First, let’s define f as an actual function:
julia> f = (x, y) -> x + y * log(y)
#11 (generic function with 1 method)
You can broadcast this function over p and q to create a grid:
julia> f.(p, q')
100×100 Array{Float64,2}:
...
But you actually don’t need to! In fact, Plots.jl already knows how to plot the contour of a function if you just pass it the input vectors p and q and the function itself:
julia> using Plots
julia> n = 100
100
julia> q = range(0, stop = 200, length = n)
0.0:2.0202020202020203:200.0
julia> p = range(0, stop = 200, length =n )
0.0:2.0202020202020203:200.0
julia> f = (x, y) -> x + y * log(y)
#11 (generic function with 1 method)
julia> contour(p, q, f)
Note that we also don’t need to generate p_grid or q_grid because Plots.jl is smart enough to work directly from the vectors.