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gnannsumpw

Calculate the sum of strided array elements, ignoring NaN values and using pairwise summation.

Installation

npm install @stdlib/blas-ext-base-gnannsumpw

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

gnannsumpw( N, x, strideX, out, strideOut )

Computes the sum of strided array elements, ignoring NaN values and using pairwise summation.

var x = [ 1.0, -2.0, NaN, 2.0 ];
var out = [ 0.0, 0 ];

var v = gnannsumpw( x.length, x, 1, out, 1 );
// returns [ 1.0, 3 ]

The function has the following parameters:

• N: number of indexed elements.
• x: input array.
• strideX: stride length for x.
• out: output array whose first element is the sum and whose second element is the number of non-NaN elements.
• strideOut: stride length for out.

The N and stride parameters determine which elements are accessed at runtime. For example, to compute the sum of every other element in the strided array:

var x = [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ];
var out = [ 0.0, 0 ];

var v = gnannsumpw( 4, x, 2, out, 1 );
// returns [ 5.0, 2 ]

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

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

var x0 = new Float64Array( [ 2.0, 1.0, NaN, -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 out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

var v = gnannsumpw( 4, x1, 2, out1, 1 );
// returns <Float64Array>[ 5.0, 4 ]

gnannsumpw.ndarray( N, x, strideX, offsetX, out, strideOut, offsetOut )

Computes the sum of strided array elements, ignoring NaN values and using pairwise summation and alternative indexing semantics.

var x = [ 1.0, -2.0, NaN, 2.0 ];
var out = [ 0.0, 0 ];

var v = gnannsumpw.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns [ 1.0, 3 ]

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetOut: starting index for out.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the sum of every other element starting from the second element:

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

var v = gnannsumpw.ndarray( 4, x, 2, 1, out, 2, 1 );
// returns [ 0.0, 5.0, 0.0, 4.0 ]

Notes

• If N <= 0, both functions return a sum equal to 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.
• Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array-base/accessor).
• Depending on the environment, the typed versions (dnannsumpw, snannsumpw, etc.) are likely to be significantly more performant.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var bernoulli = require( '@stdlib/random-base-bernoulli' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var gnannsumpw = require( '@stdlib/blas-ext-base-gnannsumpw' );

function rand() {
    if ( bernoulli( 0.5 ) < 1 ) {
        return discreteUniform( 0, 100 );
    }
    return NaN;
}

var x = filledarrayBy( 10, 'generic', rand );
console.log( x );

var out = [ 0.0, 0 ];
gnannsumpw( x.length, x, 1, out, 1 );
console.log( out );

References

• Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.

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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.

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License

See LICENSE.

Copyright

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