About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

sasumpw

Calculate the sum of absolute values (L1 norm) of single-precision floating-point strided array elements using pairwise summation.

The L1 norm is defined as

$$\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert$$

Installation

npm install @stdlib/blas-ext-base-sasumpw

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 sasumpw = require( '@stdlib/blas-ext-base-sasumpw' );

sasumpw( N, x, stride )

Computes the sum of absolute values (L1 norm) of single-precision floating-point strided array elements using pairwise summation.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = sasumpw( N, x, 1 );
// returns 5.0

The function has the following parameters:

• N: number of indexed elements.
• x: input Float32Array.
• stride: index increment for x.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the sum of absolute values of every other element in x,

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = sasumpw( 4, x, 2 );
// 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 x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = sasumpw( 4, x1, 2 );
// returns 9.0

sasumpw.ndarray( N, x, stride, offset )

Computes the sum of absolute values (L1 norm) of single-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = sasumpw.ndarray( N, x, 1, 0 );
// returns 5.0

The function has the following additional parameters:

• offset: starting index for x.

While typed array views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the sum of absolute values of every other value in x starting from the second value

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = sasumpw.ndarray( 4, x, 2, 1 );
// returns 9.0

Notes

• If N <= 0, both functions return 0.0.
• In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array-filled-by' );
var sasumpw = require( '@stdlib/blas-ext-base-sasumpw' );

var x = filledarrayBy( 10, 'float32', discreteUniform( 0, 100 ) );
console.log( x );

var v = sasumpw( x.length, x, 1 );
console.log( v );

---

References

• Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.

---

See Also

• @stdlib/blas-base/sasum: compute the sum of absolute values (L1 norm).
• @stdlib/blas-ext/base/dasumpw: calculate the sum of absolute values (L1 norm) of double-precision floating-point strided array elements using pairwise summation.
• @stdlib/blas-ext/base/gasumpw: calculate the sum of absolute values (L1 norm) of strided array elements using pairwise summation.
• @stdlib/blas-ext/base/ssumpw: calculate the sum of single-precision floating-point strided array elements using pairwise summation.

---

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

---

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.