gdot

Calculate the dot product of two vectors.

The dot product (or scalar product) is defined as

Usage

var gdot = require( '@stdlib/blas/base/gdot' );

gdot( N, x, strideX, y, strideY )

Calculates the dot product of vectors x and y.

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

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

The function has the following parameters:

N: number of indexed elements.
x: first input Array or typed array.
strideX: index increment for x.
y: second input Array or 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 calculate the dot product of every other value in x and the first N elements of y in reverse order,

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 N = floor( x.length / 2 );

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

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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 );

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

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

Calculates the dot product of x and y using alternative indexing semantics.

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

var z = gdot.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 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

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 N = floor( x.length / 2 );

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

Notes

If N <= 0 both functions return 0.0.
gdot() corresponds to the BLAS level 1 function ddot with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (ddot, sdot, etc.) are likely to be significantly more performant.

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var Uint8ClampedArray = require( '@stdlib/array/uint8c' );
var gdot = require( '@stdlib/blas/base/gdot' );

var x;
var y;
var i;

x = new Float64Array( 10 );
y = new Uint8ClampedArray( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu()*500.0 );
    y[ i ] = round( randu()*255.0 );
}
console.log( x );
console.log( y );

// Compute the dot product:
var dot = gdot.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( dot );