# g = lambda r, q : # initial distribution r0 = 1. dr0 = 0 # Q0 = np.random.normal(loc=0.9, scale=1., size=(n,)) # generate grid loc = 2.5 scale = 0.3 qgrid_size = 1000 qgrid = np.linspace(0, 15, qgrid_size) rho0 = n * norm.pdf(qgrid, loc=loc, scale=scale) t_end = 24 #60 pms.init_equations(T_r, U_r, T_q, U_q, g) pms.init_meso(r0, dr0, rho0, qgrid, t_end, n_eval=400) pms.simulate_meso(method="RK45", atol=1.e-8, rtol=1.e-8, use_upwind=True) #pms.simulate_meso_own() pms.name = "onion" #save_plots( plt, pms, "meso") pms.plot_g(levels=100) plt.show() pms.plot_veff_img(detail=500) plt.show() pms.plot_particle_paths_meso_time()
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()