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sasum

Compute the sum of absolute values (L1 norm).

The L1 norm is defined as

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

Installation

npm install @stdlib/blas-base-sasum

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

sasum( N, x, stride )

Computes the sum of absolute values.

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

var x = new Float32Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var sum = sasum( x.length, x, 1 );
// returns 19.0

The function has the following parameters:

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

The N and stride parameters determine which elements in x are used to compute the sum. For example, to sum every other value,

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

var x = new Float32Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var sum = sasum( 4, x, 2 );
// returns 10.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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

// Initial array:
var x0 = new Float32Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

// Create an offset view:
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Sum every other value:
var sum = sasum( 3, x1, 2 );
// returns 12.0

If either N is less than or equal to 0, the function returns 0.

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

Computes the sum of absolute values using alternative indexing semantics.

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

var x = new Float32Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var sum = sasum.ndarray( x.length, x, 1, 0 );
// returns 19.0

The function has the following additional parameters:

• offset: starting index.

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 sum the last three elements,

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

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

var sum = sasum.ndarray( 3, x, 1, x.length-3 );
// returns 15.0

// Using a negative stride to sum from the last element:
sum = sasum.ndarray( 3, x, -1, x.length-1 );
// returns 15.0

Notes

• If N <= 0, both functions return 0.
• sasum() corresponds to the BLAS level 1 function sasum.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var sasum = require( '@stdlib/blas-base-sasum' );

var opts = {
    'dtype': 'float32'
};
var x = discreteUniform( 10, -100, 100, opts );
console.log( x );

var out = sasum( x.length, x, 1 );
console.log( out );

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C APIs

Usage

#include "stdlib/blas/base/sasum.h"

c_sasum( N, *X, stride )

Computes the sum of absolute values.

const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };

float sum = c_sasum( 8, x, 1 );
// returns 36.0f

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] float* input array.
• stride: [in] CBLAS_INT index increment for X.

float c_sasum( const CBLAS_INT N, const float *X, const CBLAS_INT stride );

c_sasum_ndarray( N, *X, stride, offset )

Computes the sum of absolute values using alternative indexing semantics.

const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };

float sum = c_sasum_ndarray( 8, x, -1, 7 );
// returns 36.0f

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] float* input array.
• stride: [in] CBLAS_INT index increment for X.
• offset: [in] CBLAS_INT starting index for X.

float c_sasum_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT stride, const CBLAS_INT offset );

Examples

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

int main( void ) {
    // Create a strided array:
    const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };

    // Specify the number of elements:
    const int N = 8;

    // Specify a stride:
    const int stride = 1;

    // Compute the sum of absolute values:
    float sum = c_sasum( N, x, stride );

    // Print the result:
    printf( "sum: %f\n", sum );

    // Compute the sum of absolute values:
    sum = c_sasum_ndarray( N, x, -stride, N-1 );

    // Print the result:
    printf( "sum: %f\n", sum );
}

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See Also

• @stdlib/blas-base/dasum: compute the sum of absolute values (L1 norm).
• @stdlib/blas-base/gasum: compute the sum of absolute values (L1 norm).

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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.