time-to-botec/squiggle/node_modules/@stdlib/stats/base/dsnanmeanpn/README.md

<!--

@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.

-->

# dsnanmeanpn

> Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array, ignoring `NaN` values, using a two-pass error correction algorithm with extended accumulation, and returning an extended precision result.

<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@82d9e19462d218125d72a829a523c81f20e43234/lib/node_modules/@stdlib/stats/base/dsnanmeanpn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var dsnanmeanpn = require( '@stdlib/stats/base/dsnanmeanpn' );
```

#### dsnanmeanpn( N, x, stride )

Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x`, ignoring `NaN` values, using a two-pass error correction algorithm with extended accumulation, and returning an extended precision result.

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

var x = new Float32Array( [ 1.0, -2.0, NaN, 2.0 ] );
var N = x.length;

var v = dsnanmeanpn( 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, NaN ] );
var N = floor( x.length / 2 );

var v = dsnanmeanpn( 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, NaN ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var N = floor( x0.length / 2 );

var v = dsnanmeanpn( N, x1, 2 );
// returns 1.25
```

#### dsnanmeanpn.ndarray( N, x, stride, offset )

Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array, ignoring `NaN` values and using a two-pass error correction algorithm with extended accumulation and alternative indexing semantics.

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

var x = new Float32Array( [ 1.0, -2.0, NaN, 2.0 ] );
var N = x.length;

var v = dsnanmeanpn.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, NaN ] );
var N = floor( x.length / 2 );

var v = dsnanmeanpn.ndarray( N, x, 2, 1 );
// returns 1.25
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `NaN`.
-   If every indexed element is `NaN`, both functions return `NaN`.
-   Accumulated intermediate values are stored as double-precision floating-point numbers.

</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 dsnanmeanpn = require( '@stdlib/stats/base/dsnanmeanpn' );

var x;
var i;

x = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    if ( randu() < 0.2 ) {
        x[ i ] = NaN;
    } else {
        x[ i ] = round( (randu()*100.0) - 50.0 );
    }
}
console.log( x );

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

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958][@neely:1966a].
-   Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036][@schubert:2018a].

</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

[@neely:1966a]: https://doi.org/10.1145/365719.365958

[@schubert:2018a]: https://doi.org/10.1145/3221269.3223036

</section>

<!-- /.links -->