smeanwd

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

The arithmetic mean is defined as

mu equals StartFraction 1 Over n EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts x Subscript i

Usage

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

smeanwd( N, x, strideX )

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

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

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

var v = smeanwd( 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 the strided array 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 = smeanwd( 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 = smeanwd( 4, x1, 2 );
// returns 1.25

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

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

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

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

var v = smeanwd.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 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 = smeanwd.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 smeanwd = require( '@stdlib/stats/base/smeanwd' );

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

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

C APIs

Usage

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

stdlib_strided_smeanwd( N, *X, strideX )

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

const float x[] = { 1.0f, 2.0f, 3.0f };

float v = stdlib_strided_smeanwd( 3, x, 1 );
// returns 2.0f

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.
float stdlib_strided_smeanwd( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );

stdlib_strided_smeanwd_ndarray( N, *X, strideX, offsetX )

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

const float x[] = { 1.0f, 2.0f, 3.0f };

float v = stdlib_strided_smeanwd_ndarray( 4, x, 1, 0 );
// returns 2.0f

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.
float stdlib_strided_smeanwd_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/stats/base/smeanwd.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:
    float v = stdlib_strided_smeanwd( N, x, strideX );

    // Print the result:
    printf( "mean: %f\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

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