Nested Functions vs Object-Oriented Programming: k-D Tree example and relative performance

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My colleagues tend to criticize my use of nested functions in MATLAB, likening that to the professional no-no of modifying global variables. To placate those peers, I'll recode those methods that use nested functions into a handle-based object-oriented methods. Now, they accept that the current properties are accessible to the object's methods.
However, I have a specific instance where the nested functions implementation outperforms the handle-based object-oriented programming style: k-D Trees.
Here is the benchmark code run from the command window.
pdat = randn(130001,3); % position data
tic;a_tree = kDTree(pdat); disp(toc) % 9.0822 seconds
tic;i_tree = ikdtree(pdat);disp(toc) % 1.0869 seconds
I'm seeking insights into what is causing these performance differences.

Accepted Answer

per isakson
per isakson on 14 Aug 2020
Edited: per isakson on 14 Aug 2020
On my R2018b,Win10 the diffence is even bigger
% 18.585, 0.79143
% 18.937, 0.75923
The profiling result of get_root_index shows
that assigning values to the properties, LeftIndices and RightIndices, takes nearly all the time.
It's a known fact that assigning values to properties is slow in Matlab. See Is MATLAB OOP slow or am I doing something wrong? and Numerical operations are slow on class properties versus in workspace.
The execution engine (/JIT) is The Mathworks' trade secret.
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