time-to-botec

README.md (6597B)

---

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 # smeanli
 
 > Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean 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@fcea3760d526dcb339d39f08234705c4d6e44bbf/lib/node_modules/@stdlib/stats/base/smeanli/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var smeanli = require( '@stdlib/stats/base/smeanli' );
 ```
 
 #### smeanli( N, x, stride )
 
 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x` using a one-pass trial mean algorithm.
 
 ```javascript
 var Float32Array = require( '@stdlib/array/float32' );
 
 var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
 var N = x.length;
 
 var v = smeanli( N, x, 1 );
 // returns ~0.3333
 ```
 
 The function has the following parameters:
 
 -   **N**: number of indexed elements.
 -   **x**: input [`Float32Array`][@stdlib/array/float32].
 -   **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 Float32Array = require( '@stdlib/array/float32' );
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
 var N = floor( x.length / 2 );
 
 var v = smeanli( 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 Float32Array = require( '@stdlib/array/float32' );
 var floor = require( '@stdlib/math/base/special/floor' );
 
 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 N = floor( x0.length / 2 );
 
 var v = smeanli( N, x1, 2 );
 // returns 1.25
 ```
 
 #### smeanli.ndarray( N, x, stride, offset )
 
 Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm and alternative indexing semantics.
 
 ```javascript
 var Float32Array = require( '@stdlib/array/float32' );
 
 var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
 var N = x.length;
 
 var v = smeanli.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 Float32Array = require( '@stdlib/array/float32' );
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 var N = floor( x.length / 2 );
 
 var v = smeanli.ndarray( N, x, 2, 1 );
 // returns 1.25
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   If `N <= 0`, both functions return `NaN`.
 -   The underlying algorithm is a specialized case of Welford's algorithm. Similar to the method of assumed mean, the first strided array element is used as a trial mean. The trial mean is subtracted from subsequent data values, and the average deviations used to adjust the initial guess. Accordingly, the algorithm's accuracy is best when data is **unordered** (i.e., the data is **not** sorted in either ascending or descending order such that the first value is an "extreme" value).
 
 </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 Float32Array = require( '@stdlib/array/float32' );
 var smeanli = require( '@stdlib/stats/base/smeanli' );
 
 var x;
 var i;
 
 x = new Float32Array( 10 );
 for ( i = 0; i < x.length; i++ ) {
     x[ i ] = round( (randu()*100.0) - 50.0 );
 }
 console.log( x );
 
 var v = smeanli( x.length, x, 1 );
 console.log( v );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 * * *
 
 <section class="references">
 
 ## 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][@welford:1962a].
 -   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][@vanreeken:1968a].
 -   Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154][@ling:1974a].
 
 </section>
 
 <!-- /.references -->
 
 <section class="links">
 
 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
 
 [@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32
 
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 
 [@welford:1962a]: https://doi.org/10.1080/00401706.1962.10490022
 
 [@vanreeken:1968a]: https://doi.org/10.1145/362929.362961
 
 [@ling:1974a]: https://doi.org/10.2307/2286154
 
 </section>
 
 <!-- /.links -->