dsmeanwd

Calculate the arithmetic mean of a single-precision floating-point strided array using Welford's algorithm with extended accumulation and returning an extended precision result.

The arithmetic mean is defined as

Installation

npm install @stdlib/stats-strided-dsmeanwd

Usage

var dsmeanwd = require( '@stdlib/stats-strided-dsmeanwd' );

dsmeanwd( N, x, strideX )

Computes the arithmetic mean of a single-precision floating-point strided array x using Welford's algorithm with extended accumulation and returning an extended precision result.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = dsmeanwd( x.length, x, 1 );
// returns ~0.3333

The function has the following parameters:

• N: number of indexed elements.
• x: input Float32Array.
• strideX: stride length for x.

The N and stride parameters determine which elements in x are accessed at runtime. For example, to compute the arithmetic mean of every other element in x,

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = dsmeanwd( 4, x, 2 );
// returns 1.25

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

var Float32Array = require( '@stdlib/array-float32' );

var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = dsmeanwd( 4, x1, 2 );
// returns 1.25

dsmeanwd.ndarray( N, x, strideX, offsetX )

Computes the arithmetic mean of a single-precision floating-point strided array using Welford's algorithm with extended accumulation and alternative indexing semantics and returning an extended precision result.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = dsmeanwd.ndarray( x.length, x, 1, 0 );
// returns ~0.33333

The function has the following additional parameters:

• offset: starting index for x.

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 calculate the arithmetic mean for every other value in x starting from the second value

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = dsmeanwd.ndarray( 4, x, 2, 1 );
// returns 1.25

Notes

• If N <= 0, both functions return NaN.
• Accumulated intermediate values are stored as double-precision floating-point numbers.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dsmeanwd = require( '@stdlib/stats-strided-dsmeanwd' );

var x = discreteUniform( 10, -50, 50, {
    'dtype': 'float32'
});
console.log( x );

var v = dsmeanwd( x.length, x, 1 );
console.log( v );

C APIs

Usage

#include "stdlib/stats/strided/dsmeanwd.h"

stdlib_strided_dsmeanwd( N, *X, strideX )

Computes the arithmetic mean of a single-precision floating-point strided array using Welford's algorithm with extended accumulation and returning an extended precision result.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

double v = stdlib_strided_dsmeanwd( 4, x, 2 );
// returns 4.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] float* input array.
• strideX: [in] CBLAS_INT stride length for X.

double stdlib_strided_dsmeanwd( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );

stdlib_strided_dsmeanwd_ndarray( N, *X, strideX, offsetX )

Computes the arithmetic mean of a single-precision floating-point strided array using Welford's algorithm with extended accumulation and alternative indexing semantics and returning an extended precision result.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

double v = stdlib_strided_dsmeanwd_ndarray( 4, x, 2, 0 );
// returns 4.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] float* input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.

double stdlib_strided_dsmeanwd_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/stats/strided/dsmeanwd.h"
#include <stdio.h>

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

    // Specify the number of elements:
    const int N = 4;

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

    // Compute the arithmetic mean:
    double v = stdlib_strided_dsmeanwd( N, x, strideX );

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

References

• Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." Technometrics 4 (3). Taylor & Francis: 419–20. doi:10.1080/00401706.1962.10490022.
• van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." Communications of the ACM 11 (3): 149–50. doi:10.1145/362929.362961.

See Also

• @stdlib/stats-strided/dmeanwd: calculate the arithmetic mean of a double-precision floating-point strided array using Welford's algorithm.
• @stdlib/stats-strided/dsmean: calculate the arithmetic mean of a single-precision floating-point strided array using extended accumulation and returning an extended precision result.
• @stdlib/stats-strided/dsnanmeanwd: calculate the arithmetic mean of a single-precision floating-point strided array, ignoring NaN values, using Welford's algorithm with extended accumulation, and returning an extended precision result.
• @stdlib/stats-strided/meanwd: calculate the arithmetic mean of a strided array using Welford's algorithm.
• @stdlib/stats-strided/smeanwd: calculate the arithmetic mean of a single-precision floating-point strided array using Welford's algorithm.

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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