Re: FindRoot / Jacobian

*To*: mathgroup at smc.vnet.net*Subject*: [mg84307] Re: FindRoot / Jacobian*From*: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>*Date*: Tue, 18 Dec 2007 05:34:42 -0500 (EST)*References*: <fk73ub$6el$1@smc.vnet.net>

Here is how you can solve your problem: solU=(E^((-I)*p-(2*ArcTan[Tan[q/2]/Sqrt[3]])/Sqrt[3])*(1+E^((2*I)*p)))/2 solV=Sin[p]/E^((2*ArcTan[Tan[q/2]/Sqrt[3]])/Sqrt[3]) solutions=Table[FindRoot[solU==N[u]&&solV==N[v],{{p,0},{q,0}}],{u,-\[Pi],\[Pi],(2\[Pi])/70},{v,-\[Pi],\[Pi],(2\[Pi])/70}]; You can do a quick visualisation of the solutions with the following graphics: Graphics[{Map[Point,#,{2}],Map[Line,#],Map[Line,Transpose[#]]}&[{p,q}/.solutions//Chop]] Stephen Luttrell West Malvern, UK <sigmundv at gmail.com> wrote in message news:fk73ub$6el$1 at smc.vnet.net... > Dear readers, > > Consider the following expressions: > > solU = (E^((-I)*p - (2*ArcTan[Tan[q/2]/Sqrt[3]])/Sqrt[3])*(1 + > E^((2*I)*p)))/2 > > solV = Sin[p]/E^((2*ArcTan[Tan[q/2]/Sqrt[3]])/Sqrt[3]) > > I then want to solve the system of equations (u = solU, v = solV) > numerically on a grid (u,v) \in (-pi,pi). For that purpose I use > FindRoot, and execute the following: > > u1 = Pi; du = 2*Pi/70; > > uvPts1 = Flatten[Table[{u, v}, {u, u1 + du, u2 - du, du}, {v, v1 + > du, > v2 - du, dv}], 1]; > > uvNew = {p, q} /. Table[FindRoot[{solU == uvPts1[[i, 1]], solV == > uvPts1[[i, 2]]}, {p, > -2}, {q, 1+I}], {i, Length[uvPts1]}]; > > This gives me a p-value and a q-value for each point on the grid, no > problem. However, I get the wrong solution at some of the grid points. > Since I get several of the following type of messages, this would be > expected: > > FindRoot::jsing:Encountered a singular Jacobian at the point {p,q} = \ > {-10.4516+0.784848 \[ImaginaryI],108.092+104.013 \[ImaginaryI]}. Try \ > perturbing the initial point(s). >> > > Then I would like to know if there is any 'nice' way to handle these > 'singular Jacobian' errors? Does there exist any kind of 'event > handler', as in NDSolve? > > Kind regards, > Sigmund Vestergaard >