Re: Option instead of a function argument: is it possible?

*To*: mathgroup at smc.vnet.net*Subject*: [mg98053] Re: [mg98037] Option instead of a function argument: is it possible?*From*: "David Park" <djmpark at comcast.net>*Date*: Sun, 29 Mar 2009 02:43:21 -0500 (EST)*References*: <27334345.1238240356951.JavaMail.root@m02>

Alexei, eq1 = x'[t] == -y[t] - x[t]^2; eq2 = y'[t] == 2 x[t] - y[t]^3; Options[trajectory2] = {TrajectoryAccuracyGoal -> Automatic, TrajectoryMaxSteps -> 10000}; trajectory2[eq1_, eq2_, point_, tmax_, OptionsPattern[]] := Module[{s, eq3, eq4, accuracyGoal, maxSteps}, accuracyGoal = OptionValue[TrajectoryAccuracyGoal]; maxSteps = OptionValue[TrajectoryMaxSteps]; eq3 = x[0] == point[[1]]; eq4 = y[0] == point[[2]]; s = NDSolve[{eq1, eq2, eq3, eq4}, {x, y}, {t, tmax}, AccuracyGoal -> accuracyGoal, MaxSteps -> maxSteps]; ParametricPlot[Evaluate[{x[t], y[t]} /. s], {t, 0, tmax}, PlotRange -> All]] trajectory2[eq1, eq2, {1, 1}, 30] trajectory2[eq1, eq2, {1, 1}, 30, TrajectoryMaxSteps -> 200, TrajectoryAccuracyGoal -> 2] David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Alexei Boulbitch [mailto:Alexei.Boulbitch at iee.lu] Dear Community, If we need to write functions depending upon several parameters the latter are usually passed to the function as its arguments. I wonder however, if you know a way to pass some parameters to a function in the same way as options are passed to operators in Mathematica. That is, if the default value of the parameter in question is OK, you do not even mention such a parameter among the function arguments. If you need to specify such a parameter you include an argument having the form Option->optionValue. Let me explain precisely within a simple example what I would like to: 1. Consider a function that solves a system of 2 ordinary differential equations and draws a trajectory on the (x, y) plane: trajectory1[eq1_, eq2_, point_, tmax_] := Module[{s, eq3, eq4}, eq3 = x[0] == point[[1]]; eq4 = y[0] == point[[2]]; s = NDSolve[{eq1, eq2, eq3, eq4}, {x, y}, {t, tmax}]; ParametricPlot[Evaluate[{x[t], y[t]} /. s], {t, 0, tmax}, PlotRange -> All]] Equations can be fixed say, like these: eq1 = x'[t] == -y[t] - x[t]^2; eq2 = y'[t] == 2 x[t] - y[t]^3; and initial conditions are passed by the parameter point. The function can be called: trajectory1[eq1, eq2, {1, 1}, 30] 2. Assume now that I need to specify the accuracy goal and MaxSteps parameters. Then the function will take a slightly different form: trajectory2[eq1_, eq2_, point_, tmax_, accuracyGoal_, maxSteps_] := Module[{s, eq3, eq4}, eq3 = x[0] == point[[1]]; eq4 = y[0] == point[[2]]; s = NDSolve[{eq1, eq2, eq3, eq4}, {x, y}, {t, tmax}, AccuracyGoal -> accuracyGoal, MaxSteps -> maxSteps]; ParametricPlot[Evaluate[{x[t], y[t]} /. s], {t, 0, tmax}, PlotRange -> All]] and also called: trajectory2[eq1, eq2, {1, 1}, 30, 10, 1000] However, I would like to achieve a function trajectory3[eq1_, eq2_, point_, tmax_] that can be addressed both as trajectory3[eq1, eq2, {1, 1}, 30] (if I agree with the default values of the AccuracyGoal and MaxSteps) and as trajectory3[eq1, eq2, {1, 1}, 30, AccuracyGoal->10, MaxSteps->10000], if a change in these options is necessary. Is it possible? Best regards, Alexei -- Alexei Boulbitch, Dr., habil. Senior Scientist IEE S.A. ZAE Weiergewan 11, rue Edmond Reuter L-5326 Contern Luxembourg Phone: +352 2454 2566 Fax: +352 2454 3566 Website: www.iee.lu This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you are not the intended recipient and have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal from your system. Thank you for your co-operation.