コード例 #1
0
import src.Results as Results
import scipy.stats

tend = 50

params = openloop.params.Params(tend)
init_state = numpy.array([0.5, 400])

# Specify the linear model
linsystems = params.cstr_model.get_nominal_linear_systems(params.h)
opoint = 1  # which nominal model to use
A = linsystems[opoint].A
B = linsystems[opoint].B
b = linsystems[opoint].b

lin_cstr = LLDS.LLDS(A, B, params.C2, params.Q, params.R2)  # KF object

# Plant initialisation
params.xs[:, 0] = init_state
params.linxs[:, 0] = init_state - b

# Simulate plant
state_noise_dist = scipy.stats.multivariate_normal(
    cov=params.Q)  # state distribution
meas_noise_dist = scipy.stats.multivariate_normal(
    cov=lin_cstr.R)  # measurement distribution
params.ys2[:, 0] = params.C2 @ params.xs[:, 0] + meas_noise_dist.rvs(
)  # measure from actual plant

# Filter setup
kfmeans = numpy.zeros([2, params.N])
コード例 #2
0
# Set the state space model
A = linsystems[opoint].A
B = linsystems[opoint].B
b = linsystems[opoint].b  # offset from the origin

# Set point
ysp = linsystems[opoint].op[0] - b[0]  # Medium concentration
H = numpy.matrix([1, 0])  # only attempt to control the concentration
x_off, usp = LQR.offset(A, numpy.matrix(B), params.C2, H,
                        numpy.matrix([ysp]))  # control offset
ysp = x_off
usp = numpy.array([usp])

# Set up the KF
kf_cstr = LLDS.LLDS(A, B, params.C2, params.Q,
                    params.R2)  # set up the KF object (measuring both states)
state_noise_dist = scipy.stats.multivariate_normal(cov=params.Q)
meas_noise_dist = scipy.stats.multivariate_normal(cov=params.R2)

# First time step of the simulation
params.xs[:,
          0] = init_state - b  # set simulation starting point to the random initial state
params.ys2[:, 0] = params.C2 @ params.xs[:, 0] + meas_noise_dist.rvs(
)  # measure from actual plant
temp = kf_cstr.init_filter(init_state - b, params.init_state_covar,
                           params.ys2[:, 0])  # filter
params.kfmeans[:, 0], params.kfcovars[:, :, 0] = temp

horizon = 150
params.us[0] = MPC.mpc_lqr(params.kfmeans[:, 0], horizon, A, numpy.matrix(B),
                           params.QQ, params.RR, numpy.array([0, 0]),
dt = 0.1
T = 400
A = numpy.eye(6)  # state transition
A[0, 4] = dt
A[1, 0] = dt
A[2, 5] = dt
A[3, 2] = dt
B = numpy.zeros(6)  # input transition
C = numpy.zeros([2, 6])  # state observation
C[0, 1] = 1.0
C[1, 3] = 1.0
sigmaQ = 0.00001  # standard deviation of process noise
sigmaR = 50.0  # standard deviation of measurement noise
Q = sigmaQ**2 * numpy.eye(6)  # process noise covariance
R = sigmaR**2 * numpy.eye(2)  # measurement noise covariance
model = LLDS.LLDS(A, B, C, Q, R)

# Specify initial conditions
init_covar = numpy.eye(6)  # vague prior covar
init_mean = numpy.zeros(6)  # vague prior mean

# Read in correct data
visiblestates_path = pathlib.Path("visiblestates.csv")
if visiblestates_path.is_file():
    visiblestates = pandas.read_csv(
        "visiblestates.csv",
        header=None).as_matrix()  # read in the ideal answers
    filtercovar_file = pandas.read_csv("filtercovar.csv",
                                       header=None).as_matrix()
    filtercovar = numpy.reshape(filtercovar_file, [6, 6, T],
                                order='F')  # read in the ideal answers
def main(mcN=1, linear=True, pf=False):
    tend = 80
    params = closedloop_scenarios_single.closedloop_params.Params(
        tend)  # end time of simulation

    # Get the linear model
    linsystems = params.cstr_model.get_nominal_linear_systems(
        params.h)  # cstr_model comes from params.jl
    opoint = 1  # the specific operating point we are going to use for control

    init_state = numpy.array([0.55, 450
                              ])  # random initial point near operating point

    # Set the state space model
    A = linsystems[opoint].A
    B = linsystems[opoint].B
    b = linsystems[opoint].b  # offset from the origin

    # Set point
    ysp = linsystems[opoint].op[0] - b[0]  # Medium concentration
    H = numpy.matrix([1, 0])  # only attempt to control the concentration
    x_off, usp = LQR.offset(A, numpy.matrix(B), params.C2, H,
                            numpy.matrix([ysp]))  # control offset
    ysp = x_off
    usp = numpy.array([usp])

    # Noise distributions
    state_noise_dist = scipy.stats.multivariate_normal(cov=params.Q)
    meas_noise_dist = scipy.stats.multivariate_normal(cov=params.R2)

    # PF functions
    def f(x, u, w):
        return params.cstr_model.run_reactor(x, u, params.h) + w

    def g(x):
        return params.C2 @ x  # state observation

    cstr_pf = PF.Model(f, g)

    # Set up the KF
    kf_cstr = LLDS.LLDS(
        A, B, params.C2, params.Q,
        params.R2)  # set up the KF object (measuring both states)

    # Setup MPC
    horizon = 150

    # add state constraints
    aline = 10  # slope of constraint line ax + by + c = 0
    if linear:
        cline = -411  # negative of the y axis intercept
    else:
        cline = -404  # negative of the y axis intercept
    bline = 1

    if linear:
        lim_u = 10000
    else:
        lim_u = 20000

    mcdists = numpy.zeros([2, mcN])
    xconcen = numpy.zeros([params.N, mcN])
    mcerrs = numpy.zeros(mcN)
    particles = None

    for mciter in range(mcN):
        # First time step of the simulation
        if linear:
            params.xs[:,
                      0] = init_state - b  # set simulation starting point to the random initial state
            params.ys2[:,
                       0] = params.C2 @ params.xs[:, 0] + meas_noise_dist.rvs(
                       )  # measure from actual plant
            temp = kf_cstr.init_filter(init_state - b, params.init_state_covar,
                                       params.ys2[:, 0])  # filter
            params.kfmeans[:, 0], params.kfcovars[:, :, 0] = temp
        else:
            params.xs[:,
                      0] = init_state  # set simulation starting point to the random initial state
            params.ys2[:,
                       0] = params.C2 @ params.xs[:, 0] + meas_noise_dist.rvs(
                       )  # measure from actual plant
            temp = kf_cstr.init_filter(init_state - b, params.init_state_covar,
                                       params.ys2[:, 0] - b)  # filter
            params.kfmeans[:, 0], params.kfcovars[:, :, 0] = temp

        if pf:
            nP = 200
            prior_dist = scipy.stats.multivariate_normal(
                mean=init_state,
                cov=params.init_state_covar)  # prior distribution

            particles = PF.init_pf(prior_dist, nP,
                                   2)  # initialise the particles

            particles = PF.init_filter(particles, params.ys2[:, 0],
                                       meas_noise_dist, cstr_pf)
            params.pfmeans[:, 0], params.pfcovars[:, :,
                                                  0] = PF.get_stats(particles)

            params.us[0] = MPC.mpc_mean(params.pfmeans[:, 0] - b, horizon, A,
                                        numpy.matrix(B), b, aline, bline,
                                        cline, params.QQ, params.RR, ysp,
                                        usp[0], lim_u,
                                        1000.0)  # get the controller input
        else:
            params.us[0] = MPC.mpc_mean(params.kfmeans[:, 0], horizon, A,
                                        numpy.matrix(B), b, aline, bline,
                                        cline, params.QQ, params.RR, ysp,
                                        usp[0], lim_u,
                                        1000.0)  # get the controller input
        for t in range(1, params.N):
            if linear:
                params.xs[:, t] = A @ params.xs[:, t - 1] + B * params.us[
                    t - 1] + state_noise_dist.rvs()
                params.ys2[:,
                           t] = params.C2 @ params.xs[:, t] + meas_noise_dist.rvs(
                           )  # measure from actual plant
                params.kfmeans[:,
                               t], params.kfcovars[:, :,
                                                   t] = kf_cstr.step_filter(
                                                       params.kfmeans[:,
                                                                      t - 1],
                                                       params.kfcovars[:, :,
                                                                       t - 1],
                                                       params.us[t - 1],
                                                       params.ys2[:, t])
            else:
                params.xs[:, t] = params.cstr_model.run_reactor(
                    params.xs[:, t - 1], params.us[t - 1], params.h)
                params.xs[:, t] += state_noise_dist.rvs()  # actual plant
                params.ys2[:,
                           t] = params.C2 @ params.xs[:, t] + meas_noise_dist.rvs(
                           )  # measure from actual plant
                params.kfmeans[:,
                               t], params.kfcovars[:, :,
                                                   t] = kf_cstr.step_filter(
                                                       params.kfmeans[:,
                                                                      t - 1],
                                                       params.kfcovars[:, :,
                                                                       t - 1],
                                                       params.us[t - 1],
                                                       params.ys2[:, t] - b)
            if pf:
                PF.pf_filter(particles, params.us[t - 1], params.ys2[:, t],
                             state_noise_dist, meas_noise_dist, cstr_pf)
                params.pfmeans[:,
                               t], params.pfcovars[:, :,
                                                   t] = PF.get_stats(particles)

            if t % 10 == 0:
                if pf:
                    params.us[t] = MPC.mpc_mean(params.pfmeans[:, t] - b,
                                                horizon, A, numpy.matrix(B), b,
                                                aline, bline, cline, params.QQ,
                                                params.RR, ysp, usp[0], lim_u,
                                                1000.0)
                else:
                    params.us[t] = MPC.mpc_mean(params.kfmeans[:,
                                                               t], horizon, A,
                                                numpy.matrix(B), b, aline,
                                                bline, cline, params.QQ,
                                                params.RR, ysp, usp[0], lim_u,
                                                1000.0)
                if params.us[t] is None or numpy.isnan(params.us[t]):
                    break
            else:
                params.us[t] = params.us[t - 1]

        for i in range(len(params.kfmeans[0])):
            params.kfmeans[:, i] += b
            if linear:
                params.xs[:, i] += b
                params.ys2[:, i] += b

        if mcN > 1:
            xconcen[:, mciter] = params.xs[0, :]
            mcerrs[mciter] = Results.calc_error1(params.xs, ysp[0] + b[0])
            Results.get_mc_res(params.xs, params.kfcovars, [aline, cline],
                               mcdists, mciter, params.h)
        if mcN == 1:
            # Plot the results
            if pf:
                Results.plot_tracking1(params.ts, params.xs, params.ys2,
                                       params.pfmeans, params.us, 2,
                                       ysp[0] + b[0])
                Results.plot_ellipses2(params.ts, params.xs, params.pfmeans,
                                       params.pfcovars, [aline, cline],
                                       linsystems[1].op, True,
                                       -2.0 * numpy.log(1 - 0.9), 1, "best")
            else:
                Results.plot_tracking1(params.ts, params.xs, params.ys2,
                                       params.kfmeans, params.us, 2,
                                       ysp[0] + b[0])
                Results.plot_ellipses2(params.ts, params.xs, params.kfmeans,
                                       params.kfcovars, [aline, cline],
                                       linsystems[1].op, True,
                                       -2.0 * numpy.log(1 - 0.9), 1, "best")
            Results.check_constraint(params.ts, params.xs, [aline, cline])
            Results.calc_error1(params.xs, ysp[0] + b[0])
            Results.calc_energy(params.us, 0.0)
            plt.show()

    if mcN != 1:
        print("The absolute MC average error is: ", sum(abs(mcerrs)) / mcN)
        if linear:
            if pf:
                numpy.savetxt("linmod_pf_mean_mc2.csv", xconcen, delimiter=",")
            else:
                numpy.savetxt("linmod_kf_mean_mc2.csv", xconcen, delimiter=",")
        else:
            if pf:
                numpy.savetxt("nonlinmod_pf_mean_mc2.csv",
                              xconcen,
                              delimiter=",")
            else:
                numpy.savetxt("nonlinmod_kf_mean_mc2.csv",
                              xconcen,
                              delimiter=",")

    nocount = len(mcdists[0]) - numpy.count_nonzero(mcdists[0])
    filteredResults = numpy.zeros([2, mcN - nocount])
    counter = 0
    for k in range(mcN):
        if mcdists[0, k] != 0.0:
            filteredResults[:, counter] = mcdists[:, k]
            counter += 1

    if linear:
        if pf:
            numpy.savetxt("linmod_pf_mean_mc.csv",
                          filteredResults,
                          delimiter=",",
                          fmt="%f")
        else:
            numpy.savetxt("linmod_kf_mean_mc.csv",
                          filteredResults,
                          delimiter=",",
                          fmt="%f")
    else:
        if pf:
            numpy.savetxt("nonlinmod_pf_mean_mc.csv",
                          filteredResults,
                          delimiter=",",
                          fmt="%f")
        else:
            numpy.savetxt("nonlinmod_kf_mean_mc.csv",
                          filteredResults,
                          delimiter=",",
                          fmt="%f")
コード例 #5
0
import src.Results as Results
import scipy.stats

tend = 50

params = openloop.params.Params(tend)
init_state = numpy.array([0.5, 400])

# Specify the linear model
linsystems = params.cstr_model.get_nominal_linear_systems(params.h)
opoint = 1  # which nominal model to use
A = linsystems[opoint].A
B = linsystems[opoint].B
b = linsystems[opoint].b

lin_cstr = LLDS.LLDS(A, B, params.C1, params.Q, params.R1)  # KF object

# Plant initialisation
params.xs[:, 0] = init_state
params.linxs[:, 0] = init_state - b

# Simulate plant
state_noise_dist = scipy.stats.multivariate_normal(
    cov=params.Q)  # state distribution
meas_noise_dist = scipy.stats.multivariate_normal(
    cov=params.R1)  # measurement distribution
params.ys1[0] = params.C1 @ params.xs[:, 0] + meas_noise_dist.rvs(
)  # measure from actual plant

# Filter setup
kfmeans = numpy.zeros([2, params.N])
def main(nine, mcN=1, linear=True, pf=False, numerical=False):
    if nine == 90:
        k_squared = 4.6052
        plot_setting = 0
    elif nine == 99:
        k_squared = 9.21
        plot_setting = 1
    elif nine == 999:
        k_squared = 13.8155
        plot_setting = 2
    else:
        return None

    tend = 80
    params = closedloop_scenarios_single.closedloop_params.Params(
        tend)  # end time of simulation

    # Get the linear model
    linsystems = params.cstr_model.get_nominal_linear_systems(
        params.h)  # cstr_model comes from params.jl
    opoint = 1  # the specific operating point we are going to use for control

    init_state = numpy.array([0.55, 450
                              ])  # random initial point near operating point

    # Set the state space model
    A = linsystems[opoint].A
    B = linsystems[opoint].B
    b = linsystems[opoint].b  # offset from the origin

    # Set point
    ysp = linsystems[opoint].op[0] - b[0]  # Medium concentration
    H = numpy.matrix([1, 0])  # only attempt to control the concentration
    x_off, usp = LQR.offset(A, numpy.matrix(B), params.C2, H,
                            numpy.matrix([ysp]))  # control offset
    ysp = x_off
    usp = numpy.array([usp])

    # PF functions
    def f(x, u, w):
        return params.cstr_model.run_reactor(x, u, params.h) + w

    def g(x):
        return params.C2 @ x  # state observation

    cstr_pf = PF.Model(f, g)

    nP = 200
    if numerical:
        nP = 500

    # Set up for numerical
    Ndiv = len(range(0, tend, 3))
    kldiv = numpy.zeros(
        Ndiv)  # Kullback-Leibler Divergence as a function of time
    basediv = numpy.zeros(Ndiv)  # Baseline
    unidiv = numpy.zeros(Ndiv)  # Uniform comparison
    klts = numpy.zeros(Ndiv)
    ndivcounter = 0
    temp_states = numpy.zeros([2, nP])

    # Set up the KF
    kf_cstr = LLDS.LLDS(
        A, B, params.C2, params.Q,
        params.R2)  # set up the KF object (measuring both states)
    state_noise_dist = scipy.stats.multivariate_normal(cov=params.Q)
    meas_noise_dist = scipy.stats.multivariate_normal(cov=params.R2)

    # Setup MPC
    horizon = 150
    # add state constraints
    aline = 10  # slope of constraint line ax + by + c = 0
    cline = -411  # negative of the y axis intercept
    bline = 1
    e = cline

    growvar = True
    if linear:
        limu = 10000
    else:
        limu = 20000

    mcdists = numpy.zeros([2, mcN])
    xconcen = numpy.zeros([params.N, mcN])
    mcerrs = numpy.zeros(mcN)

    mciter = -1

    particles = None
    while mciter < mcN - 1:
        # First time step of the simulation
        if linear:
            params.xs[:,
                      0] = init_state - b  # set simulation starting point to the random initial state
            params.ys2[:,
                       0] = params.C2 @ params.xs[:, 0] + meas_noise_dist.rvs(
                       )  # measure from actual plant
            temp = kf_cstr.init_filter(init_state - b, params.init_state_covar,
                                       params.ys2[:, 0])  # filter
            params.kfmeans[:, 0], params.kfcovars[:, :, 0] = temp
        else:
            params.xs[:,
                      0] = init_state  # set simulation starting point to the random initial state
            params.ys2[:,
                       0] = params.C2 @ params.xs[:, 0] + meas_noise_dist.rvs(
                       )  # measure from actual plant
            temp = kf_cstr.init_filter(init_state - b, params.init_state_covar,
                                       params.ys2[:, 0] - b)  # filter
            params.kfmeans[:, 0], params.kfcovars[:, :, 0] = temp

        if pf:
            if linear:
                prior_dist = scipy.stats.multivariate_normal(
                    mean=init_state - b,
                    cov=params.init_state_covar)  # prior distribution
            else:
                prior_dist = scipy.stats.multivariate_normal(
                    mean=init_state,
                    cov=params.init_state_covar)  # prior distribution
            particles = PF.init_pf(prior_dist, nP,
                                   2)  # initialise the particles

            particles = PF.init_filter(particles, params.ys2[:, 0],
                                       meas_noise_dist, cstr_pf)
            params.pfmeans[:, 0], params.pfcovars[:, :,
                                                  0] = PF.get_stats(particles)

            if linear:
                params.us[0] = MPC.mpc_var(params.pfmeans[:, 0],
                                           params.kfcovars[:, :,
                                                           0], horizon, A,
                                           numpy.matrix(B), b, aline, bline, e,
                                           params.QQ, params.RR, ysp, usp[0],
                                           limu, 1000.0, params.Q, k_squared,
                                           growvar)  # get controller input
            else:
                params.us[0] = MPC.mpc_var(params.pfmeans[:, 0] - b,
                                           params.kfcovars[:, :,
                                                           0], horizon, A,
                                           numpy.matrix(B), b, aline, bline, e,
                                           params.QQ, params.RR, ysp, usp[0],
                                           limu, 1000.0, params.Q, k_squared,
                                           growvar)  # get controller input
        else:
            params.us[0] = MPC.mpc_var(params.kfmeans[:, 0],
                                       params.kfcovars[:, :, 0], horizon, A,
                                       numpy.matrix(B), b, aline, bline, e,
                                       params.QQ, params.RR, ysp, usp[0], limu,
                                       1000.0, params.Q, k_squared,
                                       growvar)  # get the controller input

        if numerical:
            kldiv[ndivcounter] = Auxiliary.kl(particles.x, particles.w,
                                              params.pfmeans[:, 0],
                                              params.pfcovars[:, :,
                                                              0], temp_states)
            basediv[ndivcounter] = Auxiliary.klbase(params.pfmeans[:, 0],
                                                    params.pfcovars[:, :, 0],
                                                    temp_states, nP)
            unidiv[ndivcounter] = Auxiliary.kluniform(params.pfmeans[:, 0],
                                                      params.pfcovars[:, :, 0],
                                                      temp_states, nP)
            klts[ndivcounter] = 0.0
            ndivcounter += 1
        status = True
        for t in range(1, params.N):
            if linear:
                params.xs[:, t] = A @ params.xs[:, t - 1] + B * params.us[
                    t - 1] + state_noise_dist.rvs()  # actual plant
                params.ys2[:,
                           t] = params.C2 @ params.xs[:, t] + meas_noise_dist.rvs(
                           )  # measure from actual plant
                params.kfmeans[:,
                               t], params.kfcovars[:, :,
                                                   t] = kf_cstr.step_filter(
                                                       params.kfmeans[:,
                                                                      t - 1],
                                                       params.kfcovars[:, :,
                                                                       t - 1],
                                                       params.us[t - 1],
                                                       params.ys2[:, t])
            else:
                params.xs[:, t] = params.cstr_model.run_reactor(
                    params.xs[:, t - 1],
                    params.us[t - 1],
                    params.h,
                )
                params.xs[:, t] += state_noise_dist.rvs()  # actual plant
                params.ys2[:,
                           t] = params.C2 @ params.xs[:, t] + meas_noise_dist.rvs(
                           )  # measure from actual plant
                params.kfmeans[:,
                               t], params.kfcovars[:, :,
                                                   t] = kf_cstr.step_filter(
                                                       params.kfmeans[:,
                                                                      t - 1],
                                                       params.kfcovars[:, :,
                                                                       t - 1],
                                                       params.us[t - 1],
                                                       params.ys2[:, t] - b)
            if pf:
                PF.pf_filter(particles, params.us[t - 1], params.ys2[:, t],
                             state_noise_dist, meas_noise_dist, cstr_pf)
                params.pfmeans[:,
                               t], params.pfcovars[:, :,
                                                   t] = PF.get_stats(particles)

            if t % 10 == 0:
                if pf:
                    if linear:
                        params.us[t] = MPC.mpc_var(
                            params.pfmeans[:,
                                           t], params.pfcovars[:, :,
                                                               t], horizon, A,
                            numpy.matrix(B), b, aline, bline, e, params.QQ,
                            params.RR, ysp, usp[0], limu, 1000, params.Q,
                            k_squared, growvar)  # controller input
                    else:
                        params.us[t] = MPC.mpc_var(
                            params.pfmeans[:, t] - b,
                            params.pfcovars[:, :, t], horizon, A,
                            numpy.matrix(B), b, aline, bline, e, params.QQ,
                            params.RR, ysp, usp[0], limu, 1000, params.Q,
                            k_squared, growvar)  # controller input
                else:
                    params.us[t] = MPC.mpc_var(params.kfmeans[:, t],
                                               params.kfcovars[:, :,
                                                               t], horizon, A,
                                               numpy.matrix(B), b, aline,
                                               bline, e, params.QQ, params.RR,
                                               ysp, usp[0], limu, 1000,
                                               params.Q, k_squared,
                                               growvar)  # get controller input

                if params.us[t] is None or numpy.isnan(params.us[t]):
                    status = False
                    break
            else:
                params.us[t] = params.us[t - 1]

            if numerical and params.ts[t] in range(0, tend, 3):
                kldiv[ndivcounter] = Auxiliary.kl(particles.x, particles.w,
                                                  params.pfmeans[:, t],
                                                  params.pfcovars[:, :, t],
                                                  temp_states)
                basediv[ndivcounter] = Auxiliary.klbase(
                    params.pfmeans[:, t], params.pfcovars[:, :, t],
                    temp_states, nP)
                unidiv[ndivcounter] = Auxiliary.kluniform(
                    params.pfmeans[:, t], params.pfcovars[:, :, t],
                    temp_states, nP)
                klts[ndivcounter] = params.ts[t]
                ndivcounter += 1

        if not status:
            continue
        else:
            mciter += 1
        for i in range(len(params.kfmeans[0])):
            params.kfmeans[:, i] += b
            if linear:
                params.xs[:, i] += b
                params.ys2[:, i] += b

        if mcN > 1:
            xconcen[:, mciter] = params.xs[0, :]
            mcerrs[mciter] = Results.calc_error1(params.xs, ysp[0] + b[0])
            mcdists = Results.get_mc_res(params.xs, params.kfcovars,
                                         [aline, cline], mcdists, mciter,
                                         params.h)

        if mcN == 1:
            # Plot the results
            if numerical:
                Results.plot_kl_div(klts, kldiv, basediv, unidiv, False)
                Results.plot_kl_div(klts, kldiv, basediv, unidiv, True)
                print("The average divergence for the baseline is: ",
                      1.0 / len(klts) * sum(basediv))
                print("The average divergence for the approximation is: ",
                      1.0 / len(klts) * sum(kldiv))
                print("The average divergence for the uniform is: ",
                      1.0 / len(klts) * sum(unidiv))
            elif pf:
                Results.plot_tracking1(params.ts, params.xs, params.ys2,
                                       params.pfmeans, params.us, 2,
                                       ysp[0] + b[0])
                plt.savefig(
                    "/home/ex/Documents/CSC/report/results/Figure_8-25_python.pdf",
                    bbox_inches="tight")
                Results.plot_ellipses2(params.ts, params.xs, params.pfmeans,
                                       params.pfcovars, [aline, cline],
                                       linsystems[1].op, True,
                                       -2.0 * numpy.log(1 - 0.9), plot_setting,
                                       "best")
                plt.savefig(
                    "/home/ex/Documents/CSC/report/results/Figure_8-26_python.pdf",
                    bbox_inches="tight")
                Results.check_constraint(params.ts, params.xs, [aline, cline])
                Results.calc_error1(params.xs, ysp[0] + b[0])
                Results.calc_energy(params.us, 0.0)
            else:
                Results.plot_tracking1(params.ts, params.xs, params.ys2,
                                       params.kfmeans, params.us, 2,
                                       ysp[0] + b[0])
                plt.savefig(
                    "/home/ex/Documents/CSC/report/results/Figure_8-19_python.pdf",
                    bbox_inches="tight")
                Results.plot_ellipses2(params.ts, params.xs, params.kfmeans,
                                       params.kfcovars, [aline, cline],
                                       linsystems[opoint].op, True, k_squared,
                                       plot_setting, "best")
                plt.savefig(
                    "/home/ex/Documents/CSC/report/results/Figure_8-20_python.pdf",
                    bbox_inches="tight")
                Results.check_constraint(params.ts, params.xs, [aline, cline])
                Results.calc_error1(params.xs, ysp[0] + b[0])
                Results.calc_energy(params.us, 0.0)

            plt.show()

    if mcN != 1:
        print("The absolute MC average error is: ", sum(abs(mcerrs)) / mcN)
        if linear:
            if pf:
                numpy.savetxt("linmod_pf_var{}_mc2.csv".format(nine),
                              xconcen,
                              delimiter=",",
                              fmt="%f")
            else:
                numpy.savetxt("linmod_kf_var{}_mc2.csv".format(nine),
                              xconcen,
                              delimiter=",",
                              fmt="%f")
        else:
            if pf:
                numpy.savetxt("nonlinmod_pf_var{}_mc2.csv".format(nine),
                              xconcen,
                              delimiter=",",
                              fmt="%f")
            else:
                numpy.savetxt("nonlinmod_kf_var{}_mc2.csv".format(nine),
                              xconcen,
                              delimiter=",",
                              fmt="%f")

        nocount = len(mcdists[0]) - numpy.count_nonzero(mcdists[0])
        filteredResults = numpy.zeros([2, mcN - nocount])
        counter = 0
        for k in range(mcN):
            if mcdists[0, k] != 0.0:
                filteredResults[:, counter] = mcdists[:, k]
                counter += 1

        if linear:
            if pf:
                numpy.savetxt("linmod_pf_var{}_mc.csv".format(nine),
                              filteredResults,
                              delimiter=",",
                              fmt="%f")
            else:
                numpy.savetxt("linmod_kf_var{}_mc.csv".format(nine),
                              filteredResults,
                              delimiter=",",
                              fmt="%f")
        else:
            if pf:
                numpy.savetxt("nonlinmod_pf_var{}_mc.csv".format(nine),
                              filteredResults,
                              delimiter=",",
                              fmt="%f")
            else:
                numpy.savetxt("nonlinmod_kf_var{}_mc.csv".format(nine),
                              filteredResults,
                              delimiter=",",
                              fmt="%f")