#collapse
# imports
# using Plots; plotlyjs()
using PlotlyJS

# from IPython.display import HTML
# HTML(fig.to_html()) # where fig = plotly.plot(...)

f(x, y) = x^2 + 2y^2

x = 6

xlim=[-10, x]
ylim=[-10, 10]

xs = LinRange(xlim..., 101)
ys = LinRange(ylim..., 101)
zs = [f(x, y) for x in xs, y in ys]

y = 4
dy = 4
f_y(y) = 4y

#collapse
# built interactive plot
traces = GenericTrace[]

push!(traces, PlotlyJS.surface(x=xs, y=ys, z=zs,
        showscale=false, opacity=0.8))
push!(traces, PlotlyJS.surface(x=[x, x+0.001], y=ylim, z=[[maximum(zs), minimum(zs)] [maximum(zs), minimum(zs)]],
        showscale=false, colorscale="Greys", opacity=0.2))
push!(traces, PlotlyJS.scatter3d(x=fill(x, size(ys)), y=ys, z=[x^2 + 2y^2 for y in ys],
        showlegend=false, mode="lines", line=attr(color="red", width=2)))

for y in ys[1:5:end]
    push!(traces, PlotlyJS.scatter3d(x=fill(x, 2),y=[y-dy, y+dy], z=[f(x,y)-f_y(y)*dy, f(x,y)+f_y(y)*dy],
            visible=false, showlegend=false, mode="lines", line=attr(color="orange", width=5)))
end

scene = attr(
        xaxis = attr(range=[-10,10]),
        yaxis = attr(range=[-10,10]),
        zaxis = attr(range=[-50,300]),
        aspectratio = attr(x=1, y=1, z=1)
    )

layout = Layout(
    sliders=[attr(
        steps=[
            attr(
                label=round(y, digits=2),
                method="update",
                args=[attr(visible=[fill(true, 3); fill(false, i-1); true; fill(false, 101-i)])]
            )
            for (i, y) in enumerate(ys[1:5:end])
        ],
        active = y,
        currentvalue_prefix="x = 6, y = ",
        # pad_t=40
    )],
    scene = scene,
)

p = PlotlyJS.plot(traces, layout)

#collapse
# plot partial derivative of f with respect to y, f_y
traces = GenericTrace[]

push!(traces, PlotlyJS.surface(x=xs, y=ys, z=zs,
        showscale=false, opacity=0.8))
push!(traces, PlotlyJS.surface(x=ylim, y=ylim, z=[[0, 0] [0, 0]],
        showscale=false, colorscale="Greys", opacity=0.3))
push!(traces, PlotlyJS.surface(x=xs, y=ys, z=[f_y(y) for x in xs, y in ys],
        showscale=false))

plot(traces, Layout(scene=scene))

f_x(x) = 2x

traces = GenericTrace[]

push!(traces, PlotlyJS.surface(x=xs, y=ys, z=zs,
        showscale=false, opacity=0.8))
push!(traces, PlotlyJS.surface(x=ylim, y=ylim, z=[[0, 0] [0, 0]],
        showscale=false, colorscale="Greys", opacity=0.3))
push!(traces, PlotlyJS.surface(x=xs, y=ys, z=[f_x(x) for x in xs, y in ys],
        showscale=false))

plot(traces, Layout(scene=scene))

#collapse
# plot partial derivative of f with respect to y, f_y
traces = GenericTrace[]

push!(traces, PlotlyJS.surface(x=ylim, y=ylim, z=[[0, 0] [0, 0]],
        showscale=false, colorscale="Greys", opacity=0.3))
push!(traces, PlotlyJS.surface(x=xs, y=ys, z=[f_y(y) for x in xs, y in ys],
        showscale=false))
push!(traces, PlotlyJS.scatter3d(x=[-7, 4], y=[5, 5], z=[f_y(5), f_y(5)],
        showlegend=false, mode="lines", line=attr(color="orange", width=5)))

p = plot(traces, Layout(scene=scene))

#collapse
# built interactive plot
traces = GenericTrace[]

push!(traces, PlotlyJS.surface(x=xs, y=ys, z=zs,
        showscale=false, opacity=0.8))

for x in xs[1:5:end]
    push!(traces, PlotlyJS.surface(x=[x, x+0.001], y=ylim, z=[[maximum(zs), minimum(zs)] [maximum(zs), minimum(zs)]],
            visible=false, showscale=false, colorscale="Greys", opacity=0.2))

    push!(traces, PlotlyJS.scatter3d(x=fill(x, size(ys)), y=ys, z=[x^2 + 2y^2 for y in ys],
            visible=false, showlegend=false, mode="lines", line=attr(color="red", width=2)))

    push!(traces, PlotlyJS.scatter3d(x=fill(x, 2),y=[y-dy, y+dy], z=[f(x,y)-f_y(y)*dy, f(x,y)+f_y(y)*dy],
            visible=false, showlegend=false, mode="lines", line=attr(color="orange", width=5)))
end

layout = Layout(
    sliders=[attr(
        steps=[
            attr(
                label=round(x, digits=2),
                method="update",
                args=[attr(visible=[fill(true, 1); fill(false, 3*(i-1)); fill(true, 3); fill(false, 3*(101-i))])]
            )
            for (i, x) in enumerate(xs[1:5:end])
        ],
        active = x,
        currentvalue_prefix="x = 6, y = ",
        # pad_t=40
    )],
    scene = scene,
)

p = PlotlyJS.plot(traces, layout)

g(x, y) = x^2 + 2y^2 - x*y

zs = [g(x, y) for x in xs, y in ys]

g_x(x, y) = 2x - y
g_y(x, y) = 4y - x

#collapse
# built interactive plot
traces = GenericTrace[]

push!(traces, PlotlyJS.surface(x=xs, y=ys, z=zs,
        showscale=false, opacity=0.8))

for x in xs
    push!(traces, PlotlyJS.surface(x=[x, x+0.001], y=ylim, z=[[maximum(zs), minimum(zs)] [maximum(zs), minimum(zs)]],
            visible=false, showscale=false, colorscale="Greys", opacity=0.2))

    push!(traces, PlotlyJS.scatter3d(x=fill(x, size(ys)), y=ys, z=[g(x, y) for y in ys],
            visible=false, showlegend=false, mode="lines", line=attr(color="red", width=2)))

    push!(traces, PlotlyJS.scatter3d(x=fill(x, 2),y=[y-dy, y+dy], z=[g(x,y)-g_y(x, y)*dy, g(x,y)+g_y(x, y)*dy],
            visible=false, showlegend=false, mode="lines", line=attr(color="orange", width=5)))
end

layout = Layout(
    sliders=[attr(
        steps=[
            attr(
                label=round(x, digits=2),
                method="update",
                args=[attr(visible=[fill(true, 1); fill(false, 3*(i-1)); fill(true, 3); fill(false, 3*(101-i))])]
            )
            for (i, x) in enumerate(xs)
        ],
        active = x,
        currentvalue_prefix="x = 6, y = ",
        # pad_t=40
    )],
    scene = scene,
)

p = PlotlyJS.plot(traces, layout)