Best practice of passing a large number of parameters to functions

Question

I have a number of functions that all take a large number of parameters. I am wondering what is the best practice of passing these parameters to those functions. I could, of course, simply specify the parameters outside the functions, as in (note that, in the actual example, there are far more parameters)

mu=1;
sigma=1;
lb=0;
ub=10;
f[x_] := PDF[LogNormalDistribution[mu, sigma],x]

However, I would prefer to explicitly pass the parameters to the functions. In Python, I would use a dictionary. In Mathematica, one possibility would be a replacement rule.

par={mu->1,sigma->1,lb->0,ub->10};
f[x_,par_] := PDF[LogNormalDistribution[mu, sigma],x]/.par

However, this can cause warnings if a function only takes numerical arguments, e.g.

Plot[f[x,par],{x,lb,ub}]/.par

Plot::plln: Limiting value lb in {x,lb,ub} is not a machine-sized real number. >>

The plotting actually, works, though.

Also, passing parameters using replacement rules seems to be inefficient, since - if possible - evaluations are done symbolically, and only then are values substituted for variables.

Answer 1

Basic proposal

There are a number of options and their attractiveness will depend on the scenario for their use, therefore it is difficult to make any broad recommendations of best practice.

I will say that generally it is not recommended to rely on global assignments as in your first example, because this method scales poorly and because it is easy to make mistakes and get invalid results.

One approach you might consider is this:

Options[defs] = {mu -> 1, sigma -> 1, lb -> 0, ub -> 10};
f[x_, OptionsPattern[defs]] := 
  PDF[LogNormalDistribution[OptionValue[mu], OptionValue[sigma]], x]

Now you can call f with one argument:

f[1.6]

0.216668

Or you can override values with explicit Options:

f[1.6, mu -> 1.7]

0.117023

You can also quickly change a value using SetOptions:

SetOptions[defs, sigma -> 2]

{mu -> 1, sigma -> 2, lb -> 0, ub -> 10}

f[1.6]

0.120368

Note: making assignments to the Option names (e.g. mu = 1) will break your code.
Consider either Protect-ing these Symbols or using Strings instead, e.g. "mu" -> 1.

One disadvantage of this method is that it lengthens definitions. Sometimes using With makes these more clear:

f[x_, OptionsPattern[defs]] := 
  With[{mu = OptionValue[mu], sigma = OptionValue[sigma]}, 
    PDF[LogNormalDistribution[mu, sigma], x]
  ]

This can be streamlined using listWith from: Constructing symbol definitions for With:

SetAttributes[listWith, HoldAll];
listWith[(set : Set | SetDelayed)[L_, R_], body_] :=
  set @@@ Thread[Hold @@@ {L, R}, Hold] /. _[x__] :> With[{x}, body]

Now:

f[x_, OptionsPattern[defs]] := 
  listWith[{mu, sigma} = OptionValue[{mu, sigma}],
    PDF[LogNormalDistribution[mu, sigma], x]
  ]

---

Automation

Manual specification

Although this will not work with String parameter names here is a method to further automate function construction:

SetAttributes[defWithOpts, HoldAll]
defWithOpts[
  sym_Symbol,
  opts : {__Symbol},
  (set : Set | SetDelayed)[h_[args___], RHS_]
] :=
  set[
    h[args, OptionsPattern[sym]],
    listWith[opts = OptionValue[opts], RHS]
  ]

Now:

defWithOpts[def, {mu, sigma},
  g[x_] := PDF[LogNormalDistribution[mu, sigma], x]
]

And the definition that was created:

?g

Global`g

g[x_, OptionsPattern[def]] := 
  listWith[{mu, sigma} = OptionValue[{mu, sigma}], 
    PDF[LogNormalDistribution[mu, sigma], x]]

For code specific to String parameter names see: How to write complex function definitions at run time?

Automatic detection

Yet another idea for automation, built on the assumption that you will first define the Options list (with dummy values if necessary) then the functions. It works by finding all cases of parameter (Option) names within the right-hand-side of the definition.

SetAttributes[defAutoOpts, HoldAll]
defAutoOpts[
  sym_Symbol: defs,
  (set : Set | SetDelayed)[h_[args___], RHS_]
] :=
  Cases[Unevaluated@RHS, Alternatives @@ Options[sym][[All, 1]], {-1}, Heads -> True] //
    set[h[args, OptionsPattern[sym]], listWith[# = OptionValue[#], RHS]] &

Now you can do this:

defAutoOpts[
  h[x_] := PDF[LogNormalDistribution[mu, sigma], x]
]

Which creates:

h[x_, OptionsPattern[defs]] := 
  listWith[{mu, sigma} = OptionValue[{mu, sigma}], 
    PDF[LogNormalDistribution[mu, sigma], x]]

You can also call defAutoOpts[defs2, . . .] to use a different parameter list.

Answer 2

In V10, another option is to use Association.

par=<|"mu"->1,"sigma"->1,"lb"->0,"ub"->10|>;

f[x_, p_Association:par] := PDF[LogNormalDistribution[p["mu"], p["sigma"]], x]

Plot[f[x, ##], {x, #lb, #ub}] &@par

Another form for Plot is:

Plot[f[x, par], {x, par@"lb", par@"ub"}]

And as @Mr.Wizard commented, you can use the default value for par, omitting it:

Plot[f[x], {x, par@"lb", par@"ub"}]

I like Associations because notation is much simpler than Options rule. The disadvantage is that they don't have filters as Options, and Associations do not accept pattern tests.