dmeanpn

Calculate the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm.

The arithmetic mean is defined as

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

Usage

var dmeanpn = require( '@stdlib/stats/base/dmeanpn' );

dmeanpn( N, x, strideX )

Computes the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm.

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

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

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

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

Computes the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm and alternative indexing semantics.

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

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

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

Notes

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var dmeanpn = require( '@stdlib/stats/base/dmeanpn' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( (randu()*100.0) - 50.0 );
}
console.log( x );

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

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C APIs

Usage

#include "stdlib/stats/base/dmeanpn.h"

stdlib_strided_dmeanpn( N, *X, strideX )

Computes the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm.

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

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

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 for X.

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

stdlib_strided_dmeanpn_ndarray( N, *X, strideX, offsetX )

Computes the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm and alternative indexing semantics.

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

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

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

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

Examples

#include "stdlib/stats/base/dmeanpn.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 arithmetic mean:
    double v = stdlib_strided_dmeanpn( N, x, strideX );

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

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References

• Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." Communications of the ACM 9 (7). Association for Computing Machinery: 496–99. doi:10.1145/365719.365958.
• Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In Proceedings of the 30th International Conference on Scientific and Statistical Database Management. New York, NY, USA: Association for Computing Machinery. doi:10.1145/3221269.3223036.

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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/dnanmeanpn: calculate the arithmetic mean of a double-precision floating-point strided array, ignoring NaN values and using a two-pass error correction algorithm.
• @stdlib/stats/base/meanpn: calculate the arithmetic mean of a strided array using a two-pass error correction algorithm.
• @stdlib/stats/base/smeanpn: calculate the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm.