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tests.py
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tests.py
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import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import lib as lib
import inputs as inputs
def check_random_walker_1D(tm_sigma, prob_density=None, alpha=None, N_steps=50000):
"""
Check for lib.random_walker() function with 1D input using visual inspection.
Parameters
----------
tm_sigma : float
Initial guess of the initial trial move variance for lib.random_walker()
prob_density : function or None
Probability density distribution for random_walker()
If None, it uses a Gaussian probability density distribution
alpha : np.ndarray
Parameters for prob_density()
If None, alpha=np.array([1])
N_steps : int
Number of steps of the random walker
Returns
-------
None
"""
if prob_density is None: prob_density = Gaussian
if alpha is None: alpha = np.array([1])
x_points, acceptance_probability, acceptance_ratio = lib.random_walker(prob_density, alpha, N_steps, np.zeros(1), tm_sigma)
plt.hist(x_points, bins=40, density=True)
xmin, xmax = np.min(x_points), np.max(x_points)
x = np.linspace(xmin, xmax, 1000)
plt.plot(x, prob_density(x, alpha), "--")
plt.xlim(xmin, xmax)
plt.xlabel("r")
plt.ylabel("Probability density function")
plt.tight_layout()
plt.show()
x1 = np.linspace(1, N_steps, N_steps)
print(x.shape, acceptance_probability.shape)
plt.scatter(x1, acceptance_probability, s=1)
plt.plot(x1, acceptance_ratio*np.ones(N_steps), 'r')
plt.ylim(0, 1)
plt.xlabel("step")
plt.ylabel("Acceptance probability")
plt.tight_layout()
plt.show()
graph=sns.jointplot(x=x1, y=acceptance_probability, s=1, hue_norm=(0,1))
graph.ax_joint.axhline(y=acceptance_ratio, c='r')
plt.show()
return
def check_random_walker_3D(tm_sigma, prob_density=None, alpha=None, N_steps=50000):
"""
Check for lib.random_walker() function with 3D input using visual inspection.
Parameters
----------
tm_sigma : float
Initial guess of the initial trial move variance for lib.random_walker()
prob_density : function or None
Probability density distribution for random_walker()
If None, it uses a Gaussian probability density distribution
alpha : np.ndarray
Parameters for prob_density()
If None, alpha=np.array([1])
N_steps : int
Number of steps of the random walker
Returns
-------
None
"""
if prob_density is None: prob_density = lambda x,y,z,std: Gaussian(x,std)*Gaussian(y,std)*Gaussian(z,std)
if alpha is None: alpha = np.array([1])
x_points = lib.random_walker(prob_density, alpha, N_steps, np.zeros(3), tm_sigma)
plt.hist(x_points[:,0], bins=40, density=True, alpha=0.3, label="r1")
plt.hist(x_points[:,1], bins=40, density=True, alpha=0.3, label="r2")
plt.hist(x_points[:,2], bins=40, density=True, alpha=0.3, label="r3")
plt.xlabel("r_i")
plt.ylabel("Probability density function")
plt.legend()
plt.tight_layout()
plt.show()
return
def check_random_walkers_1D(tm_sigma, prob_density=None, alpha=None, N_steps=50000):
"""
Check for lib.random_walker() function with 3D input using visual inspection.
Parameters
----------
tm_sigma : float
Initial guess of the initial trial move variance for lib.random_walker()
prob_density : function or None
Probability density distribution for random_walker()
If None, it uses a Gaussian probability density distribution
alpha : np.ndarray
Parameters for prob_density()
If None, alpha=np.array([1])
N_steps : int
Number of steps of the random walker
Returns
-------
None
"""
if prob_density is None: prob_density = Gaussian
if alpha is None: alpha = np.array([1])
x_points = lib.random_walkers(prob_density, alpha, N_steps, np.zeros((3,1)), tm_sigma)
plt.hist(x_points[:,0,0], bins=40, density=True, alpha=0.3, label="RW 1")
plt.hist(x_points[:,1,0], bins=40, density=True, alpha=0.3, label="RW 2")
plt.hist(x_points[:,2,0], bins=40, density=True, alpha=0.3, label="RW 3")
xmin, xmax = np.min(x_points), np.max(x_points)
x = np.linspace(xmin, xmax, 1000)
plt.plot(x, prob_density(x, alpha), "--")
plt.xlim(xmin, xmax)
plt.xlabel("r_i")
plt.ylabel("Probability density function")
plt.legend()
plt.tight_layout()
plt.show()
return
def monitor_ar_hydrogen(trial_move, N_walkers=10000, N_steps=10000):
"""
Plots a histogram of the acceptance ratio for hydrogen for all the random walkers.
Parameters
----------
trial_move : float
Standard deviation that defines the trial move according to a normal distribution
N_walkers : int
Number of random walkers
N_steps : int
Number of steps that each random walker takes
Returns
-------
None
"""
L_start = 5
dim = 3
alpha = np.array([1])
prob_density = inputs.prob_density_Hydrogen_atom
init_points = lib.rand_init_point(L_start, dim, N_walkers)
_, _, acceptance_ratio = lib.random_walkers(prob_density, alpha, N_steps, init_points, trial_move)
plt.hist(acceptance_ratio, bins=40, density=True)
plt.xlabel("acceptance ratio")
plt.ylabel("density of walkers")
plt.show()
return
def Gaussian(x, std):
"""
Returns the probability of x in a 1D Gaussian distribution of
zero mean and standard deviation of std.
Parameters
----------
x : float
Variable of the Gaussian distribution
std : float
Standard deviation of the aussian distribution
Returns
-------
f : float
Probability of x in a 1D Gaussian distribution N(0, std)
"""
f = np.exp(-x**2/(2*std**2))/(std*np.sqrt(2*np.pi))
return f
if __name__ == '__main__':
print("CHECK acceptance ratio Hydrogen (tm_sigma=opt)...")
opt_sigma = lib.find_optimal_trial_move(inputs.prob_density_Hydrogen_atom,np.array([1]),3,2)
print("The optimal trial move is: ", opt_sigma)
monitor_ar_hydrogen(opt_sigma)
print("DONE")
print("CHECK GAUSSIAN 1D (tm_sigma=opt)...")
opt_sigma = lib.find_optimal_trial_move(Gaussian,np.array([1]),1,1)
print("The optimal trial move is: ", opt_sigma)
check_random_walker_1D(opt_sigma)
print("DONE")
print("CHECK X^2*GAUSSIAN 1D (tm_sigma=opt)...")
f = lambda x, std: std*x**2*Gaussian(x, std)
opt_sigma = lib.find_optimal_trial_move(f,np.array([1]),1,1)
print("The optimal trial move is: ", opt_sigma)
check_random_walker_1D(opt_sigma, prob_density=f)
print("DONE")
print("CHECK GAUSSIAN 1D (tm_sigma=1)...")
check_random_walker_1D(1)
print("DONE")
print("CHECK X^2*GAUSSIAN 1D (tm_sigma=1)...")
f = lambda x, std: std*x**2*Gaussian(x, std)
check_random_walker_1D(1, prob_density=f)
print("DONE")
print("CHECK X^2*GAUSSIAN 1D (tm_sigma=0.1)...")
f = lambda x, std: std*x**2*Gaussian(x, std)
check_random_walker_1D(0.1, prob_density=f)
print("DONE")
print("CHECK X^2*GAUSSIAN 1D (tm_sigma=0.01)...")
f = lambda x, std: std*x**2*Gaussian(x, std)
check_random_walker_1D(0.01, prob_density=f)
print("DONE")
print("CHECK GAUSSIAN 3D (tm_sigma=1)...")
check_random_walker_3D(1)
print("DONE")
print("CHECK GAUSSIAN 1D WITH MULTIPLE RANDOM WALKERS (tm_sigma=1)...")
check_random_walkers_1D(1)
print("DONE")