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44 changes: 16 additions & 28 deletions lib/node_modules/@stdlib/stats/base/variance/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -98,7 +98,7 @@ The use of the term `n-1` is commonly referred to as Bessel's correction. Note,
var variance = require( '@stdlib/stats/base/variance' );
```

#### variance( N, correction, x, stride )
#### variance( N, correction, x, strideX )

Computes the [variance][variance] of a strided array `x`.

Expand All @@ -115,17 +115,14 @@ The function has the following parameters:
- **N**: number of indexed elements.
- **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
- **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 [variance][variance] of every other element in `x`,
The `N` and strideX parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [variance][variance] 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 = variance( N, 1, x, 2 );
var v = variance( 4, 1, x, 2 );
// returns 6.25
```

Expand All @@ -135,18 +132,15 @@ 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 = variance( N, 1, x1, 2 );
var v = variance( 4, 1, x1, 2 );
// returns 6.25
```

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

Computes the [variance][variance] of a strided array using alternative indexing semantics.

Expand All @@ -160,17 +154,14 @@ var v = variance.ndarray( N, 1, x, 1, 0 );

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 [variance][variance] 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 [variance][variance] for every other element in the strided array 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 = variance.ndarray( N, 1, x, 2, 1 );
var v = variance.ndarray( 4, 1, x, 2, 1 );
// returns 6.25
```

Expand All @@ -183,6 +174,7 @@ var v = variance.ndarray( N, 1, 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]).
- If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.
- Depending on the environment, the typed versions ([`dvariance`][@stdlib/stats/base/dvariance], [`svariance`][@stdlib/stats/base/svariance], etc.) are likely to be significantly more performant.

Expand All @@ -197,18 +189,12 @@ var v = variance.ndarray( N, 1, 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 variance = require( '@stdlib/stats/base/variance' );

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 = variance( x.length, 1, x, 1 );
Expand Down Expand Up @@ -250,6 +236,8 @@ console.log( v );

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

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

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

<!-- <related-links> -->
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -21,11 +21,18 @@
// 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 variance = require( './../lib/variance.js' );
var variance = require( './../lib/main.js' );


// VARIABLES //

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


// FUNCTIONS //
Expand All @@ -38,13 +45,7 @@ var variance = require( './../lib/variance.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 variance = require( './../lib/ndarray.js' );


// VARIABLES //

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


// FUNCTIONS //

/**
Expand All @@ -38,13 +45,7 @@ var variance = 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
30 changes: 14 additions & 16 deletions lib/node_modules/@stdlib/stats/base/variance/docs/repl.txt
Original file line number Diff line number Diff line change
@@ -1,9 +1,9 @@

{{alias}}( N, correction, x, stride )
{{alias}}( N, correction, x, strideX )
Computes the variance of a strided array.

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

Indexing is relative to the first index. To introduce an offset, use a typed
array view.
Expand All @@ -30,8 +30,8 @@
x: Array<number>|TypedArray
Input array.

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

Returns
-------
Expand All @@ -45,22 +45,21 @@
> {{alias}}( x.length, 1, x, 1 )
~4.3333

// 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, 1, x, stride )
> {{alias}}( 3, 1, x, 2 )
~4.3333

// 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, 1, x1, stride )
> {{alias}}( 3, 1, x1, 2 )
~4.3333

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

{{alias}}.ndarray( N, correction, x, strideX, offsetX )
Computes the variance of a strided array using alternative indexing
semantics.

Expand Down Expand Up @@ -88,10 +87,10 @@
x: Array<number>|TypedArray
Input array.

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

offset: integer
offsetX: integer
Starting index.

Returns
Expand All @@ -108,8 +107,7 @@

// 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, 1, x, 2, 1 )
> {{alias}}.ndarray( 3, 1, x, 2, 1 )
~4.3333

See Also
Expand Down
17 changes: 11 additions & 6 deletions lib/node_modules/@stdlib/stats/base/variance/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 `variance`.
Expand All @@ -32,7 +37,7 @@ interface Routine {
* @param N - number of indexed elements
* @param correction - degrees of freedom adjustment
* @param x - input array
* @param stride - stride length
* @param strideX - stride length
* @returns variance
*
* @example
Expand All @@ -41,16 +46,16 @@ interface Routine {
* var v = variance( x.length, 1, x, 1 );
* // returns ~4.3333
*/
( N: number, correction: number, x: NumericArray, stride: number ): number;
( N: number, correction: number, x: InputArray, strideX: number ): number;

/**
* Computes the variance of a strided array using alternative indexing semantics.
*
* @param N - number of indexed elements
* @param correction - degrees of freedom adjustment
* @param x - input array
* @param stride - stride length
* @param offset - starting index
* @param strideX - stride length
* @param offsetX - starting index
* @returns variance
*
* @example
Expand All @@ -68,7 +73,7 @@ interface Routine {
* @param N - number of indexed elements
* @param correction - degrees of freedom adjustment
* @param x - input array
* @param stride - stride length
* @param strideX - stride length
* @returns variance
*
* @example
Expand Down
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 variance = require( './index' );


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

variance( x.length, 1, x, 1 ); // $ExpectType number
variance( x.length, 1, 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 @@ -101,6 +103,7 @@ import variance = require( './index' );
const x = new Float64Array( 10 );

variance.ndarray( x.length, 1, x, 1, 0 ); // $ExpectType number
variance.ndarray( x.length, 1, 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/variance/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 variance = 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 = variance( x.length, 1, x, 1 );
Expand Down
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