggemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 1, 1.0, y, -2, 2 );
// y => [ 39.0, 8.0, 23.0, 10.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   `ggemv()` corresponds to the [BLAS][blas] level 2 function [`dgemv`][dgemv] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dgemv`][@stdlib/blas/base/dgemv], [`sgemv`][@stdlib/blas/base/sgemv], etc.) are likely to be significantly more performant.
-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array-base/accessor`][@stdlib/array/base/accessor]).

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

var M = 3;
var N = 3;

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

ggemv( 'row-major', 'no-transpose', M, N, 1.0, A, N, x, 1, 1.0, y, 1 );
console.log( y );

ggemv.ndarray( 'no-transpose', M, N, 1.0, A, N, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
console.log( y );
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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* * *

## 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].

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## License

See [LICENSE][stdlib-license].


## Copyright

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

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

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

[dgemv]: https://www.netlib.org/lapack/explore-html/d7/dda/group__gemv_ga4ac1b675072d18f902db8a310784d802.html

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

[@stdlib/blas/base/dgemv]: https://www.npmjs.com/package/@stdlib/blas-base-dgemv

[@stdlib/blas/base/sgemv]: https://www.npmjs.com/package/@stdlib/blas-base-sgemv

[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor

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