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# sgemv

> Perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`.

<section class="usage">

## Usage

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

#### sgemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )

Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, 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, 1.0 ] );
var y = new Float32Array( [ 1.0, 1.0 ] );

sgemv( 'row-major', 'no-transpose', 2, 3, 1.0, A, 3, x, 1, 1.0, y, 1 );
// y => <Float32Array>[ 7.0, 16.0 ]
```

The function has the following parameters:

-   **order**: storage layout.
-   **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
-   **M**: number of rows in the matrix `A`.
-   **N**: number of columns in the matrix `A`.
-   **α**: scalar constant.
-   **A**: input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].
-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
-   **x**: input [`Float32Array`][mdn-float32array].
-   **sx**: stride length for `x`.
-   **β**: scalar constant.
-   **y**: output [`Float32Array`][mdn-float32array].
-   **sy**: stride length for `y`.

The stride parameters determine how operations are performed. 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, 2.0, 3.0, 4.0 ] );
var x = new Float32Array( [ 1.0, 0.0, 1.0, 0.0 ] );
var y = new Float32Array( [ 1.0, 0.0, 1.0, 0.0 ] );

sgemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x, 2, 1.0, y, 2 );
// y => <Float32Array>[ 4.0, 0.0, 8.0, 0.0 ]
```

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( [ 0.0, 1.0, 1.0 ] );
var y0 = new Float32Array( [ 0.0, 1.0, 1.0 ] );
var A = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 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

sgemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x1, -1, 1.0, y1, -1 );
// y0 => <Float32Array>[ 0.0, 8.0, 4.0 ]
```

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

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

Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`, using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are vectors, 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, 1.0 ] );
var y = new Float32Array( [ 1.0, 1.0 ] );

sgemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
// y => <Float32Array>[ 7.0, 16.0 ]
```

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( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );
var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0 ] );

sgemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 1, 1.0, y, -2, 2 );
// y => <Float32Array>[ 39, 8, 23, 10 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float32'
};

var M = 3;
var N = 3;

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

sgemv( 'row-major', 'no-transpose', M, N, 1.0, A, N, x, -1, 1.0, y, -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/sgemv.h"
```

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

Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` matrix.

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

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

c_sgemv( CblasColMajor, CblasNoTrans, 3, 3, 1.0f, A, 3, x, 1, 1.0f, y, 1 );
```

The function accepts the following arguments:

-   **layout**: `[in] CBLAS_LAYOUT` storage layout.
-   **trans**: `[in] CBLAS_TRANSPOSE` specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
-   **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.
-   **A**: `[in] float*` input matrix.
-   **LDA**: `[in] CBLAS_INT` stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
-   **X**: `[in] float*` first input vector.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **beta**: `[in] float` scalar constant.
-   **Y**: `[inout] float*` second input vector.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.

```c
void c_sgemv( const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE trans, const CBLAS_INT M, const CBLAS_INT N, const float alpha, const float *A, const CBLAS_INT LDA, const float *X, const CBLAS_INT strideX, const float beta, float *Y, const CBLAS_INT strideY )
```

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

Performs one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`, using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are vectors, and `A` is an `M` by `N` matrix.

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

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

c_sgemv_ndarray( CblasNoTrans, 3, 3, 1.0f, A, 1, 3, 0, x, 1, 0, 1.0f, y, 1, 0 );
```

The function accepts the following arguments:

-   **trans**: `[in] CBLAS_TRANSPOSE` specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
-   **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.
-   **A**: `[in] 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`.
-   **X**: `[in] float*` first input vector.
-   **sx**: `[in] CBLAS_INT` stride length for `X`.
-   **ox**: `[in] CBLAS_INT` starting index for `X`.
-   **beta**: `[in] float` scalar constant.
-   **Y**: `[inout] float*` second input vector.
-   **sy**: `[in] CBLAS_INT` stride length for `Y`.
-   **oy**: `[in] CBLAS_INT` starting index for `Y`.

```c
void c_sgemv_ndarray( const CBLAS_TRANSPOSE trans, const CBLAS_INT M, const CBLAS_INT N, const float alpha, const float *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float beta, 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/sgemv.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Define a 3x3 matrix stored in row-major order:
    const float A[ 3*3 ] = {
        1.0f, 2.0f, 3.0f,
        4.0f, 5.0f, 6.0f,
        7.0f, 8.0f, 9.0f
    };

    // Define `x` and `y` vectors:
    const float x[ 3 ] = { 1.0f, 2.0f, 3.0f };
    float y[ 3 ] = { 1.0f, 2.0f, 3.0f };

    // Specify the number of elements along each dimension of `A`:
    const int M = 3;
    const int N = 3;

    // Perform the matrix-vector operation `y = α*A*x + β*y`:
    c_sgemv( CblasRowMajor, CblasNoTrans, M, N, 1.0f, A, M, x, 1, 1.0f, y, 1 );

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

    // Perform the matrix-vector operation `y = α*A*x + β*y` using alternative indexing semantics:
    c_sgemv_ndarray( CblasNoTrans, M, N, 1.0f, A, N, 1, 0, x, 1, 0, 1.0f, y, 1, 0 );

    // Print the result:
    for ( int i = 0; i < N; 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">

</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="links">

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

[blas-sgemv]: https://www.netlib.org/lapack/explore-html/d7/dda/group__gemv_ga0d35d880b663ad18204bb23bd186e380.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

</section>

<!-- /.links -->
