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ddot

README.md

ddot

Calculate the dot product of two double-precision floating-point vectors.

The dot product (or scalar product) is defined as

$$\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}$$

Usage

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

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

Calculates the dot product of vectors x and y.

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.
  • strideX: index increment for x.
  • y: input Float64Array.
  • 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,

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 views.

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.

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 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

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 level 1 function ddot.

Examples

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 );

See Also