From 7a0d97ddbc83a2cf49ace0237b196b7eebd26365 Mon Sep 17 00:00:00 2001 From: gururaj1512 Date: Wed, 25 Jun 2025 16:08:28 +0000 Subject: [PATCH] feat: add `stats/array/variancepn` --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: passed - task: lint_package_json status: passed - task: lint_repl_help status: passed - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: passed - task: lint_license_headers status: passed --- --- .../@stdlib/stats/array/variancepn/README.md | 180 +++++++++ .../array/variancepn/benchmark/benchmark.js | 96 +++++ .../docs/img/equation_population_mean.svg | 42 +++ .../docs/img/equation_population_variance.svg | 54 +++ .../docs/img/equation_sample_mean.svg | 43 +++ .../img/equation_unbiased_sample_variance.svg | 61 +++ .../stats/array/variancepn/docs/repl.txt | 38 ++ .../array/variancepn/docs/types/index.d.ts | 52 +++ .../stats/array/variancepn/docs/types/test.ts | 76 ++++ .../stats/array/variancepn/examples/index.js | 30 ++ .../stats/array/variancepn/lib/index.js | 42 +++ .../stats/array/variancepn/lib/main.js | 90 +++++ .../stats/array/variancepn/package.json | 70 ++++ .../stats/array/variancepn/test/test.js | 349 ++++++++++++++++++ 14 files changed, 1223 insertions(+) create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/README.md create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/benchmark/benchmark.js create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_mean.svg create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_variance.svg create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_sample_mean.svg create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_unbiased_sample_variance.svg create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/repl.txt create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/types/index.d.ts create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/docs/types/test.ts create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/examples/index.js create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/lib/index.js create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/lib/main.js create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/package.json create mode 100644 lib/node_modules/@stdlib/stats/array/variancepn/test/test.js diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/README.md b/lib/node_modules/@stdlib/stats/array/variancepn/README.md new file mode 100644 index 000000000000..654b33aead78 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/README.md @@ -0,0 +1,180 @@ + + +# variancepn + +> Calculate the [variance][variance] of an array using a two-pass algorithm. + +
+ +The population [variance][variance] of a finite size population of size `N` is given by + + + +```math +\sigma^2 = \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 [variance][variance] 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 [variance][variance], the result is biased and yields a **biased sample variance**. To compute an **unbiased sample variance** for a sample of size `n`, + + + +```math +s^2 = \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 variance and population variance. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators. + +
+ + + +
+ +## Usage + +```javascript +var variancepn = require( '@stdlib/stats/array/variancepn' ); +``` + +#### variancepn( x\[, correction] ) + +Computes the variance of an array. + +```javascript +var x = [ 1.0, -2.0, 2.0 ]; + +var v = variancepn( x ); +// returns ~4.3333 +``` + +The function has the following parameters: + +- **x**: input array. +- **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 `N` corresponds to the number of array elements and `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). Default: `1.0`. + +By default, the function computes the sample [variance][variance]. To use adjust the degrees of freedom when computing the [variance][variance], provide a `correction` argument. + +```javascript +var x = [ 1.0, -2.0, 2.0 ]; + +var v = variancepn( x, 0.0 ); +// returns ~2.8889 +``` + +
+ + + +
+ +## Notes + +- If provided an empty array, the function returns `NaN`. +- If provided a `correction` argument which is greater than or equal to the number of elements in a provided input array, the function returns `NaN`. +- The function supports array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]). + +
+ + + +
+ +## Examples + + + +```javascript +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); +var variancepn = require( '@stdlib/stats/array/variancepn' ); + +var x = discreteUniform( 10, -50, 50, { + 'dtype': 'float64' +}); +console.log( x ); + +var v = variancepn( x ); +console.log( v ); +``` + +
+ + + +* * * + +
+ +## 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]. + +
+ + + + + +
+ +
+ + + + + +
+ +[variance]: https://en.wikipedia.org/wiki/Variance + +[@neely:1966a]: https://doi.org/10.1145/365719.365958 + +[@schubert:2018a]: https://doi.org/10.1145/3221269.3223036 + +[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor + +
+ + diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/array/variancepn/benchmark/benchmark.js new file mode 100644 index 000000000000..fa86965bd7c6 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/benchmark/benchmark.js @@ -0,0 +1,96 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +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 variancepn = require( './../lib' ); + + +// VARIABLES // + +var options = { + 'dtype': 'generic' +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var x = uniform( len, -10, 10, options ); + return benchmark; + + function benchmark( b ) { + var v; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + v = variancepn( x, 1.0 ); + if ( isnan( v ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( v ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var len; + var min; + var max; + var f; + var i; + + min = 1; // 10^min + max = 6; // 10^max + + for ( i = min; i <= max; i++ ) { + len = pow( 10, i ); + f = createBenchmark( len ); + bench( pkg+':len='+len, f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_mean.svg b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_mean.svg new file mode 100644 index 000000000000..4bbdf0d2a56f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_mean.svg @@ -0,0 +1,42 @@ + +mu equals StartFraction 1 Over upper N EndFraction sigma-summation Underscript i equals 0 Overscript upper N minus 1 Endscripts x Subscript i + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_variance.svg b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_variance.svg new file mode 100644 index 000000000000..4130ba0750d2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_population_variance.svg @@ -0,0 +1,54 @@ + +sigma squared equals StartFraction 1 Over upper N EndFraction sigma-summation Underscript i equals 0 Overscript upper N minus 1 Endscripts left-parenthesis x Subscript i Baseline minus mu right-parenthesis squared + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_sample_mean.svg b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_sample_mean.svg new file mode 100644 index 000000000000..aea7a5f6687a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_sample_mean.svg @@ -0,0 +1,43 @@ + +x overbar equals StartFraction 1 Over n EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts x Subscript i + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_unbiased_sample_variance.svg b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_unbiased_sample_variance.svg new file mode 100644 index 000000000000..1ae1283e7fb1 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/img/equation_unbiased_sample_variance.svg @@ -0,0 +1,61 @@ + +s squared equals StartFraction 1 Over n minus 1 EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis x Subscript i Baseline minus x overbar right-parenthesis squared + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/repl.txt b/lib/node_modules/@stdlib/stats/array/variancepn/docs/repl.txt new file mode 100644 index 000000000000..2267e4603240 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/repl.txt @@ -0,0 +1,38 @@ + +{{alias}}( x[, correction] ) + Computes the variance of an array using a two-pass algorithm. + + If provided an empty array, the function returns `NaN`. + + Parameters + ---------- + x: Array|TypedArray + Input array. + + correction: number (optional) + 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 according to `N - c` where `N` corresponds to the number + of array elements and `c` corresponds to the provided degrees of freedom + adjustment. When computing the 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, 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). + Default: 1.0. + + Returns + ------- + out: number + Variance. + + Examples + -------- + > var x = [ 1.0, -2.0, 2.0 ]; + > {{alias}}( x, 1.0 ) + ~4.3333 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/array/variancepn/docs/types/index.d.ts new file mode 100644 index 000000000000..7f4e021840bd --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/types/index.d.ts @@ -0,0 +1,52 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +// TypeScript Version: 4.1 + +/// + +import { NumericArray, Collection, AccessorArrayLike } from '@stdlib/types/array'; + +/** +* Input array. +*/ +type InputArray = NumericArray | Collection | AccessorArrayLike; + +/** +* Computes the variance of an array using a two-pass algorithm. +* +* ## Notes +* +* - Setting the correction parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the variance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the variance of a population, setting the correction parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample variance, setting the correction 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). +* +* @param x - input array +* @param correction - degrees of freedom adjustment (default: 1.0) +* @returns variance +* +* @example +* var x = [ 1.0, -2.0, 2.0 ]; +* +* var v = variancepn( x, 1.0 ); +* // returns ~4.3333 +*/ +declare function variancepn( x: InputArray, correction?: number ): number; + + +// EXPORTS // + +export = variancepn; diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/docs/types/test.ts b/lib/node_modules/@stdlib/stats/array/variancepn/docs/types/test.ts new file mode 100644 index 000000000000..625843dfbfe5 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/docs/types/test.ts @@ -0,0 +1,76 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +import AccessorArray = require( '@stdlib/array/base/accessor' ); +import variancepn = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + const x = new Float64Array( 10 ); + + variancepn( x ); // $ExpectType number + variancepn( new AccessorArray( x ) ); // $ExpectType number + + variancepn( x, 1.0 ); // $ExpectType number + variancepn( new AccessorArray( x ), 1.0 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is not a numeric array... +{ + variancepn( 10 ); // $ExpectError + variancepn( '10' ); // $ExpectError + variancepn( true ); // $ExpectError + variancepn( false ); // $ExpectError + variancepn( null ); // $ExpectError + variancepn( undefined ); // $ExpectError + variancepn( {} ); // $ExpectError + variancepn( ( x: number ): number => x ); // $ExpectError + + variancepn( 10, 1.0 ); // $ExpectError + variancepn( '10', 1.0 ); // $ExpectError + variancepn( true, 1.0 ); // $ExpectError + variancepn( false, 1.0 ); // $ExpectError + variancepn( null, 1.0 ); // $ExpectError + variancepn( undefined, 1.0 ); // $ExpectError + variancepn( {}, 1.0 ); // $ExpectError + variancepn( ( x: number ): number => x, 1.0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a number... +{ + const x = new Float64Array( 10 ); + + variancepn( x, '10' ); // $ExpectError + variancepn( x, true ); // $ExpectError + variancepn( x, false ); // $ExpectError + variancepn( x, null ); // $ExpectError + variancepn( x, [] ); // $ExpectError + variancepn( x, {} ); // $ExpectError + variancepn( x, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + const x = new Float64Array( 10 ); + + variancepn(); // $ExpectError + variancepn( x, 1.0, {} ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/examples/index.js b/lib/node_modules/@stdlib/stats/array/variancepn/examples/index.js new file mode 100644 index 000000000000..2a44c6a9c238 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/examples/index.js @@ -0,0 +1,30 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +'use strict'; + +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); +var variancepn = require( './../lib' ); + +var x = discreteUniform( 10, -50, 50, { + 'dtype': 'float64' +}); +console.log( x ); + +var v = variancepn( x ); +console.log( v ); diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/lib/index.js b/lib/node_modules/@stdlib/stats/array/variancepn/lib/index.js new file mode 100644 index 000000000000..f493ef0f97de --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/lib/index.js @@ -0,0 +1,42 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +'use strict'; + +/** +* Compute the variance of an array using a two-pass algorithm. +* +* @module @stdlib/stats/array/variancepn +* +* @example +* var variance = require( '@stdlib/stats/array/variancepn' ); +* +* var x = [ 1.0, -2.0, 2.0 ]; +* +* var v = variance( x, 1.0 ); +* // returns ~4.3333 +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/lib/main.js b/lib/node_modules/@stdlib/stats/array/variancepn/lib/main.js new file mode 100644 index 000000000000..3260b3844933 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/lib/main.js @@ -0,0 +1,90 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +'use strict'; + +// MODULES // + +var isCollection = require( '@stdlib/assert/is-collection' ); +var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive; +var dtypes = require( '@stdlib/array/dtypes' ); +var dtype = require( '@stdlib/array/dtype' ); +var contains = require( '@stdlib/array/base/assert/contains' ); +var join = require( '@stdlib/array/base/join' ); +var strided = require( '@stdlib/stats/base/variancepn' ).ndarray; +var format = require( '@stdlib/string/format' ); + + +// VARIABLES // + +var IDTYPES = dtypes( 'real_and_generic' ); +var GENERIC_DTYPE = 'generic'; + + +// MAIN // + +/** +* Computes the standard deviation of an array using a two-pass algorithm. +* +* ## Method +* +* - This implementation uses a two-pass approach, as suggested by Neely (1966). +* +* ## 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](https://doi.org/10.1145/365719.365958). +* - 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](https://doi.org/10.1145/3221269.3223036). +* +* @param {NumericArray} x - input array +* @param {number} [correction=1.0] - degrees of freedom adjustment +* @throws {TypeError} first argument must be an array-like object +* @throws {TypeError} first argument must have a supported data type +* @throws {TypeError} second argument must be a number +* @returns {number} variance +* +* @example +* var x = [ 1.0, -2.0, 2.0 ]; +* +* var v = variancepn( x, 1.0 ); +* // returns ~4.3333 +*/ +function variancepn( x ) { + var correction; + var dt; + if ( !isCollection( x ) ) { + throw new TypeError( format( 'invalid argument. First argument must be an array-like object. Value: `%s`.', x ) ); + } + dt = dtype( x ) || GENERIC_DTYPE; + if ( !contains( IDTYPES, dt ) ) { + throw new TypeError( format( 'invalid argument. First argument must have one of the following data types: "%s". Data type: `%s`.', join( IDTYPES, '", "' ), dt ) ); + } + if ( arguments.length > 1 ) { + correction = arguments[ 1 ]; + if ( !isNumber( correction ) ) { + throw new TypeError( format( 'invalid argument. Second argument must be a number. Value: `%s`.', correction ) ); + } + } else { + correction = 1.0; + } + return strided( x.length, correction, x, 1, 0 ); +} + + +// EXPORTS // + +module.exports = variancepn; diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/package.json b/lib/node_modules/@stdlib/stats/array/variancepn/package.json new file mode 100644 index 000000000000..c1765daad751 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/package.json @@ -0,0 +1,70 @@ +{ + "name": "@stdlib/stats/array/variancepn", + "version": "0.0.0", + "description": "Calculate the variance of an array using a two-pass algorithm.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "statistics", + "stats", + "mathematics", + "math", + "variance", + "var", + "deviation", + "dispersion", + "sample variance", + "unbiased", + "stdev", + "std", + "standard deviation", + "array" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/stats/array/variancepn/test/test.js b/lib/node_modules/@stdlib/stats/array/variancepn/test/test.js new file mode 100644 index 000000000000..9710c42944d8 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/array/variancepn/test/test.js @@ -0,0 +1,349 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' ); +var BooleanArray = require( '@stdlib/array/bool' ); +var Complex128Array = require( '@stdlib/array/complex128' ); +var variancepn = require( './../lib/main.js' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof variancepn, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 1', function test( t ) { + t.strictEqual( variancepn.length, 1, 'returns expected value' ); + t.end(); +}); + +tape( 'the function throws an error if provided a first argument which is not an array-like object', function test( t ) { + var values; + var i; + + values = [ + '5', + 5, + NaN, + true, + false, + null, + void 0, + {}, + function noop() {} + ]; + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + variancepn( value ); + }; + } +}); + +tape( 'the function throws an error if provided a first argument which is not an array-like object (correction)', function test( t ) { + var values; + var i; + + values = [ + '5', + 5, + NaN, + true, + false, + null, + void 0, + {}, + function noop() {} + ]; + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + variancepn( value, 1.0 ); + }; + } +}); + +tape( 'the function throws an error if provided a first argument which has an unsupported data type', function test( t ) { + var values; + var i; + + values = [ + new BooleanArray( 4 ), + new Complex128Array( 4 ) + ]; + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + variancepn( value ); + }; + } +}); + +tape( 'the function throws an error if provided a first argument which has an unsupported data type (correction)', function test( t ) { + var values; + var i; + + values = [ + new BooleanArray( 4 ), + new Complex128Array( 4 ) + ]; + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + variancepn( value, 1.0 ); + }; + } +}); + +tape( 'the function throws an error if provided a second argument which is not a number', function test( t ) { + var values; + var i; + + values = [ + '5', + true, + false, + null, + void 0, + [], + {}, + function noop() {} + ]; + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + variancepn( [ 1, 2, 3 ], value ); + }; + } +}); + +tape( 'the function calculates the population variance of a strided array', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ]; + v = variancepn( x, 0.0 ); + t.strictEqual( v, 53.5/x.length, 'returns expected value' ); + + x = [ -4.0, -4.0 ]; + v = variancepn( x, 0.0 ); + t.strictEqual( v, 0.0, 'returns expected value' ); + + x = [ NaN, 4.0 ]; + v = variancepn( x, 0.0 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function calculates the population variance of a strided array (accessors)', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ]; + v = variancepn( toAccessorArray( x ), 0.0 ); + t.strictEqual( v, 53.5/x.length, 'returns expected value' ); + + x = [ -4.0, -4.0 ]; + v = variancepn( toAccessorArray( x ), 0.0 ); + t.strictEqual( v, 0.0, 'returns expected value' ); + + x = [ NaN, 4.0 ]; + v = variancepn( toAccessorArray( x ), 0.0 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function calculates the population variance of an array (array-like object)', function test( t ) { + var x; + var v; + + x = { + 'length': 6, + '0': 1.0, + '1': -2.0, + '2': -4.0, + '3': 5.0, + '4': 0.0, + '5': 3.0 + }; + v = variancepn( x, 0.0 ); + t.strictEqual( v, 53.5/x.length, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function calculates the sample variance of an array (default)', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ]; + v = variancepn( x ); + t.strictEqual( v, 53.5/(x.length-1), 'returns expected value' ); + + x = [ -4.0, -4.0 ]; + v = variancepn( x ); + t.strictEqual( v, 0.0, 'returns expected value' ); + + x = [ NaN, 4.0 ]; + v = variancepn( x ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function calculates the sample variance of an array (default, accessors)', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ]; + v = variancepn( toAccessorArray( x ) ); + t.strictEqual( v, 53.5/(x.length-1), 'returns expected value' ); + + x = [ -4.0, -4.0 ]; + v = variancepn( toAccessorArray( x ) ); + t.strictEqual( v, 0.0, 'returns expected value' ); + + x = [ NaN, 4.0 ]; + v = variancepn( toAccessorArray( x ) ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function calculates the sample variance of an array', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ]; + v = variancepn( x, 1.0 ); + t.strictEqual( v, 53.5/(x.length-1), 'returns expected value' ); + + x = [ -4.0, -4.0 ]; + v = variancepn( x, 1.0 ); + t.strictEqual( v, 0.0, 'returns expected value' ); + + x = [ NaN, 4.0 ]; + v = variancepn( x, 1.0 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function calculates the sample variance of an array (accessors)', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ]; + v = variancepn( toAccessorArray( x ), 1.0 ); + t.strictEqual( v, 53.5/(x.length-1), 'returns expected value' ); + + x = [ -4.0, -4.0 ]; + v = variancepn( toAccessorArray( x ), 1.0 ); + t.strictEqual( v, 0.0, 'returns expected value' ); + + x = [ NaN, 4.0 ]; + v = variancepn( toAccessorArray( x ), 1.0 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an empty array, the function returns `NaN`', function test( t ) { + var v = variancepn( [] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided an empty array, the function returns `NaN` (accessors)', function test( t ) { + var v = variancepn( toAccessorArray( [] ) ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided an array containing a single element, the function returns `0` when computing the population variance', function test( t ) { + var v = variancepn( [ 1.0 ], 0.0 ); + t.strictEqual( v, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided an array containing a single element, the function returns `0` when computing the population variance (accessors)', function test( t ) { + var v = variancepn( toAccessorArray( [ 1.0 ] ), 0.0 ); + t.strictEqual( v, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided a `correction` parameter which is greater than or equal to the input array length, the function returns `NaN`', function test( t ) { + var x; + var v; + + x = [ 1.0, -2.0, -4.0, 5.0, 3.0 ]; + + v = variancepn( x, x.length ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + v = variancepn( x, x.length+1 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided a `correction` parameter which is greater than or equal to the input array length, the function returns `NaN` (accessors)', function test( t ) { + var x; + var v; + + x = toAccessorArray( [ 1.0, -2.0, -4.0, 5.0, 3.0 ] ); + + v = variancepn( x, x.length ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + v = variancepn( x, x.length+1 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +});