https://github.com/stdlib-js/blas-base-saxpy
Multiply a vector x by a constant and add the result to y.
https://github.com/stdlib-js/blas-base-saxpy
add algebra alpha array axpy blas daxpy javascript level-1 linear math mathematics ndarray node node-js nodejs saxpy stdlib subroutines vector
Last synced: about 1 year ago
JSON representation
Multiply a vector x by a constant and add the result to y.
- Host: GitHub
- URL: https://github.com/stdlib-js/blas-base-saxpy
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T18:06:21.000Z (almost 5 years ago)
- Default Branch: main
- Last Pushed: 2025-01-11T03:41:26.000Z (over 1 year ago)
- Last Synced: 2025-01-11T04:28:38.046Z (over 1 year ago)
- Topics: add, algebra, alpha, array, axpy, blas, daxpy, javascript, level-1, linear, math, mathematics, ndarray, node, node-js, nodejs, saxpy, stdlib, subroutines, vector
- Language: C
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 724 KB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# saxpy
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Multiply a vector `x` by a constant `alpha` and add the result to `y`.
## Installation
```bash
npm install @stdlib/blas-base-saxpy
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## 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 => [ 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 => [ 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.
```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 => [ 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 => [ 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 => [ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```
## Notes
- If `N <= 0` or `alpha == 0`, both functions return `y` unchanged.
- `saxpy()` corresponds to the [BLAS][blas] level 1 function [`saxpy`][saxpy].
## Examples
```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 );
```
* * *
## C APIs
### 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 );
```
### Examples
```c
#include "stdlib/blas/base/saxpy.h"
#include
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 ] );
}
}
```
* * *
## See Also
- [`@stdlib/blas-base/daxpy`][@stdlib/blas/base/daxpy]: multiply a vector `x` by a constant and add the result to `y`.
- [`@stdlib/blas-base/gaxpy`][@stdlib/blas/base/gaxpy]: multiply a vector `x` by a constant and add the result to `y`.
* * *
## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/blas-base-saxpy
[test-image]: https://github.com/stdlib-js/blas-base-saxpy/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/blas-base-saxpy/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-base-saxpy/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/blas-base-saxpy?branch=main
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[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[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-saxpy/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-base-saxpy/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-base-saxpy/tree/umd
[umd-readme]: https://github.com/stdlib-js/blas-base-saxpy/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/blas-base-saxpy/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-base-saxpy/blob/esm/README.md
[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
[@stdlib/blas/base/daxpy]: https://github.com/stdlib-js/blas-base-daxpy
[@stdlib/blas/base/gaxpy]: https://github.com/stdlib-js/blas-base-gaxpy