Re: Using Map with a function of more than 1 argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg64255] Re: [mg64241] Using Map with a function of more than 1 argument*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Wed, 8 Feb 2006 03:53:47 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200602070836.DAA29926@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

Before spending too much time "rolling your own", you may want to take a look at David Park's add-on package Cardano3 (based on his DrawGraphics add-on). See: http://home.earthlink.net/~djmp/Mathematica.html You can find a few examples of use of this package also on the Files page at http://www.math.umass.edu/Courses/Math_421/ (not all the notebooks there involve Cardano3, and none are evaluated, so you'll need Park's package). See, especially, IntroComplexGraphics.nb, VisualizeFunctions.nb, RiemannSphere.nb, ExponentialLogFunctions.nb, Poles.nb. Matt wrote: > Hello Mathematica group, > I'm starting down the path of trying to come up with my own complex > mapping function. I'm aware of CartesianMap and PolarMap, but I've > been frustrated by those because of the lack of fine control I seem to > have (I say 'seem to have' because it might very well be the case that > I'm not aware of some of the finer points of these two functions). The > fine control that is lacking, is for example, the fact that within > CartesianMap, if I want to specify different colors for the lines, I > can't really. Let's say I went with the default of $Lines which is I > believe 25. In order to have the lines draw in 25 different colours, I > believe I'd have to supply 25 color primitives to PlotStyle. If I > supply less than 25, then the color primitives are recycled. My first > plan of attack was to take the Graphics object that is output by > CartesianMap and try to manipulate the coloring primitive for each line > drawn based upon starting and ending points (i.e. within a 'Line', if > the first point's x value and the last point's x value were 'close', > than I knew I was dealing with a vertical line, or if the first point's > y value and the last points y value were 'close', then I knew I was > dealing with a horizontal line). So, given the Graphics object output > by > > graphicOne = CartesianMap[#1 & , {-1, 1}, {-1, 1}, Lines -> theLines, > ImageSize -> {500, Automatic}, PlotStyle -> {RGBColor[1, 0, 0], > RGBColor[0, 0, 1]}, > PlotPoints -> thePlotPoints]; > > I was hoping that invoking something like > > Position[graphicOne, ({RGBColor[__], {Line[_]}})? > ((Print[Abs[First[#1[[2,1]]][[1,1]] - Last[#1[[2,1]]][[1,1]]]]; > Abs[First[#1[[2,1]]][[1,1]] - Last[#1[[2,1]]][[1,1]]] < 1.*^-9) & > )] > > would give me the positions of all of the horizontal lines, but then, > it seems that my lack of familiarity with Mathematica's rules for > working with accuracy and precision, led to results that made no sense > (i.e. it returned every Line as a match, instead of just the ones where > the x-coordinates were 'close'). Even worse than that, I realized that > my attempt was doomed to failure because even if I could get that > approach to work for a rectangular domain, it would not work once I had > applied a function that resulted in a graphic where the lines were > curved, twisted and traveling back over themselves. It was at this > point that I decided to just work with single lines (i.e. graph a > single curve, then operate on each of the points contained within the > 'Line' object and then graph the result in another graphic). > > So, as a first step towards my goal, I thought, "OK, I need to write a > function that will be able to be used with Map on a list of points and > return the 'transformed' points as well as accept an arbitrary function > that will operate on each of the points." > > Here is what I have thus far: > > Clear[f, g]; > f[z_, func_] := Module[{result}, result = func[Complex[Sequence @@ z]]; > {Re[result], Im[result]}]; > g[z_] := f[z, #1^2 & ]; > > Which, using 'g', I can use Map on a list of ordered pairs: > > g /@ {{x,y}, {x,y}, {x,y}, {x,y}, etc.} > > If I wanted to use Sin, I would redefine g as follows: > > g[z_] := f[z, Sin]; > > then reapply to the list of ordered pairs. So, I'm wondering if > there's a way to accomplish my task without the intermediary function > definition 'g'? Also, if what I'm attempting is totally wrong, I'd > appreciate any pointers as to the correct 'path' as well. > > Thanks, > > Matt > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Using Map with a function of more than 1 argument***From:*"Matt" <anonmous69@netscape.net>

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