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Apache-2.0\n\nCopyright (c) 2023 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--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe 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.\u003c/p\u003e\n  \u003cp\u003eThe 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.\u003c/p\u003e\n  \u003cp\u003eWhen 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.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# nullaryLoopOrder\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Reorder ndarray dimensions and associated strides for loop interchange.\n\n\u003c!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"intro\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003c!-- Package usage documentation. --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/ndarray-base-nullary-loop-interchange-order\n```\n\nAlternatively,\n\n-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar nullaryLoopOrder = require( '@stdlib/ndarray-base-nullary-loop-interchange-order' );\n```\n\n#### nullaryLoopOrder( shape, stridesX )\n\nReorders [ndarray][@stdlib/ndarray/ctor] dimensions and associated strides for [loop interchange][loop-interchange].\n\n```javascript\n// Define an array shape:\nvar shape = [ 2, 2 ];\n\n// Define array strides:\nvar stridesX = [ 2, 1 ]; // row-major\n\n// Resolve the loop interchange order:\nvar o = nullaryLoopOrder( shape, stridesX );\n// returns {...}\n```\n\nThe function returns an object having the following properties:\n\n-   **sh**: ordered dimensions.\n-   **sx**: array strides sorted in loop order.\n-   **idx**: dimension indices sorted in loop order.\n\nFor all returned arrays, the first element corresponds to the innermost loop, and the last element corresponds to the outermost loop.\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003c!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n## Notes\n\n-   When iterating over the elements of a multi-dimensional array, accessing elements which are closer in memory can improve performance. To this end, [loop interchange][loop-interchange] is a technique used in [loop nest optimization][loop-nest-optimization] to improve locality of reference and take advantage of CPU cache.\n\n    The purpose of this function is to order [ndarray][@stdlib/ndarray/ctor] dimensions according to the magnitude of array strides. By using the ordered dimensions and associated strides, one can construct nested loops (one for each dimension) such that the innermost loop iterates over the dimension in which array elements are closest in memory and the outermost loop iterates over the dimension in which array elements are farthest apart in memory. As a consequence, element iteration is optimized to minimize cache misses and ensure locality of reference.\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003c!-- Package usage examples. --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar array = require( '@stdlib/ndarray-array' );\nvar loopOrder = require( '@stdlib/ndarray-base-nullary-loop-interchange-order' );\n\n// Create an ndarray:\nvar x = array( [ [ 1, 2 ], [ 3, 4 ] ] );\n\n// Resolve loop interchange data:\nvar o = loopOrder( x.shape, x.strides );\n// returns {...}\n\nconsole.log( o );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"references\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\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 \u0026copy; 2016-2025. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/ndarray-base-nullary-loop-interchange-order.svg\n[npm-url]: https://npmjs.org/package/@stdlib/ndarray-base-nullary-loop-interchange-order\n\n[test-image]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/ndarray-base-nullary-loop-interchange-order/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/ndarray-base-nullary-loop-interchange-order?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/ndarray-base-nullary-loop-interchange-order.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/ndarray-base-nullary-loop-interchange-order/main\n\n--\u003e\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/ndarray-base-nullary-loop-interchange-order/tree/deno\n[deno-readme]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/tree/umd\n[umd-readme]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/tree/esm\n[esm-readme]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/ndarray-base-nullary-loop-interchange-order/main/LICENSE\n\n[loop-interchange]: https://en.wikipedia.org/wiki/Loop_interchange\n\n[loop-nest-optimization]: https://en.wikipedia.org/wiki/Loop_nest_optimization\n\n[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/ndarray-ctor\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fndarray-base-nullary-loop-interchange-order","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fndarray-base-nullary-loop-interchange-order","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fndarray-base-nullary-loop-interchange-order/lists"}