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sdsdot

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

The dot product (or scalar product) is defined as

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

Installation

npm install @stdlib/blas-base-sdsdot

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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 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 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 views.

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.

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 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 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 level 1 function sdsdot.

Examples

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 );

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C APIs

Usage

#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.

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.

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.

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.

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

#include "stdlib/blas/base/sdsdot.h"
#include <stdio.h>

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 );
}

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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.

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See Also

• @stdlib/blas-base/ddot: calculate the dot product of two double-precision floating-point vectors.
• @stdlib/blas-base/dsdot: calculate the dot product with extended accumulation and result of two single-precision floating-point vectors.
• @stdlib/blas-base/sdot: calculate the dot product of two single-precision floating-point vectors.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.