How to plot quiver plot over heatmap

I am trying to plot a quiver plot (a vector field) over a heatmap. My only reference after one day of research is this old notebook: ExamplePlots.jl/quiver.ipynb at master · JuliaPlots/ExamplePlots.jl · GitHub

My function is

initial_c(x, y, z) = (exp(-x^2 - y^2))

Is there a way to do this and even print out the values of every vector for the respective grid point?

Plots.jl examples

Example 1:

using ForwardDiff
using Plots

f(x, y) = exp(-(x^2 + y^2))
u(x, y) = ForwardDiff.derivative(Base.Fix2(f, y), x) # = f_x(x, y)
v(x, y) = ForwardDiff.derivative(Base.Fix1(f, x), y) # = f_y(x, y)

xlim = (-1.7, 1.7)
ylim = (-1.7, 1.7)
xs = range(xlim...; length=200)
ys = range(ylim...; length=200)

c = 0.5
x = range(-1.5, 1.5; length=11)
y = range(-1.5, 1.5; length=11)
X, Y = reim(complex.(x', y)) # meshgrid
U, V = c*u.(x', y), c*v.(x', y)

heatmap(xs, ys, f)
quiver!(vec(X-U/2), vec(Y-V/2); quiver=(vec(U), vec(V)), color=:cyan)
plot!(; xlim, ylim, size=(450, 400))

Example2:

using ForwardDiff
using Plots

f(x, y) = y * exp(-(x^2 + y^2))
u(x, y) = -ForwardDiff.derivative(Base.Fix2(f, y), x) # = f_x(x, y)
v(x, y) = -ForwardDiff.derivative(Base.Fix1(f, x), y) # = f_y(x, y)

xlim = (-2.2, 2.2)
ylim = (-2.2, 2.2)
xs = range(xlim...; length=200)
ys = range(ylim...; length=200)

c = 0.5
x = range(-2.0, 2.0; length=13)
y = range(-2.0, 2.0; length=13)
X, Y = reim(complex.(x', y)) # meshgrid
U, V = c*u.(x', y), c*v.(x', y)

heatmap(xs, ys, f)
quiver!(vec(X-U/2), vec(Y-V/2); quiver=(vec(U), vec(V)), color=:cyan)
plot!(; xlim, ylim, size=(450, 400))

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