# Check if all the packages are installed or not
cond = "Gadfly" in keys(Pkg.installed()) &&
    "Colors" in keys(Pkg.installed()) &&
    "ODEInterface" in keys(Pkg.installed()) &&
    "ForwardDiff" in keys(Pkg.installed());
@assert cond "Please check if the following package(s) are installed:\
    Gadfly\
    Colors\
    ODEInterface\
    ForwardDiff"

# Load all the required packages
using Gadfly
using Colors
using ODEInterface
using ForwardDiff
@ODEInterface.import_huge
loadODESolvers();

######################## Function for saving plots #################################
# Input:
# fileName = Name of the file where the plot is to be stored
#            (with or without extension)
# f_e = Array containing function evaluations as columns for each solver
# err = Array containing errors as columns for each solver
# solverNames = Array containing the names of solvers used in respective order
# plotSize = size of the plot to be created
###################################################################################
function savePlotPNG(
        fileName, f_e, err, solverNames,
        plotSize = [30cm, 30cm]
    )

    numOfLayers = length(solverNames)

    if !contains(fileName, ".")
        fileName = string(fileName, ".png")
    end

    plotColorsHex = [
        "#4D4D4D", "#5DA5DA", "#FAA43A", "#60BD68",
        "#F17CB0", "#B2912F", "#B276B2", "#DECF3F", "#F15854",
    ]
    plotColors = [parse(Colorant, c) for c in plotColorsHex]

    majorFontSize = 24pt
    minorFontSize = 20pt
    pointSize = 5pt

    myplot = plot(
        Scale.x_log10, Scale.y_log10,
        Coord.cartesian(xflip = true, xmin = -11),
        Guide.manual_color_key("Legend", solverNames, plotColorsHex[1:numOfLayers]),
        Guide.xlabel("error"), Guide.ylabel("#Function evaluations"),
        Theme(
            major_label_font_size = majorFontSize, panel_stroke = colorant"black",
            minor_label_font_size = minorFontSize, key_title_font_size = majorFontSize,
            key_label_font_size = minorFontSize, key_position = :top, key_max_columns = 1
        )
    )

    for i in 1:numOfLayers
        push!(
            myplot, layer(
                x = err[:, i], y = f_e[:, i], Geom.point, Geom.path,
                Theme(default_color = plotColors[i], default_point_size = pointSize)
            )
        )
    end

    draw(PNG(fileName, plotSize[1], plotSize[2]), myplot)
    return nothing
end

# Define the right-hand function for automatic differentiation
function vdpolAD(x)
    return [x[2], ((1 - x[1]^2) * x[2] - x[1]) * 1.0e6]
end

# Define the system for the solver
function vdpol(t, x, dx)
    dx[:] = vdpolAD(x)
    return nothing
end

# Define the Jacobian function using AD
function getJacobian(t, x, J)
    J[:, :] = ForwardDiff.jacobian(vdpolAD, x)
    return nothing
end

# Flag to check whether plot is to be generated and saved or not
# Also checks if all solvers are successful
printFlag = true;

# Initial conditions
t0 = 0.0; T = [1.0:11.0;]; x0 = [2.0, 0.0];

# Get "reference solution"
f = open("vdpolRefSol.txt");
lines = readlines(f);

x_ref = Array{Float64}(11);

tmp = Array{Float64}(22);
counter = 1;
for l in lines
    tmp[counter] = parse(Float64, l)
    counter += 1
end

x_ref = tmp[1:2:end];

close(f)

# Store the solver names for plotting
solverNames = ["RADAU", "RADAU5", "SEULEX"];

# Initialize the variables for plots
# f_e = number of function evaluations
f_e = zeros(33, 3);
# err = error wrt ref solution over all time steps and components
err = zeros(33, 3);
# flops = Floating point operations
flops = zeros(33, 3);

# Weights for computing flops
dim = 2; # dimension of the system
flopsRHS = 5; # Counted
flopsLU = ceil(2 * ((dim)^3) / 3); # As per LU algorithm (can be less)
flopsFW_BW = (dim)^2; # As per FW/BW algorithm (can be less)
flopsJac = ceil(1.5 * flopsRHS); # A guess at the moment

for i in 0:32

    # Set the tolerance for current run
    Tol = 10^(-2 - i / 4)

    # Set solver options
    opt = OptionsODE(
        OPT_EPS => 1.11e-16, OPT_ATOL => Tol, OPT_RTOL => Tol,
        OPT_RHS_CALLMODE => RHS_CALL_INSITU,
        OPT_JACOBIMATRIX => getJacobian
    )

    # Store the stats of the last t_end
    # for computing flops
    stats = Dict{AbstractString, Any}

    # Restart the solution for each end time
    # to ensure a more accurate solution
    # compared to dense output

    # Solve using RADAU
    x_radau = Array{Float64}(11)
    for j in 1:11
        (t, x, retcode, stats) = radau(vdpol, t0, T[j], x0, opt)
        # If solver fails do not continue further
        if retcode != 1
            println("Solver RADAU failed")
            printFlag = false
            break
        end
        x_radau[j] = x[1]
        f_e[i + 1, 1] = stats.vals[13]
    end
    # If solver fails do not continue further
    if !printFlag
        break
    end
    err[i + 1, 1] = norm(x_radau - x_ref, Inf)
    flops[i + 1, 1] = stats["no_rhs_calls"] * flopsRHS +
        stats["no_fw_bw_subst"] * flopsFW_BW +
        stats["no_jac_calls"] * flopsJac +
        stats["no_lu_decomp"] * flopsLU

    # Solve using RADAU5
    x_radau5 = Array{Float64}(11)
    for j in 1:11
        (t, x, retcode, stats) = radau5(vdpol, t0, T[j], x0, opt)
        # If solver fails do not continue further
        if retcode != 1
            println("Solver RADAU5 failed")
            printFlag = false
            break
        end
        x_radau5[j] = x[1]
        f_e[i + 1, 2] = stats.vals[13]
    end
    # If solver fails do not continue further
    if !printFlag
        break
    end
    err[i + 1, 2] = norm(x_radau5 - x_ref, Inf)
    flops[i + 1, 2] = stats["no_rhs_calls"] * flopsRHS +
        stats["no_fw_bw_subst"] * flopsFW_BW +
        stats["no_jac_calls"] * flopsJac +
        stats["no_lu_decomp"] * flopsLU

    # Solve using SEULEX
    x_seulex = Array{Float64}(11)
    for j in 1:11
        (t, x, retcode, stats) = seulex(vdpol, t0, T[j], x0, opt)
        # If solver fails do not continue further
        if retcode != 1
            println("Solver seulex failed")
            printFlag = false
            break
        end
        x_seulex[j] = x[1]
        f_e[i + 1, 3] = stats.vals[13]
    end
    # If solver fails do not continue further
    if !printFlag
        break
    end
    # Get the error over all the components and
    err[i + 1, 3] = norm(x_seulex - x_ref, Inf)
    flops[i + 1, 3] = stats["no_rhs_calls"] * flopsRHS +
        stats["no_fw_bw_subst"] * flopsFW_BW +
        stats["no_jac_calls"] * flopsJac +
        stats["no_lu_decomp"] * flopsLU
end

# Save the plot in PNG format
# if all the solvers were successful
if printFlag
    savePlotPNG("vdpolPrecisionTest", f_e, err, solverNames)
else
    println("Plot cannot be generated due to failure")
end

## Old reference solution
Tol = 1.0e-14;
# for Tol < 1e-14 we get the error "TOLERANCES ARE TOO SMALL"
opt = OptionsODE(
    OPT_EPS => 1.11e-16, OPT_RTOL => Tol, OPT_ATOL => Tol,
    OPT_RHS_CALLMODE => RHS_CALL_INSITU,
    OPT_JACOBIMATRIX => getJacobian
);

# Store only the desired component
# Here, only the first component is desired
# The second component is the first derivative of the first component
# due to the fact that it is a second order system.
# Hence error will be taken over the first component only.
x_ref = Array{Float64}(11);

for i in 1:11
    (t, x, retcode, stats) = seulex(vdpol, t0, T[i], x0, opt)
    if retcode != 1
        printFlag = false
        break
    end
    x_ref[i] = x[1]
end
