npm package: @stdlib/blas-base-ggemm
Description: Perform the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is either `op(X) = X` or `op(X) = X^T`.
Author: The Stdlib Authors
Latest version: 0.1.1

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# ggemm

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

> Perform the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is one of the `op(X) = X`, or `op(X) = X^T`.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### ggemm( ord, ta, tb, M, N, K, α, A, lda, B, ldb, β, C, ldc )

Performs the matrix-matrix operation `C = α*op(A)*op(B) + β*C` where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `α` and `β` are scalars, `A`, `B`, and `C` are matrices, with `op(A)` an `M` by `K` matrix, `op(B)` a `K` by `N` matrix, and `C` an `M` by `N` matrix.

```javascript
var A = [ 1.0, 2.0, 3.0, 4.0 ];
var B = [ 1.0, 1.0, 0.0, 1.0 ];
var C = [ 1.0, 2.0, 3.0, 4.0 ];

ggemm( 'row-major', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 2, B, 2, 1.0, C, 2 );
// C => [ 2.0, 5.0, 6.0, 11.0 ]
```

The function has the following parameters:

-   **ord**: storage layout.
-   **ta**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
-   **tb**: specifies whether `B` should be transposed, conjugate-transposed, or not transposed.
-   **M**: number of rows in the matrix `op(A)` and in the matrix `C`.
-   **N**: number of columns in the matrix `op(B)` and in the matrix `C`.
-   **K**: number of columns in the matrix `op(A)` and number of rows in the matrix `op(B)`.
-   **α**: scalar constant.
-   **A**: first input matrix stored in linear memory.
-   **lda**: stride of the first dimension of `A` (leading dimension of `A`).
-   **B**: second input matrix stored in linear memory.
-   **ldb**: stride of the first dimension of `B` (leading dimension of `B`).
-   **β**: scalar constant.
-   **C**: third input matrix stored in linear memory.
-   **ldc**: stride of the first dimension of `C` (leading dimension of `C`).

The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to perform matrix multiplication of two subarrays

```javascript
var A = [ 1.0, 2.0, 0.0, 0.0, 3.0, 4.0, 0.0, 0.0 ];
var B = [ 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0 ];
var C = [ 1.0, 2.0, 3.0, 4.0 ];

ggemm( 'row-major', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 4, B, 4, 1.0, C, 2 );
// C => [ 2.0, 5.0, 6.0, 11.0 ]
```

<!-- lint disable maximum-heading-length -->

#### ggemm.ndarray( ta, tb, M, N, K, α, A, sa1, sa2, oa, B, sb1, sb2, ob, β, C, sc1, sc2, oc )

Performs the matrix-matrix operation `C = α*op(A)*op(B) + β*C`, using alternative indexing semantics and where `op(X)` is either `op(X) = X` or `op(X) = X^T`, `α` and `β` are scalars, `A`, `B`, and `C` are matrices, with `op(A)` an `M` by `K` matrix, `op(B)` a `K` by `N` matrix, and `C` an `M` by `N` matrix.

```javascript
var A = [ 1.0, 2.0, 3.0, 4.0 ];
var B = [ 1.0, 1.0, 0.0, 1.0 ];
var C = [ 1.0, 2.0, 3.0, 4.0 ];

ggemm.ndarray( 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 2, 1, 0, B, 2, 1, 0, 1.0, C, 2, 1, 0 );
// C => [ 2.0, 5.0, 6.0, 11.0 ]
```

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`.
-   **sb1**: stride of the first dimension of `B`.
-   **sb2**: stride of the second dimension of `B`.
-   **ob**: starting index for `B`.
-   **sc1**: stride of the first dimension of `C`.
-   **sc2**: stride of the second dimension of `C`.
-   **oc**: starting index for `C`.

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 A = [ 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ];
var B = [ 0.0, 1.0, 0.0, 1.0, 1.0 ];
var C = [ 0.0, 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ];

ggemm.ndarray( 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 1, 2, 2, B, 1, 2, 1, 1.0, C, 1, 2, 3 );
// C => [ 0.0, 0.0, 0.0, 2.0, 6.0, 5.0, 11.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   `ggemm()` corresponds to the [BLAS][blas] level 3 function [`dgemm`][dgemm] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dgemm`][@stdlib/blas/base/dgemm], [`sgemm`][@stdlib/blas/base/sgemm], 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 ggemm = require( '@stdlib/blas-base-ggemm' );

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

var M = 3;
var N = 4;
var K = 2;

var A = discreteUniform( M*K, 0, 10, opts ); // 3x2
var B = discreteUniform( K*N, 0, 10, opts ); // 2x4
var C = discreteUniform( M*N, 0, 10, opts ); // 3x4

ggemm( 'row-major', 'no-transpose', 'no-transpose', M, N, K, 1.0, A, K, B, N, 1.0, C, N );
console.log( C );

ggemm.ndarray( 'no-transpose', 'no-transpose', M, N, K, 1.0, A, K, 1, 0, B, N, 1, 0, 1.0, C, N, 1, 0 );
console.log( C );
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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* * *

## Notice

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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-ggemm/main/LICENSE

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

[dgemm]: https://www.netlib.org/lapack/explore-html/dd/d09/group__gemm_ga1e899f8453bcbfde78e91a86a2dab984.html

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