蒙特卡罗积分法--mathematica

直接上 mathematica代码

"Monte Carlo积分法（蒙特卡罗积分法）"
monteCarlo[f_, indvar_, m_, a_, b_, n_] :=
  Module[{
     g, x, xr, yr, area, lim, areaave, y1, y2},
  g = f /. indvar -> x;
  lim = Length[n];
  area = Table[0, {
     k, 1, lim}];
  For[k = 1, k <= lim, k++,
   For[couter = 0; i = 1, i <= n[[k]], i++,
    xr = a + (b - a)*RandomReal[];
    yr = m*RandomReal[];
    If[yr <= g /. x -> xr, couter += 1;];
    area[[k]] = m*(b - a)*couter/n[[k]]]];
  areaave = 
   Sum[n[[i]]*area[[i]], {
     i, 1, lim}]/Sum[n[[i]], {
     i, 1, lim}];
  y1 = Integrate[g, {
     x, a, b}] // N;
  (*y2=Integrate[g,{
     x,a,b}];*)
  data = {
     {
     HoldForm[\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(a\), \(b\)]\(f \
\[DifferentialD]indvar\)\)]}, Join[{
     "PointNum"}, n], 
    Join[{
     "Approx"}, area], 
    Join[{
     "Err"}, area - y1], {
     "AreaAverage", areaave}, {
     "Integrate", 
     y1}};
  Grid[data, 
   Background -> {
     None, {
     Lighter[Orange, .9], {
     White, 
       Lighter[Blend[{
     Blue, Green}], .8]}}}, 
   Dividers -> {
     {
     Darker[Gray, .6], {
     Lighter[Gray, .5]}, 
      Darker[Gray, .6]}, {
     Darker[Gray, .6], Darker[Gray, .6], {
     False},
       Darker[Gray, .6]}}, Alignment -> Center, 
   Frame -> Darker[Gray, .6]]
  ]
Pnumber = Table[k*10^2, {
     k, 1, 15, 2}];
monteCarlo[z*Sqrt[1 - z], z, 0.5, 0, 1, Pnumber]
monteCarlo[x*E^(-2 x^2), x, 0.5, 0, 1, Pnumber]
monteCarlo[Sin[y] E^Cos[y], y, 0.5, \[Pi]/2, \[Pi], Pnumber]
monteCarlo[2 x*ArcSin[x^2], x, 0.5, 0, 1/Sqrt[2], Pnumber]

运行结果：