ipynb Cheat Sheet#

Maths#

A smooth system can generally be represented as \(\dot{x} = f(x,u)\).

\[\begin{split} \left.\frac{\partial f}{\partial x}\right|_{\sigma=0}=\left[\begin{array}{cc} 0 & 1 \\ -i / e & 0 \end{array}\right] \Rightarrow \operatorname{eig}\left(\frac{\partial f}{\partial x}\right) \pm i \sqrt{\frac{g}{e}} \end{split}\]

And numbered (https://jupyterbook.org/en/stable/content/math.html)

(1)#\[w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}\]

or this

(2)#\[ w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1} \]

Now I can refer to (1) or (2) with

{eq}`my_other_label`

Some special content blocks#

Note

Here is a note!

Warning

Here is a warning!

Here is some more info…

For more info expand me

Here is some more info…

Hiden cells#

Add a tag to the cell.

Hide code cell content 
# hidden with In browser (View -> Cell Toolbar -> Tags)
# Add ""

# Activate the enironment
import Pkg 
Pkg.activate(@__DIR__); # activate the env in the directory 
# Pkg.instantiate()

  Activating project at `/__w/CMU-16-745/CMU-16-745/optimalcontrol`

Look a pretty plot with hidden input

Hide code cell source 
using Plots


# our first plot is just a normal one 
x = -10:.001:10 
# now let's plot multiple 
plot(x, sin.(x), label = "sin(x)", xlabel = "x label",
     ylabel = "y label", xlim = (-5,5), ylim = (-2, 2))
# now I use plot! to modify my existing plot
plot!(x, cos.(x), label = "cos(x)")
scatter!(randn(100), randn(100), label = "random scatter points")

[ Info: Precompiling IJuliaExt [2f4121a4-3b3a-5ce6-9c5e-1f2673ce168a]

# You can copy this

using Plots 

@gif for i in 1:50
    plot(sin, 0, i * 2pi / 10)
end

[ Info: Saved animation to /__w/CMU-16-745/CMU-16-745/optimalcontrol/tmp.gif

using Random
anim = @animate for i in 1:50
    Random.seed!(123)
    scatter(cumsum(randn(i)), ms=i, lab="", alpha = 1 - i/50, 
        xlim=(0,50), ylim=(-5, 7))
end
gif(anim, fps=15)

[ Info: Saved animation to /__w/CMU-16-745/CMU-16-745/optimalcontrol/tmp.gif

# Interative plots don't display in html. Gues that makes sense ...
# import Pkg; Pkg.add("Plotly");
# using Plots
# plotly()
# x = range(0, 10, length=100)
# y = sin.(x)
# plot(x, y)
# @show x

# @show A = [1 2 3.0; 4 5 6]
# @show A = [1 2 3]
# @show A = range(1, 10)

# x = [1 2 3]
# y = [4 5 6]
# plot(x',y',label="sin(x)")