npm package: @stdlib/blas-base-gaxpy
Description: Multiply a vector `x` by a constant and add the result to `y`.
Author: The Stdlib Authors
Latest version: 0.3.1

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# gaxpy

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

> Multiply `x` by a constant `alpha` and add the result to `y`.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### gaxpy( N, alpha, x, strideX, y, strideY )

Multiplies `x` by a constant `alpha` and adds the result to `y`.

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

gaxpy( x.length, alpha, x, 1, y, 1 );
// y => [ 6.0, 11.0, 16.0, 21.0, 26.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: `numeric` constant.
-   **x**: first input array.
-   **strideX**: index increment for `x`.
-   **y**: second input array.
-   **strideY**: index increment for `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other value in `x` by `alpha` and add the result to the first `N` elements of `y` in reverse order,

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

gaxpy( 3, 5.0, x, 2, y, -1 );
// y => [ 26.0, 16.0, 6.0, 1.0, 1.0, 1.0 ]
```

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, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// 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*3 ); // start at 4th element

gaxpy( 3, 5.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

#### gaxpy.ndarray( N, alpha, x, strideX, offsetX, y, strideY, offsetY )

Multiplies `x` by a constant `alpha` and adds the result to `y` using alternative indexing semantics.

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

gaxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => [ 6.0, 11.0, 16.0, 21.0, 26.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetY**: 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, to multiply every other value in `x` by a constant `alpha` starting from the second value and add to the last `N` elements in `y` where `x[i] -> y[n]`, `x[i+2] -> y[n-1]`,...,

```javascript
var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];

gaxpy.ndarray( 3, 5.0, x, 2, 1, y, -1, y.length-1 );
// y => [ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0` or `alpha == 0`, both functions return `y` unchanged.
-   `gaxpy()` corresponds to the [BLAS][blas] level 1 function [`daxpy`][daxpy] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`daxpy`][@stdlib/blas/base/daxpy], [`saxpy`][@stdlib/blas/base/saxpy], 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 gaxpy = require( '@stdlib/blas-base-gaxpy' );

var opts = {
    'dtype': 'generic'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );

gaxpy.ndarray( x.length, 5.0, x, 1, 0, y, -1, y.length-1 );
console.log( y );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/blas-base/daxpy`][@stdlib/blas/base/daxpy]</span><span class="delimiter">: </span><span class="description">multiply a vector `x` by a constant and add the result to `y`.</span>
-   <span class="package-name">[`@stdlib/blas-base/saxpy`][@stdlib/blas/base/saxpy]</span><span class="delimiter">: </span><span class="description">multiply a vector `x` by a constant and add the result to `y`.</span>

</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].

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

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

[daxpy]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html

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

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

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

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