stats-strided-dstdevtk

Calculate the standard deviation of a double-precision floating-point strided array using a one-pass textbook algorithm.

https://github.com/stdlib-js/stats-strided-dstdevtk

Science Score: 57.0%

This score indicates how likely this project is to be science-related based on various indicators:

✓
CITATION.cff file
Found CITATION.cff file
✓
codemeta.json file
Found codemeta.json file
✓
.zenodo.json file
Found .zenodo.json file
✓
DOI references
Found 3 DOI reference(s) in README
○
Academic publication links
○
Academic email domains
○
Institutional organization owner
○
JOSS paper metadata
○
Scientific vocabulary similarity
Low similarity (14.2%) to scientific vocabulary

Keywords

deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation spread standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

Last synced: 4 months ago · JSON representation ·

Repository

Calculate the standard deviation of a double-precision floating-point strided array using a one-pass textbook algorithm.

Basic Info

Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 919 KB

Statistics

Stars: 0
Watchers: 2
Forks: 0
Open Issues: 0
Releases: 0

Topics

deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation spread standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

Created 10 months ago · Last pushed 5 months ago

Metadata Files

Readme Changelog Contributing License Code of conduct Citation Security

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

dstdevtk

Calculate the standard deviation of a double-precision floating-point strided array using a one-pass textbook algorithm.

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by ```math \sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} ``` where the population mean is given by ```math \mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i ``` Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`, ```math s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} ``` where the sample mean is given by ```math \bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i ``` The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.

## Installation ```bash npm install @stdlib/stats-strided-dstdevtk ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage ```javascript var dstdevtk = require( '@stdlib/stats-strided-dstdevtk' ); ``` #### dstdevtk( N, correction, x, strideX ) Computes the [standard deviation][standard-deviation] of a double-precision floating-point strided array `x` using a one-pass textbook algorithm. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); var v = dstdevtk( x.length, 1.0, x, 1 ); // returns ~2.0817 ``` 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 [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] 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 corrected sample [standard deviation][standard-deviation], 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 [`Float64Array`][@stdlib/array/float64]. - **strideX**: stride length for `x`. The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [standard deviation][standard-deviation] of every other element in `x`, ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] ); var v = dstdevtk( 4, 1.0, x, 2 ); // returns 2.5 ``` Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. ```javascript var Float64Array = require( '@stdlib/array-float64' ); 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 v = dstdevtk( 4, 1.0, x1, 2 ); // returns 2.5 ``` #### dstdevtk.ndarray( N, correction, x, strideX, offsetX ) Computes the [standard deviation][standard-deviation] of a double-precision floating-point strided array using a one-pass textbook algorithm and alternative indexing semantics. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); var v = dstdevtk.ndarray( x.length, 1.0, x, 1, 0 ); // returns ~2.0817 ``` The function has the following additional parameters: - **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 [standard deviation][standard-deviation] for every other element in `x` starting from the second element ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); var v = dstdevtk.ndarray( 4, 1.0, x, 2, 1 ); // returns 2.5 ```

## Notes - If `N <= 0`, both functions return `NaN`. - 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 computing a negative variance due to floating-point rounding errors!). In short, no single "best" algorithm for computing the standard deviation 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.

## Examples ```javascript var discreteUniform = require( '@stdlib/random-array-discrete-uniform' ); var dstdevtk = require( '@stdlib/stats-strided-dstdevtk' ); var x = discreteUniform( 10, -50, 50, { 'dtype': 'float64' }); console.log( x ); var v = dstdevtk( x.length, 1.0, x, 1 ); console.log( v ); ```

## C APIs

### Usage ```c #include "stdlib/stats/strided/dstdevtk.h" ``` #### stdlib_strided_dstdevtk( N, correction, \*X, strideX ) Computes the [standard deviation][standard-deviation] of a double-precision floating-point strided array using a one-pass textbook algorithm. ```c const double x[] = { 1.0, -2.0, 2.0 }; double v = stdlib_strided_dstdevtk( 3, 1.0, x, 1 ); // returns ~2.0817 ``` The function accepts the following arguments: - **N**: `[in] CBLAS_INT` number of indexed elements. - **correction**: `[in] double` 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 [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] 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 corrected sample [standard deviation][standard-deviation], 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**: `[in] double*` input array. - **strideX**: `[in] CBLAS_INT` stride length for `X`. ```c double stdlib_strided_dstdevtk( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX ); ``` #### stdlib_strided_dstdevtk_ndarray( N, correction, \*X, strideX, offsetX ) Computes the [standard deviation][standard-deviation] of a double-precision floating-point strided array using a one-pass textbook algorithm and alternative indexing semantics. ```c const double x[] = { 1.0, -2.0, 2.0 }; double v = stdlib_strided_dstdevtk_ndarray( 3, 1.0, x, 1, 0 ); // returns ~2.0817 ``` The function accepts the following arguments: - **N**: `[in] CBLAS_INT` number of indexed elements. - **correction**: `[in] double` 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 [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] 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 corrected sample [standard deviation][standard-deviation], 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**: `[in] double*` input array. - **strideX**: `[in] CBLAS_INT` stride length for `X`. - **offsetX**: `[in] CBLAS_INT` starting index for `X`. ```c double stdlib_strided_dstdevtk_ndarray( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX ); ```

### Examples ```c #include "stdlib/stats/strided/dstdevtk.h" #include int main( void ) { // Create a strided array: const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 }; // Specify the number of elements: const int N = 4; // Specify the stride length: const int strideX = 2; // Compute the variance: double v = stdlib_strided_dstdevtk( N, 1.0, x, strideX ); // Print the result: printf( "sample standard deviation: %lf\n", v ); } ```

## References - Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154][@ling:1974a].

* * * ## Notice This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more. For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

Owner

Name: stdlib
Login: stdlib-js
Kind: organization

Website: https://stdlib.io
Twitter: stdlibjs
Repositories: 3,692
Profile: https://github.com/stdlib-js

Standard library for JavaScript.

Citation (CITATION.cff)

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
  metadata from this file.

type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

GitHub Events

Total

Member event: 1
Push event: 25
Create event: 6

Last Year

Member event: 1
Push event: 25
Create event: 6

Issues and Pull Requests

Last synced: 10 months ago

All Time

Total issues: 0
Total pull requests: 0
Average time to close issues: N/A
Average time to close pull requests: N/A
Total issue authors: 0
Total pull request authors: 0
Average comments per issue: 0
Average comments per pull request: 0
Merged pull requests: 0
Bot issues: 0
Bot pull requests: 0

Past Year

Issues: 0
Pull requests: 0
Average time to close issues: N/A
Average time to close pull requests: N/A
Issue authors: 0
Pull request authors: 0
Average comments per issue: 0
Average comments per pull request: 0
Merged pull requests: 0
Bot issues: 0
Bot pull requests: 0

View more stats

Top Authors

Issue Authors

Pull Request Authors

Top Labels

Issue Labels

Pull Request Labels

Dependencies

.github/workflows/benchmark.yml actions

actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite

.github/workflows/cancel.yml actions

styfle/cancel-workflow-action 85880fa0301c86cca9da44039ee3bb12d3bedbfa composite

.github/workflows/close_pull_requests.yml actions

superbrothers/close-pull-request 9c18513d320d7b2c7185fb93396d0c664d5d8448 composite

.github/workflows/examples.yml actions

actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite

.github/workflows/npm_downloads.yml actions

actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite
actions/upload-artifact 5d5d22a31266ced268874388b861e4b58bb5c2f3 composite
distributhor/workflow-webhook 48a40b380ce4593b6a6676528cd005986ae56629 composite

.github/workflows/productionize.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite
stdlib-js/bundle-action main composite
stdlib-js/transform-errors-action main composite

.github/workflows/publish.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
JS-DevTools/npm-publish 19c28f1ef146469e409470805ea4279d47c3d35c composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite
styfle/cancel-workflow-action 85880fa0301c86cca9da44039ee3bb12d3bedbfa composite

.github/workflows/test.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite

.github/workflows/test_bundles.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite
denoland/setup-deno 041b854f97b325bd60e53e9dc2de9cb9f9ac0cba composite

.github/workflows/test_coverage.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite
codecov/codecov-action 84508663e988701840491b86de86b666e8a86bed composite
distributhor/workflow-webhook 48a40b380ce4593b6a6676528cd005986ae56629 composite

.github/workflows/test_install.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite

.github/workflows/test_published_package.yml actions

8398a7/action-slack 28ba43ae48961b90635b50953d216767a6bea486 composite
actions/checkout 8ade135a41bc03ea155e62e844d188df1ea18608 composite
actions/setup-node b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 composite

package.json npm

@stdlib/array-float64 ^0.2.2 development
@stdlib/assert-is-browser ^0.2.2 development
@stdlib/bench-harness ^0.2.2 development
@stdlib/math-base-assert-is-nan ^0.2.2 development
@stdlib/math-base-special-pow ^0.3.0 development
@stdlib/random-array-discrete-uniform ^0.2.1 development
@stdlib/random-array-uniform ^0.2.1 development
istanbul ^0.4.1 development
proxyquire ^2.0.0 development
tap-min git+https://github.com/Planeshifter/tap-min.git development
tape git+https://github.com/kgryte/tape.git#fix/globby development
@stdlib/assert-is-error ^0.2.2
@stdlib/blas-base-shared ^0.1.0
@stdlib/math-base-special-sqrt ^0.2.2
@stdlib/napi-argv ^0.2.2
@stdlib/napi-argv-double ^0.2.1
@stdlib/napi-argv-int64 ^0.2.2
@stdlib/napi-argv-strided-float64array ^0.2.2
@stdlib/napi-create-double ^0.0.2
@stdlib/napi-export ^0.2.2
@stdlib/stats-strided-dvariancetk github:stdlib-js/stats-strided-dvariancetk#main
@stdlib/strided-base-stride2offset ^0.1.0
@stdlib/utils-define-nonenumerable-read-only-property ^0.2.2
@stdlib/utils-library-manifest ^0.2.2
@stdlib/utils-try-require ^0.2.2

ecosyste.ms

Data

Tools

Indexes

Applications

Experiments

Open Source Science

stats-strided-dstdevtk

Science Score: 57.0%

Keywords

Repository

Basic Info

Statistics

Topics

Metadata Files

README.md

dstdevtk

Owner

Citation (CITATION.cff)

GitHub Events

Total

Last Year

Issues and Pull Requests

All Time

Past Year

Top Authors

Issue Authors

Pull Request Authors

Top Labels

Issue Labels

Pull Request Labels

Dependencies