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Compile succeeds and then fails with a simple change.

W. Craig Carter, MIT
Posted 12 years ago

The following works just fine:

positions = RandomReal[{-200, 200}, {1000, 2}];

example1 = Compile[{{positions, _Real, 2}},
  Block[{distanceMat, distanceMatCubed, differenceMat, ret},
   differenceMat = Outer[Subtract, N[positions], N[positions], 1] ;
   distanceMat = 
    Map[#.# &, differenceMat, {2}] + IdentityMatrix[Length[positions]];
   distanceMatCubed = distanceMat^3;
   (*{
   Total[-12 differenceMat ( 1-distanceMatCubed)/distanceMat^7],
   Total[(1-2distanceMatCubed)/distanceMat^6]
   }*)

   Total[-12 differenceMat ( 1 - distanceMatCubed)/distanceMat^7]
   ]
  ]

Timing[example1[positions];]

However, this doesn't:

example2 = Compile[{{positions, _Real, 2}},
  Block[{distanceMat, distanceMatCubed, differenceMat, ret},
   differenceMat = Outer[Subtract, N[positions], N[positions], 1] ;
   distanceMat = 
    Map[#.# &, differenceMat, {2}] + IdentityMatrix[Length[positions]];
   distanceMatCubed = distanceMat^3;
   {
    Total[-12 differenceMat ( 1 - distanceMatCubed)/distanceMat^7],
    Total[(1 - 2 distanceMatCubed)/distanceMat^6]
    }
   ]
  ]

Timing[example2[positions];]

Looking at the CompilePrint, the offending line appears to be:

MainEvaluate[ Hold[List][ T(R2)6, T(R1)12]]

Where T(R2)6 = Total[ T(R3)11, I12]] and T(R1)12 = Total[ T(R2)11, I12]] appear to be valid results.

Perhaps, I need to coerce the final result type... but I am not sure how to do this. Any advice? Thanks, Craig
POSTED BY: W. Craig Carter
4 Replies
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It fails because the two totals do not have compatible dimensions, so creating that final List involves an object that is not a proper tensor. Compile gets upset when handling nontensorial objects. Very, very upset.
POSTED BY: Daniel Lichtblau

I do not know why it fails when the compile result is multi-dimensions list.
POSTED BY: Nasser M. Abbasi

Thanks Nassar, I've fixed the particles and positions typo in the original post. Your solution will work: I suppose that I can Partition the result. However, the Dimensions of the two Lists that are getting Flattened are different, but it is doable. Thanks.

However, I am still curious as to why it fails.

Thanks, Craig

PS: I believe that my N[positions] in the compile statement is redundant...
POSTED BY: W. Craig Carter

btw, you meant to write example[particles] and not example[positions]

As for the problem, it seems relating to the list at the end. Simply putting Flatten at the end, removes the error and not it works. 

    particles = RandomReal[{-200, 200}, {1000, 2}];
    example = Compile[{{positions, _Real, 2}}, 
      Block[{distanceMat, distanceMatCubed, differenceMat, ret},
         differenceMat = Outer[Subtract, N[positions], N[positions], 1];
         distanceMat = Map[#.# &, differenceMat, {2}] + IdentityMatrix[Length[positions]];
         distanceMatCubed = distanceMat^3;   
         Flatten@{Total[-12 differenceMat (1 - distanceMatCubed)/distanceMat^7], 
                      Total[(1 - 2 distanceMatCubed)/distanceMat^6]}
     ]
  ]
   example[particles]
POSTED BY: Nasser M. Abbasi
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