update PF docs

docs/src/analysis/parameterized_functions.md

@@ -12,7 +12,7 @@ pf = ParameterizedFunction(f,params)
 
 The form for `f` is `f(t,u,params,du)` where `params` is any type which defines
 the parameters (it does not have to be an array, and it can be any user-defined
-type as well). The resulting `ParameterizedFunction` has the function call 
+type as well). The resulting `ParameterizedFunction` has the function call
 `pf(t,u,params,du)` which matches the original function, and a call `pf(t,u,du)`
 which uses internal parameters which can be used with a differential equation solver.
 Note that the internal parameters can be modified at any time via the field: `pf.p = ...`.
@@ -121,6 +121,49 @@ parameters affect the model. Thus ParameterizedFunctions, when coupled with the
 solvers, forms the backbone of functionality such as parameter estimation, parameter
 sensitivity analysis, and bifurcation analysis.
 
+## Extra Little Tricks
+
+There are some extra little tricks you can do. Since `@ode_def` is a macro,
+you cannot directly make the parameters something that requires a runtime value.
+Thus the following will error:
+
+```julia
+vec = rand(1,4)
+f = @ode_def LotkaVolterraExample begin
+dx = ax - bxy
+dy = -cy + dxy
+end a=>vec[1] b=>vec[2] c=>vec[3] d=vec[4]
+```
+
+To do the same thing, instead initialize it with values of the same type, and simply
+replace them:
+
+```julia
+vec = rand(1,4)
+f = @ode_def LotkaVolterraExample begin
+dx = ax - bxy
+dy = -cy + dxy
+end a=>1.0 b=>1.0 c=>1.0 d=vec[4]
+f.a,f.b,f.c = vec[1:3]
+```
+
+Notice that when using `=`, it can inline expressions. It can even inline expressions
+of time, like `d=3*t` or `d=2π`. However, do not use something like `d=3*x` as that will
+fail to transform the `x`.
+
+In addition, one can also use their own function inside of the macro. For example:
+
+```julia
+f(x,y,d) = erf(x*y/d)
+NJ = @ode_def FuncTest begin
+  dx = a*x - b*x*y
+  dy = -c*y + f(x,y,d)
+end a=>1.5 b=>1 c=3 d=4
+```
+
+will do fine. The symbolic derivatives will not work unless you define a derivative
+for `f`.
+
 ## Extra Optimizations
 
 Because the ParameterizedFunction defined by the macro holds the definition at a