"""This file contains the various potential functions we have defined."""

import numpy as np
import math
try:
    import cPickle as pickle
except:
    import pickle


def cosine_potential(coords):
    """
    Calculate the Potential Energy and Force of Cos(x).

    Parameters:
    -----------

    coords  : float (or array of floats)
            Location


    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    F       : float (or array of floats)
              Force

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
	
    if hasattr(coords, "__len__") is True:
	V = np.zeros_like(coords)
	F = np.zeros_like(coords)
	for i in range(0,coords.size):
		if coords[i]<np.pi:
			V[i] = np.cos(coords[i]) * 3.0
    			F[i] = np.sin(coords[i]) * 3.0
		else:
			V[i] = np.cos(coords[i]) * 2.0 - 1.0
			F[i] = np.sin(coords[i]) * 2.0
    else:
	if coords<np.pi:

                V = np.cos(coords) * 3.0
                F = np.sin(coords) * 3.0
        else:
                V = np.cos(coords) * 2.0 - 1.0
                F = np.sin(coords) * 2.0
    Event=''
    if hasattr(coords, "__len__") is False and coords < -2.0:
        Trigger = True
        Event = 'A'
    elif hasattr(coords, "__len__") is False and coords > 8.28:
        Trigger = True
        Event = 'B'
    else:
        Trigger = False

    return (V, F, Trigger, Event)


def two_gaussian_potential(coords):
    """
    Calculate the force and potential based on location (1-D).

    Parameters:
    -----------

    coords  :  array of floats
               X and Y coordinates


    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    F       : float (or array of floats)
              Force

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    V = (-5 * np.exp(-(coords - 2/0.75)**2) -
         10*np.exp(-(coords + 2/0.75)**2))
    F = ((-5 * 2 * -1 * (coords - 2/0.75) * np.exp(-(coords - 2/0.75)**2) -
         10 * 2 * -1 * (coords + 2/0.75) * np.exp(-(coords + 2/0.75)**2)) *
         (-1))
    Event='A'
    if type(coords) is np.float64 and coords < -2.0:
        Trigger = True
    else:
        Trigger = False

    return (V, F, Trigger, Event)


def pv_2D_potential(x, y):
    """
    Calculate the force and potential based on location (2-D).

    Parameters:
    -----------

    x       : array of floats
              X coordinates

    y       : array of floats
              Y coordinates

    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    Fpot    : float (or array of floats)
              Force in x and y direction

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    if hasattr(x, "__len__") is True:

        V = np.zeros([y.size, x.size])
        Fx = np.empty([y.size, x.size])
        Fy = np.empty([y.size, x.size])
        for k in range(0, y.size - 1):
            for j in range(0, x.size - 1):
                V[k, j] = (np.cos(2*math.pi*x[j])*(1 + 4*y[k]) +
                           math.pi*y[k]**2 - 0.75*np.cos(2*math.pi*x[j]/3))
                Fx = (((2*math.pi/3*0.75)*np.sin(2*math.pi*x[j]/3) -
                      2*math.pi*(1+4*y[k])*np.sin(2*math.pi*x[j])))
                Fy = ((2*math.pi*y[k]+4*np.cos(2*math.pi*x[j])))
        Fpotx = Fx * -1
        Fpoty = Fy * -1
        Trigger = False

    else:

        V = (np.cos(2*math.pi*x)*(1+4*y) + math.pi*y**2 -
             0.75*np.cos(2*math.pi*x/3))
        Fpotx = (((2*math.pi/3*0.75)*np.sin(2*math.pi*x/3) -
                 2*math.pi*(1+4*y)*np.sin(2*math.pi*x)))*-1
        Fpoty = ((2*math.pi*y+4*np.cos(2*math.pi*x)))*-1

        if x < 0.75 and y > 0:
            Trigger = True
            Event = 'A'
        elif x > 2.25 and y > 0:
            Trigger = True
            Event = 'B'
        else:
            Trigger = False
    Fpot = np.array([Fpotx, Fpoty])
    return (V, Fpot, Trigger, Event)

def C_Cl_potential(x, y):
    """
    Calculate the force and potential based on location (2-D).

    Parameters:
    -----------

    x       : array of floats
              X coordinates

    y       : array of floats
              Y coordinates

    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    Fpot    : float (or array of floats)
              Force in x and y direction

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    pot = pickle.load(open("kfpotential.p", "rb"))
    if hasattr(x, "__len__") is True:

        V = np.zeros([y.size, x.size])
        Fx = np.empty([y.size, x.size])
        Fy = np.empty([y.size, x.size])
        for k in range(0, y.size - 1):
            for j in range(0, x.size - 1):
                V[k, j] = pot(k, j)
                Fy = pot(k, j, dx=1)
                Fx = pot(k, j, dy=1)
        Fpotx = Fx * -1
        Fpoty = Fy * -1
        Trigger = False

    else:

        V[k, j] = pot(k, j)
        Fy = pot(k, j, dx=1)
        Fx = pot(k, j, dy=1)
        Fpotx = Fx * -1
        Fpoty = Fy * -1

        if x > 0.25 and y < 0.20:
            Trigger = True
        else:
            Trigger = False
    Fpot = np.array([Fpotx, Fpoty])
    Event=''
    return (V, Fpot, Trigger, Event)


def muller_brown_potential(x, y):
    """
    Calculate the force and potential based on location (2-D).

    Parameters:
    -----------

    x       : array of floats
              X coordinates

    y       : array of floats
              Y coordinates

    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    Fpot    : float (or array of floats)
              Force in x and y direction

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    if type(x) is not np.float64:

        V = np.zeros([y.size, x.size])
        Fx = np.empty([y.size, x.size])
        Fy = np.empty([y.size, x.size])
        A = np.array([-200.0, -100.0, -170.0, 15.0])
        a = np.array([-1.0, -1.0, -6.50, 0.7])
        b = np.array([0.0, 0.0, 11.0, 0.6])
        c = np.array([-10.0, -10.0, -6.50, 0.7])
        x0 = np.array([1.0, 0.0, -0.50, -1.0])
        y0 = np.array([0.0, 0.5, 1.50, 1.0])
        for k in range(0, y.size - 1):
            for j in range(0, x.size - 1):
                V[k, j] = sum(A * np.exp(a*(x[j]-x0)**2 +
                                         b*(x[j]-x0)*(y[k]-y0) +
                                         c*(y[k]-y0)**2))
                Fx = (-400*np.exp(-1*(-1+x[j])**2 - 10*y[k]**2)*(-1+x[j]) -
                      200*np.exp(-x[j]**2-10*(-0.5+x[j])**2)*x[j] +
                      170*np.exp(-6.5*(0.5+x[j])**2+11*(0.5+x[j])*(-1.5+y[k]) -
                      6.5*(-1.5+y[k])**2)*(-13*(0.5+x[j])+11*(-1/5+y[k])) -
                      15*np.exp(0.7*(1+x[j])**2+0.6*(1+x[j])*(y[k]-1) +
                      0.7*(y[k]-1)**2)*(1.4*(1+x[j])+0.6*(y[k]-1)))
                Fy = (170*np.exp(-6.5*(0.5+x[j])**2 +
                      11*(0.5+x[j])*(-1.5+y[k]) -
                      6.5*(y[k]-1.5)**2)*(11*(0.5+x[j])-13*(y[k]-1.5)) -
                      15*np.exp(0.7*(1+x[j])**2+0.6*(1+x[j])*(y[k]-1) +
                      0.7*(y[k]-1)**2)*(0.6*(x[j]+1)+1.4*(y[k]-1)) -
                      1000*np.exp(-x[j]**2-10*(y[k]-0.5)**2)*(y[k]-0.5) -
                      4000*np.exp(-1*(x[j]-1)**2-10*y[k]**2)*y[k])
        Fpotx = Fx * -1
        Fpoty = Fy * -1
        Trigger = False

    else:

        V = sum(A * np.exp(a * (x-x0)**2 + b * (x-x0)*(y-y0) +
                           c * (y-y0)**2))
        Fpotx = (-400*np.exp(-1*(-1+x)**2 - 10*y**2)*(-1+x) -
                 200*np.exp(-x**2-10*(-0.5+x)**2)*x +
                 170*np.exp(-6.5*(0.5+x)**2+11*(0.5+x)*(-1.5+y) -
                 6.5*(-1.5+y)**2)*(-13*(0.5+x)+11*(-1/5+y)) -
                 15*np.exp(0.7*(1+x)**2+0.6*(1+x)*(y-1) +
                 0.7*(y-1)**2)*(1.4*(1+x)+0.6*(y-1)))
        Fpoty = (170*np.exp(-6.5*(0.5+x)**2 +
                 11*(0.5+x)*(-1.5+y) -
                 6.5*(y-1.5)**2)*(11*(0.5+x)-13*(y-1.5)) -
                 15*np.exp(0.7*(1+x)**2+0.6*(1+x)*(y-1) +
                 0.7*(y-1)**2)*(0.6*(x+1)+1.4*(y-1)) -
                 1000*np.exp(-x**2-10*(y-0.5)**2)*(y-0.5) -
                 4000*np.exp(-1*(x-1)**2-10*y**2)*y)

        if x > 0.4 and y < 0.1:
            Trigger = True
        else:
            Trigger = False
    Fpot = np.array([Fpotx, Fpoty])
    Event=''
    return (V, Fpot, Trigger)


def get_potential_dict():
    """Return a dictionary of all of the available potential functions."""
    potential_dict = {'cosine_potential': cosine_potential,
                      'two_gaussian_potential': two_gaussian_potential,
                      'pv_2D_potential': pv_2D_potential,
                      'muller_brown_potential': muller_brown_potential,
                      'C_Cl_potential': C_Cl_potential}

    dimension_dict = {'cosine_potential': '1-D Potential',
                      'two_gaussian_potential': '1-D Potential',
                      'pv_2D_potential': '2-D Potential',
                      'muller_brown_potential': '2-D Potential',
                      'C_Cl_potential': '2-D Potential'}

    return potential_dict, dimension_dict


def get_GUI_presets_dict():
    """Return a dictionary of all of the available potential functions."""
    preset_dict = {'cosine_potential': np.array([3.14,-6.28,12.57,0.01,0,
                                                    0,0,0]).astype(str),
                      'two_gaussian_potential': np.array([2.67,-4,4,0.01,
                                                          0,0,0,0]).astype(str),
                      'pv_2D_potential': np.array([1.5,0,3.0,0.01,0.6,-2.0,
                                                   2.0,0.01]).astype(str),
                      'muller_brown_potential': np.array([0,0,0,0,0,0,0,
                                                          0]).astype(str),
                      'C_Cl_potential': np.array([0,0,0,0,0,0,0,0]).astype(str)
                    }

    return preset_dict


def two_gaussian_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    vold = vnew
    bcbias = 0
    is_periodic = False
    if (coords < -4.3193):

        vnew = 100.0 * (coords+4.0)**4.0 - 1.690133
        f2 = -100.0 * 4.0 * (coords+4.0)**3.0
        bcbias = vnew - vold

    elif (coords > 4.25882):

        vnew = 100.0 * (coords-4.0)**4.0 - 0.845067
        f2 = -100.0 * 4.0 * (coords-4.0)**3.0
        bcbias = vnew - vold

    return (vnew, f2, coords, bcbias, is_periodic)


def pv_2D_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    if (coords[0] < 0):
        coords[0] = coords[0] + 3

    elif (coords[0] > 3.0):
        coords[0] = coords[0] - 3
    bcbias = 0
    is_periodic_x = True
    is_periodic_y = False
    is_periodic = np.array([is_periodic_x, is_periodic_y])
    return (vnew, f2, coords, bcbias, is_periodic)


def C_Cl_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    bcbias = 0
    is_periodic_x = False
    is_periodic_y = False
    is_periodic = np.array([is_periodic_x, is_periodic_y])
    return (vnew, f2, coords, bcbias, is_periodic)


def LJ_potential_bc(vnew,f2,coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    bcbias = 0
    return (vnew, f2, coords, bcbias)


def mb_2D_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    bcbias = 0
    is_periodic_x = False
    is_periodic_y = False
    is_periodic = np.array([is_periodic_x, is_periodic_y])
    return (vnew, f2, coords, bcbias, is_periodic)


def cosine_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    # if (coords < -2*np.pi):
        # coords = coords + 6*np.pi

    if (coords > 2*np.pi):
        vnew = 100*(coords-2*np.pi)**4+1.0
    	f2 = -4.0*100.0*(coords-2*np.pi)**3
    bcbias = 0
    is_periodic = False
    return (vnew, f2, coords, bcbias, is_periodic)


def get_boundary_condition_dict():
    """Return a dictionary of all of the available potential functions."""
    bc_dict = {'cosine_potential': cosine_potential_bc,
               'two_gaussian_potential': two_gaussian_potential_bc,
               'pv_2D_potential': pv_2D_potential_bc,
               'muller_brown_potential': mb_2D_potential_bc,
               'LJ_potential': LJ_potential_bc,
               'C_Cl_potential': C_Cl_potential_bc}

    return bc_dict

"""This file contains the various potential functions we have defined."""

import numpy as np
import math
try:
    import cPickle as pickle
except:
    import pickle


def cosine_potential(coords):
    """
    Calculate the Potential Energy and Force of Cos(x).

    Parameters:
    -----------

    coords  : float (or array of floats)
            Location


    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    F       : float (or array of floats)
              Force

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
	
    if hasattr(coords, "__len__") is True:
	V = np.zeros_like(coords)
	F = np.zeros_like(coords)
	for i in range(0,coords.size):
		if coords[i]<np.pi:
			V[i] = np.cos(coords[i]) * 3.0
    			F[i] = np.sin(coords[i]) * 3.0
		else:
			V[i] = np.cos(coords[i]) * 2.0 - 1.0
			F[i] = np.sin(coords[i]) * 2.0
    else:
	if coords<np.pi:

                V = np.cos(coords) * 3.0
                F = np.sin(coords) * 3.0
        else:
                V = np.cos(coords) * 2.0 - 1.0
                F = np.sin(coords) * 2.0
    Event=''
    if hasattr(coords, "__len__") is False and coords < -2.0:
        Trigger = True
        Event = 'A'
    elif hasattr(coords, "__len__") is False and coords > 8.28:
        Trigger = True
        Event = 'B'
    else:
        Trigger = False

    return (V, F, Trigger, Event)


def two_gaussian_potential(coords):
    """
    Calculate the force and potential based on location (1-D).

    Parameters:
    -----------

    coords  :  array of floats
               X and Y coordinates


    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    F       : float (or array of floats)
              Force

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    V = (-5 * np.exp(-(coords - 2/0.75)**2) -
         10*np.exp(-(coords + 2/0.75)**2))
    F = ((-5 * 2 * -1 * (coords - 2/0.75) * np.exp(-(coords - 2/0.75)**2) -
         10 * 2 * -1 * (coords + 2/0.75) * np.exp(-(coords + 2/0.75)**2)) *
         (-1))
    Event='A'
    if type(coords) is np.float64 and coords < -2.0:
        Trigger = True
    else:
        Trigger = False

    return (V, F, Trigger, Event)


def pv_2D_potential(x, y):
    """
    Calculate the force and potential based on location (2-D).

    Parameters:
    -----------

    x       : array of floats
              X coordinates

    y       : array of floats
              Y coordinates

    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    Fpot    : float (or array of floats)
              Force in x and y direction

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    if hasattr(x, "__len__") is True:

        V = np.zeros([y.size, x.size])
        Fx = np.empty([y.size, x.size])
        Fy = np.empty([y.size, x.size])
        for k in range(0, y.size - 1):
            for j in range(0, x.size - 1):
                V[k, j] = (np.cos(2*math.pi*x[j])*(1 + 4*y[k]) +
                           math.pi*y[k]**2 - 0.75*np.cos(2*math.pi*x[j]/3))
                Fx = (((2*math.pi/3*0.75)*np.sin(2*math.pi*x[j]/3) -
                      2*math.pi*(1+4*y[k])*np.sin(2*math.pi*x[j])))
                Fy = ((2*math.pi*y[k]+4*np.cos(2*math.pi*x[j])))
        Fpotx = Fx * -1
        Fpoty = Fy * -1
        Trigger = False

    else:

        V = (np.cos(2*math.pi*x)*(1+4*y) + math.pi*y**2 -
             0.75*np.cos(2*math.pi*x/3))
        Fpotx = (((2*math.pi/3*0.75)*np.sin(2*math.pi*x/3) -
                 2*math.pi*(1+4*y)*np.sin(2*math.pi*x)))*-1
        Fpoty = ((2*math.pi*y+4*np.cos(2*math.pi*x)))*-1

        if x < 0.75 and y > 0:
            Trigger = True
            Event = 'A'
        elif x > 2.25 and y > 0:
            Trigger = True
            Event = 'B'
        else:
            Trigger = False
    Fpot = np.array([Fpotx, Fpoty])
    return (V, Fpot, Trigger, Event)

def C_Cl_potential(x, y):
    """
    Calculate the force and potential based on location (2-D).

    Parameters:
    -----------

    x       : array of floats
              X coordinates

    y       : array of floats
              Y coordinates

    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    Fpot    : float (or array of floats)
              Force in x and y direction

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    pot = pickle.load(open("kfpotential.p", "rb"))
    if hasattr(x, "__len__") is True:

        V = np.zeros([y.size, x.size])
        Fx = np.empty([y.size, x.size])
        Fy = np.empty([y.size, x.size])
        for k in range(0, y.size - 1):
            for j in range(0, x.size - 1):
                V[k, j] = pot(k, j)
                Fy = pot(k, j, dx=1)
                Fx = pot(k, j, dy=1)
        Fpotx = Fx * -1
        Fpoty = Fy * -1
        Trigger = False

    else:

        V[k, j] = pot(k, j)
        Fy = pot(k, j, dx=1)
        Fx = pot(k, j, dy=1)
        Fpotx = Fx * -1
        Fpoty = Fy * -1

        if x > 0.25 and y < 0.20:
            Trigger = True
        else:
            Trigger = False
    Fpot = np.array([Fpotx, Fpoty])
    Event=''
    return (V, Fpot, Trigger, Event)


def muller_brown_potential(x, y):
    """
    Calculate the force and potential based on location (2-D).

    Parameters:
    -----------

    x       : array of floats
              X coordinates

    y       : array of floats
              Y coordinates

    Returns:
    --------

    V       : float (or array of floats)
              Potential Energy

    Fpot    : float (or array of floats)
              Force in x and y direction

    Trigger : Boolean
              Has rare event occurred (True) or not (False)

    """
    if type(x) is not np.float64:

        V = np.zeros([y.size, x.size])
        Fx = np.empty([y.size, x.size])
        Fy = np.empty([y.size, x.size])
        A = np.array([-200.0, -100.0, -170.0, 15.0])
        a = np.array([-1.0, -1.0, -6.50, 0.7])
        b = np.array([0.0, 0.0, 11.0, 0.6])
        c = np.array([-10.0, -10.0, -6.50, 0.7])
        x0 = np.array([1.0, 0.0, -0.50, -1.0])
        y0 = np.array([0.0, 0.5, 1.50, 1.0])
        for k in range(0, y.size - 1):
            for j in range(0, x.size - 1):
                V[k, j] = sum(A * np.exp(a*(x[j]-x0)**2 +
                                         b*(x[j]-x0)*(y[k]-y0) +
                                         c*(y[k]-y0)**2))
                Fx = (-400*np.exp(-1*(-1+x[j])**2 - 10*y[k]**2)*(-1+x[j]) -
                      200*np.exp(-x[j]**2-10*(-0.5+x[j])**2)*x[j] +
                      170*np.exp(-6.5*(0.5+x[j])**2+11*(0.5+x[j])*(-1.5+y[k]) -
                      6.5*(-1.5+y[k])**2)*(-13*(0.5+x[j])+11*(-1/5+y[k])) -
                      15*np.exp(0.7*(1+x[j])**2+0.6*(1+x[j])*(y[k]-1) +
                      0.7*(y[k]-1)**2)*(1.4*(1+x[j])+0.6*(y[k]-1)))
                Fy = (170*np.exp(-6.5*(0.5+x[j])**2 +
                      11*(0.5+x[j])*(-1.5+y[k]) -
                      6.5*(y[k]-1.5)**2)*(11*(0.5+x[j])-13*(y[k]-1.5)) -
                      15*np.exp(0.7*(1+x[j])**2+0.6*(1+x[j])*(y[k]-1) +
                      0.7*(y[k]-1)**2)*(0.6*(x[j]+1)+1.4*(y[k]-1)) -
                      1000*np.exp(-x[j]**2-10*(y[k]-0.5)**2)*(y[k]-0.5) -
                      4000*np.exp(-1*(x[j]-1)**2-10*y[k]**2)*y[k])
        Fpotx = Fx * -1
        Fpoty = Fy * -1
        Trigger = False

    else:

        V = sum(A * np.exp(a * (x-x0)**2 + b * (x-x0)*(y-y0) +
                           c * (y-y0)**2))
        Fpotx = (-400*np.exp(-1*(-1+x)**2 - 10*y**2)*(-1+x) -
                 200*np.exp(-x**2-10*(-0.5+x)**2)*x +
                 170*np.exp(-6.5*(0.5+x)**2+11*(0.5+x)*(-1.5+y) -
                 6.5*(-1.5+y)**2)*(-13*(0.5+x)+11*(-1/5+y)) -
                 15*np.exp(0.7*(1+x)**2+0.6*(1+x)*(y-1) +
                 0.7*(y-1)**2)*(1.4*(1+x)+0.6*(y-1)))
        Fpoty = (170*np.exp(-6.5*(0.5+x)**2 +
                 11*(0.5+x)*(-1.5+y) -
                 6.5*(y-1.5)**2)*(11*(0.5+x)-13*(y-1.5)) -
                 15*np.exp(0.7*(1+x)**2+0.6*(1+x)*(y-1) +
                 0.7*(y-1)**2)*(0.6*(x+1)+1.4*(y-1)) -
                 1000*np.exp(-x**2-10*(y-0.5)**2)*(y-0.5) -
                 4000*np.exp(-1*(x-1)**2-10*y**2)*y)

        if x > 0.4 and y < 0.1:
            Trigger = True
        else:
            Trigger = False
    Fpot = np.array([Fpotx, Fpoty])
    Event=''
    return (V, Fpot, Trigger)


def get_potential_dict():
    """Return a dictionary of all of the available potential functions."""
    potential_dict = {'cosine_potential': cosine_potential,
                      'two_gaussian_potential': two_gaussian_potential,
                      'pv_2D_potential': pv_2D_potential,
                      'muller_brown_potential': muller_brown_potential,
                      'C_Cl_potential': C_Cl_potential}

    dimension_dict = {'cosine_potential': '1-D Potential',
                      'two_gaussian_potential': '1-D Potential',
                      'pv_2D_potential': '2-D Potential',
                      'muller_brown_potential': '2-D Potential',
                      'C_Cl_potential': '2-D Potential'}

    return potential_dict, dimension_dict


def get_GUI_presets_dict():
    """Return a dictionary of all of the available potential functions."""
    preset_dict = {'cosine_potential': np.array([3.14,-6.28,12.57,0.01,0,
                                                    0,0,0]).astype(str),
                      'two_gaussian_potential': np.array([2.67,-4,4,0.01,
                                                          0,0,0,0]).astype(str),
                      'pv_2D_potential': np.array([1.5,0,3.0,0.01,0.6,-2.0,
                                                   2.0,0.01]).astype(str),
                      'muller_brown_potential': np.array([0,0,0,0,0,0,0,
                                                          0]).astype(str),
                      'C_Cl_potential': np.array([0,0,0,0,0,0,0,0]).astype(str)
                    }

    return preset_dict


def two_gaussian_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    vold = vnew
    bcbias = 0
    is_periodic = False
    if (coords < -4.3193):

        vnew = 100.0 * (coords+4.0)**4.0 - 1.690133
        f2 = -100.0 * 4.0 * (coords+4.0)**3.0
        bcbias = vnew - vold

    elif (coords > 4.25882):

        vnew = 100.0 * (coords-4.0)**4.0 - 0.845067
        f2 = -100.0 * 4.0 * (coords-4.0)**3.0
        bcbias = vnew - vold

    return (vnew, f2, coords, bcbias, is_periodic)


def pv_2D_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    if (coords[0] < 0):
        coords[0] = coords[0] + 3

    elif (coords[0] > 3.0):
        coords[0] = coords[0] - 3
    bcbias = 0
    is_periodic_x = True
    is_periodic_y = False
    is_periodic = np.array([is_periodic_x, is_periodic_y])
    return (vnew, f2, coords, bcbias, is_periodic)


def C_Cl_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    bcbias = 0
    is_periodic_x = False
    is_periodic_y = False
    is_periodic = np.array([is_periodic_x, is_periodic_y])
    return (vnew, f2, coords, bcbias, is_periodic)


def LJ_potential_bc(vnew,f2,coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    bcbias = 0
    return (vnew, f2, coords, bcbias)


def mb_2D_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    bcbias = 0
    is_periodic_x = False
    is_periodic_y = False
    is_periodic = np.array([is_periodic_x, is_periodic_y])
    return (vnew, f2, coords, bcbias, is_periodic)


def cosine_potential_bc(vnew, f2, coords):
    """
    Apply Boundary Condition to the potential, force, and coordinates.

    Parameters:
    -----------
    vnew       : float (or array of floats)
                 Potential Energy

    f2         : float (or array of floats)
                 Force

    coords     : float
                 coordinates

    Returns:
    --------

    vnew       : float (or array of floats)
                 Adjusted potential energy from boundary condition

    F          : float (or array of floats)
                 Adjusted force from boundary condition

    coords     : float
                 adjusted coordinates from boundary condition

    bcbias     : float
                 bias applied strictly from the boundary condition
    """
    # if (coords < -2*np.pi):
        # coords = coords + 6*np.pi

    if (coords > 2*np.pi):
        vnew = 100*(coords-2*np.pi)**4+1.0
    	f2 = -4.0*100.0*(coords-2*np.pi)**3
    bcbias = 0
    is_periodic = False
    return (vnew, f2, coords, bcbias, is_periodic)


def get_boundary_condition_dict():
    """Return a dictionary of all of the available potential functions."""
    bc_dict = {'cosine_potential': cosine_potential_bc,
               'two_gaussian_potential': two_gaussian_potential_bc,
               'pv_2D_potential': pv_2D_potential_bc,
               'muller_brown_potential': mb_2D_potential_bc,
               'LJ_potential': LJ_potential_bc,
               'C_Cl_potential': C_Cl_potential_bc}

    return bc_dict

This file contains the various potential functions we have defined. Calculate the Potential Energy and Force of Cos(x).      Parameters:     -----------      coords  : float (or array of floats)             Location       Returns:     --------      V       : float (or array of floats)               Potential Energy      F       : float (or array of floats)               Force      Trigger : Boolean               Has rare event occurred (True) or not (False) Calculate the force and potential based on location (1-D).      Parameters:     -----------      coords  :  array of floats                X and Y coordinates       Returns:     --------      V       : float (or array of floats)               Potential Energy      F       : float (or array of floats)               Force      Trigger : Boolean               Has rare event occurred (True) or not (False) Calculate the force and potential based on location (2-D).      Parameters:     -----------      x       : array of floats               X coordinates      y       : array of floats               Y coordinates      Returns:     --------      V       : float (or array of floats)               Potential Energy      Fpot    : float (or array of floats)               Force in x and y direction      Trigger : Boolean               Has rare event occurred (True) or not (False) Calculate the force and potential based on location (2-D).      Parameters:     -----------      x       : array of floats               X coordinates      y       : array of floats               Y coordinates      Returns:     --------      V       : float (or array of floats)               Potential Energy      Fpot    : float (or array of floats)               Force in x and y direction      Trigger : Boolean               Has rare event occurred (True) or not (False) Calculate the force and potential based on location (2-D).      Parameters:     -----------      x       : array of floats               X coordinates      y       : array of floats               Y coordinates      Returns:     --------      V       : float (or array of floats)               Potential Energy      Fpot    : float (or array of floats)               Force in x and y direction      Trigger : Boolean               Has rare event occurred (True) or not (False) Return a dictionary of all of the available potential functions. Return a dictionary of all of the available potential functions. Apply Boundary Condition to the potential, force, and coordinates.      Parameters:     -----------     vnew       : float (or array of floats)                  Potential Energy      f2         : float (or array of floats)                  Force      coords     : float                  coordinates      Returns:     --------      vnew       : float (or array of floats)                  Adjusted potential energy from boundary condition      F          : float (or array of floats)                  Adjusted force from boundary condition      coords     : float                  adjusted coordinates from boundary condition      bcbias     : float                  bias applied strictly from the boundary condition Apply Boundary Condition to the potential, force, and coordinates.      Parameters:     -----------     vnew       : float (or array of floats)                  Potential Energy      f2         : float (or array of floats)                  Force      coords     : float                  coordinates      Returns:     --------      vnew       : float (or array of floats)                  Adjusted potential energy from boundary condition      F          : float (or array of floats)                  Adjusted force from boundary condition      coords     : float                  adjusted coordinates from boundary condition      bcbias     : float                  bias applied strictly from the boundary condition Apply Boundary Condition to the potential, force, and coordinates.      Parameters:     -----------     vnew       : float (or array of floats)                  Potential Energy      f2         : float (or array of floats)                  Force      coords     : float                  coordinates      Returns:     --------      vnew       : float (or array of floats)                  Adjusted potential energy from boundary condition      F          : float (or array of floats)                  Adjusted force from boundary condition      coords     : float                  adjusted coordinates from boundary condition      bcbias     : float                  bias applied strictly from the boundary condition Apply Boundary Condition to the potential, force, and coordinates.      Parameters:     -----------     vnew       : float (or array of floats)                  Potential Energy      f2         : float (or array of floats)                  Force      coords     : float                  coordinates      Returns:     --------      vnew       : float (or array of floats)                  Adjusted potential energy from boundary condition      F          : float (or array of floats)                  Adjusted force from boundary condition      coords     : float                  adjusted coordinates from boundary condition      bcbias     : float                  bias applied strictly from the boundary condition Apply Boundary Condition to the potential, force, and coordinates.      Parameters:     -----------     vnew       : float (or array of floats)                  Potential Energy      f2         : float (or array of floats)                  Force      coords     : float                  coordinates      Returns:     --------      vnew       : float (or array of floats)                  Adjusted potential energy from boundary condition      F          : float (or array of floats)                  Adjusted force from boundary condition      coords     : float                  adjusted coordinates from boundary condition      bcbias     : float                  bias applied strictly from the boundary condition Apply Boundary Condition to the potential, force, and coordinates.      Parameters:     -----------     vnew       : float (or array of floats)                  Potential Energy      f2         : float (or array of floats)                  Force      coords     : float                  coordinates      Returns:     --------      vnew       : float (or array of floats)                  Adjusted potential energy from boundary condition      F          : float (or array of floats)                  Adjusted force from boundary condition      coords     : float                  adjusted coordinates from boundary condition      bcbias     : float                  bias applied strictly from the boundary condition # if (coords < -2*np.pi): # coords = coords + 6*np.pi Return a dictionary of all of the available potential functions.