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Apache-2.0\n\nCopyright (c) 2018 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>\n  <p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p>\n  <p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# LOWESS\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> Locally-weighted polynomial regression via the LOWESS algorithm.\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/stats-lowess\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar lowess = require( '@stdlib/stats-lowess' );\n```\n\n#### lowess( x, y\\[, opts] )\n\nFor [input arrays][mdn-array] and/or [typed arrays][mdn-typed-array] `x` and `y`, the function returns an object holding the ordered input values `x` and smoothed values for `y`.\n\n<!-- eslint-disable array-element-newline -->\n\n```javascript\nvar x = [\n    4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,\n    14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,\n    20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25\n];\nvar y = [\n    2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,\n    26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,\n    32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85\n];\n\nvar out = lowess( x, y );\n/* returns\n    {\n        'x': [\n            4,\n            4,\n            7,\n            7,\n            ...,\n            24,\n            24,\n            24,\n            25\n        ],\n        'y': [\n            ~4.857,\n            ~4.857,\n            ~13.1037,\n            ~13.1037,\n            ...,\n            ~79.102,\n            ~79.102,\n            ~79.102,\n            ~84.825\n        ]\n    }\n*/\n```\n\nThe function accepts the following `options`:\n\n-   **f**: positive `number` specifying the smoothing span, i.e., the proportion of points which influence smoothing at each value. Larger values correspond to more smoothing. Default: `2/3`.\n-   **nsteps**: `number` of iterations in the robust fit (fewer iterations translates to faster function execution). If set to zero, the nonrobust fit is returned. Default: `3`.\n-   **delta**: nonnegative `number` which may be used to reduce the number of computations. Default: 1/100th of the range of `x`.\n-   **sorted**: `boolean` indicating if the input array `x` is sorted. Default: `false`.\n\nBy default, smoothing at each value is determined by `2/3` of all other points. To choose a different smoothing span, set the `f` option.\n\n<!-- eslint-disable array-element-newline -->\n\n```javascript\nvar x = [\n    4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,\n    14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,\n    20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25\n];\nvar y = [\n    2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,\n    26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,\n    32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85\n];\n\nvar out = lowess( x, y, {\n    'f': 0.2\n});\n/* returns\n    {\n        'x': [\n            4,\n            4,\n            7,\n            ...,\n            24,\n            24,\n            25\n        ],\n        'y': [\n            ~6.03,\n            ~6.03,\n            ~12.68,\n            ...,\n            ~82.575,\n            ~82.575,\n            ~93.028\n        ]\n    }\n*/\n```\n\nBy default, three iterations of locally weighted regression fits are calculated after the initial fit. To set a different number of iterations for the robust fit, set the `nsteps` option.\n\n<!-- eslint-disable array-element-newline -->\n\n```javascript\nvar x = [\n    4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,\n    14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,\n    20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25\n];\nvar y = [\n    2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,\n    26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,\n    32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85\n];\n\nvar out = lowess( x, y, {\n    'nsteps': 20\n});\n/* returns\n    {\n        'x': [\n            4,\n            ...,\n            25\n        ],\n        'y': [\n            ~4.857,\n            ...,\n            ~84.825\n        ]\n    }\n*/\n```\n\nTo save computations, set the `delta` option. For cases where one has a large number of (x,y)-pairs, carrying out regression calculations for all points is not likely to be necessary. By default, `delta` is set to 1/100th of the range of the values in `x`. In this case, if the values in `x` were uniformly scattered over the entire range, the locally weighted regression would be calculated at approximately 100 points. On the other hand, for small data sets with less than 100 observations, one can safely set the option to zero so calculations are made for each data point.\n\n<!-- eslint-disable array-element-newline -->\n\n```javascript\nvar x = [\n    4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,\n    14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,\n    20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25\n];\nvar y = [\n    2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,\n    26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,\n    32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85\n];\n\nvar out = lowess( x, y, {\n    'delta': 0.0\n});\n/* returns\n    {\n        'x': [\n            4,\n            ...,\n            25\n        ],\n        'y': [\n            ~4.857,\n            ...,\n            ~84.825\n        ]\n    }\n*/\n```\n\nIf the elements of `x` are sorted in ascending order, set the `sorted` option to `true`.\n\n<!-- eslint-disable array-element-newline -->\n\n```javascript\nvar x = [\n    4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,\n    14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,\n    20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25\n];\nvar y = [\n    2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,\n    26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,\n    32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85\n];\n\nvar out = lowess( x, y, {\n    'sorted': true\n});\n/* returns\n    {\n        'x': [\n            4,\n            ...,\n            25\n        ],\n        'y': [\n            ~4.857,\n            ...,\n            ~84.825\n        ]\n    }\n*/\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar randn = require( '@stdlib/random-base-randn' );\nvar Float64Array = require( '@stdlib/array-float64' );\nvar plot = require( '@stdlib/plot-ctor' );\nvar lowess = require( '@stdlib/stats-lowess' );\n\nvar x;\nvar y;\nvar i;\n\n// Create some data...\nx = new Float64Array( 100 );\ny = new Float64Array( x.length );\nfor ( i = 0; i < x.length; i++ ) {\n    x[ i ] = i;\n    y[ i ] = ( 0.5*i ) + ( 10.0*randn() );\n}\n\nvar opts = {\n    'delta': 0\n};\n\nvar out = lowess( x, y, opts );\nvar h = plot( [ x, out.x ], [ y, out.y ] );\n\nh.lineStyle = [ 'none', '-' ];\nh.symbols = [ 'closed-circle', 'none' ];\n\nh.view( 'stdout' );\n```\n\n</section>\n\n<!-- /.examples -->\n\n<section class=\"references\">\n\n## References\n\n-   Cleveland, William S. 1979. \"Robust Locally and Smoothing Weighted Regression Scatterplots.\" _Journal of the American Statistical Association_ 74 (368): 829–36. doi:[10.1080/01621459.1979.10481038][@cleveland:1979].\n-   Cleveland, William S. 1981. \"Lowess: A program for smoothing scatterplots by robust locally weighted regression.\" _American Statistician_ 35 (1): 54–55. doi:[10.2307/2683591][@cleveland:1981].\n\n</section>\n\n<!-- /.references -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\n\n* * *\n\n## Notice\n\nThis package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.\n\nFor more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright &copy; 2016-2024. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-lowess.svg\n[npm-url]: https://npmjs.org/package/@stdlib/stats-lowess\n\n[test-image]: https://github.com/stdlib-js/stats-lowess/actions/workflows/test.yml/badge.svg?branch=v0.2.1\n[test-url]: https://github.com/stdlib-js/stats-lowess/actions/workflows/test.yml?query=branch:v0.2.1\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-lowess/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/stats-lowess?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/stats-lowess.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/stats-lowess/main\n\n-->\n\n[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg\n[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/stats-lowess/tree/deno\n[deno-readme]: https://github.com/stdlib-js/stats-lowess/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/stats-lowess/tree/umd\n[umd-readme]: https://github.com/stdlib-js/stats-lowess/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/stats-lowess/tree/esm\n[esm-readme]: https://github.com/stdlib-js/stats-lowess/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/stats-lowess/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-lowess/main/LICENSE\n\n[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array\n\n[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays\n\n[@cleveland:1979]: https://doi.org/10.1080/01621459.1979.10481038\n\n[@cleveland:1981]: https://doi.org/10.2307/2683591\n\n</section>\n\n<!-- /.links -->\n","_attachments":{},"homepage":"https://stdlib.io","bugs":{"url":"https://github.com/stdlib-js/stdlib/issues"},"license":"Apache-2.0"}