Giving an arbitrary number of arguments to Manipulate using Apply
- To: mathgroup at smc.vnet.net
- Subject: [mg94635] Giving an arbitrary number of arguments to Manipulate using Apply
- From: "Yoichi Aso" <aso at caltech.edu>
- Date: Thu, 18 Dec 2008 07:22:03 -0500 (EST)
Hello,
I have a problem with using Manipulate and Apply.
I'd like to ask for your advice on this.
Here is what I want to do:
I have a list of expressions, expr, and a list of variables, vars.
Each element of expr is a function of variables in vars.
For example, expr={Sin[a x], x^2+b, - b x}; vars = {x,a,b}.
Now, I want to write a function which takes expr and vars as arguments
and does the following.
First, it adds together the elements of expr to make a new function, newFunc.
Then it creates a Manipulate object with sliders for all the variables in vars.
The first argument of the Manipulate is a Plot of newFunc as a
function of the first variable
in vars.The value of the other variables are determined by the
sliders. Along with the plot,
the value of the first variable is shown as a Text object in the plot.
Here is a code I came up with to implement the above task.
testFunc[expr_, vars_] := Module[{newFunc, args, i, p},
newFunc = Apply[Plus, expr] /. vars[[1]] -> p;
args :=
Join[{Plot[newFunc, {p, 0, 10}, Epilog -> Text[vars[[1]], {5, 1}]]},
Table[{vars[[i]], 0, 10}, {i, 1, Length[vars]}]];
Apply[Manipulate, args]
]
However, when I execute, for example,
testFunc[{Sin[a x], b + x^2, -b x}, {x, a, b}]
it shows nothing in the plot area.
I'm guessing it is because Join tries to evaluate the arguments, and
at this moment, Plot cannot draw a graph
because the variables a and b do not have numerical values.
I enclosed the Join with Hold and used ReleaseHold around the Apply,
but still no plot shown.
I used Apply because I don't know the length of vars in advance.
I'd appreciate it if anyone can suggest a solution to this problem.
Thank you in advance,
Yoichi
--
----------------------------------------
Yoichi Aso
LIGO Laboratory, California Institute of Technology
aso at caltech.edu or asoy01 at gmail.com