# sdsdot
> Calculate the dot product of two single-precision floating-point vectors with extended accumulation.
The [dot product][dot-product] (or scalar product) is defined as
## 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.
```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
```
## Notes
- If `N <= 0`, both functions return `scalar`.
- `sdsdot()` corresponds to the [BLAS][blas] level 1 function [`sdsdot`][sdsdot].
## Examples
```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 );
```
* * *
## 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].
[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://www.npmjs.com/package/@stdlib/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
