CODEWITHSUNDEEP
integrationwolfram-mathematica
James J
James J

Reputation: 131

How to use Nintegrate in mathematica whose integrand contains elements from a 1d array that need to be accessed by index

I am trying to evaluate the following integral:

Integral

where the issue lies with variables like F since it is defined as F[x_, y_] := f[x, y]/(2*Cto[Norm[x]]*Cto[Norm[y]]) and Cto[x_] := C_t[[Round[x]]] where C_t is a 1d array and x and y are two vector and I need to access the element of C_t corresponding to the integer of the magnitude of x for example. However, this gives me the following errors when evaluating the integral:

Ci = Flatten[Import["Downloads/ctjulien.txt", "table"]]
Cp = Flatten[Import["Downloads/clphiphi.txt", "table"]]
Subscript[C, t] = Flatten[Import["Downloads/ctobs.txt", "table"]]



Lp[a_] := 1052*{Cos[a], Sin[a]}
vL[L_] := {L, 0}
l[l1_, \[CapitalPhi]1_] := 
 l1*{Cos[\[CapitalPhi]1], Sin[\[CapitalPhi]1]}
Cii[x_] := Ci[[Round[x]]]
f[x_, y_] := Cii[Norm[x]]*Dot[x + y, x] + Cii[Norm[y]]*Dot[x + y, y]
Cto[x_] := Subscript[C, t][[Round[x]]]
F[x_, y_] := f[x, y]/(2*Cto[Norm[x]]*Cto[Norm[y]])
Cpp[x_] := Cp[[Round[x]]]

NIntegrate[l1*F[l[l1,\[CapitalPhi]],{L,0}-l[l1,\[CapitalPhi]]]*F[Lp[\[CapitalPhi]p],{L,0}-Lp[\[CapitalPhi]p]]*(Dot[Lp[\[CapitalPhi]p],Lp[\[CapitalPhi]p]-l[l1,\[CapitalPhi]]]*If[Norm[Lp[\[CapitalPhi]p]-l[l1,\[CapitalPhi]]]<=2900,Cpp[Norm[Lp[\[CapitalPhi]p]-l[l1,\[CapitalPhi]]]],0]*f[-{L,0}+l[l1,\[CapitalPhi]],{L,0}-Lp[\[CapitalPhi]p]]+Dot[Lp[\[CapitalPhi]p],Lp[\[CapitalPhi]p]-l[{L,0}-l[l1,\[CapitalPhi]],\[CapitalPhi]]]*If[Norm[Lp[\[CapitalPhi]p]-l[{L,0}-l[l1,\[CapitalPhi]],\[CapitalPhi]]]<=2900,Cpp[Norm[Lp[\[CapitalPhi]p]-l[{L,0}-l[l1,\[CapitalPhi]],\[CapitalPhi]]]],0]*f[-l[l1,\[CapitalPhi]],{L,0}-Lp[\[CapitalPhi]p]]),{\[CapitalPhi],-Pi,Pi},{\[CapitalPhi]p,-Pi,Pi},{l1,2,3000}]

Errors

Upvotes: 0

Views: 226

Answers (1)

Bill
Bill

Reputation: 3957

This isn't anywhere near an answer yet, but it is a start. Watch out for Subscript and greek characters and use those appropriately when you test this.

If you insert in front of your code

Ci =Table[RandomInteger[{1,10}],{3000}];
Cp =Table[RandomInteger[{1,10}],{3000}];
Ct =Table[RandomInteger[{1,10}],{3000}];

then you can try to test your code without having your data files present.

If you then test your code you get a stream of "The expression Round[Abs[2+L]] cannot be used as a part" but if you instead insert in front of your code L=2 or some other integer assignment then that error goes away

If you use NIntegrate[yourlongexpression...] then you get a stream of "Round[Sqrt[Abs[l1 Cos[phi]]^2+Abs[l1 Sin[phi]]^2 cannot be used as a part" If you instead use fun[phi_?NumericQ, phip_?NumericQ, l1_?NumericQ]:=yourlongexpression; NIntegrate[fun[phi,phip,l1]...] then that error goes away.

If you use Table[fun[phi,phip,l1],{phi,-Pi,Pi,Pi/2},{phip,-Pi,Pi,Pi/2},{l1,2,10}] instead of your integral and you look carefully at the output then you should see the word List appearing a number of times. That means you have somelist[[0]] somewhere in your code and Mathematica subscripts all start with 1, not with 0 and that has to be tracked down and fixed.

That is probably the first three or four levels of errors that need to found and fixed.

Upvotes: 1

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