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copied!<blockquote> <p>Can you redefine an arithmetic operator in MATLAB?... Yes</p> <p><strong>Should</strong> you redefine an arithmetic operator in MATLAB?... Eh, probably not.</p> </blockquote> <p>Why? Because every other function in MATLAB expects that the arithmetic operator will behave as defined by the built-in implementation.</p> <p>I've answered a few other related questions that have dealt with overloading arithmetic operators and shadowing built-in behavior, which I definitely suggest reading through first to understand the details, difficulties, and pitfalls involved in such an approach:</p> <ul> <li><a href="https://stackoverflow.com/q/5365464/52738">MATLAB: Is it possible to overload operators on native constructs (cells, structs, etc)?</a></li> <li><a href="https://stackoverflow.com/q/2425251/52738">How do I get real integer overflows in MATLAB/Octave?</a></li> </ul> <p>And now that I'm done with my disclaimer, I'll hand you the gun with which to potentially shoot yourself in the foot... ;)</p> <hr> <p>Arithmetic operators in MATLAB have functional equivalents that are called behind the scenes when you invoke them, which are listed <a href="http://www.mathworks.com/help/matlab/arithmetic-operators.html" rel="nofollow noreferrer">here</a>. The arraywise power operator <code>.^</code> calls the built-in <a href="http://www.mathworks.com/help/matlab/ref/power.html" rel="nofollow noreferrer"><code>power</code></a> function when invoked.</p> <p>Now, there will be a separate <code>power</code> function defined for each <a href="https://www.mathworks.com/help/matlab/numeric-types.html" rel="nofollow noreferrer">data type</a> that uses it. This function will be placed in an <code>@type</code> directory, which you can see by using the <a href="https://www.mathworks.com/help/matlab/ref/which.html" rel="nofollow noreferrer"><code>which</code></a> function to look at the different <code>power</code> functions that exist:</p> <pre><code>>> which power -all built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@single\power) % single method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@double\power) % double method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@char\power) % char method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@int64\power) % int64 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@int32\power) % int32 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@int16\power) % int16 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@int8\power) % int8 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@uint64\power) % uint64 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@uint32\power) % uint32 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@uint16\power) % uint16 method built-in (C:\Program Files\MATLAB\R2010b\toolbox\matlab\ops\@uint8\power) % uint8 method </code></pre> <p>If your variables <code>x</code> and <code>y</code> are going to be of type <a href="https://www.mathworks.com/help/matlab/ref/double.html" rel="nofollow noreferrer"><code>double</code></a> (as they are by default in MATLAB), then you will have to shadow the built-in <code>@double\power</code> function. You can do this by creating a directory (we'll call it <code>temp</code>), creating a subdirectory within that called <code>@double</code>, and then placing the following custom <code>power</code> function in that subdirectory:</p> <pre><code>function result = power(x, y) result = sign(x).*abs(builtin('power', x, y)); end </code></pre> <p>Now, based on the <a href="https://www.mathworks.com/help/matlab/matlab_prog/function-precedence-order.html" rel="nofollow noreferrer">function precedence order</a> MATLAB follows, if you add the directory <code>temp</code> to the <a href="http://www.mathworks.com/help/matlab/matlab_env/what-is-the-matlab-search-path.html" rel="nofollow noreferrer">MATLAB path</a>, or if you simply change the <a href="http://www.mathworks.com/help/matlab/ref/cd.html" rel="nofollow noreferrer">current working directory</a> to <code>temp</code>, then the above custom <code>power</code> function will be called instead of the built-in one when using the <code>.^</code> operator on double variables.</p>

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