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# dger

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

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### dger( ord, 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 Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dger( 'row-major', 2, 3, 1.0, x, 1, y, 1, A, 3 );
// A => <Float64Array>[ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]
```

The function has the following parameters:

-   **ord**: 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 [`Float64Array`][mdn-float64array].
-   **sx**: stride length for `x`.
-   **y**: an `N` element [`Float64Array`][mdn-float64array].
-   **sy**: stride length for `y`.
-   **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
-   **lda**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `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 Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 0.0, 1.0, 0.0 ] );
var y = new Float64Array( [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ] );

dger( 'column-major', 2, 3, 1.0, x, 2, y, 2, A, 2 );
// A => <Float64Array>[ 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.

<!-- eslint-disable stdlib/capitalized-comments -->

```javascript
var Float64Array = require( '@stdlib/array/float64' );

// Initial arrays...
var x0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
var y0 = new Float64Array( [ 0.0, 1.0, 1.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dger( 'column-major', 2, 3, 1.0, x1, -1, y1, -1, A, 2 );
// A => <Float64Array>[ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]
```

#### dger.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 Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dger.ndarray( 2, 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
// A => <Float64Array>[ 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 Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 0.0, 0.0, 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );
var x = new Float64Array( [ 0.0, 1.0, 0.0, 1.0, 0.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ] );

dger.ndarray( 2, 3, 1.0, x, 2, 1, y, 2, 1, A, 1, 2, 2 );
// A => <Float64Array>[ 0.0, 0.0, 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float64'
};

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 );

dger( 'row-major', M, N, 1.0, x, 1, y, 1, A, N );
console.log( A );

dger.ndarray( M, N, 1.0, x, 1, 0, y, 1, 0, A, 1, M, 0 );
console.log( A );

```

</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/dger.h"
```

#### c_dger( 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"

double A[ 3*4 ] = {
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0
};

const double x[ 3 ] = { 1.0, 4.0, 0.0 };
const double y[ 4 ] = { 0.0, 1.0, 2.0, 3.0 };

c_dger( CblasRowMajor, 3, 4, 1.0, 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] double` scalar constant.
-   **X**: `[in] double*` an `M` element vector.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **Y**: `[in] double*` an `N` element vector.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
-   **A**: `[inout] double*` 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_dger( const CBLAS_LAYOUT layout, const CBLAS_INT M, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY, double *A, const CBLAS_INT LDA );
```

#### c_dger_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"

double A[ 3*4 ] = {
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0
};

const double x[ 3 ] = { 1.0, 4.0, 0.0 };
const double y[ 4 ] = { 0.0, 1.0, 2.0, 3.0 };

c_dger_ndarray( 3, 4, 1.0, 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] double` scalar constant.
-   **X**: `[in] double*` an `M` element vector.
-   **sx**: `[in] CBLAS_INT` stride length for `X`.
-   **ox**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[in] double*` an `N` element vector.
-   **sy**: `[in] CBLAS_INT` stride length for `Y`.
-   **oy**: `[in] CBLAS_INT` starting index for `Y`.
-   **A**: `[inout] double*` 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_dger( onst CBLAS_INT M, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA );
```

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

int main( void ) {
   // Define a 3x4 matrix stored in row-major order:
   double A[ 3*4 ] = {
      0.0, 0.0, 0.0, 0.0,
      0.0, 0.0, 0.0, 0.0,
      0.0, 0.0, 0.0, 0.0
   };
   // Define `x` and `y^T` vectors:
   const double x[ 3 ] = { 1.0, 4.0, 0.0 };      // M
   const double y[ 4 ] = { 0.0, 1.0, 2.0, 3.0 }; // 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_dger( CblasRowMajor, M, N, 1.0, 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] = %lf\n", i, j, A[ (i*N)+j ] );
      }
   }
}
```

</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-dger]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d15/group__double__blas__level2_ga458222e01b4d348e9b52b9343d52f828.html

[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array

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

</section>

<!-- /.links -->
