apps121025_test_liouville.app06_volume_calc

Using 4 particle, calculate the area.

''' Using 4 particle, calculate the area.
'''
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mp

from .app04_nrm_setup import kep_particle

def main_cal(withplot=False, figure=None):

    ### Reference condition at t=0.  For 2D.
    pos0ref = np.array([1.2317, 0, 0])
    vel0ref = np.array([-0.52318 * 0.5, 0.52318 * np.sqrt(3./4), 0])

    ### Reference condition at t=3e5.
    pos1ref, vel1ref = kep_particle(pos0ref, vel0ref)
    pos1ref = pos1ref[-1, :]
    vel1ref = vel1ref[-1, :]

    posdel = np.array([0.0001, 0.0001, 0])    # Dr at t=0
    veldel = np.array([0.0001, 0.0001, 0])      # Dv at t=0

    npart = 4

    pos0list = np.zeros([3, npart])
    pos1list = np.zeros([3, npart])

    vel0list = np.zeros([3, npart])
    vel1list = np.zeros([3, npart])

    for n in range(npart):  ###  Test particles
        ### Calculate the position and velocity
        ### from the parameters defined above.
        ### Position (and velocity) should have
        ### the uniformly random from pos0ref \pm posdel/2.

        posx = np.random.uniform(low=-posdel[0] / 2., high=posdel[0] / 2.) + pos0ref[0]
        posy = np.random.uniform(low=-posdel[1] / 2., high=posdel[1] / 2.) + pos0ref[1]
        velx = np.random.uniform(low=-veldel[0] / 2., high=veldel[0] / 2.) + vel0ref[0]
        vely = np.random.uniform(low=-veldel[1] / 2., high=veldel[1] / 2.) + vel0ref[1]

        pos = np.array([posx, posy, 0])
        vel = np.array([velx, vely, 0])

        pos0list[:, n] = pos
        vel0list[:, n] = vel

        pos1, vel1 = kep_particle(pos, vel)
        pos1list[:, n] = pos1[-1, :]
        vel1list[:, n] = vel1[-1, :]

    if withplot:
        if figure == None:
            figure = plt.figure()
        ax = figure.add_subplot(241)
        ax.scatter(pos0list[0, :] - pos0ref[0], pos0list[1, :] - pos0ref[1], marker='.')
        ax.set_xlabel('X')
        ax.set_ylabel('Y')
        ax = figure.add_subplot(242)
        ax.scatter(vel0list[0, :] - vel0ref[0], vel0list[1, :] - vel0ref[1], marker='.')
        ax.set_xlabel('Vx')
        ax.set_ylabel('Vy')
        ax = figure.add_subplot(243)
        ax.scatter(pos0list[0, :] - pos0ref[0], vel0list[0, :] - vel0ref[0], marker='.')
        ax.set_xlabel('X')
        ax.set_ylabel('Vx')
        ax = figure.add_subplot(244)
        ax.scatter(pos0list[1, :] - pos0ref[1], vel0list[1, :] - vel0ref[1], marker='.')
        ax.set_xlabel('Y')
        ax.set_ylabel('Vy')

        ax = figure.add_subplot(245)
        ax.scatter(pos1list[0, :] - pos1ref[0], pos1list[1, :] - pos1ref[1], marker='.')
        ax.set_xlabel('X')
        ax.set_ylabel('Y')
        drbox = mp.Rectangle([-posdel[0]/2., -posdel[1]/2.], posdel[0], posdel[1], color='none', ec='red')
        ax.add_patch(drbox)

        ax = figure.add_subplot(246)
        ax.scatter(vel1list[0, :] - vel1ref[0], vel1list[1, :] - vel1ref[1], marker='.')
        ax.set_xlabel('Vx')
        ax.set_ylabel('Vy')
        drbox = mp.Rectangle([-veldel[0]/2., -veldel[1]/2.], veldel[0], veldel[1], color='none', ec='red')
        ax.add_patch(drbox)

        ax = figure.add_subplot(247)
        ax.scatter(pos1list[0, :] - pos1ref[0], vel1list[0, :] - vel1ref[0], marker='.')
        ax.set_xlabel('X')
        ax.set_ylabel('Vx')
        drbox = mp.Rectangle([-posdel[0]/2., -veldel[0]/2.], posdel[0], veldel[0], color='none', ec='red')
        ax.add_patch(drbox)

        ax = figure.add_subplot(248)
        ax.scatter(pos1list[1, :] - pos1ref[1], vel1list[1, :] - vel1ref[1], marker='.')
        ax.set_xlabel('Y')
        ax.set_ylabel('Vy')
        drbox = mp.Rectangle([-posdel[1]/2., -veldel[1]/2.], posdel[1], veldel[1], color='none', ec='red')
        ax.add_patch(drbox)


    # Volume calculation
    from irfpy.util.graminan import Graminan
    ### 4-D space (x, y, vx, vy) for each particle.

    # At t=0
    px0 = pos0list[0, :] - pos0ref[0]
    py0 = pos0list[1, :] - pos0ref[1]
    vx0 = vel0list[0, :] - vel0ref[0]
    vy0 = vel0list[1, :] - vel0ref[1]

    G0 = Graminan([px0, py0, vx0, vy0])   # Indeed, transpose is needed, but in this case, no problem as G.Transpose = G.
    print("Phase space volume (T=0)", G0.get_volume())

    # At t=3e4
    px1 = pos1list[0, :] - pos1ref[0]
    py1 = pos1list[1, :] - pos1ref[1]
    vx1 = vel1list[0, :] - vel1ref[0]
    vy1 = vel1list[1, :] - vel1ref[1]
    G1 = Graminan([px1, py1, vx1, vy1])   # Indeed, transpose is needed, but in this case, no problem as G.Transpose = G.
    print("Phase space volume (T=3e4)", G1.get_volume())

    return (G0.get_volume(), G1.get_volume())

def main():
    nexam = 100
    vol0 = np.zeros([nexam])
    vol1 = np.zeros([nexam])

    fig = plt.figure(figsize=(16, 8))
    for iexam in range(nexam):
        v0, v1 = main_cal(withplot=True, figure=fig)
        vol0[iexam] = v0
        vol1[iexam] = v1
        print(v0, v1)
    fig.savefig('app06_volume_calc0.png')

    plt.figure()
    plt.scatter(np.log10(vol0), np.log10(vol1))
    plt.plot([-20, -15], [-20, -15])
    plt.xlabel('Log phasevolume t=0')
    plt.ylabel('Log phasevolume t=1')
    plt.savefig('app06_volume_calc1.png')
    

if __name__ == "__main__":
    import time
    t0 = time.time()
    main()
    print('Time ellapsed', time.time() - t0)