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Re: Mathematica Numerical Integration and For Loop
*To*: mathgroup at smc.vnet.net
*Subject*: [mg81978] Re: Mathematica Numerical Integration and For Loop
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Mon, 8 Oct 2007 00:05:50 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <fea9tf$k99$1@smc.vnet.net>
General wrote:
> I have a function which I have numerically integrated in Mathematica. I would like to be able to change a parameter of that function and re-evaluate that integral and then record the answer.
>
> Since this needs to be done for vary small changes of that independent variable it would be impossible for me to sit down and do it one by one.
>
> I am thinking of using a for loop but I cannot understand how to use it in my case.
>
> I would appreciate anyones help/
>
> Here is the form of the function that I am integrating
>
> NIntegrate[
> ref[\[lambda], \[Theta], \[Phi], \[Pi]/5, (2 \[Pi])/5], {\[Theta],
> 0, \[Pi]}, {\[Phi], 0, 2 \[Pi]}]
>
> I would like to be able to change the first variable within my ref function. This is lambda. So I want lambda to take different values within a range of 0 to 10 with increments of 0.01 and then store the output of the numerical integration. I would then like to plot lambda against the values obtained from the numerical integration.
Forget about the for-loop construction and use *Table* instead. Below, I
have cooked up a fully working example (though not very interesting from
the mathematical point of view).
(* First, we define a function with a check on each variable to ensure
that f will be called by *NIntegrate* only if its arguments are
numeric. *)
f[x_?NumericQ, y_?NumericQ, p_?NumericQ] := Exp[-x + y] Sin[p]
(* Then, we construct a list of points. Each point is a pair of values
that hold the value of p and the result of the numerical integration. *)
data = Table[{p,
NIntegrate[f[x, y, p], {x, 0, \[Infinity]}, {y, 0, 1}]}, {p, 1,
10, 1/10}];
(* Finally, we plot this list of pairs with *ListPlot*. *)
ListPlot[data]
Regards,
--
Jean-Marc
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