https://github.com/stdlib-js/blas-base-sger

Perform the rank 1 operation `A = α*x*y^T + A`.
https://github.com/stdlib-js/blas-base-sger
algebra array blas float float32 float32array javascript level-2 linear math mathematics ndarray node node-js nodejs sger stdlib subroutines
Last synced: 4 months ago
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Perform the rank 1 operation `A = α*x*y^T + A`.
Host: GitHub
URL: https://github.com/stdlib-js/blas-base-sger
Owner: stdlib-js
License: apache-2.0
Created: 2025-07-02T10:10:56.000Z (4 months ago)
Default Branch: main
Last Pushed: 2025-07-07T15:23:17.000Z (4 months ago)
Last Synced: 2025-07-07T16:44:54.565Z (4 months ago)
Topics: algebra, array, blas, float, float32, float32array, javascript, level-2, linear, math, mathematics, ndarray, node, node-js, nodejs, sger, stdlib, subroutines
Language: JavaScript
Homepage: https://github.com/stdlib-js/stdlib
Size: 407 KB
Stars: 0
Watchers: 0
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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# sger

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

> Perform the rank 1 operation `A = α*x*y^T + A`.

## Installation

```bash

npm install @stdlib/blas-base-sger

```

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 sger = require( '@stdlib/blas-base-sger' );

```

#### sger( order, M, N, α, x, sx, y, sy, A, lda )

Performs the rank 1 operation `A = α*x*y^T + A`, where `α` is a scalar, `x` is an `M` element vector, `y` is an `N` element vector, and `A` is an `M` by `N` matrix.

```javascript

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

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

var x = new Float32Array( [ 1.0, 1.0 ] );

var y = new Float32Array( [ 1.0, 1.0, 1.0 ] );

sger( 'row-major', 2, 3, 1.0, x, 1, y, 1, A, 3 );

// A => [ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]

```

The function has the following parameters:

-   **order**: storage layout.

-   **M**: number of rows in the matrix `A`.

-   **N**: number of columns in the matrix `A`.

-   **α**: scalar constant.

-   **x**: an `M` element [`Float32Array`][mdn-float32array].

-   **sx**: stride length for `x`.

-   **y**: an `N` element [`Float32Array`][mdn-float32array].

-   **sy**: stride length for `y`.

-   **A**: input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].

-   **lda**: stride of the first dimension of `A` (leading dimension of `A`).

The stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to iterate over every other element in `x` and `y`,

```javascript

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

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

var x = new Float32Array( [ 1.0, 0.0, 1.0, 0.0 ] );

var y = new Float32Array( [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ] );

sger( 'column-major', 2, 3, 1.0, x, 2, y, 2, A, 2 );

// A => [ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

```

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( [ 0.0, 1.0, 1.0 ] );

var y0 = new Float32Array( [ 0.0, 1.0, 1.0, 1.0 ] );

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

// 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*1 ); // start at 2nd element

sger( 'column-major', 2, 3, 1.0, x1, -1, y1, -1, A, 2 );

// A => [ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

```

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

Performs the rank 1 operation `A = α*x*y^T + A`, using alternative indexing semantics and where `α` is a scalar, `x` is an `M` element vector, `y` is an `N` element vector, and `A` is an `M` by `N` matrix.

```javascript

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

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

var x = new Float32Array( [ 1.0, 1.0 ] );

var y = new Float32Array( [ 1.0, 1.0, 1.0 ] );

sger.ndarray( 2, 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );

// A => [ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]

```

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

var A = new Float32Array( [ 0.0, 0.0, 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );

var x = new Float32Array( [ 0.0, 1.0, 0.0, 1.0, 0.0 ] );

var y = new Float32Array( [ 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ] );

sger.ndarray( 2, 3, 1.0, x, 2, 1, y, 2, 1, A, 1, 2, 2 );

// A => [ 0.0, 0.0, 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

```

## Notes

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

## Examples

```javascript

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );

var sger = require( '@stdlib/blas-base-sger' );

var opts = {

    'dtype': 'float32'

};

var M = 3;

var N = 5;

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

var x = discreteUniform( M, 0, 255, opts );

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

sger( 'row-major', M, N, 1.0, x, 1, y, 1, A, N );

console.log( A );

sger.ndarray( M, N, 1.0, x, 1, 0, y, 1, 0, A, 1, M, 0 );

console.log( A );

```

* * *

## C APIs

### Usage

```c

#include "stdlib/blas/base/sger.h"

```

#### c_sger( layout, M, N, alpha, \*X, strideX, \*Y, strideY, \*A, LDA )

Performs the rank 1 operation `A = alpha*x*y^T + A`, where `alpha` is a scalar, `X` is an `M` element vector, `Y` is an `N` element vector, and `A` is an `M`-by-`N` matrix.

```c

#include "stdlib/blas/base/shared.h"

float A[ 3*4 ] = {

   0.0f, 0.0f, 0.0f, 0.0f,

   0.0f, 0.0f, 0.0f, 0.0f,

   0.0f, 0.0f, 0.0f, 0.0f

};

const float x[ 3 ] = { 1.0f, 4.0f, 0.0f };

const float y[ 4 ] = { 0.0f, 1.0f, 2.0f, 3.0f };

c_sger( CblasRowMajor, 3, 4, 1.0f, x, 1, y, 1, A, 4 );

```

The function accepts the following arguments:

-   **layout**: `[in] CBLAS_LAYOUT` storage layout.

-   **M**: `[in] CBLAS_INT` number of rows in the matrix `A`.

-   **N**: `[in] CBLAS_INT` number of columns in the matrix `A`.

-   **alpha**: `[in] float` scalar constant.

-   **X**: `[in] float*` an `M` element vector.

-   **strideX**: `[in] CBLAS_INT` stride length for `X`.

-   **Y**: `[in] float*` an `N` element vector.

-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.

-   **A**: `[inout] float*` input matrix.

-   **LDA**: `[in] CBLAS_INT` stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).

```c

void c_sger( const CBLAS_LAYOUT layout, const CBLAS_INT M, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const float *Y, const CBLAS_INT strideY, float *A, const CBLAS_INT LDA );

```

#### c_sger_ndarray( M, N, alpha, \*X, sx, ox, \*Y, sy, oy, \*A, sa1, sa2, oa )

Performs the rank 1 operation `A = alpha*x*y^T + A`, using alternative indexing semantics and where `alpha` is a scalar, `X` is an `M` element vector, `Y` is an `N` element vector, and `A` is an `M`-by-`N` matrix.

```c

#include "stdlib/blas/base/shared.h"

float A[ 3*4 ] = {

   0.0f, 0.0f, 0.0f, 0.0f,

   0.0f, 0.0f, 0.0f, 0.0f,

   0.0f, 0.0f, 0.0f, 0.0f

};

const float x[ 3 ] = { 1.0f, 4.0f, 0.0f };

const float y[ 4 ] = { 0.0f, 1.0f, 2.0f, 3.0f };

c_sger_ndarray( 3, 4, 1.0f, x, 1, 0, y, 1, 0, A, 4, 1, 0 );

```

The function accepts the following arguments:

-   **layout**: `[in] CBLAS_LAYOUT` storage layout.

-   **M**: `[in] CBLAS_INT` number of rows in the matrix `A`.

-   **N**: `[in] CBLAS_INT` number of columns in the matrix `A`.

-   **alpha**: `[in] float` scalar constant.

-   **X**: `[in] float*` an `M` element vector.

-   **sx**: `[in] CBLAS_INT` stride length for `X`.

-   **ox**: `[in] CBLAS_INT` starting index for `X`.

-   **Y**: `[in] float*` an `N` element vector.

-   **sy**: `[in] CBLAS_INT` stride length for `Y`.

-   **oy**: `[in] CBLAS_INT` starting index for `Y`.

-   **A**: `[inout] float*` input matrix.

-   **sa1**: `[in] CBLAS_INT` stride of the first dimension of `A`.

-   **sa2**: `[in] CBLAS_INT` stride of the second dimension of `A`.

-   **oa**: `[in] CBLAS_INT` starting index for `A`.

```c

void c_sger_ndarray( const CBLAS_INT M, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, float *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA );

```

### Examples

```c

#include "stdlib/blas/base/sger.h"

#include "stdlib/blas/base/shared.h"

#include 

int main( void ) {

   // Define a 3x4 matrix stored in row-major order:

   float A[ 3*4 ] = {

      0.0f, 0.0f, 0.0f, 0.0f,

      0.0f, 0.0f, 0.0f, 0.0f,

      0.0f, 0.0f, 0.0f, 0.0f

   };

   // Define `x` and `y^T` vectors:

   const float x[ 3 ] = { 1.0f, 4.0f, 0.0f };       // M

   const float y[ 4 ] = { 0.0f, 1.0f, 2.0f, 3.0f }; // N

   // Specify the number of rows and columns:

   const int M = 3;

   const int N = 4;

   // Specify stride lengths:

   const int strideX = 1;

   const int strideY = 1;

   // Perform operation:

   c_sger( CblasRowMajor, M, N, 1.0f, x, strideX, y, strideY, A, N );

   // Print the result:

   for ( int i = 0; i < M; i++ ) {

      for ( int j = 0; j < N; j++ ) {

         printf( "A[%i,%i] = %f\n", i, j, A[ (i*N)+j ] );

      }

   }

   // Perform operation using alternative indexing semantics:

   c_sger( CblasRowMajor, M, N, 1.0f, x, strideX, 0, y, 0, strideY, A, N, 1, 0 );

   // Print the result:

   for ( int i = 0; i < M; i++ ) {

      for ( int j = 0; j < N; j++ ) {

         printf( "A[%i,%i] = %f\n", i, j, A[ (i*N)+j ] );

      }

   }

}

```

* * *

## 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].

[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-base-sger.svg

[npm-url]: https://npmjs.org/package/@stdlib/blas-base-sger

[test-image]: https://github.com/stdlib-js/blas-base-sger/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/blas-base-sger/actions/workflows/test.yml?query=branch:main

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-base-sger/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/blas-base-sger?branch=main

[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im

[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-sger/tree/deno

[deno-readme]: https://github.com/stdlib-js/blas-base-sger/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/blas-base-sger/tree/umd

[umd-readme]: https://github.com/stdlib-js/blas-base-sger/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/blas-base-sger/tree/esm

[esm-readme]: https://github.com/stdlib-js/blas-base-sger/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/blas-base-sger/blob/main/branches.md

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

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

[blas-sger]: https://www.netlib.org/lapack/explore-html/d8/d75/group__ger_ga95baec6bb0a84393d7bc67212b566ab0.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
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