# ddot
> Calculate the dot product of two double-precision floating-point vectors.
The [dot product][dot-product] (or scalar product) is defined as
## Usage
```javascript
var ddot = require( '@stdlib/blas/base/ddot' );
```
#### ddot( N, x, strideX, y, strideY )
Calculates the dot product of vectors `x` and `y`.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );
var z = ddot( x.length, x, 1, y, 1 );
// returns -5.0
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Float64Array`][@stdlib/array/float64].
- **strideX**: index increment for `x`.
- **y**: input [`Float64Array`][@stdlib/array/float64].
- **strideY**: index increment for `y`.
The `N` and strides 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 Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var z = ddot( 3, 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 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*3 ); // start at 4th element
var z = ddot( 3, x1, -2, y1, 1 );
// returns 128.0
```
#### ddot.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
Calculates the dot product of `x` and `y` using alternative indexing semantics.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 4.0, 2.0, -3.0, 5.0, -1.0 ] );
var y = new Float64Array( [ 2.0, 6.0, -1.0, -4.0, 8.0 ] );
var z = ddot.ndarray( x.length, 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 Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var z = ddot.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// returns 128.0
```
## Notes
- If `N <= 0`, both functions return `0.0`.
- `ddot()` corresponds to the [BLAS][blas] level 1 function [`ddot`][ddot].
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ddot = require( '@stdlib/blas/base/ddot' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );
var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );
var out = ddot.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( out );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/blas/base/ddot.h"
```
#### c_ddot( N, \*X, strideX, \*Y, strideY )
Computes the dot product of two double-precision floating-point vectors.
```c
const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };
double v = c_ddot( 5, x, 1, y, 1 );
// returns -5.0
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **X**: `[in] double*` first input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **Y**: `[in] double*` second input array.
- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
```c
double c_ddot( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );
```
#### c_ddot_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )
Computes the dot product of two double-precision floating-point vectors using alternative indexing semantics.
```c
const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0 };
double v = c_ddot_ndarray( 5, x, -1, 4, y, -1, 4 );
// returns -5.0
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **X**: `[in] double*` first input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
- **Y**: `[in] double*` second input array.
- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
- **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
```c
double c_ddot_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY. const CBLAS_INT offsetY );
```
### Examples
```c
#include "stdlib/blas/base/ddot.h"
#include
int main( void ) {
// Create strided arrays:
const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
const double y[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
// Specify the number of elements:
const int N = 8;
// Specify strides:
const int strideX = 1;
const int strideY = -1;
// Compute the dot product:
double d = c_ddot( N, x, strideX, y, strideY );
// Print the result:
printf( "dot product: %lf\n", d );
// Compute the dot product:
d = c_ddot_ndarray( N, x, strideX, 0, y, strideY, N-1 );
// Print the result:
printf( "dot product: %lf\n", d );
}
```
[dot-product]: https://en.wikipedia.org/wiki/Dot_product
[blas]: http://www.netlib.org/blas
[ddot]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html
[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[@stdlib/blas/base/dsdot]: https://github.com/stdlib-js/blas/tree/main/base/dsdot
[@stdlib/blas/base/gdot]: https://github.com/stdlib-js/blas/tree/main/base/gdot
[@stdlib/blas/base/sdot]: https://github.com/stdlib-js/blas/tree/main/base/sdot
[@stdlib/blas/base/sdsdot]: https://github.com/stdlib-js/blas/tree/main/base/sdsdot
[@stdlib/blas/ddot]: https://github.com/stdlib-js/blas/tree/main/ddot
