# 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 the strided arrays 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 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 z = sdsdot( 3, 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' );
// 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 z = sdsdot( 3, 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 offset 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 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 z = sdsdot.ndarray( 3, 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var sdsdot = require( '@stdlib/blas/base/sdsdot' );
var opts = {
'dtype': 'float32'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );
var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );
var out = sdsdot( x.length, 0.0, x, 1, y, -1 );
console.log( out );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/blas/base/sdsdot.h"
```
#### c_sdsdot( N, scalar, \*X, strideX, \*Y, strideY )
Calculates the dot product of vectors `x` and `y` with extended accumulation.
```c
const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
const float y[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
float v = c_sdsdot( 5, 0.0f, x, 1, y, -1 );
// returns -120.0f
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **scalar**: `[in] float` scalar constant to add to dot product.
- **X**: `[in] float*` first input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **Y**: `[in] float*` second input array.
- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
```c
float c_sdsdot( const CBLAS_INT N, const float scalar, const float *X, const CBLAS_INT strideX, const float *Y, const CBLAS_INT strideY );
```
#### c_sdsdot_ndarray( N, scalar, \*X, strideX, offsetX, \*Y, strideY, offsetY )
Calculates the dot product of vectors `x` and `y` with extended accumulation using alternative indexing semantics.
```c
const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
const float y[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
float v = c_sdsdot_ndarray( 5, 0.0f, x, 1, 0, y, -1, 7 );
// returns -80.0f
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **scalar**: `[in] float` scalar constant to add to dot product.
- **X**: `[in] float*` first input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
- **Y**: `[in] float*` second input array.
- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
- **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
```c
float c_sdsdot_ndarray( const CBLAS_INT N, const float scalar, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
```
### Examples
```c
#include "stdlib/blas/base/sdsdot.h"
#include
int main( void ) {
// Create strided arrays:
const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
const float y[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
// Specify the number of indexed elements:
const int N = 8;
// Specify strides:
const int strideX = 1;
const int strideY = -1;
// Compute the dot product:
float d = c_sdsdot( N, 0.0f, x, strideX, y, strideY );
// Print the result:
printf( "dot product: %f\n", d );
// Compute the dot product:
d = c_sdsdot_ndarray( N, 0.0f, x, strideX, 0, y, strideY, 7 );
// Print the result:
printf( "dot product: %f\n", d );
}
```
* * *
## 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
[@stdlib/blas/base/ddot]: https://github.com/stdlib-js/blas/tree/main/base/ddot
[@stdlib/blas/base/dsdot]: https://github.com/stdlib-js/blas/tree/main/base/dsdot
[@stdlib/blas/base/sdot]: https://github.com/stdlib-js/blas/tree/main/base/sdot
