Re: Problem with compiled function (is this a bug?)

*To*: mathgroup at smc.vnet.net*Subject*: [mg65578] Re: [mg65570] Problem with compiled function (is this a bug?)*From*: "Carl K. Woll" <carlw at wolfram.com>*Date*: Sun, 9 Apr 2006 04:32:04 -0400 (EDT)*References*: <200604080445.AAA25147@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

szhorvat at gmail.com wrote: > I have a problem with the following compiled function: > > cpl = Compile[{x,y}, Table[Ceiling[Norm[{i, j} - Ceiling[{ > x, y}/2]]], {i, 1, x}, {j, 1, y}]] > > When trying to use this function (for example, as idx = cpl[100,100]), > I get the following error: > > CompiledFunction::"cfte" : > Compiled expression 49 Sqrt[2] should be a rank 1 tensor of > machine-size integers. > > CompiledFunction::cfex: External evaluation error at instruction 23; > proceeding with uncompiled evaluation. > > I get the same error even if I try to specify that all variables are > Reals: > > cpl = Compile[{{x, _Real}, {y, _Real}}, Table[Ceiling[Norm[{i, j} - > Ceiling[{ > x, y}/2]]], {i, 1, x}, {j, 1, y}], {{i, _Real}, {j, _Real}}] > > Is this a bug in Mathematica? If not, what is the right way to compile > this function? Does this error occur with earlier versions than 5.2? > > I'd like to use this function to generate indices for a matrix whose > values I want to average radially (ie. I'd like to compute the mean > values in the ring around the center of the matrix). Unofrtunately this > function takes more than 16 seconds on an 500x500 matrix on my machine > which seems unrealistically long for such a simple function. I need to > use the function interactively on many datasets, often much larger than > 500x500. > > Szabolcs Horvat I think the problem is that Norm is a relatively new function (version 5) and it hasn't been incorporated into Compile. Witness: In[1]:= cpl=Compile[{x,y}, Table[Ceiling[Norm[{i,j}-Ceiling[{x,y}/2]]],{i,1,x},{j,1,y}]]; In[2]:= cpl[[4]] Out[2]= {{1, 5}, {28, 1, 4}, {28, 0, 5}, {7, -1, 8}, {62, 5, 4, 8, 2, 0}, {7, 0, 9}, {11, 9, 6}, {4, 18}, {7, 0, 9}, {11, 9, 7}, {4, 14}, {65, 6, 7, 2, 4}, {65, 0, 1, 3, 1}, {7, 1, 9}, {7, 2, 10}, {15, 0, 9, 2}, {15, 0, 10, 3}, {92, 260, 3, 0, 2, 3, 0, 3, 3, 0, 4}, {92, 273, 3, 0, 4, 3, 1, 1, 3, 1, 5}, {91, 49, 3, 1, 5, 2, 1, 1}, {91, 41, 2, 1, 1, 2, 1, 5}, {51, 4, 5, 4}, {55, Norm, 2, 1, 4, 2, 1, 5}, {64, 8, 5, 0}, {5, 7, 4, -13}, {5, 6, 5, -17}, {2}} You'll see that a Norm is buried amidst the compile code, indicating that it wasn't compiled. One workaround is to use (Sqrt[#.#]&) instead of Norm, as Dot and Sqrt are compilable: cpl2 = Compile[{x, y}, Table[Ceiling[(Sqrt[#.#] &)[{i, j} - Ceiling[{x, y}/2]]], {i, 1, x}, {j, 1, y}]]; In[4]:= cpl2[[4]] Out[4]= {{1, 5}, {28, 1, 4}, {28, 0, 5}, {7, 0, 9}, {62, 5, 4, 2, 0}, {7, 0, 10}, {11, 10, 6}, {4, 21}, {7, 0, 10}, {11, 10, 7}, {4, 17}, {65, 6, 7, 2, 2}, {65, 0, 1, 3, 1}, {7, 1, 10}, {7, 2, 11}, {15, 0, 10, 2}, {15, 0, 11, 4}, {92, 260, 3, 0, 2, 3, 0, 4, 3, 0, 3}, {92, 273, 3, 0, 3, 3, 1, 1, 3, 1, 3}, {91, 49, 3, 1, 3, 2, 1, 1}, {91, 41, 2, 1, 1, 2, 1, 3}, {51, 2, 3, 2}, {89, 2, 2, 10}, {15, 0, 10, 3}, {91, 55, 3, 0, 3, 3, 0, 2}, {91, 49, 3, 0, 2, 2, 0, 10}, {63, 9, 10, 0}, {5, 7, 4, -16}, {5, 6, 5, -20}, {2}} However, it seems to me that you ought to be able to optimize this function so that even without Compile it would be much faster. For example: cpl3[x_, y_] := Ceiling[Sqrt[ N[Outer[Plus, (Range[x] - Ceiling[x/2])^2, (Range[y] - Ceiling[y/2])^2]]]] Some tests: In[12]:= r1=cpl2[1000,1000];//Timing r2=cpl3[1000,1000];//Timing r1===r2 Out[12]= {2.391 Second,Null} Out[13]= {0.125 Second,Null} Out[14]= True The uncompiled function cpl3 seems to meet your speed requirements. Carl Woll Wolfram Research

**References**:**Problem with compiled function (is this a bug?)***From:*szhorvat@gmail.com