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Calculate the arithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm.

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smeankbn

Calculate thearithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm.

Thearithmetic mean is defined as

$$\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i$$

Installation

npm install @stdlib/stats-base-smeankbn

Alternatively,

To load the package in a website via ascript tag without installation and bundlers, use theES Module available on theesm branch (seeREADME).
If you are using Deno, visit thedeno branch (seeREADME for usage intructions).
For use in Observable, or in browser/node environments, use theUniversal Module Definition (UMD) build available on theumd branch (seeREADME).

Thebranches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

varsmeankbn=require('@stdlib/stats-base-smeankbn');

smeankbn( N, x, strideX )

Computes thearithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm.

varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([1.0,-2.0,2.0]);varv=smeankbn(x.length,x,1);// returns ~0.3333

The function has the following parameters:

N: number of indexed elements.
x: inputFloat32Array.
strideX: stride length forx.

TheN and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute thearithmetic mean of every other element inx,

varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([1.0,2.0,2.0,-7.0,-2.0,3.0,4.0,2.0]);varv=smeankbn(4,x,2);// returns 1.25

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

varFloat32Array=require('@stdlib/array-float32');varx0=newFloat32Array([2.0,1.0,2.0,-2.0,-2.0,2.0,3.0,4.0]);varx1=newFloat32Array(x0.buffer,x0.BYTES_PER_ELEMENT*1);// start at 2nd elementvarv=smeankbn(4,x1,2);// returns 1.25

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

Computes thearithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics.

varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([1.0,-2.0,2.0]);varv=smeankbn.ndarray(x.length,x,1,0);// returns ~0.33333

The function has the following additional parameters:

offsetX: starting index forx.

Whiletyped 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 thearithmetic mean for every other element inx starting from the second element

varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([2.0,1.0,2.0,-2.0,-2.0,2.0,3.0,4.0]);varv=smeankbn.ndarray(4,x,2,1);// returns 1.25

Notes

IfN <= 0, both functions returnNaN.

Examples

vardiscreteUniform=require('@stdlib/random-array-discrete-uniform');varsmeankbn=require('@stdlib/stats-base-smeankbn');varx=discreteUniform(10,-50,50,{'dtype':'float32'});console.log(x);varv=smeankbn(x.length,x,1);console.log(v);

C APIs

Usage

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

stdlib_strided_smeankbn( N, *X, strideX )

Computes thearithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm.

constfloatx[]= {1.0f,2.0f,3.0f,4.0f,5.0f,6.0f,7.0f,8.0f };floatv=stdlib_strided_smeankbn(4,x,2 );// returns 4.0f

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 forX.

floatstdlib_strided_smeankbn(constCBLAS_INTN,constfloat*X,constCBLAS_INTstrideX );

stdlib_strided_smeankbn_ndarray( N, *X, strideX, offsetX )

Computes thearithmetic mean of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics.

constfloatx[]= {1.0f,2.0f,3.0f,4.0f,5.0f,6.0f,7.0f,8.0f };floatv=stdlib_strided_smeankbn_ndarray(4,x,2,0 );// returns 4.0f

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 forX.
offsetX:[in] CBLAS_INT starting index forX.

floatstdlib_strided_smeankbn_ndarray(constCBLAS_INTN,constfloat*X,constCBLAS_INTstrideX,constCBLAS_INToffsetX );

Examples

#include"stdlib/stats/base/smeankbn.h"#include<stdio.h>intmain(void ) {// Create a strided array:constfloatx[]= {1.0f,2.0f,3.0f,4.0f,5.0f,6.0f,7.0f,8.0f };// Specify the number of elements:constintN=4;// Specify the stride length:constintstrideX=2;// Compute the arithmetic mean:floatv=stdlib_strided_smeankbn(N,x,strideX );// Print the result:printf("mean: %f\n",v );}

References

Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums."Zeitschrift Für Angewandte Mathematik Und Mechanik 54 (1): 39–51. doi:10.1002/zamm.19740540106.

Notice

This package is part ofstdlib, 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 developstdlib, see the main projectrepository.