npm install @stdlib/ndarray-base-loop-interchange-order

Alternatively,

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• For use in Observable, or in browser/node environments, use theUniversal Module Definition (UMD) build available on theumd branch (seeREADME).

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varloopOrder=require('@stdlib/ndarray-base-loop-interchange-order');

Reordersndarray dimensions and associated strides forloop interchange.

// Define an array shape:varshape=[2,2];// Define the strides for the input arrays:varstridesX=[2,1];// row-majorvarstridesY=[4,2];// row-major// Define the strides for the output array:varstridesZ=[1,2];// column-major// Resolve the loop interchange order:varo=loopOrder(shape,[stridesX,stridesY,stridesZ]);// returns [...]

The function returns an array having the following elements:

[ <shape>, ...<strides> ]

where

• shape: dimensions sorted in loop order.
• ...strides: strides for each respective ndarray sorted in loop order.

For all returned arrays, the first element corresponds to the innermost loop, and the last element corresponds to the outermost loop.

• 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 is a technique used inloop nest optimization to improve locality of reference and take advantage of CPU cache.

  The purpose of this function is to orderndarray 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.

• Cache performance may be degraded if the layout order (i.e., row-major or column-major) differs for the input and outputndarrays. This function is intended to optimize cache performance for the most common layout order. Accordingly, if the outputndarray has a different layout order (e.g., if the inputndarrays are row-major and the outputndarray is column-major), cache misses are likely for the outputndarray. In general, to ensure best performance, input and outputndarrays should have the same layout order.

• The function assumes that the input and outputndarrays have the same shape. Hence, loop interchange order should only be determinedafter broadcasting.

This package is part ofstdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to developstdlib, see the main projectrepository.

SeeLICENSE.

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