Re: real valued function from complex
- To: mathgroup at smc.vnet.net
- Subject: [mg37405] Re: [mg37354] real valued function from complex
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Sat, 26 Oct 2002 02:04:29 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
It seems to me that:
Plot[Evaluate[{Re[D[Zeta[1/
2 + I*t], t]], Re[Zeta[1/2 + I*t]]}], {t, 0, 40}, PlotStyle ->
{RGBColor[
1, 0, 0], RGBColor[0, 0, 1]}]
should give you what you want?
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/
On Friday, October 25, 2002, at 03:46 PM,
strgh at mimosa.csv.warwick.ac.uk () wrote:
> I want to define a real-valued function f[t_] from the
> values of a complex-valued function on a line parametrised
> by t, and then be able to handle f like any other real
> function (differentiate it etc.)
>
> A cute example is:
>
> Clear[rz, drz];
> rz[t_] := Re[Zeta[1/2 + I*t]];
> drz[t_] := D[rz[t], t] (* the sort of thing I want to do *)
>
> so that
>
> Plot[{drz[t], Im[Zeta[1/2 + I*t]]}, {t, 0, 40},
> PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}]
>
> will work (it doesn't).
> I can get a quick & dirty numerical approximation in this case
> (including, as a reality check, the original function I'm
> differentiating) using something like
>
> Clear[rz, iz, rztable, plotzeta];
> rz[t_] := Re[Zeta[1/2 + I*t]];
> iz[t_] := Im[Zeta[1/2 + I*t]];
> rztable[tmin_, tmax_] :=
> Table[{t, rz[t]}, {t, tmin, tmax, (tmax - tmin)/50}];
> plotzeta[tmin_, tmax_] := Module[{rzapprox},
> rzapprox = Interpolation[rztable[tmin, tmax]];
> Plot[{rzapprox'[t], rz[t], iz[t]}, {t, 0, 40},
> PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 1, 0],
> RGBColor[0, 0, 1]}]
> ]
>
> plotzeta[0, 40]
>
> However I'd prefer to leave the numerical approximations
> till the last minute (i.e. plotting), and the interpolation
> table would need tweaking on a case-by-case basis.
> Any other suggestions? (sorry if there is an "obvious" answer).
> -- Ewart Shaw
> --
> J.E.H.Shaw [Ewart Shaw] strgh at uk.ac.warwick TEL: +44 2476
> 523069
> Department of Statistics, University of Warwick, Coventry CV4 7AL,
> U.K.
> http://www.warwick.ac.uk/statsdept/Staff/JEHS/
> 3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[) <#:3
> 6 2
>
>
>