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# gaxpby

> Multiply a strided array `x` by a constant and add the result to a strided array `y` multiplied by a constant.

<section class="intro">

This BLAS extension implements the operation

<!-- <equation class="equation" label="eq:axpby" align="center" raw="\mathbf{y} = \alpha \mathbf{x} + \beta \mathbf{y}" alt="Equation for axpby operation."> -->

<!-- </equation> -->

This API is complementary to the package [`@stdlib/blas/base/gaxpy`][@stdlib/blas/base/gaxpy] and is a common BLAS extension in libraries such as Intel MKL, OpenBLAS, and others.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### gaxpby( N, alpha, x, strideX, beta, y, strideY )

Multiplies a strided array `x` by a constant and adds the result to a strided array `y` multiplied by a constant.

```javascript
var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var y = [ 2.0, 3.0, 4.0, 5.0, 6.0 ];

gaxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
// y => [ 9.0, 16.0, 23.0, 30.0, 37.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: first scalar constant.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideX**: stride length for `x`.
-   **beta**: second scalar constant.
-   **y**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideY**: stride length for `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other element in `x` by `alpha` and add to every other element in `y` multiplied by `beta`:

```javascript
var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var y = [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ];

gaxpby( 3, 5.0, x, 2, 2.0, y, 2 );
// y => [ 19.0, 8.0, 33.0, 10.0, 47.0, 12.0 ]
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

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

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// 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*2 ); // start at 3rd element

gaxpby( 3, 5.0, x1, 1, 2.0, y1, 1 );
// y0 => <Float64Array>[ 7.0, 8.0, 28.0, 35.0, 42.0, 12.0 ]
```

#### gaxpby.ndarray( N, alpha, x, strideX, offsetX, beta, y, strideY, offsetY )

Multiplies a strided array `x` by a constant and adds the result to a strided array `y` multiplied by a constant using alternative indexing semantics.

```javascript
var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var y = [ 2.0, 3.0, 4.0, 5.0, 6.0 ];

gaxpby.ndarray( x.length, 5.0, x, 1, 0, 2.0, y, 1, 0 );
// y => [ 9.0, 16.0, 23.0, 30.0, 37.0 ]
```

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 the last three elements of `x` by `alpha` and add to the last three elements of `y` multiplied by `beta`:

```javascript
var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var y = [ 6.0, 7.0, 8.0, 9.0, 10.0 ];

gaxpby.ndarray( 3, 5.0, x, 1, x.length-3, 2.0, y, 1, y.length-3 );
// y => [ 6.0, 7.0, 31.0, 38.0, 45.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `y` unchanged.
-   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 gaxpby = require( '@stdlib/blas/ext/base/gaxpby' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( x );

var y = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( y );

gaxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
console.log( y );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

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<section class="links">

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

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

[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor

[@stdlib/blas/base/gaxpy]: https://github.com/stdlib-js/blas/tree/main/base/gaxpy

<!-- <related-links> -->

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</section>

<!-- /.links -->
