gasum

Compute the sum of absolute values (L1 norm).

The L1 norm is defined as

double-vertical-bar bold x double-vertical-bar Subscript 1 Baseline equals sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts StartAbsoluteValue x Subscript i Baseline EndAbsoluteValue

Usage

var gasum = require( '@stdlib/blas/base/gasum' );

gasum( N, x, stride )

Computes the sum of absolute values.

var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

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

The function accepts the following parameters:

  • N: number of elements to sum.
  • x: input Array or typed array.
  • 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 floor = require( '@stdlib/math/base/special/floor' );

var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

var N = floor( x.length / 2 );
var stride = 2;

var sum = gasum( N, x, stride );
// returns 10.0

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

var Float64Array = require( '@stdlib/array/float64' );

var floor = require( '@stdlib/math/base/special/floor' );

// Initial array...
var x0 = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

// Create an offset view...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var N = floor( x0.length / 2 );

// Sum every other value...
var sum = gasum( N, x1, 2 );
// returns 12.0

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

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

Computes the sum of absolute values, with alternative indexing semantics.

var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];

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

The function accepts 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 Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

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

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

Notes

  • If N <= 0, both functions return 0.
  • gasum() corresponds to the BLAS level 1 function dasum with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (dasum, sasum, etc.) are likely to be significantly more performant.

Examples

var round = require( '@stdlib/math/base/special/round' );
var randu = require( '@stdlib/random/base/randu' );
var gasum = require( '@stdlib/blas/base/gasum' );

var rand;
var sign;
var x;
var i;

x = new Array( 100 );
for ( i = 0; i < x.length; i++ ) {
    rand = round( randu()*100.0 );
    sign = randu();
    if ( sign < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    x[ i ] = sign * rand;
}
console.log( gasum( x.length, x, 1 ) );