Python DiscretePMS Examples

Example #1

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from scipy.stats import norm

from init_plot_settings import init_plot_settings
from save_state import save_plots

init_plot_settings(plt)

pms = DiscretePMS()

n = 250

# masses
m_r = 20.
m_q = 10. / n

# stiffness
kappa_r = 1.
kappa_q = 1.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #2

File: example_onion_meso.py Project: SteffenPL/PartiallyKineticSystems

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from scipy.stats import norm

from init_plot_settings import init_plot_settings
from save_state import save_plots

init_plot_settings(plt)

pms = DiscretePMS()

n = 100

# masses
m_r = 2.
m_q = 1. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #3

File: example_onion.py Project: SteffenPL/PartiallyKineticSystems

Created on Thu Jul 25 09:44:55 2019

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from init_plot_settings import init_plot_settings
from save_state import save_plots

init_plot_settings(plt)

dpms = DiscretePMS()

n = 100

# masses
m_r = 2.
m_q = 1. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #4

def analyse_variance(example_name):

    dpms = DiscretePMS()
    dpms.name = example_name

    n_particles = 2**np.arange(2, 7)
    mean_vec = []
    var_vec = []

    n_mc = 50
    for n in n_particles:

        if dpms.name == "linear":

            # masses
            m_r = 2.
            m_q = 10. / n

            # stiffness
            kappa_r = 1.
            kappa_q = 1 / n

            # forces
            U_r = lambda r, dr: 0.5 * kappa_r * r**2
            T_r = lambda r, dr: 0.5 * m_r * dr**2

            U_q = lambda q, dq: 0.5 * kappa_q * q**2
            T_q = lambda q, dq: 0.5 * m_q * dq**2

            # constraint
            g = lambda r, q: q - r

            t_end = 23
            r0 = 1.
            dr0 = 0.

            mean = 2.0
            scale = 1.0

        if dpms.name == "onion":
            # masses
            m_r = 2.
            m_q = 1. / n

            # stiffness
            kappa_r = 1.
            kappa_q = 0.0 / n

            # forces
            U_r = lambda r, dr: 0.5 * kappa_r * r**2
            T_r = lambda r, dr: 0.5 * m_r * dr**2

            U_q = lambda q, dq: 0.5 * kappa_q * q**2
            T_q = lambda q, dq: 0.5 * m_q * dq**2

            # constraint
            factor = 1.
            # g = lambda r, q : factor*q/(1+r**2) - q**3
            g = lambda r, q: -factor * sp.sin(0.1 * q) / (1 + r**2) + 0.1 * q

            t_end = 20
            r0 = 1.
            dr0 = 0.

            mean = 0.9
            scale = 1.0

        r_end = np.zeros(shape=(n_mc, ))

        dpms.init_equations(T_r, U_r, T_q, U_q, g)

        # colors in plots
        col_min = np.array([0., 0.6, 0.9])
        col_max = np.array([0.6, 0., 0.9])

        for i in range(0, n_mc):

            # initial distribution

            Q0 = np.random.normal(loc=mean, scale=scale, size=(n, ))

            dpms.init_state(r0, dr0, Q0, t_end)
            dpms.simulate()

            r_end[i] = dpms.r[-1]
            p = i / (n_mc - 1)

            plt.plot(dpms.sol.t,
                     dpms.r,
                     color=p * col_min + (1. - p) * col_max,
                     lw=0.3)

        # calucate mean and variance at t_end

        cur_mean = 1 / n_mc * np.sum(r_end)
        cur_var = 1 / (n_mc - 1) * np.sum((r_end - cur_mean)**2)

        mean_vec.append(cur_mean)
        var_vec.append(cur_var)

        plt.xlabel(r"$t$")
        plt.ylabel(r"$r(t)$")
        plt.title("heavy system (%d samples, %d particles)" % (n_mc, n))
        plt.savefig(
            gen_name(dpms, "disc") + ("_mc%d_n%d" % (n_mc, n)) + ".pdf")
        plt.show()

    plt.loglog(n_particles,
               var_vec,
               label=r"$\mathrm{Var}[ r(t_\text{end} ) ]$")
    plt.loglog(n_particles, 1. / n_particles, label=r"$n^{-1}$")
    plt.xlabel(r"$\log(n)$")
    plt.title("variance of the heavy system")
    #plt.ylabel(r"$\log$")
    plt.legend()
    plt.savefig(gen_name(dpms, "disc") + ("_variance_mc%d" % (n_mc)) + ".pdf")
    plt.show()

Example #5

File: example_singular_stoch.py Project: SteffenPL/PartiallyKineticSystems

"""
Created on Thu Jul 25 09:44:55 2019

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from init_plot_settings import init_plot_settings
from save_state import save_plots
init_plot_settings(plt)

dpms = DiscretePMS()

n = 50

# masses
m_r = 2.
m_q = 1. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #6

Created on Thu Jul 25 09:44:55 2019

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from init_plot_settings import init_plot_settings
from save_state import save_plots

init_plot_settings(plt)

dpms = DiscretePMS()

n = 100

# masses
m_r = 2.
m_q = 1. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #7

"""



import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS


from init_plot_settings import init_plot_settings

init_plot_settings(plt)


dpms = DiscretePMS()



n = 100

# masses
m_r = 2.
m_q = 1. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2

Example #8

File: example_singular_meso.py Project: SteffenPL/PartiallyKineticSystems

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from scipy.stats import norm

from init_plot_settings import init_plot_settings
from save_state import save_plots

init_plot_settings(plt)

pms = DiscretePMS()

n = 100

# masses
m_r = 2.
m_q = 1. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #9

Created on Thu Jul 25 09:44:55 2019

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from init_plot_settings import init_plot_settings
from save_state import save_plots

init_plot_settings(plt)

dpms = DiscretePMS()

n = 100

# masses
m_r = 2.
m_q = 10. / n

# stiffness
kappa_r = 1.
kappa_q = 1 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2

Example #10

File: uni-kl.de 2019-08-14-12-40-12).py Project: SteffenPL/PartiallyKineticSystems

Created on Thu Jul 25 09:44:55 2019

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from init_plot_settings import init_plot_settings
from save_state import save_plots, basepath

init_plot_settings(plt)

dpms = DiscretePMS()

n_particles = 2**np.arange(2, 9)
mean_vec = []
var_vec = []

n_mc = 50

for n in n_particles:

    # masses
    m_r = 2.
    m_q = 1. / n

    # stiffness
    kappa_r = 1.

Example #11

File: demo_meso.py Project: SteffenPL/PartiallyKineticSystems

@author: plunder
"""

import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
from discrete_pms import DiscretePMS

from scipy.stats import norm

from init_plot_settings import init_plot_settings

init_plot_settings(plt)

dpms = DiscretePMS()

n = 100

# masses
m_r = 2.
m_q = 10. / n

# stiffness
kappa_r = 1.
kappa_q = 0.0 / n

# forces
U_r = lambda r, dr: 0.5 * kappa_r * r**2
T_r = lambda r, dr: 0.5 * m_r * dr**2