time-to-botec/squiggle/node_modules/@stdlib/blas/base/gaxpy/README.md

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# gaxpy

> Multiply `x` by a constant `alpha` and add the result to `y`.

<section class="usage">

## Usage

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

#### gaxpy( N, alpha, x, strideX, y, strideY )

Multiplies `x` by a constant `alpha` and adds the result to `y`.

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

gaxpy( x.length, alpha, x, 1, y, 1 );
// y => [ 6.0, 11.0, 16.0, 21.0, 26.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: `numeric` constant.
-   **x**: input [`array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideX**: index increment for `x`.
-   **y**: input [`array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideY**: index increment for `y`.

The `N` and `stride` parameters determine which elements in `x` and `y` are accessed at runtime. For example, to multiply every other value in `x` by `alpha` and add the result to the first `N` elements of `y` in reverse order,

```javascript
var floor = require( '@stdlib/math/base/special/floor' );

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

var alpha = 5.0;
var N = floor( x.length / 2 );

gaxpy( N, alpha, x, 2, y, -1 );
// y => [ 26.0, 16.0, 6.0, 1.0, 1.0, 1.0 ]
```

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' );
var floor = require( '@stdlib/math/base/special/floor' );

// 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*3 ); // start at 4th element

var N = floor( x0.length / 2 );

gaxpy( N, 5.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

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

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

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

gaxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => [ 6.0, 11.0, 16.0, 21.0, 26.0 ]
```

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 `offsetX` and `offsetY` parameters support indexing semantics based on starting indices. For example, to multiply every other value in `x` by a constant `alpha` starting from the second value and add to the last `N` elements in `y` where `x[i] -> y[n]`, `x[i+2] -> y[n-1]`,...,

```javascript
var floor = require( '@stdlib/math/base/special/floor' );

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 ];

var alpha = 5.0;
var N = floor( x.length / 2 );

gaxpy.ndarray( N, alpha, x, 2, 1, y, -1, y.length-1 );
// y => [ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0` or `alpha == 0`, both functions return `y` unchanged.
-   `gaxpy()` corresponds to the [BLAS][blas] level 1 function [`daxpy`][daxpy] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`daxpy`][@stdlib/blas/base/daxpy], [`saxpy`][@stdlib/blas/base/saxpy], etc.) are likely to be significantly more performant.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var gaxpy = require( '@stdlib/blas/base/gaxpy' );

var x;
var y;
var i;

x = [];
y = [];
for ( i = 0; i < 10; i++ ) {
    x.push( round( randu()*100.0 ) );
    y.push( round( randu()*10.0 ) );
}
console.log( x );
console.log( y );

gaxpy.ndarray( x.length, 5.0, x, 1, 0, y, -1, y.length-1 );
console.log( y );
```

</section>

<!-- /.examples -->

<section class="links">

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

[daxpy]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html

[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/blas/base/daxpy]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/daxpy

[@stdlib/blas/base/saxpy]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/saxpy

</section>

<!-- /.links -->