@stdlib/blas-ext-base-dasumpw

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

https://github.com/stdlib-js/blas-ext-base-dasumpw

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

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Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
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abs absolute blas extended javascript l1-norm l1norm manhattan math mathematics node node-js nodejs norm statistics stats stdlib sum taxicab total

Created over 4 years ago · Last pushed 8 months ago

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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!

dasumpw

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

The [_L1_ norm][l1norm] is defined as ```math \|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert ```

## Installation ```bash npm install @stdlib/blas-ext-base-dasumpw ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] 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 ```javascript var dasumpw = require( '@stdlib/blas-ext-base-dasumpw' ); ``` #### dasumpw( N, x, strideX ) Computes the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); var v = dasumpw( x.length, x, 1 ); // returns 5.0 ``` The function has the following parameters: - **N**: number of indexed elements. - **x**: input [`Float64Array`][@stdlib/array/float64]. - **strideX**: stride length 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: ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] ); var v = dasumpw( 4, x, 2 ); // returns 9.0 ``` Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element var v = dasumpw( 4, x1, 2 ); // returns 9.0 ``` #### dasumpw.ndarray( N, x, strideX, offsetX ) Computes the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation and alternative indexing semantics. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); var v = dasumpw.ndarray( x.length, x, 1, 0 ); // returns 5.0 ``` The function has the following additional parameters: - **offsetX**: starting index for `x`. While [`typed array`][mdn-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 element starting from the second element: ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); var v = dasumpw.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 ```javascript var discreteUniform = require( '@stdlib/random-array-discrete-uniform' ); var dasumpw = require( '@stdlib/blas-ext-base-dasumpw' ); var x = discreteUniform( 10, -100, 100, { 'dtype': 'float64' }); console.log( x ); var v = dasumpw( x.length, x, 1 ); console.log( v ); ```

## C APIs

### Usage ```c #include "stdlib/blas/ext/base/dasumpw.h" ``` #### stdlib_strided_dasumpw( N, \*X, strideX ) Computes the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation. ```c const double x[] = { 1.0, 2.0, 3.0, 4.0 } double v = stdlib_strided_dasumpw( 4, x, 1 ); // returns 10.0 ``` The function accepts the following arguments: - **N**: `[in] CBLAS_INT` number of indexed elements. - **X**: `[in] double*` input array. - **strideX**: `[in] CBLAS_INT` stride length for `X`. ```c double stdlib_strided_dasumpw( const CBLAS_INT N, const double *X, const CBLAS_INT strideX ); ``` #### stdlib_strided_dasumpw_ndarray( N, \*X, strideX, offsetX ) Computes the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation and alternative indexing semantics. ```c const double x[] = { 1.0, 2.0, 3.0, 4.0 } double v = stdlib_strided_dasumpw_ndarray( 4, x, 1, 0 ); // returns 10.0 ``` The function accepts the following arguments: - **N**: `[in] CBLAS_INT` number of indexed elements. - **X**: `[in] double*` input array. - **strideX**: `[in] CBLAS_INT` stride length for `X`. - **offsetX**: `[in] CBLAS_INT` starting index for `X`. ```c double stdlib_strided_dasumpw_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX ); ```

### Examples ```c #include "stdlib/blas/ext/base/dasumpw.h" #include int main( void ) { // Create a strided array: const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 }; // Specify the number of indexed elements: const int N = 8; // Specify a stride: const int strideX = 1; // Compute the sum: double v = stdlib_strided_dasumpw( N, x, strideX ); // Print the result: printf( "sumabs: %lf\n", 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][@higham:1993a].

* * * ## Notice This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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npmjs.org: @stdlib/blas-ext-base-dasumpw

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

Homepage: https://stdlib.io
License: Apache-2.0
Latest release: 0.2.2
published over 1 year ago

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@stdlib/blas-ext-base-dasumpw

Science Score: 39.0%

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