text:
# ===============================
# Written by AAE
# TU Delft, Spring 2014
# simulkade.com
# ===============================

# %% ====================== 1D CARTESIAN MESH =======================
"""
m = createMesh1D(Nx::Int, Width::Real)
It creates a uniform mesh on a 1D Cartesian domain.

Inputs:

   + Nx: number of cells in the domain (integer)
	 + Width: width or length of the domain (Real)

Outputs:

   + m: a mesh structure

Usage:

Nx=10
Lx=1.0
m=createMesh1D(Nx, Lx)
"""
function createMesh1D(Nx::Int, Width::Real)
    # builds a uniform 1D mesh:
    # Nx is the number of cells in x (horizontal) direction
    # Width is the domain length in x direction

    # mesh dimension

    # cell size is dx
    dx = Width/Nx

    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    MeshStructure(1,
    		[Nx],
    		CellSize(dx*ones(Nx+2), [0.0], [0.0]),
    		CellLocation([1:Nx;]*dx.-dx/2,[0.0],[0.0]),
    		FaceLocation([0:Nx;]*dx,[0.0],[0.0]),
    		[1],
    		[1])
end

"""
m = createMesh1D(facelocationX::Array{Real,1})
It creates a non/uniform mesh on a 1D Cartesian domain.

Inputs:

   + facelocationX: location of the the cell boundaries on
	 the x-axis.

Outputs:

   + m: a mesh structure

Usage:

	x= [0.0, 1.0, 1.4, 2.5, 4.1, 6.0, 10.0]
	m=createMesh1D(x)
"""
function createMesh1D{T<:Real}(facelocationX::Array{T,1})
    # builds a uniform 1D mesh:
    # facelocationX is the location of each cell face
    # mesh dimension
    # cell size is dx
    Nx = length(facelocationX)-1
    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    MeshStructure(1,
    		[Nx],
    		CellSize(
                [
                    facelocationX[2]-facelocationX[1];
    		        facelocationX[2:end]-facelocationX[1:end-1];
    		        facelocationX[end]-facelocationX[end-1]
                ],
                [0.0], [0.0]),
    		CellLocation(
                0.5*(facelocationX[2:end]+facelocationX[1:end-1]),
                [0.0],[0.0]),
    		FaceLocation(facelocationX,[0.0],[0.0]),
    		[1],
    		[1])
end

# %% ================= 1D CYLINDRICAL MESH ==========================
"""
m = createMeshCylindrical1D(Nr::Int, Radius::Real)
It creates a uniform mesh on a 1D Radial domain.

Inputs:

   + Nr: number of cells in the domain (integer)
	 + Radius: Radius of the domain (Real)

Outputs:

   + m: a mesh structure

Usage:

Nr=10
R=1.0
m=createMesh1D(Nr, R)
"""
function createMeshCylindrical1D(Nr::Int, Radius::Real)
# builds a uniform 1D cylindrical mesh:
# Nx is the number of cells in r (radial) direction
# Radius is the domain length in r direction
# mesh dimension
# cell size is dr
dr = Radius/Nr
# numbering system of cells, like the single index numbering of Matlab
# +2 is added to account for the ghost cells that are added at
# the boundaries
MeshStructure(1.5,
		[Nr],
		CellSize(dr*ones(Nr+2), [0.0], [0.0]),
		CellLocation([1:Nr;]*dr.-dr/2.0,[0.0],[0.0]),
		FaceLocation([0:Nr;]*dr,[0.0],[0.0]),
		[1],
		[1])
end

"""
m = createMeshCylindrical1D(facelocationR::Array{Real,1})
It creates a non/uniform mesh on a 1D radial domain.

Inputs:

   + facelocationX: location of the the cell boundaries on
	 the r-axis.

Outputs:

   + m: a mesh structure

Usage:

	r= [0.1, 1.0, 1.4, 2.5, 4.1, 6.0, 10.0]
	m=createMeshCylindrical1D(r)
"""
function createMeshCylindrical1D{T<:Real}(facelocationR::Array{T,1})
    # builds a uniform 1D cylindrical mesh:
    # Nx is the number of cells in r (radial) direction
    # Radius is the domain length in r direction
    # mesh dimension
    # cell size is dr
    Nr = length(facelocationR)-1
    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    MeshStructure(1.5,
    		[Nr],
    		CellSize(
                [
                    facelocationR[2]-facelocationR[1];
                    facelocationR[2:end]-facelocationR[1:end-1];
        		    facelocationR[end]-facelocationR[end-1]],
                [0.0], [0.0]),
    		CellLocation(
                0.5*(facelocationR[2:end]+facelocationR[1:end-1]),
                [0.0],[0.0]),
    		FaceLocation(facelocationR,[0.0],[0.0]),
    		[1],
    		[1])
end

# %% ========================= 2D CARTESIAN MESH ==========================
"""
m = createMesh2D(Nx::Int, Ny::Int, Width::Real, Height::Real)
It creates a uniform mesh on a 2D Cartesian domain.

Inputs:

   + Nx: number of cells in the x-direction (integer)
   + Ny: number of cells in the y-direction (integer)
	 + Width: length of the domain in the x-direction (Real)
   + Height: length of the domain in the y-direction (Real)

Outputs:

   + m: a mesh structure

Usage:

Nx=10
Ny=15
Lx=1.0
Ly=2.5
m=createMesh2D(Nx, Ny, Lx, Ly)
"""
function createMesh2D(Nx::Int, Ny::Int, Width::Real, Height::Real)
    # builds a uniform 2D mesh:
    # Nx is the number of cells in x (horizontal) direction
    # Width is the domain length in x direction

    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    # cell size is dx
    dx = Width/Nx
    dy = Height/Ny
    G=reshape([1:(Nx+2)*(Ny+2);], Nx+2, Ny+2)
    MeshStructure(2,
    	[Nx, Ny],
    	CellSize(dx*ones(Nx+2), dy*ones(Ny+2), [0.0]),
    	CellLocation([1:Nx;]*dx.-dx/2.0,[1:Ny;]*dy.-dy/2.0,[0.0]),
    	FaceLocation([0:Nx;]*dx,[0:Ny;]*dy,[0.0]),
    	G[[1,end],[1,end]][:],
    	[1])
end

"""
Creates a mesh on a 2D Cartesian domain with specified face locations

m = createMesh2D(faceLocationX, faceLocationY)

Inputs:

   + faceLocationX (Vector of reals): face locations along horizontal axis
   + faceLocationY (Vector of reals): face locations along vertical axis

Outputs:

   + m: a mesh structure

Usage:

fX = [0.0; 0.05; 0.1:0.1:1.0;]
fY = [0.0; 0.05; 0.12; 0.2:0.2:3.0;]

m=createMesh2D(fx, fy)
"""
function createMesh2D{T<:Real}(facelocationX::Array{T,1}, facelocationY::Array{T,1})
    Nx = length(facelocationX)-1
    Ny = length(facelocationY)-1
    G=reshape([1:(Nx+2)*(Ny+2);], Nx+2, Ny+2)
    MeshStructure(2,
    	[Nx, Ny],
    	CellSize(
            [
                facelocationX[2]-facelocationX[1];
                facelocationX[2:end]-facelocationX[1:end-1];
                facelocationX[end]-facelocationX[end-1]
            ],
        	[
                facelocationY[2]-facelocationY[1];
                facelocationY[2:end]-facelocationY[1:end-1];
                facelocationY[end]-facelocationY[end-1]
            ],
        	[0.0]),
    	CellLocation(
            0.5*(facelocationX[2:end]+facelocationX[1:end-1]),
            0.5*(facelocationY[2:end]+facelocationY[1:end-1]),
            [0.0]),
    	FaceLocation(facelocationX, facelocationY, [0.0]),
    	G[[1,end],[1,end]][:],
    	[1])
end

# %% ========================= 2D RADIAL MESH ==============================
"""
Builds a uniform radial (polar coordinates) 2D mesh:

m = createMeshRadial2D(Nr, Ntheta, Radius, Angle)

Inputs:

    + Nr (Integer): number of cells in r (radial) direction
    + Ntheta (Integer): number of cells in angular direction
    + Radius (Real): domain length in r (radial) direction
    + Angle (Real): angular domain size (in radians)

Outputs:

    + m: a mesh structure

"""
function createMeshRadial2D(Nr::Int, Ntheta::Int, Radius::Real, Angle::Real)
    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    # cell size is dx, dy
    if Angle>2*pi
    	Angle = 2*pi
    	warn("The domain size adjusted to match a maximum of 2π.")
    end
    dr = Radius/Nr
    dtheta = Angle/Ntheta
    G=reshape([1:(Nr+2)*(Ntheta+2);], Nr+2, Ntheta+2)
    MeshStructure(2.8,
    	[Nr, Ntheta],
    	CellSize(dr*ones(Nr+2), dtheta*ones(Ntheta+2), [0.0]),
    	CellLocation(
            [1:Nr;]*dr.-dr/2.0,
            [1:Ntheta;]*dtheta.-dtheta/2.0,
            [0.0]),
    	FaceLocation([0:Nr;]*dr,[0:Ntheta;]*dtheta,[0.0]),
    	G[[1,end],[1,end]][:],
    	[1])
end

"""
Creates a mesh on a 2D radial (polar coordinates) domain with specified face
locations

m = createMesh2D(faceLocationR, faceLocationTheta)

Inputs:

   + faceLocationR (Vector of reals): face locations along radial axis
   + faceLocationTheta (Vector of reals): face locations along angular axis

Outputs:

   + m: a mesh structure

Usage:

fR = [0.0; 0.05; 0.1:0.1:1.0;]
fΘ = [0.0; 0.05; 0.12; 0.2:0.2:π;]

m=createMesh2D(fR, fΘ)
"""
function createMeshRadial2D{T<:Real}(facelocationR::Array{T,1}, facelocationTheta::Array{T,1})
    if facelocationTheta[end]>2.0*pi
    	facelocationTheta = facelocationTheta/facelocationTheta[end]*(2.0*pi)
    	warn("The domain size adjusted to match a maximum of 2π.")
    end
    Nx = length(facelocationR)-1
    Ny = length(facelocationTheta)-1
    G=reshape([1:(Nx+2)*(Ny+2);], Nx+2, Ny+2)
    MeshStructure(2.8,
    	[Nx, Ny],
    	CellSize(
            [
                facelocationR[2]-facelocationR[1];
                facelocationR[2:end]-facelocationR[1:end-1];
                facelocationR[end]-facelocationR[end-1]
            ],
    	[
            facelocationTheta[2]-facelocationTheta[1];
            facelocationTheta[2:end]-facelocationTheta[1:end-1];
            facelocationTheta[end]-facelocationTheta[end-1]
        ],
    	[0.0]),
    	CellLocation(
            0.5*(facelocationR[2:end]+facelocationR[1:end-1]),
            0.5*(facelocationTheta[2:end]+facelocationTheta[1:end-1]),
            [0.0]),
    	FaceLocation(facelocationR, facelocationTheta, [0.0]),
    	G[[1,end],[1,end]][:],
    	[1])
end

# %% ===================== 2D CYLINDRICAL MESH ==========================
"""
Builds a uniform cylindrical 2D mesh

m = createMeshCylindrical2D(Nr, Nz, Radius, Height)

Inputs:
    + Nr (Integer): number of cells in r (radial) direction
    + Nz (Integer): number of cells in z (axial, vertical) direction
    + Radius (Real): radius of the cylinder
    + Height (Real): height of the cylinder

Output:

    + m: a mesh structure
"""
function createMeshCylindrical2D(Nr::Int, Nz::Int, Radius::Real, Height::Real)
    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    # cell size is dr, dz
    dr = Radius/Nr
    dz = Height/Nz
    G=reshape([1:(Nr+2)*(Nz+2);], Nr+2, Nz+2)
    MeshStructure(2.5,
    	[Nr, Nz],
    	CellSize(dr*ones(Nr+2), dz*ones(Nz+2), [0.0]),
    	CellLocation([1:Nr;]*dr.-dr/2.0,[1:Nz;]*dz.-dz/2.0,[0.0]),
    	FaceLocation([0:Nr;]*dr,[0:Nz;]*dz,[0.0]),
    	G[[1,end],[1,end]][:],
    	[1])
end

"""
Creates a mesh on a 2D cylindrical domain with specified face
locations

m = createMesh2D(faceLocationR, faceLocationZ)

Inputs:

   + faceLocationR (Vector of reals): face locations along radial axis
   + faceLocationZ (Vector of reals): face locations along vertical axis

Outputs:

   + m: a mesh structure

Usage:

fR = [0.0; 0.05; 0.1:0.1:1.0;]
fZ = [0.0; 0.05; 0.12; 0.2:0.2:3.0;]

m=createMesh2D(fR, fZ)
"""
function createMeshCylindrical2D{T<:Real}(facelocationR::Array{T,1}, facelocationY::Array{T,1})
    Nx = length(facelocationR)-1
    Ny = length(facelocationY)-1
    G=reshape([1:(Nx+2)*(Ny+2);], Nx+2, Ny+2)
    MeshStructure(2.5,
    	[Nx, Ny],
    	CellSize(
            [
                facelocationR[2]-facelocationR[1];
                facelocationR[2:end]-facelocationR[1:end-1];
                facelocationR[end]-facelocationR[end-1]
            ],
    	    [
                facelocationY[2]-facelocationY[1];
                facelocationY[2:end]-facelocationY[1:end-1];
                facelocationY[end]-facelocationY[end-1]
            ],
    	[0.0]),
    	CellLocation(
            0.5*(facelocationR[2:end]+facelocationR[1:end-1]),
            0.5*(facelocationY[2:end]+facelocationY[1:end-1]),
            [0.0]),
    	FaceLocation(facelocationR, facelocationY, [0.0]),
    	G[[1,end],[1,end]][:],
    	[1])
end

# %% ========================== 3D CARTESIAN MESH ============================
"""
Creates a uniform 3D mesh:

m = createMesh3D(Nx, Ny, Nz, Width, Height, Depth)

Inputs:

    + Nx (int): number of cells in horizontal direction
    + Ny (int): number of cells in vertical direction
    + Nz (int): number of cells in depth direction
    + Width, Height, Depth (reals): size of each dimension

Output:

    + m: a mesh structure

"""
function createMesh3D(Nx::Int, Ny::Int, Nz::Int, Width::Real, Height::Real, Depth::Real)
    # numbering system of cells, like the single index numbering of Matlab
    # +2 is added to account for the ghost cells that are added at
    # the boundaries
    dx = Width/Nx
    dy = Height/Ny
    dz = Depth/Nz
    G=reshape([1:(Nx+2)*(Ny+2)*(Nz+2);], Nx+2, Ny+2, Nz+2)
    MeshStructure(3,
    	[Nx, Ny, Nz],
    	CellSize(dx*ones(Nx+2), dy*ones(Ny+2), dz*ones(Nz+2)),
    	CellLocation(
            [1:Nx;]*dx.-dx/2.0,
            [1:Ny;]*dy.-dy/2.0,
            [1:Nz;]*dz.-dz/2.0),
    	FaceLocation([0:Nx;]*dx, [0:Ny;]*dy, [0:Nz;]*dz),
    	G[[1,end],[1,end],[1,end]][:],                         # corners
    	[                                                      # edges
            G[[1, end], [1, end], 2:Nz+1][:];
        	G[[1, end], 2:Ny+1, [1, end]][:];
        	G[2:Nx+1, [1, end], [1, end]][:]
        ])
end

"""
Creates a mesh on a 3D Cartesian domain with specified faces
locations

m = createMesh2D(faceLocationX, faceLocationY, faceLocationZ)

Inputs:

   + faceLocationX (Vector of reals): face locations along horizontal direction
   + faceLocationY (Vector of reals): face locations along vertical direction
   + faceLocationZ (Vector of reals): face locations along depth direction

Outputs:

   + m: a mesh structure

Usage:

```julia
fX = [0.0; 0.05; 0.1:0.1:1.0;]
fY = [0.0; 0.05; 0.12; 0.2:0.2:3.0;]
fz = [0.0:0.1:0.5;]

m=createMesh2D(fX, fY, fZ)
```
"""
function createMesh3D{T<:Real}(facelocationX::Array{T,1}, facelocationY::Array{T,1}, facelocationZ::Array{T,1})
Nx = length(facelocationX)-1
Ny = length(facelocationY)-1
Nz = length(facelocationZ)-1
G=reshape([1:(Nx+2)*(Ny+2)*(Nz+2);], Nx+2, Ny+2, Nz+2)
MeshStructure(3,
	[Nx, Ny, Nz],
	CellSize([facelocationX[2]-facelocationX[1]; facelocationX[2:end]-facelocationX[1:end-1]; facelocationX[end]-facelocationX[end-1]],
	  [facelocationY[2]-facelocationY[1]; facelocationY[2:end]-facelocationY[1:end-1]; facelocationY[end]-facelocationY[end-1]],
	  [facelocationZ[2]-facelocationZ[1]; facelocationZ[2:end]-facelocationZ[1:end-1]; facelocationZ[end]-facelocationZ[end-1]]),
	CellLocation(0.5*(facelocationX[2:end]+facelocationX[1:end-1]),
	  0.5*(facelocationY[2:end]+facelocationY[1:end-1]),
	  0.5*(facelocationZ[2:end]+facelocationZ[1:end-1])),
	FaceLocation(facelocationX, facelocationY, facelocationZ),
	G[[1,end],[1,end],[1,end]][:],
	[G[[1, end], [1, end], 2:Nz+1][:];
	G[[1, end], 2:Ny+1, [1, end]][:];
	G[2:Nx+1, [1, end], [1, end]][:]])
end

# TODO: docstring for uniform cylindrical 3D mesh
# TODO: formatting for uniform cylindrical 3D mesh
# %% ================== 3D CYLINDRICAL MESH ===================================
function createMeshCylindrical3D(Nr::Int, Ntheta::Int, Nz::Int, Radius::Real, Angle::Real, Height::Real)
# builds a uniform 3D mesh:
# Nr is the number of cells in x direction
# Ntheta is the number of cells in y direction
# Nz is the number of cells in z direction
# Radius is the domain length in x direction
# Angle is the domain length in y direction
# Depth is the domain length in z direction

# numbering system of cells, like the single index numbering of Matlab
# +2 is added to account for the ghost cells that are added at
# the boundaries
if Angle>2*pi
	Angle = 2*pi
	println("The domain size adjusted to match a maximum of 2*pi.")
end
dr = Radius/Nr
dtheta = Angle/Ntheta
dz = Height/Nz
G=reshape([1:(Nr+2)*(Ntheta+2)*(Nz+2);], Nr+2, Ntheta+2, Nz+2)
MeshStructure(3.2,
	[Nr, Ntheta, Nz],
	CellSize(dr*ones(Nr+2), dtheta*ones(Ntheta+2), dz*ones(Nz+2)),
	CellLocation([1:Nr;]*dr.-dr/2.0, [1:Ntheta;]*dtheta.-dtheta/2.0, [1:Nz;]*dz.-dz/2.0),
	FaceLocation([0:Nr;]*dr, [0:Ntheta;]*dtheta, [0:Nz;]*dz),
	G[[1,end],[1,end],[1,end]][:],
	[G[[1, end], [1, end], 2:Nz+1][:];
	G[[1, end], 2:Ntheta+1, [1, end]][:];
	G[2:Nr+1, [1, end], [1, end]][:]])
end

# TODO: docstring for nonuniform cylindrical 3D mesh
# TODO: formatting for nonuniform cylindrical 3D mesh
function createMeshCylindrical3D{T<:Real}(facelocationR::Array{T,1}, facelocationTheta::Array{T,1}, facelocationZ::Array{T,1})
if facelocationTheta[end]>2*pi
	facelocationTheta = facelocationTheta/facelocationTheta[end]*2.0*pi
	println("The domain size adjusted to match a maximum of 2*pi.")
end
Nx = length(facelocationR)-1
Ny = length(facelocationTheta)-1
Nz = length(facelocationZ)-1
G=reshape([1:(Nx+2)*(Ny+2)*(Nz+2);], Nx+2, Ny+2, Nz+2)
MeshStructure(3.2,
	[Nx, Ny, Nz],
	CellSize([facelocationR[2]-facelocationR[1]; facelocationR[2:end]-facelocationR[1:end-1]; facelocationR[end]-facelocationR[end-1]],
	  [facelocationTheta[2]-facelocationTheta[1]; facelocationTheta[2:end]-facelocationTheta[1:end-1]; facelocationTheta[end]-facelocationTheta[end-1]],
	  [facelocationZ[2]-facelocationZ[1]; facelocationZ[2:end]-facelocationZ[1:end-1]; facelocationZ[end]-facelocationZ[end-1]]),
	CellLocation(0.5*(facelocationR[2:end]+facelocationR[1:end-1]),
	  0.5*(facelocationTheta[2:end]+facelocationTheta[1:end-1]),
	  0.5*(facelocationZ[2:end]+facelocationZ[1:end-1])),
	FaceLocation(facelocationR, facelocationTheta, facelocationZ),
	G[[1,end],[1,end],[1,end]][:],
	[G[[1, end], [1, end], 2:Nz+1][:];
	G[[1, end], 2:Ny+1, [1, end]][:];
	G[2:Nx+1, [1, end], [1, end]][:]])
end


text:
# License for this file: MIT (expat)
# Copyright 2019, DLR Institute of System Dynamics and Control

"""
    module IdealClutch

Model of a mass controlled by a two-point controller leading to state events.

# Physical model

```
# Inertias
J1*der(w1) = emf.tau - clutch.tau
J2*der(w2) =           clutch.tau

# Clutch
engaged = time < 100 or time >= 300
if engaged
    0 = w2 - w1
else
    0 = clutch.tau
end

# Electric circuit
R.v   := V0 - C.v
R.i   := R.v/R
emf.v := emf.k*w1
C.v   := emf.v
C.i   := C*der(C.v)

tau1 = emf.k*emf.i
R.i  = C.i + emf.i

---------------------------
Sorted and solved equations:

input : x     = [w1     , w2     , integral(clutch_tau)]
        der_x = [der(w1), der(w2), clutch.tau]
output: residue

emf.v    := emf.k*w1
C.v      := emf.v
der(C.v) := emf.k*der(w1)
C.i      := C*der(C.v)
R.v      := V0 - C.v
R.i      := R.v/R
emf.i    := R.i - C.i
emf.tau  := emf.k*emf.i

residue1 := J1*der(w1) - (emf.tau - clutch.tau)
residue2 := J2*der(w2) - clutch.tau
residue3 := if engaged then w2-w1 else clutch.tau

is_constraint[1] := false
is_constraint[2] := false
is_constraint[3] := engaged
------

```

"""
module IdealClutch

import ..ModiaMath

const T1 = 100.0
const T2 = 300.0

mutable struct Model <: ModiaMath.AbstractSimulationModel
    simulationState::ModiaMath.SimulationState

    # Parameters
    V0::Float64
    J1::Float64
    J2::Float64
    R::Float64
    C::Float64
    emf_k::Float64
	T_next::Float64
	engaged::Bool

    function Model(;V0=10.0, J1 = 0.1, J2 = 0.4, w1_start = 0.0, w2_start = 10.0, R=10.0, C=2.0, emf_k = 0.25)
        simulationState = ModiaMath.SimulationState("IdealClutch", getModelResidues!, [w1_start, w2_start, 0.0], getVariableName;
		                                            structureOfDAE = ModiaMath.DAE_LinearDerivativesAndConstraints,
													is_constraint = [false, false, true],
                                                    nz=1, nw=3)

        new(simulationState, V0, J1, J2, R, C, emf_k, T1, true)
    end
end

getVariableName(model, vcat, vindex) = ModiaMath.getVariableName(model, vcat, vindex;
                                                                 xNames    = ["inertia1.w", "inertia2.w", "integral(clutch.tau)"],
																 derxNames = ["der(inertia1.w)", "der(inertia2.w)", "clutch.tau"],
                                                                 wNames    = ["capacitor.v", "capacitor.i", "engaged"])

function getModelResidues!(m::Model, t::Float64, _x::Vector{Float64}, _derx::Vector{Float64}, _r::Vector{Float64}, _w::Vector{Float64})
    sim = m.simulationState

	if ModiaMath.isInitial(sim)
	    m.T_next  = T1
    	m.engaged = true
        ModiaMath.setNextEvent!(sim, m.T_next)
    end

    if ModiaMath.isEvent(sim)
	    # engaged = time < 100 or time >= 300

		if t >= m.T_next
            if t < T2
		        m.T_next  = T2
			    m.engaged = false
            else
                m.T_next  = Inf
                m.engaged = true
	        end
	        ModiaMath.setNextEvent!(sim, m.T_next)
		end

		is_constraint    = ModiaMath.get_is_constraint(sim)
        is_constraint[3] = m.engaged
    end
	engaged = m.engaged

	V0    = m.V0
	J1    = m.J1
	J2    = m.J2
	R     = m.R
	C     = m.C
	emf_k = m.emf_k

    w1     = _x[1]
    w2     = _x[2]
    der_w1 = _derx[1]
    der_w2 = _derx[2]
    tau    = _derx[3]

    C_v     = emf_k*w1
    der_C_v = emf_k*der_w1
    C_i     = C*der_C_v
    R_v     = V0 - C_v
    R_i     = R_v/R
    emf_i   = R_i - C_i
    emf_tau = emf_k*emf_i

    _r[1] = J1*der_w1 - (emf_tau - tau)
    _r[2] = J2*der_w2 - tau
    _r[3] = engaged ? w2-w1 : tau

    _w[1] = C_v
	_w[2] = C_i
	_w[3] = engaged ? 1.0 : 0.0

    #println("... time = $t, engaged = $engaged, w1 = $w1, w2 = $w2, r3 = $(_r[3])")
    return nothing
end

end

ext: jl


text:
module MriResearchTools

using Requires
using Interpolations
using NIfTI
using ROMEO
using Statistics
using DataStructures
using ImageMorphology
using PaddedViews

include("utility.jl")
include("smoothing.jl")
include("intensitycorrection.jl")
include("VSMbasedunwarping.jl")
include("methods.jl")
include("niftihandling.jl")
include("mcpc3ds.jl")
include("romeofunctions.jl")

function __init__()
        @require FFTW="7a1cc6ca-52ef-59f5-83cd-3a7055c09341" include("laplacianunwrapping.jl")
end
laplacianunwrap(p) = @warn "FFTW is required! Type 'using FFTW' before calling this function"

export  readphase, readmag, niread, write_emptynii,
        header,
        savenii,
        estimatenoise,
        robustmask, robustmask!,
        robustrescale,
        #combine_echoes,
        calculateB0_unwrapped,
        mask_from_voxelquality,
        romeovoxelquality,
        getHIP,
        laplacianunwrap, laplacianunwrap!,
        getVSM,
        unwarp,
        thresholdforward,
        gaussiansmooth3d!, gaussiansmooth3d,
        gaussiansmooth3d_phase,
        makehomogeneous!, makehomogeneous,
        getsensitivity,
        getscaledimage,
        estimatequantile,
        RSS,
        mcpc3ds,
        unwrap, unwrap!, romeo, romeo!,
        unwrap_individual, unwrap_individual!,
        homodyne, homodyne!,
        to_dim,
        NumART2star, r2s_from_t2s

end # module


text:
### A Pluto.jl notebook ###
# v0.17.2

using Markdown
using InteractiveUtils

# ╔═╡ d9015225-b635-42ad-ae96-fe7772a031b7
using Pkg, DrWatson

# ╔═╡ 727e041b-fe08-4f7d-ad19-e3c57772c967
begin
	using GLM
	using CSV
	using Random
	using StatsBase
	using DataFrames
	using Dagitty
	using Turing
	using StatsPlots
	using StatisticalRethinking
	using StatisticalRethinkingPlots
	using Logging
end

# ╔═╡ 5a128323-2c19-4efa-989f-ff345e6a9cb3
# Pkg.update()

# ╔═╡ 078fdb65-5bd6-4b0d-b672-617f5912480d
begin
	default(labels=false)
	Logging.disable_logging(Logging.Warn);
end;

# ╔═╡ 5141dfdf-490d-479e-ac58-63c929ae8fd1
md"## 7.1 The problem with parameters."

# ╔═╡ 611c3828-f01f-4721-830b-736b28620e7e
md"### Code 7.1"

# ╔═╡ ad511be2-fd88-4aba-a830-21e242d994f1
begin
	sppnames = ["afarensis", "africanus", "habilis", "boisei",
		"rudolfensis", "ergaster", "sapiens"]
	brainvolcc = [438, 452, 612, 521, 752, 871, 1350]
	masskg = [37.0, 35.5, 34.5, 41.5, 55.5, 61.0, 53.5]
	d = DataFrame(:species => sppnames, :brain => brainvolcc, :mass => masskg)
end;

# ╔═╡ 4ee38b80-aded-40af-93ac-11a4ac2b9378
md"### Code 7.2"

# ╔═╡ 5c7f1f26-02ac-4325-a06c-8c26c75e6cf4
begin
	d[!,:mass_std] = (d.mass .- mean(d.mass))./std(d.mass)
	d[!,:brain_std] = d.brain ./ maximum(d.brain)
	d
end

# ╔═╡ 5a2f79ca-2d3e-4cd4-9de9-7c7e283a5052
md"### Code 7.3"

# ╔═╡ 94b5539b-4374-40b8-9501-8d3df49f20c3
@model function model_m7_1(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ Normal(0, 10)
    μ = @. a + b*mass_std
    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ 2aafe78c-b1b1-4963-ad89-dbe09b546d96
begin
	m7_1_ch = sample(model_m7_1(d.mass_std, d.brain_std), NUTS(), 1000)
	m7_1 = DataFrame(m7_1_ch)
	PRECIS(m7_1)
end

# ╔═╡ 45122674-c5d2-4f61-af03-c74482618e90
md"### Code 7.4"

# ╔═╡ 3b7ca48f-078f-4eef-9d0c-fa8724e711d3
X = hcat(ones(length(d.mass_std)), d.mass_std)

# ╔═╡ 40c173f3-3dbb-4907-9188-632d34b3d7cf
m = lm(X, d.brain_std)

# ╔═╡ 39dc811c-2742-4977-a203-c9fdcb5b218d
md"### Code 7.5"

# ╔═╡ 85bb82da-efe7-4b34-8af5-cf60ae6e4757
Random.seed!(12);

# ╔═╡ 53806285-ea68-4f5c-b3fb-a382a894ec56
md"## Do explicit simulation due to log_σ."

# ╔═╡ 59b9a24b-6967-418b-a4f8-e67ceb0a5474
begin
	s = [
		rand(MvNormal((@. r.a + r.b * d.mass_std), exp(r.log_σ)))
		for r ∈ eachrow(m7_1)
	]
	s = vcat(s'...);

	r = mean.(eachcol(s)) .- d.brain_std;
	resid_var = var(r, corrected=false)
	outcome_var = var(d.brain_std, corrected=false)
	1 - resid_var/outcome_var
end

# ╔═╡ ed541621-2245-49f9-9672-31e20b9b7765
md"### Code 7.6"

# ╔═╡ 47d9566c-93ec-4f70-b7b6-5586193bcdef
md"#### Function is implemented in a generic way to support any amount of b[x] coefficients."

# ╔═╡ 1e5a39c0-6b5b-4d29-826e-e68c31c8f34e
function R2_is_bad(df; sigma=missing)
    degree = ncol(df[!,r"b"])
    # build mass_std*degree matrix, with each col exponentiated to col's index
    t = repeat(d.mass_std, 1, degree)
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    s = [
        begin
            # calculate product on coefficient's vector
            b = collect(r[r"b"])
            μ = r.a .+ t * b
            s = ismissing(sigma) ? exp(r.log_σ) : sigma
            rand(MvNormal(μ, s))
        end
        for r ∈ eachrow(df)
    ]
    s = vcat(s'...);

    r = mean.(eachcol(s)) .- d.brain_std;
    v1 = var(r, corrected=false)
    v2 = var(d.brain_std, corrected=false)
    1 - v1 / v2
end

# ╔═╡ e8f6166f-20e5-40a2-a8fc-692ea8704b6d
md"### Code 7.7"

# ╔═╡ f74d5bc3-747b-4b12-9fb2-7e4a19cfe2c1
@model function model_m7_2(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ MvNormal([0, 0], 10)
    μ = @. a + b[1]*mass_std + b[2]*mass_std^2
    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ fa9522ce-d91d-4cbd-9a1a-fe63fd2b7d15
begin
	m7_2_ch = sample(model_m7_2(d.mass_std, d.brain_std), NUTS(), 10000)
	m7_2 = DataFrame(m7_2_ch)
	PRECIS(m7_2)
end

# ╔═╡ 41fc983a-9209-4ff5-b9fa-5798c7d387af
md"### Code 7.8"

# ╔═╡ 0f8d2476-7379-4bec-8a6f-e6ef81066ebb
md"#### Implemented the sample in a general way."

# ╔═╡ 4632e385-2417-4683-9e31-72825cf5501c
@model function model_m7_n(mass_std, brain_std; degree::Int)
    a ~ Normal(0.5, 1)
    b ~ MvNormal(zeros(degree), 10)
    # build matrix n*degree
    t = repeat(mass_std, 1, degree)
    # exponent its columns
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    # calculate product on coefficient's vector
    μ = a .+ t * b

    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ bf763ccd-2c72-4529-b6ac-747f39f1b9cf
begin
	m7_3_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=3), NUTS(), 1000)
	m7_3 = DataFrame(m7_3_ch)
	PRECIS(m7_3)
end

# ╔═╡ ef2e821a-d947-40e1-9855-79819aec5dbb
begin
	m7_4_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=4), NUTS(), 1000)
	m7_4 = DataFrame(m7_4_ch)
	PRECIS(m7_4)
end

# ╔═╡ e1e48fb9-bb0f-4fe6-a34e-46ea2ced2510
begin
	m7_5_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=5), NUTS(), 1000)
	m7_5 = DataFrame(m7_5_ch)
	PRECIS(m7_5)
end

# ╔═╡ bff2a56e-e799-4d50-b97b-79983df86565
@model function model_m7_6(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ MvNormal(zeros(6), 10)
    μ = @. a + b[1]*mass_std + b[2]*mass_std^2 + b[3]*mass_std^3 +
               b[4]*mass_std^4 + b[5]*mass_std^5 + b[6]*mass_std^6
    brain_std ~ MvNormal(μ, 0.001)
end

# ╔═╡ 5c26fd02-6695-4f3d-8f17-37c9b2ada2e6
begin
	m7_6_ch = sample(model_m7_6(d.mass_std, d.brain_std), NUTS(), 1000)
	m7_6 = DataFrame(m7_6_ch)
	PRECIS(m7_6)
end

# ╔═╡ 941248e9-c1ec-4d6a-8a2a-dbdd9aee17d8
md"### Code 7.10"

# ╔═╡ 97a58b2a-a200-4249-acf3-c52d28ca6aea
mass_seq = range(extrema(d.mass_std)...; length=100)

# ╔═╡ 7174161a-6536-4ec7-a89e-2c385de7052c
begin
	l = [
    	@. r.a + r.b * mass_seq
    	for r ∈ eachrow(m7_1)
	]
	l = vcat(l'...)
	μ = mean.(eachcol(l))
end

# ╔═╡ f4955154-ea66-4523-aacd-1a4beef6d41b
begin
	ci = PI.(eachcol(l))
	ci = vcat(ci'...)
end

# ╔═╡ caa5e742-7606-43fa-8ae3-a1287ff24951
scatter(d.mass_std, d.brain_std; title="1: R² = $(round(R2_is_bad(m7_1); digits=3))")

# ╔═╡ 2f524064-abcc-40a1-a21e-99a0a4636545
plot!(mass_seq, [μ μ]; fillrange=ci, c=:black, fillalpha=0.3)

# ╔═╡ 0f92b3fa-1b99-45f4-8a8e-5b7ea33a464d
md"### Reimplemented the brain_plot function to check my results."

# ╔═╡ cb2d9bdf-3cf3-48f2-a984-5440dba08ad9
function brain_plot(df; sigma=missing)
    degree = ncol(df[!,r"b"])
    # build mass_seq*degree matrix, with each col exponentiated to col's index
    t = repeat(mass_seq, 1, degree)
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    l = [
        r.a .+ t * collect(r[r"b"])
        for r ∈ eachrow(df)
    ]
    l = vcat(l'...)
    μ = mean.(eachcol(l))
    ci = PI.(eachcol(l))
    ci = vcat(ci'...)

    r2 = round(R2_is_bad(df, sigma=sigma); digits=3)
    scatter(d.mass_std, d.brain_std; title="$degree: R² = $r2")
    plot!(mass_seq, [μ μ]; fillrange=ci, c=:black, fillalpha=0.3)
end;

# ╔═╡ 29f7fc44-1d5c-4912-a0b0-07a7e97cfe26
plot(
    brain_plot(m7_1),
    brain_plot(m7_2),
    brain_plot(m7_3),
    brain_plot(m7_4),
    brain_plot(m7_5),
    brain_plot(m7_6, sigma=0.001);
    size=(1000, 600)
)

# ╔═╡ bb21db38-31cf-4e88-86d2-922d62533769
md"### Code 7.11"

# ╔═╡ 4f7bfda2-297d-432d-83c9-c931f5f62868
i = 3;

# ╔═╡ 90d5c3e8-a045-4d96-aebc-2ec99609e10b
d_minus_i = d[setdiff(1:end,i),:];

# ╔═╡ 3babf620-dd01-45ae-b21c-e46e136057f6
function brain_loo_plot(model, data; title::String)
    (a, b) = extrema(data.brain_std)
    p = scatter(data.mass_std, data.brain_std; title=title, ylim=(a-0.1, b+0.1))
    mass_seq = range(extrema(data.mass_std)...; length=100)

    for i ∈ 1:nrow(data)
        d_minus_i = data[setdiff(1:end,i),:]
        df = DataFrame(sample(
				model(d_minus_i.mass_std, d_minus_i.brain_std),
				NUTS(),
				1000))

        degree = ncol(df[!,r"b"])

        # build mass_seq*degree matrix, with each col exponentiated to col's index

        t = repeat(mass_seq, 1, degree)
        t = hcat(map(.^, eachcol(t), 1:degree)...)
        l = [
            r.a .+ t * collect(r[r"b"])
            for r ∈ eachrow(df)
        ]
        l = vcat(l'...)
        μ = mean.(eachcol(l))
        plot!(mass_seq, μ; c=:black)
    end
    p
end

# ╔═╡ 9a5d927d-e816-4f5f-a460-c89a507ce1ae
model_m7_4 = (mass, brain) -> model_m7_n(mass, brain, degree=4)

# ╔═╡ b3778ab5-03b7-4ba5-9501-3e6bb643e4d5
plot(
    brain_loo_plot(model_m7_1, d, title="m7.1"),
    brain_loo_plot(model_m7_4, d, title="m7.4");
    size=(800, 400)
)

# ╔═╡ b55cffd3-d5ce-41db-968d-0b54b1b872a7
md"## 7.2 Entropy and accuracy."

# ╔═╡ e8765238-eec6-41c0-9c8c-148c9e51aad9
md"### Code 7.12"

# ╔═╡ fd1f8ae2-6839-4f7e-9141-66824490df72
p = [0.3, 0.7];

# ╔═╡ 3a3537ec-039a-434d-a7d4-15ab41eb97d8
-sum(p .* log.(p))

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
Dagitty = "d56128e0-8113-48cd-82a0-fc808dc30d4b"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
DrWatson = "634d3b9d-ee7a-5ddf-bec9-22491ea816e1"
GLM = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StatisticalRethinking = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
StatisticalRethinkingPlots = "e1a513d0-d9d9-49ff-a6dd-9d2e9db473da"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
CSV = "~0.8.5"
Dagitty = "~0.0.1"
DataFrames = "~1.2.2"
DrWatson = "~2.4.1"
GLM = "~1.5.1"
StatisticalRethinking = "~4.0.4"
StatisticalRethinkingPlots = "~0.3.0"
StatsBase = "~0.33.10"
StatsPlots = "~0.14.26"
Turing = "~0.18.0"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[ANSIColoredPrinters]]
git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c"
uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9"
version = "0.0.1"

[[AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.0.1"

[[AbstractMCMC]]
deps = ["BangBang", "ConsoleProgressMonitor", "Distributed", "Logging", "LoggingExtras", "ProgressLogging", "Random", "StatsBase", "TerminalLoggers", "Transducers"]
git-tree-sha1 = "db0a7ff3fbd987055c43b4e12d2fa30aaae8749c"
uuid = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
version = "3.2.1"

[[AbstractPPL]]
deps = ["AbstractMCMC"]
git-tree-sha1 = "15f34cc635546ac072d03fc2cc10083adb4df680"
uuid = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
version = "0.2.0"

[[AbstractTrees]]
git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.3.4"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

[[AdvancedHMC]]
deps = ["AbstractMCMC", "ArgCheck", "DocStringExtensions", "InplaceOps", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "Setfield", "Statistics", "StatsBase", "StatsFuns", "UnPack"]
git-tree-sha1 = "0a655e9a59ee1c8bafc3af18e96d90f980b08600"
uuid = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
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[[AdvancedMH]]
deps = ["AbstractMCMC", "Distributions", "Random", "Requires"]
git-tree-sha1 = "8ad8bfddf8bb627d689ecb91599c349cbf15e971"
uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
version = "0.6.6"

[[AdvancedPS]]
deps = ["AbstractMCMC", "Distributions", "Libtask", "Random", "StatsFuns"]
git-tree-sha1 = "06da6c283cf17cf0f97ed2c07c29b6333ee83dc9"
uuid = "576499cb-2369-40b2-a588-c64705576edc"
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[[AdvancedVI]]
deps = ["Bijectors", "Distributions", "DistributionsAD", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "StatsBase", "StatsFuns", "Tracker"]
git-tree-sha1 = "130d6b17a3a9d420d9a6b37412cae03ffd6a64ff"
uuid = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
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[[ArgCheck]]
git-tree-sha1 = "dedbbb2ddb876f899585c4ec4433265e3017215a"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.1.0"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "f87e559f87a45bece9c9ed97458d3afe98b1ebb9"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.1.0"

[[Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
git-tree-sha1 = "2ff92b71ba1747c5fdd541f8fc87736d82f40ec9"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
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git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.2.0"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[TerminalLoggers]]
deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
git-tree-sha1 = "62846a48a6cd70e63aa29944b8c4ef704360d72f"
uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed"
version = "0.1.5"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[ThreadingUtilities]]
deps = ["ManualMemory"]
git-tree-sha1 = "03013c6ae7f1824131b2ae2fc1d49793b51e8394"
uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5"
version = "0.4.6"

[[Tracker]]
deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "bf4adf36062afc921f251af4db58f06235504eff"
uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
version = "0.2.16"

[[Transducers]]
deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
git-tree-sha1 = "bccb153150744d476a6a8d4facf5299325d5a442"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.67"

[[Tullio]]
deps = ["ChainRulesCore", "DiffRules", "LinearAlgebra", "Requires"]
git-tree-sha1 = "0288b7a395fc412952baf756fac94e4f28bfec65"
uuid = "bc48ee85-29a4-5162-ae0b-a64e1601d4bc"
version = "0.3.2"

[[Turing]]
deps = ["AbstractMCMC", "AdvancedHMC", "AdvancedMH", "AdvancedPS", "AdvancedVI", "BangBang", "Bijectors", "DataStructures", "Distributions", "DistributionsAD", "DocStringExtensions", "DynamicPPL", "EllipticalSliceSampling", "ForwardDiff", "Libtask", "LinearAlgebra", "MCMCChains", "NamedArrays", "Printf", "Random", "Reexport", "Requires", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Tracker", "ZygoteRules"]
git-tree-sha1 = "e22a11c2029137b35adf00a0e4842707c653938c"
uuid = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
version = "0.18.0"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "5239606cf3552aff43d79ecc75b1af1ce4625109"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.21"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "80661f59d28714632132c73779f8becc19a113f2"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.4"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
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# ╟─00000000-0000-0000-0000-000000000002


text:
using Test

@timed_testset "trained_weights/" begin
    include("trained_weights/MNIST.n1.jl")
    include("trained_weights/MNIST.WK17a_linf0.1_authors.jl")
end


text:
using Test
using Spandex

@testset "push!" begin
    local il = Intlist(10)
    push!(il, 1)
    push!(il, 7)
    push!(il, 3)
    push!(il, 2)

    @test 10 == il.capacity
    @test 4 == il.size
end

@testset "contains" begin
    local il = Intlist(10)
    push!(il, 1)
    push!(il, 7)
    push!(il, 3)
    push!(il, 2)

    @test contains(il, 1)
    @test contains(il, 2)
    @test contains(il, 3)
    @test contains(il, 7)

    @test !contains(il, 0)
    @test !contains(il, 4)
end

@testset "pop!" begin
    local il = Intlist(10)
    push!(il, 1)
    push!(il, 7)
    push!(il, 3)
    push!(il, 2)

    @test 2 == pop!(il)
    @test 3 == pop!(il)
    @test 7 == pop!(il)
    @test 1 == pop!(il)
end

@testset "pop_all!" begin
    local il = Intlist(10)
    push!(il, 1)
    push!(il, 7)
    push!(il, 3)
    push!(il, 2)

    local values = pop_all!(il)

    @test 0 == il.size

    @test 2 == values[1]
    @test 3 == values[2]
    @test 7 == values[3]
    @test 1 == values[4]
end


text:
include("rob_lib.jl")
# perimetr have all it markerito

function mark_frame_perimetr!(r::Robot)
    num_verticale = moves!(r, Sud)
    num_horizont = moves!(r, West)

    for i in 3:6
        putmarkers!(r, HorizonSide(i % 4)) # particular sides we want 1 0 3 2
    end

    Back!(r, Nord, num_verticale)
    Back!(r, Ost, num_horizont)
end

function moves!(r::Robot, side::HorizonSide)
    num_steps = 0
    while move_if_possible!(r, side)
        num_steps += 1
    end
    return num_steps
end

function putmarkers!(r::Robot, side::HorizonSide)
    while !isborder(r, side)
        move!(r, side)
        putmarker!(r)
    end
end

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text:
using Printf, Distributions, IterTools

newv(n::Int, p::Float64) = rand(Bernoulli(p), n)
runs(v::Vector{Int}) = sum((a & ~b) for (a, b) in zip(v, IterTools.chain(v[2:end], v[1])))

mrd(n::Int, p::Float64) = runs(newv(n, p)) / n

nrep = 500

for p in 0.1:0.2:1
    lim = p * (1 - p)

    println()
    for ex in 10:2:14
        n = 2 ^ ex
        sim = mean(mrd.(n, p) for _ in 1:nrep)
        @printf("nrep = %3i\tp = %4.2f\tn = %5i\np · (1 - p) = %5.3f\tsim = %5.3f\tΔ = %3.1f%%\n",
                nrep, p, n, lim, sim, lim > 0 ? abs(sim - lim) / lim * 100 : sim * 100)
    end
end

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