briochemc

using VegaLite, DataFrames

df = DataFrame(x = [0, 1, 2, 3, 4, 0, 1, 2, 3, 4], y = 1:10, style = ["A", "A", "A", "A", "A", "B", "B", "B", "B", "B"])

list_styles = ["B", "A"]
mycolors = ["#000000", "#ee00ff"]
    
p = df |>
@vlplot(
    mark={

briochemc

mutable struct ThreeVec <: AbstractVector{Float64}
    x::Float64
    y::Float64
    z::Float64
end

Base.size(V::ThreeVec) = (3,)
Base.IndexStyle(::Type{<:ThreeVec}) = IndexLinear()
using Match
Base.getindex(V::ThreeVec, i::Int) = @match i begin

briochemc

using DualNumbers, LinearAlgebra, SparseArrays, SuiteSparse

n = 10
A = randn(n, n)            # a real-valued matrix
B = randn(n, n)            # another real-valued matrix

# Create a dual-valued matrix
M = A + ε * B

# And a sparse version of it

briochemc

const x = 1.0 ;

function foo(y)
    println("x = ", x)
end

foo("a string") # should print "x = 1.0"
# Invoking foo just JIT-compiled foo to use x = 1.0 if the argument is a string.

x = 2.0 ; # modify constant

briochemc

# Error check
using LinearAlgebra, SparseArrays, SuiteSparse, BenchmarkTools, MAT
M = matread("test_matrix.mat")["M"] ;
x = matread("test_matrix.mat")["x"] ;
Mf = factorize(M) ;
sol1 = Mf \ x ;
sol2 = M \ x ;
norm(x)
norm(x - M * sol1) / norm(x)
norm(x - M * sol1)

briochemc

using LinearAlgebra, SparseArrays, SuiteSparse
using DualNumbers, DualMatrixTools
using BenchmarkTools

n = 1000 ;

y = rand(n) ;

A = sprand(n, n, 20/n) ;
i, j, v = findnz(A) ;

briochemc

# Example function to find the root of
f(x) = [(x[1] + x[2] + 1)^3, (x[1] - x[2] - 1)^3]
function f_Jac!(J, x)
    J[1, 1] = 3(x[1] + x[2] + 1)^2
    J[2, 1] = 3(x[1] - x[2] - 1)^2
    J[1, 2] = 3(x[1] + x[2] + 1)^2
    J[2, 2] = -3(x[1] - x[2] - 1)^2
    return J
end

briochemc

f1(x) = x
f2(x) = 2x
f3(x) = 3x

list_methods = [
    ("method1", :f1)
    ("method2", :f2)
    ("method3", :f3)
]

briochemc

load Downloads/CTL.mat
T = output.TR ;
f1 = figure ;
spy(T, 'w') ;
darkBackground(f1, [0 0 0], [1 1 1])

briochemc

# Here I store more data as I go, 
# which I could use to plot figures comparing methods
# the convergence speed of different methods

# I use the Rosenbrock classic example and
# Optim.jl as an iterative process which will
# call f multiple times to find its minimum
# and I plot the convergence vs time
using Optim, Cassette