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52 changes: 19 additions & 33 deletions lib/node_modules/@stdlib/stats/base/meanpw/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -51,33 +51,29 @@ The [arithmetic mean][arithmetic-mean] is defined as
var meanpw = require( '@stdlib/stats/base/meanpw' );
```

#### meanpw( N, x, stride )
#### meanpw( N, x, strideX )

Computes the [arithmetic mean][arithmetic-mean] of a strided array `x` using pairwise summation.
Computes the [arithmetic mean][arithmetic-mean] of a strided array using pairwise summation.

```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

var v = meanpw( N, x, 1 );
var v = meanpw( x.length, 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`.
- **strideX**: stride length 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`,
The `N` and stride parameters determine which elements in the strided array 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 = meanpw( N, x, 2 );
var v = meanpw( 4, x, 2 );
// returns 1.25
```

Expand All @@ -87,42 +83,35 @@ Note that indexing is relative to the first index. To introduce an offset, use [

```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 = meanpw( N, x1, 2 );
var v = meanpw( 4, x1, 2 );
// returns 1.25
```

#### meanpw.ndarray( N, x, stride, offset )
#### meanpw.ndarray( N, x, strideX, offsetX )

Computes the [arithmetic mean][arithmetic-mean] of a strided array using pairwise summation and alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

var v = meanpw.ndarray( N, x, 1, 0 );
var v = meanpw.ndarray( x.length, x, 1, 0 );
// returns ~0.33333
```

The function has the following additional parameters:

- **offset**: starting index for `x`.
- **offsetX**: 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
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 element in `x` starting from the second element

```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 = meanpw.ndarray( N, x, 2, 1 );
var v = meanpw.ndarray( 4, x, 2, 1 );
// returns 1.25
```

Expand All @@ -135,6 +124,7 @@ var v = meanpw.ndarray( N, x, 2, 1 );
## Notes

- If `N <= 0`, both functions return `NaN`.
- Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
- In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
- Depending on the environment, the typed versions ([`dmeanpw`][@stdlib/stats/strided/dmeanpw], [`smeanpw`][@stdlib/stats/strided/smeanpw], etc.) are likely to be significantly more performant.

Expand All @@ -149,18 +139,12 @@ var v = meanpw.ndarray( N, x, 2, 1 );
<!-- 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var meanpw = require( '@stdlib/stats/base/meanpw' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0) - 50.0 );
}
var x = discreteUniform( 10, -50, 50, {
'dtype': 'float64'
});
console.log( x );

var v = meanpw( x.length, x, 1 );
Expand Down Expand Up @@ -211,6 +195,8 @@ console.log( v );

[@higham:1993a]: https://doi.org/10.1137/0914050

[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor

<!-- <related-links> -->

[@stdlib/stats/strided/dmeanpw]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/strided/dmeanpw
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -21,13 +21,20 @@
// MODULES //

var bench = require( '@stdlib/bench' );
var randu = require( '@stdlib/random/base/randu' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pow = require( '@stdlib/math/base/special/pow' );
var pkg = require( './../package.json' ).name;
var meanpw = require( './../lib/meanpw.js' );


// VARIABLES //

var options = {
'dtype': 'generic'
};


// FUNCTIONS //

/**
Expand All @@ -38,13 +45,7 @@ var meanpw = require( './../lib/meanpw.js' );
* @returns {Function} benchmark function
*/
function createBenchmark( len ) {
var x;
var i;

x = [];
for ( i = 0; i < len; i++ ) {
x.push( ( randu()*20.0 ) - 10.0 );
}
var x = uniform( len, -10, 10, options );
return benchmark;

function benchmark( b ) {
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -21,13 +21,20 @@
// MODULES //

var bench = require( '@stdlib/bench' );
var randu = require( '@stdlib/random/base/randu' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pow = require( '@stdlib/math/base/special/pow' );
var pkg = require( './../package.json' ).name;
var meanpw = require( './../lib/ndarray.js' );


// VARIABLES //

var options = {
'dtype': 'generic'
};


// FUNCTIONS //

/**
Expand All @@ -38,13 +45,7 @@ var meanpw = require( './../lib/ndarray.js' );
* @returns {Function} benchmark function
*/
function createBenchmark( len ) {
var x;
var i;

x = [];
for ( i = 0; i < len; i++ ) {
x.push( ( randu()*20.0 ) - 10.0 );
}
var x = uniform( len, -10, 10, options );
return benchmark;

function benchmark( b ) {
Expand Down
32 changes: 14 additions & 18 deletions lib/node_modules/@stdlib/stats/base/meanpw/docs/repl.txt
Original file line number Diff line number Diff line change
@@ -1,12 +1,12 @@

{{alias}}( N, x, stride )
{{alias}}( N, x, strideX )
Computes the arithmetic mean of a strided array using pairwise summation.

The `N` and `stride` parameters determine which elements in `x` are accessed
at runtime.

Indexing is relative to the first index. To introduce an offset, use a typed
array view.
The `N` and stride parameters determine which elements in the strided array
are accessed at runtime.

If `N <= 0`, the function returns `NaN`.

Expand All @@ -18,8 +18,8 @@
x: Array<number>|TypedArray
Input array.

stride: integer
Index increment.
strideX: integer
Stride length.

Returns
-------
Expand All @@ -33,22 +33,19 @@
> {{alias}}( x.length, x, 1 )
~0.3333

// Using `N` and `stride` parameters:
// Using `N` and stride parameters:
> x = [ -2.0, 1.0, 1.0, -5.0, 2.0, -1.0 ];
> var N = {{alias:@stdlib/math/base/special/floor}}( x.length / 2 );
> var stride = 2;
> {{alias}}( N, x, stride )
> {{alias}}( 3, x, 2 )
~0.3333

// Using view offsets:
> var x0 = new {{alias:@stdlib/array/float64}}( [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ] );
> var x1 = new {{alias:@stdlib/array/float64}}( x0.buffer, x0.BYTES_PER_ELEMENT*1 );
> N = {{alias:@stdlib/math/base/special/floor}}( x0.length / 2 );
> stride = 2;
> {{alias}}( N, x1, stride )
> {{alias}}( 3, x1, 2 )
~-0.3333

{{alias}}.ndarray( N, x, stride, offset )

{{alias}}.ndarray( N, x, strideX, offsetX )
Computes the arithmetic mean of a strided array using pairwise summation and
alternative indexing semantics.

Expand All @@ -64,10 +61,10 @@
x: Array<number>|TypedArray
Input array.

stride: integer
Index increment.
strideX: integer
Stride length.

offset: integer
offsetX: integer
Starting index.

Returns
Expand All @@ -84,8 +81,7 @@

// Using offset parameter:
> var x = [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ];
> var N = {{alias:@stdlib/math/base/special/floor}}( x.length / 2 );
> {{alias}}.ndarray( N, x, 2, 1 )
> {{alias}}.ndarray( 3, x, 2, 1 )
~-0.3333

See Also
Expand Down
19 changes: 12 additions & 7 deletions lib/node_modules/@stdlib/stats/base/meanpw/docs/types/index.d.ts
Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,12 @@

/// <reference types="@stdlib/types"/>

import { NumericArray } from '@stdlib/types/array';
import { NumericArray, Collection, AccessorArrayLike } from '@stdlib/types/array';

/**
* Input array.
*/
type InputArray = NumericArray | Collection<number> | AccessorArrayLike<number>;

/**
* Interface describing `meanpw`.
Expand All @@ -31,7 +36,7 @@ interface Routine {
*
* @param N - number of indexed elements
* @param x - input array
* @param stride - stride length
* @param strideX - stride length
* @returns arithmetic mean
*
* @example
Expand All @@ -40,15 +45,15 @@ interface Routine {
* var v = meanpw( x.length, x, 1 );
* // returns ~0.3333
*/
( N: number, x: NumericArray, stride: number ): number;
( N: number, x: InputArray, strideX: number ): number;

/**
* Computes the arithmetic mean of a strided array using pairwise summation and alternative indexing semantics.
*
* @param N - number of indexed elements
* @param x - input array
* @param stride - stride length
* @param offset - starting index
* @param strideX - stride length
* @param offsetX - starting index
* @returns arithmetic mean
*
* @example
Expand All @@ -57,15 +62,15 @@ interface Routine {
* var v = meanpw.ndarray( x.length, x, 1, 0 );
* // returns ~0.3333
*/
ndarray( N: number, x: NumericArray, stride: number, offset: number ): number;
ndarray( N: number, x: InputArray, strideX: number, offsetX: number ): number;
}

/**
* Computes the arithmetic mean of a strided array using pairwise summation.
*
* @param N - number of indexed elements
* @param x - input array
* @param stride - stride length
* @param strideX - stride length
* @returns arithmetic mean
*
* @example
Expand Down
3 changes: 3 additions & 0 deletions lib/node_modules/@stdlib/stats/base/meanpw/docs/types/test.ts
Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,7 @@
* limitations under the License.
*/

import AccessorArray = require( '@stdlib/array/base/accessor' );
import meanpw = require( './index' );


Expand All @@ -26,6 +27,7 @@ import meanpw = require( './index' );
const x = new Float64Array( 10 );

meanpw( x.length, x, 1 ); // $ExpectType number
meanpw( x.length, new AccessorArray( x ), 1 ); // $ExpectType number
}

// The compiler throws an error if the function is provided a first argument which is not a number...
Expand Down Expand Up @@ -85,6 +87,7 @@ import meanpw = require( './index' );
const x = new Float64Array( 10 );

meanpw.ndarray( x.length, x, 1, 0 ); // $ExpectType number
meanpw.ndarray( x.length, new AccessorArray( x ), 1, 0 ); // $ExpectType number
}

// The compiler throws an error if the `ndarray` method is provided a first argument which is not a number...
Expand Down
14 changes: 4 additions & 10 deletions lib/node_modules/@stdlib/stats/base/meanpw/examples/index.js
Original file line number Diff line number Diff line change
Expand Up @@ -18,18 +18,12 @@

'use strict';

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var meanpw = require( './../lib' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0) - 50.0 );
}
var x = discreteUniform( 10, -50, 50, {
'dtype': 'float64'
});
console.log( x );

var v = meanpw( x.length, x, 1 );
Expand Down
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