From c5324e0c994b002ecbfa3ea51b0e1f8793c8abc5 Mon Sep 17 00:00:00 2001 From: Prathameshk2024 Date: Tue, 11 Aug 2026 10:25:40 +0530 Subject: [PATCH] Add dvariancepn and dvariancetk --- .../stats/base/ndarray/dvariancepn/README.md | 203 ++++++++++++++++ .../dvariancepn/benchmark/benchmark.js | 109 +++++++++ .../docs/img/equation_sample_mean.svg | 43 ++++ .../base/ndarray/dvariancepn/docs/repl.txt | 44 ++++ .../ndarray/dvariancepn/docs/types/index.d.ts | 57 +++++ .../ndarray/dvariancepn/docs/types/test.ts | 64 +++++ .../ndarray/dvariancepn/examples/index.js | 35 +++ .../base/ndarray/dvariancepn/lib/index.js | 49 ++++ .../base/ndarray/dvariancepn/lib/main.js | 74 ++++++ .../base/ndarray/dvariancepn/package.json | 75 ++++++ .../base/ndarray/dvariancepn/test/test.js | 227 ++++++++++++++++++ .../stats/base/ndarray/dvariancetk/README.md | 201 ++++++++++++++++ .../dvariancetk/benchmark/benchmark.js | 109 +++++++++ .../docs/img/equation_sample_mean.svg | 43 ++++ .../base/ndarray/dvariancetk/docs/repl.txt | 44 ++++ .../ndarray/dvariancetk/docs/types/index.d.ts | 57 +++++ .../ndarray/dvariancetk/docs/types/test.ts | 64 +++++ .../ndarray/dvariancetk/examples/index.js | 35 +++ .../base/ndarray/dvariancetk/lib/index.js | 49 ++++ .../base/ndarray/dvariancetk/lib/main.js | 74 ++++++ .../base/ndarray/dvariancetk/package.json | 75 ++++++ .../base/ndarray/dvariancetk/test/test.js | 227 ++++++++++++++++++ 22 files changed, 1958 insertions(+) create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/README.md create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/benchmark/benchmark.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/img/equation_sample_mean.svg create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/repl.txt create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/index.d.ts create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/test.ts create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/examples/index.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/index.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/main.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/package.json create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/test/test.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/README.md create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/benchmark/benchmark.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/img/equation_sample_mean.svg create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/repl.txt create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/index.d.ts create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/test.ts create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/examples/index.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/index.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/main.js create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/package.json create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/test/test.js diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/README.md new file mode 100644 index 000000000000..3a34abd7ff1a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/README.md @@ -0,0 +1,203 @@ + + +# dvariancepn + +> Calculate the [variance][variance] of a one-dimensional double-precision floating-point ndarray 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 an **uncorrected sample variance**. To compute a **corrected 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 dvariancepn = require( '@stdlib/stats/base/ndarray/dvariancepn' ); +``` + +#### dvariancepn( arrays ) + +Computes the [variance][variance] of a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. + +```javascript +var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +var correction = scalar2ndarray( 1.0, opts ); + +var v = dvariancepn( [ x, correction ] ); +// returns ~4.3333 +``` + +The function has the following parameters: + +- **arrays**: array-like object containing the following ndarrays: + + - a one-dimensional input ndarray. + - a zero-dimensional ndarray specifying the degrees of freedom adjustment. Providing a non-zero degrees of freedom adjustment has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `N` is the number of elements in the input ndarray 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 corrected 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). + +
+ + + +
+ +## Notes + +- If provided an empty one-dimensional ndarray, the function returns `NaN`. +- If `N - c` is less than or equal to `0` (where `N` corresponds to the number of elements in the input ndarray and `c` corresponds to the provided degrees of freedom adjustment), the function returns `NaN`. + +
+ + + +
+ +## Examples + + + +```javascript +var discreteUniform = require( '@stdlib/random/discrete-uniform' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var ndarray2array = require( '@stdlib/ndarray/to-array' ); +var dvariancepn = require( '@stdlib/stats/base/ndarray/dvariancepn' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = discreteUniform( [ 10 ], -50, 50, opts ); +console.log( ndarray2array( x ) ); + +var correction = scalar2ndarray( 1.0, opts ); +var v = dvariancepn( [ x, correction ] ); +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 + +
+ + diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/benchmark/benchmark.js new file mode 100644 index 000000000000..f65b406158ce --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/benchmark/benchmark.js @@ -0,0 +1,109 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var dvariancepn = require( './../lib' ); + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var correction; + var x; + + x = uniform( [ len ], -10.0, 10.0, options ); + correction = scalar2ndarray( 1.0, options ); + + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var v; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + v = dvariancepn( [ x, correction ] ); + 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( format( '%s:len=%d', pkg, len ), f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/img/equation_sample_mean.svg b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/img/equation_sample_mean.svg new file mode 100644 index 000000000000..aea7a5f6687a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/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/base/ndarray/dvariancepn/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/repl.txt new file mode 100644 index 000000000000..621573bb0995 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/repl.txt @@ -0,0 +1,44 @@ + +{{alias}}( arrays ) + Computes the variance of a one-dimensional double-precision floating-point + ndarray using a two-pass algorithm. + + If provided an empty one-dimensional ndarray, the function returns `NaN`. + + If `N - c` is less than or equal to `0` (where `N` corresponds to the number + of elements in the input ndarray and `c` corresponds to the provided degrees + of freedom adjustment), the function returns `NaN`. + + Parameters + ---------- + arrays: ArrayLikeObject + Array-like object containing the following ndarrays: + + - a one-dimensional input ndarray. + - a zero-dimensional ndarray specifying the degrees of freedom + adjustment. Providing a non-zero degrees of freedom adjustment has the + effect of adjusting the divisor during the calculation of the variance + according to `N-c` where `N` is the number of elements in the input + ndarray 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 + corrected 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). + + Returns + ------- + out: number + The variance. + + Examples + -------- + > var x = new {{alias:@stdlib/ndarray/vector/float64}}( [ 1.0, -2.0, 2.0 ] ); + > var opts = { 'dtype': 'float64' }; + > var correction = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts ); + > {{alias}}( [ x, correction ] ) + ~4.3333 + + See Also + -------- diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/index.d.ts new file mode 100644 index 000000000000..bea1ccf684f6 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/index.d.ts @@ -0,0 +1,57 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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 { float64ndarray, typedndarray } from '@stdlib/types/ndarray'; + +/** +* Computes the variance of a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. +* +* ## Notes +* +* - The function expects the following ndarrays: +* +* - a one-dimensional input ndarray. +* - a zero-dimensional ndarray specifying the degrees of freedom adjustment. +* +* @param arrays - array-like object containing ndarrays +* @returns variance +* +* @example +* var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +* +* var opts = { +* 'dtype': 'float64' +* }; +* +* var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +* var correction = scalar2ndarray( 1.0, opts ); +* +* var v = dvariancepn( [ x, correction ] ); +* // returns ~4.3333 +*/ +declare function dvariancepn( arrays: [ float64ndarray, typedndarray ] ): number; + + +// EXPORTS // + +export = dvariancepn; diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/test.ts new file mode 100644 index 000000000000..968e82b8c62a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/docs/types/test.ts @@ -0,0 +1,64 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +/* eslint-disable space-in-parens */ + +import zeros = require( '@stdlib/ndarray/zeros' ); +import scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +import dvariancepn = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + const x = zeros( [ 10 ], { + 'dtype': 'float64' + }); + const correction = scalar2ndarray( 1.0, { + 'dtype': 'float64' + }); + + dvariancepn( [ x, correction ] ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is not an array of ndarrays... +{ + dvariancepn( '10' ); // $ExpectError + dvariancepn( 10 ); // $ExpectError + dvariancepn( true ); // $ExpectError + dvariancepn( false ); // $ExpectError + dvariancepn( null ); // $ExpectError + dvariancepn( undefined ); // $ExpectError + dvariancepn( [] ); // $ExpectError + dvariancepn( {} ); // $ExpectError + dvariancepn( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + const x = zeros( [ 10 ], { + 'dtype': 'float64' + }); + const correction = scalar2ndarray( 1.0, { + 'dtype': 'float64' + }); + + dvariancepn(); // $ExpectError + dvariancepn( [ x, correction ], 10 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/examples/index.js new file mode 100644 index 000000000000..456004f88a87 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/examples/index.js @@ -0,0 +1,35 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/discrete-uniform' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var ndarray2array = require( '@stdlib/ndarray/to-array' ); +var dvariancepn = require( './../lib' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = discreteUniform( [ 10 ], -50, 50, opts ); +console.log( ndarray2array( x ) ); + +var correction = scalar2ndarray( 1.0, opts ); +var v = dvariancepn( [ x, correction ] ); +console.log( v ); diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/index.js new file mode 100644 index 000000000000..d4268424ee7f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/index.js @@ -0,0 +1,49 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. +* +* @module @stdlib/stats/base/ndarray/dvariancepn +* +* @example +* var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +* var dvariancepn = require( '@stdlib/stats/base/ndarray/dvariancepn' ); +* +* var opts = { +* 'dtype': 'float64' +* }; +* +* var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +* var correction = scalar2ndarray( 1.0, opts ); +* +* var v = dvariancepn( [ x, correction ] ); +* // returns ~4.3333 +*/ + +// MODULES // + +var main = require( '@stdlib/stats/base/ndarray/dvariancepn/lib/main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/main.js new file mode 100644 index 000000000000..8ee6bdc9753d --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/lib/main.js @@ -0,0 +1,74 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 numelDimension = require( '@stdlib/ndarray/base/numel-dimension' ); +var getStride = require( '@stdlib/ndarray/base/stride' ); +var getOffset = require( '@stdlib/ndarray/base/offset' ); +var getData = require( '@stdlib/ndarray/base/data-buffer' ); +var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' ); +var strided = require( '@stdlib/stats/strided/dvariancepn' ).ndarray; + + +// MAIN // + +/** +* Computes the variance of a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. +* +* ## Notes +* +* - The function expects the following ndarrays: +* +* - a one-dimensional input ndarray. +* - a zero-dimensional ndarray specifying the degrees of freedom adjustment. +* +* @param {ArrayLikeObject} arrays - array-like object containing ndarrays +* @returns {number} variance +* +* @example +* var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +* +* var opts = { +* 'dtype': 'float64' +* }; +* +* var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +* +* var correction = scalar2ndarray( 1.0, opts ); +* +* var v = dvariancepn( [ x, correction ] ); +* // returns ~4.3333 +*/ +function dvariancepn( arrays ) { + var correction; + var x; + + x = arrays[ 0 ]; + correction = ndarraylike2scalar( arrays[ 1 ] ); + + return strided( numelDimension( x, 0 ), correction, getData( x ), getStride( x, 0 ), getOffset( x ) ); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = dvariancepn; diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/package.json b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/package.json new file mode 100644 index 000000000000..1d6b7cca4472 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/package.json @@ -0,0 +1,75 @@ +{ + "name": "@stdlib/stats/base/ndarray/dvariance", + "version": "0.0.0", + "description": "Compute the variance of a one-dimensional double-precision floating-point ndarray.", + "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", + "spread", + "sample variance", + "unbiased", + "dvariance", + "std", + "ndarray", + "float64", + "double", + "double-precision", + "typed", + "float64array" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/test/test.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/test/test.js new file mode 100644 index 000000000000..28d0e90e1694 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancepn/test/test.js @@ -0,0 +1,227 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 Float64Array = require( '@stdlib/array/float64' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var ndarray = require( '@stdlib/ndarray/base/ctor' ); +var dvariance = require( '@stdlib/stats/base/ndarray/dvariancepn/lib' ); + + +// FUNCTIONS // + +/** +* Returns a one-dimensional ndarray. +* +* @private +* @param {Collection} buffer - underlying data buffer +* @param {NonNegativeInteger} length - number of indexed elements +* @param {integer} stride - stride length +* @param {NonNegativeInteger} offset - index offset +* @returns {ndarray} one-dimensional ndarray +*/ +function vector( buffer, length, stride, offset ) { + return new ndarray( 'float64', buffer, [ length ], [ stride ], offset, 'row-major' ); +} + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dvariance, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 1', function test( t ) { + t.strictEqual( dvariance.length, 1, 'has expected arity' ); + t.end(); +}); + +tape( 'the function calculates the variance of a one-dimensional ndarray', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array( [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, x.length, 1, 0 ), correction ] ); + expected = 53.5 / (x.length-1); + t.strictEqual( v, expected, 'returns expected value' ); + + x = new Float64Array( [ -4.0, -5.0 ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, x.length, 1, 0 ), correction ] ); + expected = 0.5; + t.strictEqual( v, expected, 'returns expected value' ); + + x = new Float64Array( [ NaN ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, x.length, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + x = new Float64Array( [ NaN, NaN ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, x.length, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an empty ndarray, the function returns `NaN`', function test( t ) { + var correction; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array( [] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, 0, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided a correction argument yielding `N-correction` less than or equal to `0`, the function returns `NaN`', function test( t ) { + var correction; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array( [ 1.0 ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, 1, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports one-dimensional ndarrays having non-unit strides', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array([ + 1.0, // 0 + 2.0, + 2.0, // 1 + -7.0, + -2.0, // 2 + 3.0, + 4.0, // 3 + 2.0 + ]); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, 4, 2, 0 ), correction ] ); + expected = 6.25; + t.strictEqual( v, expected, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports one-dimensional ndarrays having negative strides', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array([ + 1.0, // 3 + 2.0, + 2.0, // 2 + -7.0, + -2.0, // 1 + 3.0, + 4.0, // 0 + 2.0 + ]); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, 4, -2, 6 ), correction ] ); + expected = 6.25; + t.strictEqual( v, expected, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports one-dimensional ndarrays having non-zero offsets', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array([ + 2.0, + 1.0, // 0 + 2.0, + -2.0, // 1 + -2.0, + 2.0, // 2 + 3.0, + 4.0 // 3 + ]); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariance( [ vector( x, 4, 2, 1 ), correction ] ); + expected = 6.25; + t.strictEqual( v, expected, 'returns expected value' ); + + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/README.md new file mode 100644 index 000000000000..d52a9cbaad69 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/README.md @@ -0,0 +1,201 @@ + + +# dvariancetk + +> Calculate the [variance][variance] of a one-dimensional double-precision floating-point ndarray 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 an **uncorrected sample variance**. To compute a **corrected 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 dvariancetk = require( '@stdlib/stats/base/ndarray/dvariancetk' ); +``` + +#### dvariancetk( arrays ) + +Computes the [variance][variance] of a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. + +```javascript +var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +var correction = scalar2ndarray( 1.0, opts ); + +var v = dvariancetk( [ x, correction ] ); +// returns ~4.3333 +``` + +The function has the following parameters: + +- **arrays**: array-like object containing the following ndarrays: + + - a one-dimensional input ndarray. + - a zero-dimensional ndarray specifying the degrees of freedom adjustment. Providing a non-zero degrees of freedom adjustment has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `N` is the number of elements in the input ndarray 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 corrected 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). + +
+ + + +
+ +## Notes + +- If provided an empty one-dimensional ndarray, the function returns `NaN`. +- If `N - c` is less than or equal to `0` (where `N` corresponds to the number of elements in the input ndarray and `c` corresponds to the provided degrees of freedom adjustment), the function returns `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. + +
+ + + +
+ +## Examples + + + +```javascript +var discreteUniform = require( '@stdlib/random/discrete-uniform' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var ndarray2array = require( '@stdlib/ndarray/to-array' ); +var dvariancetk = require( '@stdlib/stats/base/ndarray/dvariancetk' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = discreteUniform( [ 10 ], -50, 50, opts ); +console.log( ndarray2array( x ) ); + +var correction = scalar2ndarray( 1.0, opts ); +var v = dvariancetk( [ x, correction ] ); +console.log( 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]. + +
+ + + + + +
+ +
+ + + + + +
+ +[variance]: https://en.wikipedia.org/wiki/Variance + +[@ling:1974a]: https://doi.org/10.2307/2286154 + +
+ + diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/benchmark/benchmark.js new file mode 100644 index 000000000000..f38196fb3ae2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/benchmark/benchmark.js @@ -0,0 +1,109 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var dvariancetk = require( './../lib' ); + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var correction; + var x; + + x = uniform( [ len ], -10.0, 10.0, options ); + correction = scalar2ndarray( 1.0, options ); + + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var v; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + v = dvariancetk( [ x, correction ] ); + 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( format( '%s:len=%d', pkg, len ), f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/img/equation_sample_mean.svg b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/img/equation_sample_mean.svg new file mode 100644 index 000000000000..aea7a5f6687a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/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/base/ndarray/dvariancetk/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/repl.txt new file mode 100644 index 000000000000..26f3b03f5d8f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/repl.txt @@ -0,0 +1,44 @@ + +{{alias}}( arrays ) + Computes the variance of a one-dimensional double-precision floating-point + ndarray. + + If provided an empty one-dimensional ndarray, the function returns `NaN`. + + If `N - c` is less than or equal to `0` (where `N` corresponds to the number + of elements in the input ndarray and `c` corresponds to the provided degrees + of freedom adjustment), the function returns `NaN`. + + Parameters + ---------- + arrays: ArrayLikeObject + Array-like object containing the following ndarrays: + + - a one-dimensional input ndarray. + - a zero-dimensional ndarray specifying the degrees of freedom + adjustment. Providing a non-zero degrees of freedom adjustment has the + effect of adjusting the divisor during the calculation of the variance + according to `N-c` where `N` is the number of elements in the input + ndarray 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 + corrected 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). + + Returns + ------- + out: number + The variance. + + Examples + -------- + > var x = new {{alias:@stdlib/ndarray/vector/float64}}( [ 1.0, -2.0, 2.0 ] ); + > var opts = { 'dtype': 'float64' }; + > var correction = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts ); + > {{alias}}( [ x, correction ] ) + ~4.3333 + + See Also + -------- diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/index.d.ts new file mode 100644 index 000000000000..f79a933378ad --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/index.d.ts @@ -0,0 +1,57 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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 { float64ndarray, typedndarray } from '@stdlib/types/ndarray'; + +/** +* Computes the variance of a one-dimensional double-precision floating-point ndarray. +* +* ## Notes +* +* - The function expects the following ndarrays: +* +* - a one-dimensional input ndarray. +* - a zero-dimensional ndarray specifying the degrees of freedom adjustment. +* +* @param arrays - array-like object containing ndarrays +* @returns variance +* +* @example +* var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +* +* var opts = { +* 'dtype': 'float64' +* }; +* +* var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +* var correction = scalar2ndarray( 1.0, opts ); +* +* var v = dvariancetk( [ x, correction ] ); +* // returns ~4.3333 +*/ +declare function dvariancetk( arrays: [ float64ndarray, typedndarray ] ): number; + + +// EXPORTS // + +export = dvariancetk; diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/test.ts new file mode 100644 index 000000000000..757b7897391f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/docs/types/test.ts @@ -0,0 +1,64 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +/* eslint-disable space-in-parens */ + +import zeros = require( '@stdlib/ndarray/zeros' ); +import scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +import dvariancetk = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + const x = zeros( [ 10 ], { + 'dtype': 'float64' + }); + const correction = scalar2ndarray( 1.0, { + 'dtype': 'float64' + }); + + dvariancetk( [ x, correction ] ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is not an array of ndarrays... +{ + dvariancetk( '10' ); // $ExpectError + dvariancetk( 10 ); // $ExpectError + dvariancetk( true ); // $ExpectError + dvariancetk( false ); // $ExpectError + dvariancetk( null ); // $ExpectError + dvariancetk( undefined ); // $ExpectError + dvariancetk( [] ); // $ExpectError + dvariancetk( {} ); // $ExpectError + dvariancetk( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + const x = zeros( [ 10 ], { + 'dtype': 'float64' + }); + const correction = scalar2ndarray( 1.0, { + 'dtype': 'float64' + }); + + dvariancetk(); // $ExpectError + dvariancetk( [ x, correction ], 10 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/examples/index.js new file mode 100644 index 000000000000..43d6070147b0 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/examples/index.js @@ -0,0 +1,35 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/discrete-uniform' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var ndarray2array = require( '@stdlib/ndarray/to-array' ); +var dvariancetk = require( '@stdlib/stats/base/ndarray/dvariancetk/lib' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = discreteUniform( [ 10 ], -50, 50, opts ); +console.log( ndarray2array( x ) ); + +var correction = scalar2ndarray( 1.0, opts ); +var v = dvariancetk( [ x, correction ] ); +console.log( v ); diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/index.js new file mode 100644 index 000000000000..7bee29cf53f4 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/index.js @@ -0,0 +1,49 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. +* +* @module @stdlib/stats/base/ndarray/dvariancetk +* +* @example +* var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +* var dvariancetk = require( '@stdlib/stats/base/ndarray/dvariancetk' ); +* +* var opts = { +* 'dtype': 'float64' +* }; +* +* var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +* var correction = scalar2ndarray( 1.0, opts ); +* +* var v = dvariancetk( [ x, correction ] ); +* // returns ~4.3333 +*/ + +// MODULES // + +var main = require( '@stdlib/stats/base/ndarray/dvariancetk/lib/main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/main.js new file mode 100644 index 000000000000..8ec940c95f34 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/lib/main.js @@ -0,0 +1,74 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 numelDimension = require( '@stdlib/ndarray/base/numel-dimension' ); +var getStride = require( '@stdlib/ndarray/base/stride' ); +var getOffset = require( '@stdlib/ndarray/base/offset' ); +var getData = require( '@stdlib/ndarray/base/data-buffer' ); +var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' ); +var strided = require( '@stdlib/stats/strided/dvariancetk' ).ndarray; + + +// MAIN // + +/** +* Computes the variance of a one-dimensional double-precision floating-point ndarray using a two-pass algorithm. +* +* ## Notes +* +* - The function expects the following ndarrays: +* +* - a one-dimensional input ndarray. +* - a zero-dimensional ndarray specifying the degrees of freedom adjustment. +* +* @param {ArrayLikeObject} arrays - array-like object containing ndarrays +* @returns {number} variance +* +* @example +* var Float64Vector = require( '@stdlib/ndarray/vector/float64' ); +* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +* +* var opts = { +* 'dtype': 'float64' +* }; +* +* var x = new Float64Vector( [ 1.0, -2.0, 2.0 ] ); +* +* var correction = scalar2ndarray( 1.0, opts ); +* +* var v = dvariancetk( [ x, correction ] ); +* // returns ~4.3333 +*/ +function dvariancetk( arrays ) { + var correction; + var x; + + x = arrays[ 0 ]; + correction = ndarraylike2scalar( arrays[ 1 ] ); + + return strided( numelDimension( x, 0 ), correction, getData( x ), getStride( x, 0 ), getOffset( x ) ); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = dvariancetk; diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/package.json b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/package.json new file mode 100644 index 000000000000..55e88089a57c --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/package.json @@ -0,0 +1,75 @@ +{ + "name": "@stdlib/stats/base/ndarray/dvariancetk", + "version": "0.0.0", + "description": "Compute the variance of a one-dimensional double-precision floating-point ndarray 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", + "spread", + "sample variance", + "unbiased", + "dvariancetk", + "std", + "ndarray", + "float64", + "double", + "double-precision", + "typed", + "float64array" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/test/test.js b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/test/test.js new file mode 100644 index 000000000000..99dce923ff33 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/ndarray/dvariancetk/test/test.js @@ -0,0 +1,227 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 Float64Array = require( '@stdlib/array/float64' ); +var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' ); +var ndarray = require( '@stdlib/ndarray/base/ctor' ); +var dvariancetk = require( '@stdlib/stats/base/ndarray/dvariancetk/lib' ); + + +// FUNCTIONS // + +/** +* Returns a one-dimensional ndarray . +* +* @private +* @param {Collection} buffer - underlying data buffer +* @param {NonNegativeInteger} length - number of indexed elements +* @param {integer} stride - stride length +* @param {NonNegativeInteger} offset - index offset +* @returns {ndarray} one-dimensional ndarray +*/ +function vector( buffer, length, stride, offset ) { + return new ndarray( 'float64', buffer, [ length ], [ stride ], offset, 'row-major' ); +} + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dvariancetk, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 1', function test( t ) { + t.strictEqual( dvariancetk.length, 1, 'has expected arity' ); + t.end(); +}); + +tape( 'the function calculates the variance of a one-dimensional ndarray', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array( [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, x.length, 1, 0 ), correction ] ); + expected = 53.5 / (x.length-1); + t.strictEqual( v, expected, 'returns expected value' ); + + x = new Float64Array( [ -4.0, -5.0 ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, x.length, 1, 0 ), correction ] ); + expected = 0.5; + t.strictEqual( v, expected, 'returns expected value' ); + + x = new Float64Array( [ NaN ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, x.length, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + x = new Float64Array( [ NaN, NaN ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, x.length, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an empty ndarray, the function returns `NaN`', function test( t ) { + var correction; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array( [] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, 0, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided a correction argument yielding `N-correction` less than or equal to `0`, the function returns `NaN`', function test( t ) { + var correction; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array( [ 1.0 ] ); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, 1, 1, 0 ), correction ] ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports one-dimensional ndarrays having non-unit strides', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array([ + 1.0, // 0 + 2.0, + 2.0, // 1 + -7.0, + -2.0, // 2 + 3.0, + 4.0, // 3 + 2.0 + ]); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, 4, 2, 0 ), correction ] ); + expected = 6.25; + t.strictEqual( v, expected, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports one-dimensional ndarrays having negative strides', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array([ + 1.0, // 3 + 2.0, + 2.0, // 2 + -7.0, + -2.0, // 1 + 3.0, + 4.0, // 0 + 2.0 + ]); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, 4, -2, 6 ), correction ] ); + expected = 6.25; + t.strictEqual( v, expected, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports one-dimensional ndarrays having non-zero offsets', function test( t ) { + var correction; + var expected; + var opts; + var x; + var v; + + opts = { + 'dtype': 'float64' + }; + + x = new Float64Array([ + 2.0, + 1.0, // 0 + 2.0, + -2.0, // 1 + -2.0, + 2.0, // 2 + 3.0, + 4.0 // 3 + ]); + correction = scalar2ndarray( 1.0, opts ); + + v = dvariancetk( [ vector( x, 4, 2, 1 ), correction ] ); + expected = 6.25; + t.strictEqual( v, expected, 'returns expected value' ); + + t.end(); +});