<!-- @license Apache-2.0 Copyright (c) 2020 The Stdlib Authors. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # meankbn > Calculate the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm. <section class="intro"> The [arithmetic mean][arithmetic-mean] is defined as <!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> --> <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean"> <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@a4861d8b5345a07f446bcfb2bb4bef1bc8346595/lib/node_modules/@stdlib/stats/base/meankbn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean."> <br> </div> <!-- </equation> --> </section> <!-- /.intro --> <section class="usage"> ## Usage ```javascript var meankbn = require( '@stdlib/stats/base/meankbn' ); ``` #### meankbn( N, x, stride ) Computes the [arithmetic mean][arithmetic-mean] of a strided array `x` using an improved Kahan–Babuška algorithm. ```javascript var x = [ 1.0, -2.0, 2.0 ]; var N = x.length; var v = meankbn( N, x, 1 ); // returns ~0.3333 ``` The function has the following parameters: - **N**: number of indexed elements. - **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array]. - **stride**: index increment for `x`. The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`, ```javascript var floor = require( '@stdlib/math/base/special/floor' ); var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ]; var N = floor( x.length / 2 ); var v = meankbn( N, x, 2 ); // returns 1.25 ``` Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. <!-- eslint-disable stdlib/capitalized-comments --> ```javascript var Float64Array = require( '@stdlib/array/float64' ); var floor = require( '@stdlib/math/base/special/floor' ); 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 N = floor( x0.length / 2 ); var v = meankbn( N, x1, 2 ); // returns 1.25 ``` #### meankbn.ndarray( N, x, stride, offset ) Computes the [arithmetic mean][arithmetic-mean] of a strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics. ```javascript var x = [ 1.0, -2.0, 2.0 ]; var N = x.length; var v = meankbn.ndarray( N, x, 1, 0 ); // returns ~0.33333 ``` The function has the following additional parameters: - **offset**: starting index for `x`. While [`typed array`][mdn-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][arithmetic-mean] for every other value in `x` starting from the second value ```javascript var floor = require( '@stdlib/math/base/special/floor' ); var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ]; var N = floor( x.length / 2 ); var v = meankbn.ndarray( N, x, 2, 1 ); // returns 1.25 ``` </section> <!-- /.usage --> <section class="notes"> ## Notes - If `N <= 0`, both functions return `NaN`. - Depending on the environment, the typed versions ([`dmeankbn`][@stdlib/stats/base/dmeankbn], [`smeankbn`][@stdlib/stats/base/smeankbn], etc.) are likely to be significantly more performant. </section> <!-- /.notes --> <section class="examples"> ## Examples <!-- eslint no-undef: "error" --> ```javascript var randu = require( '@stdlib/random/base/randu' ); var round = require( '@stdlib/math/base/special/round' ); var Float64Array = require( '@stdlib/array/float64' ); var meankbn = require( '@stdlib/stats/base/meankbn' ); 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 = meankbn( x.length, x, 1 ); console.log( v ); ``` </section> <!-- /.examples --> * * * <section class="references"> ## 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][@neumaier:1974a]. </section> <!-- /.references --> <section class="links"> [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray [@stdlib/stats/base/dmeankbn]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dmeankbn [@stdlib/stats/base/smeankbn]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/smeankbn [@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106 </section> <!-- /.links -->