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dnannsumpw

Calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.

Usage

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

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

Computes the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.

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

var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumpw( x.length, x, 1, out, 1 );
// returns <Float64Array>[ 1.0, 3 ]

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Float64Array.
  • strideX: stride length for x.
  • out: output Float64Array 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 Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ] );
var out = new Float64Array( 2 );

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

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

Computes the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation and alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumpw.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns <Float64Array>[ 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 Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 2.0, 1.0, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( 4 );

var v = dnannsumpw.ndarray( 4, x, 2, 1, out, 2, 1 );
// returns <Float64Array>[ 0.0, 5.0, 0.0, 4 ]

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.

Examples

var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var bernoulli = require( '@stdlib/random/base/bernoulli' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var Float64Array = require( '@stdlib/array/float64' );
var dnannsumpw = require( '@stdlib/blas/ext/base/dnannsumpw' );

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

var x = filledarrayBy( 10, 'float64', rand );
console.log( x );

var out = new Float64Array( 2 );
dnannsumpw( x.length, x, 1, out, 1 );
console.log( out );

C APIs

Usage

#include "stdlib/blas/ext/base/dnannsumpw.h"

stdlib_strided_dnannsumpw( N, *X, strideX, *n )

Computes the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.

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

const double x[] = { 1.0, 2.0, 0.0/0.0, 4.0 };
CBLAS_INT n = 0;

double v = stdlib_strided_dnannsumpw( 4, x, 1, &n );
// returns 7.0

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] double* input array.
  • strideX: [in] CBLAS_INT stride length.
  • n: [out] CBLAS_INT* pointer for storing the number of non-NaN elements.
double stdlib_strided_dnannsumpw( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, CBLAS_INT *n );

stdlib_strided_dnannsumpw_ndarray( N, *X, strideX, offsetX, *n )

Computes the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation and alternative indexing semantics.

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

const double x[] = { 1.0, 2.0, 0.0/0.0, 4.0 };
CBLAS_INT n = 0;

double v = stdlib_strided_dnannsumpw_ndarray( 4, x, 1, 0, &n );
// returns 7.0

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] double* input array.
  • strideX: [in] CBLAS_INT stride length.
  • offsetX: [in] CBLAS_INT starting index.
  • n: [out] CBLAS_INT* pointer for storing the number of non-NaN elements.
double stdlib_strided_dnannsumpw_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, CBLAS_INT *n );

Examples

#include "stdlib/blas/ext/base/dnannsumpw.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 0.0/0.0, 0.0/0.0 };

    // Specify the number of elements:
    const int N = 5;

    // Specify the stride length:
    const int strideX = 2;

    // Initialize a variable for storing the number of non-NaN elements:
    CBLAS_INT n = 0;

    // Compute the sum:
    double v = stdlib_strided_dnannsumpw( N, x, strideX, &n );

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

References

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

See Also

  • @stdlib/blas/ext/base/dnannsum: calculate the sum of double-precision floating-point strided array elements, ignoring NaN values.
  • @stdlib/blas/ext/base/dnannsumkbn: calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.
  • @stdlib/blas/ext/base/dnannsumkbn2: calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using a second-order iterative Kahan–Babuška algorithm.
  • @stdlib/blas/ext/base/dnannsumors: calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using ordinary recursive summation.
  • @stdlib/blas/ext/base/dsumpw: calculate the sum of double-precision floating-point strided array elements using pairwise summation.