# gasum
> Compute the sum of [absolute values][@stdlib/math/base/special/abs] ([_L1_ norm][l1norm]).
The [_L1_ norm][l1norm] is defined as
## Usage
```javascript
var gasum = require( '@stdlib/blas/base/gasum' );
```
#### gasum( N, x, stride )
Computes the sum of [absolute values][@stdlib/math/base/special/abs].
```javascript
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 has the following parameters:
- **N**: number of elements to sum.
- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-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,
```javascript
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`][mdn-typed-array] views.
```javascript
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][@stdlib/math/base/special/abs] using alternative indexing semantics.
```javascript
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 has the following additional parameters:
- **offset**: starting index.
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 sum the last three elements,
```javascript
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][blas] level 1 function [`dasum`][dasum] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dasum`][@stdlib/blas/base/dasum], [`sasum`][@stdlib/blas/base/sasum], etc.) are likely to be significantly more performant.
## Examples
```javascript
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 = [];
for ( i = 0; i < 100; i++ ) {
rand = round( randu()*100.0 );
sign = randu();
if ( sign < 0.5 ) {
sign = -1.0;
} else {
sign = 1.0;
}
x.push( sign*rand );
}
console.log( gasum( x.length, x, 1 ) );
```
[blas]: http://www.netlib.org/blas
[dasum]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html
[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[l1norm]: http://en.wikipedia.org/wiki/Norm_%28mathematics%29
[@stdlib/math/base/special/abs]: https://www.npmjs.com/package/@stdlib/math-base-special-abs
[@stdlib/blas/base/dasum]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/dasum
[@stdlib/blas/base/sasum]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/sasum
