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POIn Mathematica, how do I compile the function Outer[] for an arbitrary number of arguments?
 

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  1. POIn Mathematica, how do I compile the function Outer[] for an arbitrary number of arguments?
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    <p>If I want to find all possible sums from two lists <code>list1</code> and <code>list2</code>, I use the <code>Outer[]</code> function with the specification of <code>Plus</code> as the combining operator:</p> <p><code>In[1]= list1 = {a, b}; list2 = {c, d}; Outer[Plus, list1, list2]</code></p> <p><code>Out[1]= {{a + c, a + d}, {b + c, b + d}}</code></p> <p>If I want to be able to handle an arbitrary number of lists, say a list of lists,</p> <p><code>In[2]= listOfLists={list1, list2};</code></p> <p>then the only way I know how to find all possible sums is to use the <code>Apply[]</code> function (which has the short hand <code>@@</code>) along with <code>Join</code>:</p> <p><code>In[3]= argumentsToPass=Join[{Plus},listOfLists]</code></p> <p><code>Out[3]= {Plus, {a, b}, {c, d}}</code></p> <p><code>In[4]= Outer @@ argumentsToPass</code></p> <p><code>Out[4]= {{a + c, a + d}, {b + c, b + d}}</code></p> <p>or simply</p> <p><code>In[5]= Outer @@ Join[{Plus},listOfLists]</code></p> <p><code>Out[5]= {{a + c, a + d}, {b + c, b + d}}</code></p> <p>The problem comes when I try to compile:</p> <p><code>In[6]= Compile[ ..... Outer @@ Join[{Plus},listOfLists] .... ]</code></p> <p><code>Compile::cpapot: "Compilation of Outer@@Join[{Plus},listOfLists]] is not supported for the function argument Outer. The only function arguments supported are Times, Plus, or List. Evaluation will use the uncompiled function. "</code></p> <p>The thing is, I <em>am</em> using a supported function, namely <code>Plus</code>. The problem seems to be solely with the <code>Apply[]</code> function. Because if I give it a fixed number of lists to outer-plus together, it works fine</p> <p><code>In[7]= Compile[{{bob, _Integer, 1}, {joe, _Integer, 1}}, Outer[Plus, bob, joe]]</code></p> <p><code>Out[7]= CompiledFunction[{bob, joe}, Outer[Plus, bob, joe],-CompiledCode-]</code></p> <p>but as soon as I use <code>Apply</code>, it breaks</p> <p><code>In[8]= Compile[{{bob, _Integer, 1}, {joe, _Integer, 1}}, Outer @@ Join[{Plus}, {bob, joe}]]</code></p> <p><code>Out[8]= Compile::cpapot: "Compilation of Outer@@Join[{Plus},{bob,joe}] is not supported for the function argument Outer. The only function arguments supported are Times, Plus, or List. Evaluation will use the uncompiled function."</code></p> <p><strong>So my questions is</strong>: Is there a way to circumvent this error or, alternatively, a way to compute all possible sums of elements pulled from an arbitrary number of lists in a compiled function?</p> <p>(Also, I'm not sure if "compilation" is an appropriate tag. Please advise.)</p> <p>Thanks so much.</p>
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    1. USJess Riedel
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    1. COAbout how many lists are you expecting, and how long are the lists? Depending on the answer, Compile may not be the fastest way to perform this operation.
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      1. USjoebolte
 

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