npm package: @stdlib/blas-base-saxpy
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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# saxpy

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

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

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

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

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

```javascript
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

saxpy( x.length, alpha, x, 1, y, 1 );
// y => <Float32Array>[ 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**: input [`Float32Array`][mdn-float32array].
-   **strideX**: index increment for `x`.
-   **y**: output [`Float32Array`][mdn-float32array].
-   **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 Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var alpha = 5.0;

saxpy( 3, alpha, x, 2, y, -1 );
// y => <Float32Array>[ 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 Float32Array = require( '@stdlib/array-float32' );

// Initial arrays...
var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

saxpy( 3, 5.0, x1, -2, y1, 1 );
// y0 => <Float32Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

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

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

```javascript
var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

saxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => <Float32Array>[ 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 Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

var alpha = 5.0;

saxpy.ndarray( 3, alpha, x, 2, 1, y, -1, y.length-1 );
// y => <Float32Array>[ 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.
-   `saxpy()` corresponds to the [BLAS][blas] level 1 function [`saxpy`][saxpy].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float32'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

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

saxpy.ndarray( x.length, 5.0, x, 1, 0, y, -1, y.length-1 );
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
#include "stdlib/blas/base/saxpy.h"
```

#### c_saxpy( N, alpha, \*X, strideX, \*Y, strideY )

Multiplies a vector `X` by a constant and adds the result to `Y`.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f };

c_saxpy( 4, 5.0f, x, 1, y, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] float` scalar constant.
-   **X**: `[in] float*` input array.
-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
-   **Y**: `[inout] float*` output array.
-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.

```c
void c_saxpy( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, float *Y, const CBLAS_INT strideY );
```

#### c_saxpy_ndarray( N, alpha, \*X, strideX, offsetX, \*Y, strideY, offsetY )

Multiplies a vector `X` by a constant and adds the result to `Y` using alternative indexing semantics.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f };

c_saxpy_ndarray( 4, 5.0f, x, 1, 0, y, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] float` scalar constant.
-   **X**: `[in] float*` input array.
-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[inout] float*` output array.
-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.
-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.

```c
void c_saxpy_ndarray( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
```

</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
#include "stdlib/blas/base/saxpy.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
    float y[] = { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f };

    // Specify the number of elements:
    const int N = 4;

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute `a*x + y`:
    c_saxpy( N, 5.0f, x, strideX, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %i ] = %f\n", i, y[ i ] );
    }

    // Compute `a*x + y`:
    c_saxpy_ndarray( N, 5.0f, x, strideX, 1, y, strideY, 7 );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %i ] = %f\n", i, y[ i ] );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->


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

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

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

[saxpy]: http://www.netlib.org/lapack/explore-html/df/d28/group__single__blas__level1.html

[mdn-float32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array

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

<!-- <related-links> -->

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

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

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</section>

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