time-to-botec/squiggle/node_modules/@stdlib/blas/base/sdsdot/README.md

sdsdot

Calculate the dot product of two single-precision floating-point vectors with extended accumulation.

The dot product (or scalar product) is defined as

Usage

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.

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.
• strideX: index increment for x.
• y: input Float32Array.
• 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 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 views.

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.

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 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 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 level 1 function sdsdot.

Examples

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 );

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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.