how to plot nminimized result

*To*: mathgroup at smc.vnet.net*Subject*: [mg113502] how to plot nminimized result*From*: tarun dutta <tarunduttaz at gmail.com>*Date*: Sun, 31 Oct 2010 02:09:22 -0500 (EST)

p = 0.01; q = 1; n = 5; CompNum[i_] := a[i] + I b[i]; TCompNum[i_] := a[i] - I b[i]; f = Sum[SetPrecision[ Sqrt[i + 1] p CompNum[i] TCompNum[i + 1] + p CompNum[i + 1] TCompNum[i] + (q*i + i (i - 1)) CompNum[ i] TCompNum[i], Infinity], {i, 0, n}]; c = \!\( \*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(n\)] \*SuperscriptBox[\(Abs\ [CompNum[i]]\), \(2\)]\) == 1; c // TraditionalForm; dp = {a[n + 1] -> 0, b[n + 1] -> 0}; var = Table[CompNum[i], {i, 0, n}] /. a_ + I b_ -> {a, b} // Flatten; prob = Join[ComplexExpand[f] /. a_ + I b_ -> {a^2 + b^2} /. dp, {c}]; {val, res} = NMinimize[prob, var, MaxIterations -> 10000, AccuracyGoal -> 30]; // AbsoluteTiming this is my main program.for fixed value of p and q.I got the minimized value and also the variable like a[o],a[1]..etc for example(from above program) In[12]:= val Out[12]= 5.25767*10^-6 In[13]:= res Out[13]= {a[0] -> -0.805443, b[0] -> 0.591251, a[1] -> -0.00824279, b[1] -> 0.0402093, a[2] -> 0.0000547477, b[2] -> -0.000202243, a[3] -> -1.11872*10^-7, b[3] -> 3.84618*10^-7, a[4] -> 6.22738*10^-10, b[4] -> 8.88902*10^-11, a[5] -> 3.02522*10^-10, b[5] -> 3.02899*10^-10} now I want to vary the value of p from 0 to 2 for a fixed value of q.q will also vary from 0 to 5.so, program will start taking the first value of q as 0 and scan p from 0 to 2 in steps 0.01.every time i will get the corresponding {val,res}.for example q=1 p=0.01 val 5.25767*10^-6 res a[0] -> -0.805443, b[0] -> 0.591251, a[1] -> -0.00824279, b[1] -> 0.0402093, a[2] -> 0.0000547477, b[2] -> -0.000202243, a[3] -> -1.11872*10^-7, b[3] -> 3.84618*10^-7, a[4] -> 6.22738*10^-10, b[4] -> 8.88902*10^-11, a[5] -> 3.02522*10^-10, b[5] -> 3.02899*10^-10} q=1 p=0.02 val= res = now i want to check the result of res----if any a[i] and b[i] of all a[i] and b[i] is nearly equal to 1(or > o.1) and other a[i] are zero then print 'true' and also print the corresponding value of p and q if more than one a[i] and b[i] have value nearly equal to 1 then print 'false' from above example.. q=1 p=0.01 res=True because only a[0] and b[0] have nearly = to 1.we ignore all other a[i] and b[i] cause they have value in order of 10^-2 or more. so there will be some kind of table as q=1 p=0.01 res true q=1 p=0.02 res true q=1 p=0.03 res true q=1 p=0.04 res false now we only consider only the last value of p for which we get res=true after that point we get false from above example we note the value of p=0.03 for q=1 similarly q=1.1 res true p=0.01 q=1.1 res true p=0.02 q=1.1 res false p=0.03 here we note the value p=0.02,q=1.1 in this way we get a table of true value like q=1 p=0.03 q=1.1 p=0.02 .... ..... now I want to plot(contour) q vs p....... this is my problem....so how will I do all this in mathematica... help if the problem is not clear to you people just mail me... with regards, tarun