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# sdsdot

> Calculate the dot product of two single-precision floating-point vectors with extended accumulation.

<section class="intro">

The [dot product][dot-product] (or scalar product) is defined as

<!-- <equation class="equation" label="eq:dot_product" align="center" raw="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" alt="Dot product definition."> -->

<div class="equation" align="center" data-raw-text="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" data-equation="eq:dot_product">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@37cdbad9473fd050c8f7185c122a33d0f680b6c6/lib/node_modules/@stdlib/blas/base/sdsdot/docs/img/equation_dot_product.svg" alt="Dot product definition.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### sdsdot( N, scalar, x, strideX, y, strideY )

Calculates the dot product of vectors `x` and `y` with extended accumulation.

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float32Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );

var z = sdsdot( x.length, 0.0, x, 1, y, 1 );
// returns -5.0
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **scalar**: scalar constant added to the dot product.
-   **x**: input [`Float32Array`][@stdlib/array/float32].
-   **strideX**: index increment for `x`.
-   **y**: input [`Float32Array`][@stdlib/array/float32].
-   **strideY**: index increment for `y`.

The `N` and `stride` parameters determine which elements in `x` and `y` are accessed at runtime. For example, to calculate the dot product of every other value in `x` and the first `N` elements of `y` in reverse order,

```javascript
var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

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

var z = sdsdot( N, 0.0, x, 2, y, -1 );
// returns 9.0
```

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

// Initial arrays...
var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

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

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

var z = sdsdot( N, 0.0, x1, -2, y1, 1 );
// returns 128.0
```

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

Calculates the dot product of vectors `x` and `y` with extended accumulation and using alternative indexing semantics.

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float32Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );

var z = sdsdot.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
// returns -5.0
```

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 calculate the dot product of every other value in `x` starting from the second value with the last 3 elements in `y` in reverse order

```javascript
var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

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

var z = sdsdot.ndarray( N, 0.0, x, 2, 1, y, -1, y.length-1 );
// returns 128.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `scalar`.
-   `sdsdot()` corresponds to the [BLAS][blas] level 1 function [`sdsdot`][sdsdot].

</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 Float32Array = require( '@stdlib/array/float32' );
var sdsdot = require( '@stdlib/blas/base/sdsdot' );

var x;
var y;
var i;

x = new Float32Array( 10 );
y = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu() * 100.0 );
    y[ i ] = round( randu() * 10.0 );
}
console.log( x );
console.log( y );

var z = sdsdot( x.length, 0.0, x, 1, y, -1 );
console.log( z );
```

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Lawson, Charles L., Richard J. Hanson, Fred T. Krogh, and David Ronald Kincaid. 1979. "Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage \[F1]." _ACM Transactions on Mathematical Software_ 5 (3). New York, NY, USA: Association for Computing Machinery: 324–25. doi:[10.1145/355841.355848][@lawson:1979a].

</section>

<!-- /.references -->

<section class="links">

[dot-product]: https://en.wikipedia.org/wiki/Dot_product

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

[sdsdot]: http://www.netlib.org/lapack/explore-html/df/d28/group__single__blas__level1.html

[@stdlib/array/float32]: https://github.com/stdlib-js/array-float32

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

[@lawson:1979a]: https://doi.org/10.1145/355841.355848

</section>

<!-- /.links -->
