dmeanwd

Calculate the arithmetic mean of a double-precision floating-point strided array using Welford's algorithm.

The arithmetic mean is defined as

$$\mu =\frac{1}{n}\sum _{i=0}^{n-1}{x}_i$$

Usage

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

dmeanwd( N, x, strideX )

Computes the arithmetic mean of a double-precision floating-point strided array x using Welford's algorithm.

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

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

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

The function has the following parameters:

• N: number of indexed elements.
• x: input Float64Array.
• strideX: stride length for x.

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

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

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

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

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, 2.0, -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 v = dmeanwd( 4, x1, 2 );
// returns 1.25

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

Computes the arithmetic mean of a double-precision floating-point strided array using Welford's algorithm and alternative indexing semantics.

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

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

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

The function has the following additional parameters:

• offsetX: 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 element in x starting from the second element

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

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

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

Notes

• If N <= 0, both functions return NaN.

Examples

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

var x = discreteUniform( 10, -50, 50, {
    'dtype': 'float64'
});
console.log( x );

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

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C APIs

Usage

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

stdlib_strided_dmeanwd( N, *X, strideX )

Computes the arithmetic mean of a double-precision floating-point strided array using Welford's algorithm.

const double x[] = { 1.0, -2.0, 2.0 };

double v = stdlib_strided_dmeanwd( 3, x, 1 );
// returns ~0.333

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 for X.

double stdlib_strided_dmeanwd( const CBLAS_INT N, const double *X, const CBLAS_INT strideX );

stdlib_strided_dmeanwd_ndarray( N, *X, strideX, offsetX )

Computes the arithmetic mean of a double-precision floating-point strided array using Welford's algorithm and alternative indexing semantics.

const double x[] = { 1.0, -2.0, 2.0 };

double v = stdlib_strided_dmeanwd_ndarray( 3, x, 1, 0 );
// returns ~0.333

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 for X.
• offsetX: [in] CBLAS_INT starting index for X.

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

Examples

#include "stdlib/stats/strided/dmeanwd.h"
#include <stdint.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 };

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

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

    // Compute the minimum value:
    double v = stdlib_strided_dmeanwd( N, x, strideX );

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

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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.

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See Also

• @stdlib/stats/base/dmean: calculate the arithmetic mean of a double-precision floating-point strided array.
• @stdlib/stats/strided/dnanmeanwd: calculate the arithmetic mean of a double-precision floating-point strided array, using Welford's algorithm and ignoring NaN values.
• @stdlib/stats/base/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.