199 lines
5.5 KiB
Markdown
199 lines
5.5 KiB
Markdown
|
<!--
|
|||
|
|
|||
|
@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.
|
|||
|
|
|||
|
-->
|
|||
|
|
|||
|
# dmeankbn
|
|||
|
|
|||
|
> Calculate the [arithmetic mean][arithmetic-mean] of a double-precision floating-point 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@195c6d0df4074a7fb40f55cc6bc541f7b70125e7/lib/node_modules/@stdlib/stats/base/dmeankbn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
|
|||
|
<br>
|
|||
|
</div>
|
|||
|
|
|||
|
<!-- </equation> -->
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
<!-- /.intro -->
|
|||
|
|
|||
|
<section class="usage">
|
|||
|
|
|||
|
## Usage
|
|||
|
|
|||
|
```javascript
|
|||
|
var dmeankbn = require( '@stdlib/stats/base/dmeankbn' );
|
|||
|
```
|
|||
|
|
|||
|
#### dmeankbn( N, x, stride )
|
|||
|
|
|||
|
Computes the [arithmetic mean][arithmetic-mean] of a double-precision floating-point strided array `x` using an improved Kahan–Babuška algorithm.
|
|||
|
|
|||
|
```javascript
|
|||
|
var Float64Array = require( '@stdlib/array/float64' );
|
|||
|
|
|||
|
var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
|
|||
|
var N = x.length;
|
|||
|
|
|||
|
var v = dmeankbn( N, x, 1 );
|
|||
|
// returns ~0.3333
|
|||
|
```
|
|||
|
|
|||
|
The function has the following parameters:
|
|||
|
|
|||
|
- **N**: number of indexed elements.
|
|||
|
- **x**: input [`Float64Array`][@stdlib/array/float64].
|
|||
|
- **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 Float64Array = require( '@stdlib/array/float64' );
|
|||
|
var floor = require( '@stdlib/math/base/special/floor' );
|
|||
|
|
|||
|
var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
|
|||
|
var N = floor( x.length / 2 );
|
|||
|
|
|||
|
var v = dmeankbn( 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 = dmeankbn( N, x1, 2 );
|
|||
|
// returns 1.25
|
|||
|
```
|
|||
|
|
|||
|
#### dmeankbn.ndarray( N, x, stride, offset )
|
|||
|
|
|||
|
Computes the [arithmetic mean][arithmetic-mean] of a double-precision floating-point strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics.
|
|||
|
|
|||
|
```javascript
|
|||
|
var Float64Array = require( '@stdlib/array/float64' );
|
|||
|
|
|||
|
var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
|
|||
|
var N = x.length;
|
|||
|
|
|||
|
var v = dmeankbn.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 Float64Array = require( '@stdlib/array/float64' );
|
|||
|
var floor = require( '@stdlib/math/base/special/floor' );
|
|||
|
|
|||
|
var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
|
|||
|
var N = floor( x.length / 2 );
|
|||
|
|
|||
|
var v = dmeankbn.ndarray( N, x, 2, 1 );
|
|||
|
// returns 1.25
|
|||
|
```
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
<!-- /.usage -->
|
|||
|
|
|||
|
<section class="notes">
|
|||
|
|
|||
|
## Notes
|
|||
|
|
|||
|
- If `N <= 0`, both functions return `NaN`.
|
|||
|
|
|||
|
</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 dmeankbn = require( '@stdlib/stats/base/dmeankbn' );
|
|||
|
|
|||
|
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 = dmeankbn( 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
|
|||
|
|
|||
|
[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64
|
|||
|
|
|||
|
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
|
|||
|
|
|||
|
[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
<!-- /.links -->
|