Re: Plot the results of Findroot

*To*: mathgroup at smc.vnet.net*Subject*: [mg122949] Re: Plot the results of Findroot*From*: Kontopoulos Dimitris <dimitris.jp at gmail.com>*Date*: Fri, 18 Nov 2011 06:22:31 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <7BB0E96E72E84E41B24A1FF8ED13F5E6131286E80D@IE2RD2XVS581.red002.local>

hello and sorry for my late reply. i just wanted to thank you so much for your help, i ouldn't have made it alone! :) Dimitris On Nov 10, 2011, at 6:20 PM, Alexei Boulbitch wrote: > Hello, Dimitris, > One way to do what you want may be like the following. Since you do not give explicitly your equations I answer within the most simple example of two primitive equations: > > Clear[y1, y2, x1, x2, n, d]; > y1[n_] := x1 + x2 == n; > y2[d_] := x1 - x2 == d; > > Let us define a function finding its roots for any n and d: > > fR[{n_, d_}] := FindRoot[{y1[n], y2[d]}, {x1, -1}, {x2, -2}]; > > Let us check for the following list pairs {n, d} is {{1, 2}, {1, -1}, {3, -2}}. Map the function fR onto this list: > > Map[fR, {{1, 2}, {1, -1}, {3, -2}}] > > {{x1 -> 1.5, x2 -> -0.5}, {x1 -> 0., x2 -> 1.}, {x1 -> 0.5, > x2 -> 2.5}} > > Now we can package this all into one function. Its argument is a list of pairs {n, d}: > > solving[lst_List] := > Module[{fR, y1, y2}, > y1[n_] := x1 + x2 == n; > y2[d_] := x1 - x2 == d; > fR[{n_, d_}] := FindRoot[{y1[n], y2[d]}, {x1, -1}, {x2, -2}]; > Map[fR, lst] > ]; > > Now to address your second question I create an arbitrary list, lst, with the same n=1, and arbitrary d and solve it: > lst = Table[{1, RandomInteger[{-5, 5}]}, {10}] > sol = solving[lst] > > {{1, 0}, {1, -5}, {1, -1}, {1, -1}, {1, > 5}, {1, -2}, {1, -4}, {1, -4}, {1, 5}, {1, 3}} > > {{x1 -> 0.5, x2 -> 0.5}, {x1 -> -2., x2 -> 3.}, {x1 -> 0., > x2 -> 1.}, {x1 -> 0., x2 -> 1.}, {x1 -> 3., x2 -> -2.}, {x1 -> -0.5, > x2 -> 1.5}, {x1 -> -1.5, x2 -> 2.5}, {x1 -> -1.5, > x2 -> 2.5}, {x1 -> 3., x2 -> -2.}, {x1 -> 2., x2 -> -1.}} > > In order to plot x1=x1({1, d}) let us now construct the list of pairs {d,x1}. Take the i,2-nd element of the list lst and the solution for x1 (that is the i,1,2-the element) of the list of the solutions and plot it: > > lstForPlot = Table[{lst[[i, 2]], sol[[i, 1, 2]]}, {i, 1, Length[lst]}] > > {{0, 0.5}, {-5, -2.}, {-1, 0.}, {-1, 0.}, {5, > 3.}, {-2, -0.5}, {-4, -1.5}, {-4, -1.5}, {5, 3.}, {3, 2.}} > > > ListPlot[lstForPlot] > > You get a list of pairs {d,x1} plotted as the result. > There is a possible weak point here: if your equations are non-linear, it is not necessary that your initial values for FindRoot are always good. > > Hope this helps, have fun, Alexei > > > Hello everyone, > > I have a system of 21 simultaneous equations where i want to calculate > the values of x1, x2...x21 and i am trying to evaluate it by using > FindRoot. > > I have 2 problems, > 1) I want to tell FindRoot to calculate this set for a range of values > for 2 parameters (n and d) that are found in the equations > 2) I want to plot the results of x1, x2,...x20 for the range of the > parameters. > > i have named each of the 21 equations y1, y2, y3.... y21 and this is > how i wrote the command for FindRoot: > > FindRoot[{y1, y2, y2, y4, y5, y6, y7, y8, y9, y10, y11, y12, y13, y14, > y15, y16, y17, y18, y19, y20, > x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13 + > x14 + x15 + x16 + x17 + x18 + x19 + x20 + x21 == 1}, {{x1, > 0.0272275467214981, 0, 1}, {x2, 0.0271731, 0, 1}, {x3, 0.04279, 0, > 1}, {x4, 0.042534, 0, 1}, {x5, 0.0548527, 0, 1}, {x6, 0.054198, 0, > 1}, {x7, 0.0627144, 0, 1}, {x8, 0.0614572, 0, 1}, {x9, 0.066180, 0, > 1}, {x10, 0.064208, 0, 1}, {x11, 0.075882, 0, 1}, {x12, 0.062862, > 0, 1}, {x13, 0.06160, 0, 1}, {x14, 0.058231, 0, 1}, {x15, > 0.0230354, 0, 1}, {x16, 0.0250354, 0, 1}, {x17, 0.055199, 0, > 1}, {x18, 0.026367, 0, 1}, {x19, 0.028367, 0, 1}, {x20, 0.051339, > 0, 1}, {x21, 0.028735, 0, 1}}] > > > Now every time i want to find the solution for each n and d i manually > type their values > e.x. > n=10^4 > d=10^6 > > and then i get the answer from FindRoot for all the x1,x2,....x21 > > What i want to do is calculate x1,x2,...x21 for n ranging from 10^4 to > 10^9 and d ranging from 10^4 to 10^11. > > And in the end I want to plot the results (for a given d) in a graph > where the y axis is one of the x1,x2,..x21 and the x axis is n > > I tried creating a table first so i can plot its contents but it > doesn't seem to be working.... > Table[n, d, > Evaluate[MyFunction[n, d]], {n, 10^4, 10^9, 10^4}, {d, 10^4, 10^9, > 10^11}] > > I would appreciate all the tips you can give me > > Dimitris > > Alexei BOULBITCH, Dr., habil. > IEE S.A. > ZAE Weiergewan, > 11, rue Edmond Reuter, > L-5326 Contern, LUXEMBOURG > > Office phone : +352-2454-2566 > Office fax: +352-2454-3566 > mobile phone: +49 151 52 40 66 44 > > e-mail: alexei.boulbitch at iee.lu > >