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performance tuning - How can I make this program work faster?


Previous question: Can any one help me make my program work faster?


This question is an extension to the question I asked previously and referred to in the link above. I want to add spin to my system, so I changed it to the following code. the problem is that although I am using Compile, it is still very slow. I didn't change it much, so I don't understand why it is becoming so slow?


This is the code after including the spin by using the function kdfxn which acts as a delta function. gives 1 in case I have equal spin for instance if sz1 and sz2 are equal and gives 0 otherwise. The only changed I made is in chmat, the rest is the same as previous.


 nvec = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,

 18, 19, 20};
 svec = {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, \
 -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
  1, 1, 1};
  ne = 5;
  nμ = 40;
  δ = -150;
 β = 1;
  kdfxn[i_, j_] := If[i == j, 1, 0]
 avec = {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 
 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
 0, 0, 0, 0, 0, 0, 0, 0}};


 cfxn = Block[{n1a, n1b, n2a, n2b},
  With[{code = Which[
   n1a == n1b && n2a == n2b,
   Evaluate[N[1/6 (1 - 3/(n1a^2 π^2) - 3/(n2a^2 π^2))]],

   n1a == n1b && n2a != n2b,
   Evaluate[N[(4 (1 + (-1)^(n2a + n2b)) n2a n2b)/((n2a^2 - n2b^2)^2 π^2)]],

   n1a != n1b && n2a == n2b,
   Evaluate[N[(4 (1 + (-1)^(n1a + n1b)) n1a n1b)/((n1a^2 - n1b^2)^2 π^2)]],       


   True, 
   Evaluate[N[-((32 (-1 + (-1)^(n1a + n1b)) (-1 + (-1)^(n2a + n2b)) n1a n1b 
   n2a n2b)/((n1a^2 - n1b^2)^2 (n2a^2 - n2b^2)^2 π^4))]]
   ]},
   Compile[{{n1a, _Integer}, {n1b, _Integer}, {n2a, _Integer}, {n2b, 
   _Integer}},
    code,
  CompilationTarget -> "C"
   ]

    ]];

This is the same function as previous question, which I did not change, and it will be use later to calculate a matrix:


   chmat = With[{ccfxn = cfxn, kkdfxn = kdfxn}, 
   Compile[{{nm, _Integer}, {ne, _Integer}, {b, _Real}, {d, _Real}, \
   {avec, _Real, 2}, {nvec, _Real, 1}, {svec, _Real, 1}}, 
   Block[{sz0, sz1, sz2, sz3, n0, n1, n2, n3, h1, h2, tmp, tmp2, 
   tmp21, kf01, kf23, kf13, kf02}, 
   Table[n0 = Compile`GetElement[nvec, nm0];
   n1 = Compile`GetElement[nvec, nm1];

   sz0 = Compile`GetElement[svec, nm0];
   sz1 = Compile`GetElement[svec, nm1];
   tmp = 0.;
   Do[sz2 = Compile`GetElement[svec, nm2];
   sz3 = Compile`GetElement[svec, nm3];
   n2 = Compile`GetElement[nvec, nm2];
   n3 = Compile`GetElement[nvec, nm3];
   tmp2 = ccfxn[n1, n0, n3, n2];
   tmp21 = ccfxn[n1, n3, n0, n2];


   kf01 = kkdfxn[sz0, sz1];
   kf23 = kkdfxn[sz2, sz3];
   kf13 = kkdfxn[sz1, sz3];
   kf02 = kkdfxn[sz0, sz2];

   Do[
    tmp += (tmp2 kf23 kf01 - tmp21 kf13 kf02) Compile`GetElement[
       avec, j, nm3] Compile`GetElement[avec, j, nm2], {j, 1, 
     ne}], {nm2, 1, nm}, {nm3, 1, nm}];
    d tmp + 

    If[nm0 == nm1, (n0^2 Pi^2 + b Compile`GetElement[svec, nm0]), 
    0.], {nm0, 1, nm}, {nm1, 1, nm}]], CompilationTarget -> "C", 
  CompilationOptions -> {"InlineCompiledFunctions" -> True}, 
  RuntimeOptions -> "Speed"]];

and then I use the iteration method to converge the energies, which is the same as previous question and the speed is fine,:


  Table[
  hmat = chmat[nμ, ne, δ, β, avec, nvec, svec];
  {evals, evecs} = Eigensystem[hmat];
  pos = Ordering[evals][[1 ;; ne]];

  bvec = Map[x \[Function] If[Total[x] < 0, -x, x], evecs[[pos]]];
  residual = Max[Abs[avec - bvec]];
  avec = bvec;
  {residual, Total[evals[[pos]]]},
  {j, 1, 30}]

I wish some one could tell me why does it become so slow as I have included spin, and is there any way I can make it work faster?



Answer



Despite telling myself I wouldn't fix this, here you are... Your problem is that you can't Compile DownValues.


Replace kdfxn with (If[# == #2, 1, 0] &) and it'll work fine.



It might help to read up on Compile a bit so this won't be an issue in the future


P.S. KroneckerDelta already exists in the language and if you were to do your own version you'd want to use === instead of ==


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