u2[i] = ((V_ro(U[0, m[i]]) - U[1, m[i]]) / tau)
return np.array([u1, u2])
def f_u(U, m):
u1 = U[0, m] * U[1, m]
u2 = 1 / 2 * (U[1, m] ** 2) + (c_0 ** 2) * np.log(U[0, m])
return np.array([u1, u2])
a = 9
b = 16
error = np.zeros(b - a)
k_vec = np.zeros(b - a)
ref = rw.read_data("L_F_ref")
for i in range(a, b):
k = 2 ** (-i)
N = int(10 / k)
u = np.zeros([2, len(x) + 1])
u_next = np.zeros([2, len(x) + 1])
initial_velocity = V_ro(rho_up)
u[0, :] = rho_up
u[1, :] = initial_velocity
u_next[0, :] = rho_up
u_next[1, :] = initial_velocity
for n in range(N):
f = f_u(u, range(1, len(x) + 1))
s_next = s(u, range(1, len(x) + 1), n)
f = f_u(u, range(0, len(x) + 1)) # length: L/h
s_next = s(u, range(0, len(x) - 1), n) # length: L/h
#print("length of x:",len(x))
#print("length of u:",len(u[0]))
for m in range(1, len(x) - 1):
u_next[0, m] = (
(u[0, m - 1] + u[0, m + 1]) /
2) - (k /
(2 * h)) * (f[0, m + 1] - f[0, m - 1]) + (k * s_next[0, m])
u_next[1, m] = ((u[1, m - 1] + u[1, m + 1]) / 2) - (k / (2 * h)) * (
f[1, m + 1] - f[1, m - 1]) + (k * s_next[1, m]) + (
(k / (h**2)) * (u[1, m + 1] - 2 * u[1, m] + u[1, m - 1]))
u_next[0, 0] = rho_up
u_next[1, 0] = initial_velocity
u_next[:, len(x)] = u_next[:, len(x) - 1]
u = u_next
#print(n)
if (n % (N / 10) == 0):
plt.plot(x, u[0][:-1])
plt.show()
if __name__ == "__main__":
print("hei")
rw.write_data(u, "u_lax_friedrich_x3.txt")
a = rw.read_data("u_lax_friedrich_x3.txt")
print(a)
#plt.plot(x,u[0][:-1])
#plt.show()
import numpy as np
import matplotlib.pyplot as plt
import readwrite as rw
# This script makes a convergence plot for Lax-Wendroff in space
# The different step lengths we are iterating for
h_values = [2**i for i in range(3, 9)]
ref_sol = rw.read_data("Reference solution, Lax-Wendroff, x-convergence.txt"
) # Reference solution
# Constants:
k = 10**-4
sigma = 300
tau = 0.5
V_0 = 2000
rho_hat = 0.14
E = 100
c_0 = 900
mu = 10000
f_up = 32.5
f_rmp = 2
rho_up = 0.02
N = 10**4
L = 2**13
ref_sol_points = L / (
len(ref_sol[0]) - 1
) # Relationship between length of the road and length of reference solution
number_of_discretizations = len(h_values)
errors1 = np.zeros(number_of_discretizations) # Error in 1-norm
u2[i] = ((V_ro(U[0, m[i]]) - U[1, m[i]]) / tau)
return np.array([u1, u2])
def f_u(U, m):
u1 = U[0, m] * U[1, m]
u2 = 1 / 2 * (U[1, m]**2) + (c_0**2) * np.log(U[0, m])
return np.array([u1, u2])
a = 9
b = 12
error = np.zeros(b - a)
k_vec = np.zeros(b - a)
ref = rw.read_data("ber1.txt")
for i in range(a, b): #16
k = 2**(-i)
N = int(10 / k)
u = np.zeros([2, len(x) + 1]) #2 x M
u_next = np.zeros([2, len(x) + 1])
initial_velocity = V_ro(rho_up)
u[0, :] = rho_up
u[1, :] = initial_velocity
u_next[0, :] = rho_up
u_next[1, :] = initial_velocity
for n in range(N):
f = f_u(u, range(1, len(x) + 1))
s_next = s(u, range(1, len(x) + 1), n)
rho_hat = 0.14
E = 100
c_0 = 900
mu = 100
f_up = 32.5
f_rmp = 2
rho_up = 0.02
N = 10**4
# The different step lengths we are iterating for
h_values = [2**i for i in range(2, 9)]
number_of_discretizations = len(h_values)
errors2 = np.zeros(number_of_discretizations) # Error in 2-norm
ref_sol = rw.read_data("Reference solution, Lax-Friedrich, x-convergence.txt"
) # Reference solution
ref_sol_points = L / (
len(ref_sol[0]) - 1
) # Relationship between length of the road and length of reference solution
def q(t):
return f_rmp
def phi(x):
return ((2 * np.pi * (sigma**2))**(-1 / 2)) * np.exp(-(x**2) /
(2 * (sigma**2)))
def V_ro(ro):
c_0 = 54
mu = 600
f_up = 1948
f_rmp = 121
rho_up = 20
N = 1000
"""
# Lager konvergensplot for Lax-Wendroff i x-retning
#h_values = [2**i for i in range(4, 8)]
h_values = [2**i for i in range(3, 9)]
#h_values = [10, 20, 50, 100, 200, 500]
number_of_discretizations = len(h_values)
errors1 = np.zeros(number_of_discretizations) # Error in 1-norm
errors2 = np.zeros(number_of_discretizations) # Error in 2-norm
ref_sol = rw.read_data("u_lax_wendroff_x2.txt") # Reference solution
L = 2**13
ref_sol_points = L / (len(ref_sol[0]) - 1)
k = 10**-4
sigma = 300
tau = 0.5
V_0 = 2000
rho_hat = 0.14
E = 100
c_0 = 900
mu = 10000
f_up = 32.5
f_rmp = 2
rho_up = 0.02
N = 10**4
from sklearn.neural_network import MLPClassifier
import matplotlib.pyplot as plt
from readwrite import read_data, write_data
from sklearn.metrics import plot_confusion_matrix
train_images, train_labels, test_images, validation_images, validation_labels = read_data(
)
classifier = MLPClassifier(hidden_layer_sizes=(100, ),
activation='relu',
solver='adam',
alpha=0.0001,
batch_size='auto',
learning_rate='constant',
power_t=0.5,
max_iter=10,
shuffle=True,
random_state=None,
tol=0.0001,
momentum=0.9,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=10)
classifier.fit(train_images, train_labels)
plot_confusion_matrix(classifier, validation_images, validation_labels)
plt.show()
plt.savefig('mlp.png')
prediction = classifier.predict(test_images)
write_data(prediction)
import readwrite as rw
# Lager konvergensplot for Lax-Friedrichs i x-retning
k = 10**-4
L = 2**13
#h_values = [50, 100, 200, 500]
#h_values = [50, 100]
h_values = [2**i for i in range(2, 9)]
number_of_discretizations = len(h_values)
errors1 = np.zeros(number_of_discretizations) # Error in 1-norm
errors2 = np.zeros(number_of_discretizations) # Error in 2-norm
ref_sol = rw.read_data("u_lax_friedrich_x2.txt") # Reference solution
ref_sol_points = L / (len(ref_sol[0]) - 1)
sigma = 300
tau = 0.5
V_0 = 2000
rho_hat = 0.14
E = 100
c_0 = 900
mu = 100
f_up = 32.5
f_rmp = 2
rho_up = 0.02
N = 10**4
def q(t):
f_next_p1 = f_u(u,m+1) #m+1
u_half[0,m] = ((u[0,m] + u[0,m+1])/2) -(k/(2*h))*(f_next_p1[0]-f_next[0])+((k/2)*(s_next[0]+s_next_p1[0]))
u_half[1,m] = ((u[1,m] + u[1,m+1])/2) -(k/(2*h))*(f_next_p1[1]-f_next[1])+((k/2)*(s_next[1]+s_next_p1[1]))
f_half_p1 = f_u(u_half,m)
f_half_m1 = f_u(u_half,m-1)
s_half_p1 = s(u_half, m, n)
s_half_m1 = s(u_half, m-1, n)
u_next[0,m]= u[0,m] -(k/(2*h))*(f_half_p1[0]-f_half_m1[0])+((k/2)*(s_half_p1[0]+s_half_m1[0]))
u_next[1,m] = u[1,m] -(k/(2*h))*(f_half_p1[1]-f_half_m1[1])+((k/2)*(s_half_p1[1]+s_half_m1[1]))
#print(((u[0, m - 1] + u[0, m + 1]) / 2), (k / (2 * h)) * (f_next_p1[0] - f_next_m1[0]), (k * s_next[0]))
#print(((u[1,m-1]+ u[1,m+1])/2),(k/(2*h))*(f_next_p1[1]-f_next_m1[1]),(k*s_next[1]))
u_next[0,0] = u_next[0,1] -(u_next[0,2]-u_next[0,1])
u_next[1,0] = u_next[1,1] - (u_next[1,2]-u_next[1,1])
u_next[0, len(x)] = u_next[0, len(x)-1]+(u_next[0,len(x)-1]-u_next[0, len(x)-2])
u_next[1, len(x)] = u_next[1, len(x) - 1] + (u_next[1, len(x) - 1] - u_next[1, len(x) - 2])
u = u_next
#if (n % (N / 10) == 0):
# plt.plot(x, u[0][:-1])
# plt.show()
if __name__ == "__main__":
rw.write_data(u, "u_lax_wendroff_x2.txt")
a = rw.read_data("u_lax_wendroff_x2.txt")
print(a)
plt.plot(x,ref_sol[0])
plt.show()
u1 = q(n * k) * phi((m * h) - (L / 2))
u2 = ((V_ro(U[0, m]) - U[1, m]) / tau)
return np.array([u1, u2])
def f_u(U, m):
u1 = U[0, m] * U[1, m]
u2 = 1 / 2 * (U[1, m]**2) + (c_0**2) * np.log(U[0, m])
return np.array([u1, u2])
a = 5
b = 12
error = np.zeros(b - a)
k_vec = np.zeros(b - a)
ref = rw.read_data("L_W_100_0.00001_200000")
for i in range(a, b): # 16
k = 2**(-i)
N = int(2 / k)
u = np.zeros([2, len(x) + 1]) # 2 x M
u_next = np.zeros([2, len(x) + 1])
u_half = np.zeros([2, len(x) + 1])
initial_velocity = V_ro(rho_up)
u_half[0, :] = rho_up
u_half[1, :] = initial_velocity
u[0, :] = rho_up
u[1, :] = initial_velocity
u_next[0, :] = rho_up
u_next[1, :] = initial_velocity
u2[i] = ((V_ro(U[0, m[i]]) - U[1, m[i]]) / tau)
return np.array([u1, u2])
def f_u(U, m):
u1 = U[0, m] * U[1, m]
u2 = 1 / 2 * (U[1, m]**2) + (c_0**2) * np.log(U[0, m])
return np.array([u1, u2])
a = 9
b = 12
error = np.zeros(b - a)
k_vec = np.zeros(b - a)
ref = rw.read_data("ber1.txt")
index = 0
for i in range(a, b): #16
k = 2**(-i)
N = int(10 / k)
u = np.zeros([2, len(x) + 1]) #2 x M
u_next = np.zeros([2, len(x) + 1])
initial_velocity = V_ro(rho_up)
u[0, :] = rho_up
u[1, :] = initial_velocity
u_next[0, :] = rho_up
u_next[1, :] = initial_velocity
for n in range(N):
f = f_u(u, range(1, len(x) + 1))
s_next = s(u, range(1, len(x) + 1), n)
u2 = ((V_ro(U[0, m]) - U[1, m]) / tau)
return np.array([u1, u2])
def f_u(U, m):
u1 = U[0, m] * U[1, m]
u2 = 1 / 2 * (U[1, m]**2) + (c_0**2) * np.log(U[0, m])
return np.array([u1, u2])
#Declarations for convergence analysis
a = 6
b = 14
error = np.zeros(b - a) #To save difference in norm
k_vec = np.zeros(b - a) #To save k-values
ref = rw.read_data("L_W_ref_boundaries") #Load reference solution
#Scale reference solution
ref[0] = ref[0] / 1000
ref[1] = ref[1] / 0.06
for i in range(a, b): #Loop executing Lax-Wendroff with varying values of k
k = 2**(-i)
N = int(2 / k)
u = np.zeros([2, len(x) + 1])
u_next = np.zeros([2, len(x) + 1])
u_half = np.zeros([2, len(x) + 1])
initial_velocity = V_ro(rho_up)
u_half[0, :] = rho_up
u_half[1, :] = initial_velocity
