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Re: Finding positive / non-complex solutions (newbie)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg102373] Re: Finding positive / non-complex solutions (newbie)
*From*: dh <dh at metrohm.com>
*Date*: Fri, 7 Aug 2009 05:29:57 -0400 (EDT)
*References*: <h5bk5p$hl9$1@smc.vnet.net>
Dan wrote:
> Hi,
>
> This is probably easily solved because I'm very much a newbie. I have
> two equations (eqn1 and eqn2) with two variables and want to find the
> positive (non-zero, no-complex solutions) for when they both equal 0,
> as a function of two other parameters, then plot the results. So far
> (after several days work), I've found a kind of solution (it plots
> correctly), but produces an error. The error, as far as I can tell,
> is produced by the "Cases" statement, which is the function I'm using
> to find the positive solutions. This will work when the parameters
> (theta and rho) are defined, but will fall over when undefined, which
> seems to be what happens when I call Plot.
>
> Any help on this much appreciated (along with any pointers for where
> my code looks obscure / overly complex -- as I say, I'm not used to
> Mathematica).
>
> Cheers
> Dan
>
> In[1]:=
> f[rho_, t_] := Module [{Pu, Pv, pi, d , eqn1, eqn2, res, res2, pi2},
> pi = (u Pu + (1 - u) Pv)/(2 s);
> d = (Pu - Pv)/(2 s);
> eqn1 = -t pi (1 - pi) + t u (1 - u) d^2;
> eqn2 = d (rho + u + (2 pi - 1) t - (u - (1 - u)) (1 + t d)) + pi;
> res = NSolve[{eqn1 == 0, eqn2 == 0}, {Pu, Pv}];
> res2 =
> Cases[{Pu, Pv} /.
> res, {(a_Real)?Positive, (b_Real)?Positive} :> {a, b}][[1]];
> pi2 = (u res2[[1]] + (1 - u) res2[[2]])/(2 s);
> (1 - pi2)/u
> ];
>
> In[2]:= u = 0.004;
> s = 0.02;
>
> In[4]:= f[1, 0.1]
>
> Out[4]= 0.237377
>
> In[5]:= f[10, 0.1]
>
> Out[5]= 0.0081024
>
> In[6]:= LogLogPlot[{f[rho, 0.1], f[rho, 10]}, {rho, 0.01, 100}]
>
>
>
Hi Dan,
LogLogPlot first checks if it can simplify your function. Towards this
aim it calls the function with symbolic arguments. To prevent an error
message, you must define your function only for numeric arguments like e.g.:
f[rho_?NumericQ, t_?NumericQ]
Daniel
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