import matplotlib
matplotlib.use('Agg')
import functions21 as f
import numpy as np
#----------------- 1(a) ----------------------------
seed = 1094801294865
print('The seed will be:',seed)
#Initialize the RNG and plot the asked figures.
R = f.RNG(seed)
samp = R.sample(1000000)
samp1000 = samp[:1000]
sshift = samp[1:1001:1]
f.scatter(sshift, samp1000, 'Sequential Random Numbers', r'$x_{i+1}$', r'$x_i$'
,'scatter1a1',True)
f.scatter(np.linspace(0,1000,1000), samp1000, ' Random Numbers', 'i', r'$x_i$'
,'scatter1a2',True)
#plot the histogram of the sample.
f.plthist(samp, 20, 'Distribution of the RNG', 'Result', 'Probability','hist1a',
True)
np.savetxt('../seed.txt',R.state)
import matplotlib
matplotlib.use('Agg')
import numpy as np
from matplotlib import pyplot as plt
import functions21 as f
R = f.RNG(np.loadtxt('../seed.txt'))
#---------------------------- 1(b) --------------------------
#For the asked distribution values plot both the NormedGaussian and the
#histogram of a sample.
m = 3
s = 2.4
y1 = R.BoxMuller(1000, mu = m, sigma = s)
xsG = np.linspace(m - 5 * s, m + 5 * s, 10000)
ysG = f.NormedGaussian(xsG, mu = m, sig = s)
plt.hist(y1, bins=21, density=True, label='RNG')
plt.plot(xsG,ysG, label='Theoretical')
for i in range(6):
dx = i * s
fval = f.NormedGaussian(m - dx, mu = m, sig = s)
#Add the +-n\sigma-lines.
plt.plot([m - dx, m - dx], [0,fval], c='black')
plt.plot([m + dx, m + dx], [0,fval], c='black')
#Plot the y-axis in 'log' to be able to see the lines clearly
plt.yscale('log')
plt.legend()
plt.title(r'Normal distribution with $\mu=3$ and $\sigma=2.4$')
plt.xlabel(r'$x$')
plt.ylabel(r'$\mathbb{P}(x)$')
plt.savefig('1b.png',format='png')
import matplotlib
matplotlib.use('Agg')
import functions24 as f4
import numpy as np
from matplotlib import pyplot as plt
import sys
sys.path.append('../Problem1')
import functions21 as f1
#Initialize an RNG and positions if 64 * 64 particles.
R = f1.RNG(1246578543)
print('seed for c =', 1246578543)
xso, yso = [np.linspace(0, 63, 64) for i in range(2)]
xso, yso = np.meshgrid(xso, yso)
#Get the x- and y- components of S(q) from a Gaussian Random Field.
Bx, By = f4.grf2d(R)
#Counteract the normalization from scipy.fftpack.
Bx, By = Bx.real * 64, By.real * 64
#Initialize the a-values and arrays to store x, y, p_x and p_y for the first
#ten particles along the y-axis (for x=0 thus).
aval = np.linspace(0.0025, 1, 30 * 3)
da = aval[1] - aval[0]
x10, y10, px10, py10 = [np.zeros((10, 90)) for i in range(4)]
#Plot the initial positions and store the initial positions and momenta.
fig = plt.figure(dpi=50, figsize=[6.4, 6.4])
plt.scatter(xso, yso, s=1, c='black')