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

*To*: mathgroup at smc.vnet.net*Subject*: [mg98068] Re: Option instead of a function argument: is it possible?*From*: Helen Read <hpr at together.net>*Date*: Sun, 29 Mar 2009 02:46:07 -0500 (EST)*References*: <gqkv21$4dn$1@smc.vnet.net>*Reply-to*: HPR <read at math.uvm.edu>

Alexei Boulbitch wrote: > 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? Sure, you just need optional arguments to your function. Here's a simple example. f[x_, y_: 3, z_: 2] := x *y + z y and z are optional arguments. If you don't specify them, the default values (3 and 2 respectively) are used. Try evaluating these: f[x] f[x,5] f[x,-4,6] -- Helen Read University of Vermont