Skip to main content

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 ==


Comments

Post a Comment

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more

plotting - Adding a thick curve to a regionplot

Suppose we have the following simple RegionPlot: f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}] Now I'm trying to change the curve defined by $y=g[x]$ into a thick black curve, while leaving all other boundaries in the plot unchanged. I've tried adding the region $y=g[x]$ and playing with the plotstyle, which didn't work, and I've tried BoundaryStyle, which changed all the boundaries in the plot. Now I'm kinda out of ideas... Any help would be appreciated! Answer With f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 You can use Epilog to add the thick line: RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, Epilog -> (Plot[g[x], {x, 0, 2}, PlotStyle -> {Black, Thick}][[1]]), PlotStyle -> {Directive[Yellow, Opacity[0.4]], Directive[Pink, Opacity[0.4]],
Post a Comment
Read more