Skip to content

Refactor variancetk #5926

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
wants to merge 5 commits into
base: develop
Choose a base branch
from
Open
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
44 changes: 16 additions & 28 deletions lib/node_modules/@stdlib/stats/base/variancetk/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 variancetk = require( '@stdlib/stats/base/variancetk' );
```

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

Computes the [variance][variance] of a strided array `x` using a one-pass textbook algorithm.

Expand All @@ -114,17 +114,14 @@ 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 stride 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 = variancetk( N, 1, x, 2 );
var v = variancetk( 4, 1, x, 2 );
// returns 6.25
```

Expand All @@ -134,18 +131,15 @@ 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 = variancetk( N, 1, x1, 2 );
var v = variancetk( 4, 1, x1, 2 );
// returns 6.25
```

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

Computes the [variance][variance] of a strided array using a one-pass textbook algorithm and alternative indexing semantics.

Expand All @@ -158,17 +152,14 @@ var v = variancetk.ndarray( x.length, 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 element value 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 = variancetk.ndarray( N, 1, x, 2, 1 );
var v = variancetk.ndarray( 4, 1, x, 2, 1 );
// returns 6.25
```

Expand All @@ -181,6 +172,7 @@ var v = variancetk.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`.
- Some caution should be exercised when using the one-pass textbook algorithm. Literature overwhelmingly discourages the algorithm's use for two reasons: 1) the lack of safeguards against underflow and overflow and 2) the risk of catastrophic cancellation when subtracting the two sums if the sums are large and the variance small. These concerns have merit; however, the one-pass textbook algorithm should not be dismissed outright. For data distributions with a moderately large standard deviation to mean ratio (i.e., **coefficient of variation**), the one-pass textbook algorithm may be acceptable, especially when performance is paramount and some precision loss is acceptable (including a risk of returning a negative variance due to floating-point rounding errors!). In short, no single "best" algorithm for computing the variance exists. The "best" algorithm depends on the underlying data distribution, your performance requirements, and your minimum precision requirements. When evaluating which algorithm to use, consider the relative pros and cons, and choose the algorithm which best serves your needs.
- Depending on the environment, the typed versions ([`dvariancetk`][@stdlib/stats/base/dvariancetk], [`svariancetk`][@stdlib/stats/base/svariancetk], etc.) are likely to be significantly more performant.
Expand All @@ -196,18 +188,12 @@ var v = variancetk.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 variancetk = require( '@stdlib/stats/base/variancetk' );

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 = variancetk( x.length, 1, x, 1 );
Expand Down Expand Up @@ -257,6 +243,8 @@ console.log( v );

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

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

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

[@ling:1974a]: https://doi.org/10.2307/2286154
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 variancetk = require( './../lib/variancetk.js' );
var variancetk = require( './../lib/main.js' );


// VARIABLES //

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


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


// VARIABLES //

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


// FUNCTIONS //

/**
Expand All @@ -38,13 +45,7 @@ var variancetk = 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/variancetk/docs/repl.txt
Original file line number Diff line number Diff line change
@@ -1,10 +1,10 @@

{{alias}}( N, correction, x, stride )
{{alias}}( N, correction, x, strideX )
Computes the variance of a strided array using a one-pass textbook
algorithm.

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 at runtime.

Indexing is relative to the first index. To introduce an offset, use a typed
array view.
Expand All @@ -31,8 +31,8 @@
x: Array<number>|TypedArray
Input array.

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

Returns
-------
Expand All @@ -46,22 +46,21 @@
> {{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 a one-pass textbook algorithm
and alternative indexing semantics.

Expand Down Expand Up @@ -89,10 +88,10 @@
x: Array<number>|TypedArray
Input array.

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

offset: integer
offsetX: integer
Starting index.

Returns
Expand All @@ -109,8 +108,7 @@

// 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
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 `variancetk`.
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 = variancetk( 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 a one-pass textbook algorithm and 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 variancetk = require( './index' );


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

variancetk( x.length, 1, x, 1 ); // $ExpectType number
variancetk( 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 variancetk = require( './index' );
const x = new Float64Array( 10 );

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