Plot[Evaluate[compiled functions... causes problems

Question

I'm sure there is an easy solution to this, but I have beaten my head against a wall for a couple of days, so I hope someone can help.

I have compiled functions. For a minimal example let's take:

fn1 = Compile[{{t, _Real}, {x, _Real}}, Sin[t x]];
fn2 = Compile[{{t, _Real}, {x, _Real}}, Cos[t x]];

The list of functions I want to plot is dynamic, so I cannot explicitly list them. We can model this using Through, though there are many ways to do this:

Plot[Through[{fn1, fn2}[3, x]], {x, 0, 10}]

But this plots both curves with the same color because with the Hold attribute of Plot, the head Through evaluates as a single item. The standard way to fix this problem is to use Evaluate:

Plot[Evaluate@Through[{fn1, fn2}[3, x]], {x, 0, 10}]

But this gives errors:

CompiledFunction: Argument x at position 2 should be a machine-size real number.

Clearly this is because MMA is trying to Evaluate the x before a value has been assigned to it by Plot. How can we avoid this problem (other than just suppressing the warning messages)?

Answer 1

You could try using Inactive/Activate, e.g.:

With[{in = {fn1, fn2} /. CompiledFunction -> Inactive[CompiledFunction]},
    Activate @ Inactive[Plot][Through[in[3, x]], {x, 0, 10}]
]

Answer 2

And the power of the post.

Plot[Evaluate@(Hold[#[3, x]] & /@ {fn1, fn2}), {x, 0, 10}]