Generate a natural-looking function

Produce a random function that is the sum of Gaussian random variables

rpoly2 generates a random 2nd degree polynomial (as a function)

rfun(vars = ~x & y, seed = NULL, n = 0)

rpoly2(vars = ~x & y, seed = NULL)

Arguments

vars

a formula; the LHS is empty and the RHS indicates the variables used for input to the function (separated by &)

seed

seed for random number generator, passed to set.seed().

n

the number of Gaussians. By default, this will be selected randomly.

Value

a function with the appropriate number of inputs

a function defined by a 2nd degree polynomial with coefficients selected randomly according to a Unif(-1,1) distribution.

Details

rfun is an easy way to generate a natural-looking but random function with ups and downs much as you might draw on paper. In two variables, it provides a good way to produce a random landscape that is smooth. Things happen in the domain -5 to 5. The function is pretty flat outside of that. Use seed to create a fixed function that will be the same for everybody

These functions are particularly useful for teaching calculus.

Examples

f <- rfun( ~ u & v)
plotFun(f(u,v)~u&v,u=range(-5,5),v=range(-5,5))

myfun <- rfun(~ u & v, seed=1959)
g <- rpoly2( ~ x&y&z, seed=1964)
plotFun(g(x,y,z=2)~x&y,xlim=range(-5,5),ylim=range(-5,5))