matthieubulte

using Gadfly
import Cairo, Fontconfig
using Printf
using FFMPEG

#################################### This is pretty much the same code as in https://github.com/JuliaPlots/Plots.jl/blob/master/src/animation.jl
struct Animation
    dir::String
    frames::Vector{String}
    kwargs::Iterators.Pairs

matthieubulte

(* Good morning everyone, I'm currently learning ocaml for one of my CS class and needed to implement
   an avl tree using ocaml. I thought that it would be interesting to go a step further and try
   to verify the balance property of the avl tree using the type system. Here's the resulting code
   annotated for people new to the ideas of type level programming :)
*)

(* the property we are going to try to verify is that at each node of our tree, the height difference between
   the left and the right sub-trees is at most of 1. *)

matthieubulte

### A Pluto.jl notebook ###
# v0.12.21

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))

matthieubulte

using MacroTools
using Symbolics

function parse(strexpr)
    expr = Meta.parse(strexpr)
    freevars = Set()
    expr = MacroTools.postwalk(x -> begin
        if isa(x, Symbol) && !isdefined(Base, x)
            push!(freevars, Variable(x))
            Expr(:call, Variable, QuoteNode(x))

matthieubulte

using LinearAlgebra, BenchmarkTools, SparseArrays, SymbolicUtils, Symbolics

## Problem setup
const z = zeros;

wx = Float64[ 0 -1  0;
              1  0  0;
              0  0  0;];

Ak_1 = [ wx           -I   zeros(3,12);

matthieubulte

using LinearAlgebra
using BenchmarkTools
using SparseArrays

# To exploit the sparsity of the matrix as much as possible, pre-compile the multiplication operation
# to skip the matrix entries look-up. Since the matrix is sparse this might generate only a few operations
# which are all inlined.
# Note that this only works with small matrices since otherwise the size of the function will just be to
# large.
# Note that this could also be avoided, but this is another topic.

matthieubulte

# Answer to: https://twitter.com/1HaskellADay/status/875063542784958465
#
# So the Initial Value Problem (IVP) you want to solve seems to be the following
# 
# dy/dx = 3*exp(-x) - 0.4*y 
# y(x_0) = y_0      with x_0 = 0 and y_0 = 5
# 
# You then ask: what is the value of y when x = 3?
#
# This can be computed using the Runge Kutta method by feeding it

matthieubulte

(* TODO: use Random.State *)
open Random;;
open List;;

(* =========================================== General Utils = *)
let sign x = if x < 0 then -1 else 1;;

let truncate x l = sign x * min (abs x) l;;

matthieubulte

matthieubulte