sasum

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 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 accepts the following parameters:

  • N: number of elements to sum.
  • 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 floor = require( '@stdlib/math/base/special/floor' );

var x = new Float32Array( [ -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 = sasum( N, x, stride );
// 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' );
var floor = require( '@stdlib/math/base/special/floor' );

// 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

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

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

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

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

Computes the sum of absolute values, with 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 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 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 round = require( '@stdlib/math/base/special/round' );
var randu = require( '@stdlib/random/base/randu' );
var Float32Array = require( '@stdlib/array/float32' );
var sasum = require( '@stdlib/blas/base/sasum' );

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

x = new Float32Array( 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( sasum( x.length, x, 1 ) );