if __name__ == "__main__":
d = 0.025
n_min, n_max = 25, 40
size = 100
N_q = 300
N_c_list = array([i for i in range(n_min, n_max + 1)])
x_q, w_q = legendre_gauss(0, 1, N_q)
F_analytic = load(open(rel_path + "/Data_files/F.pkl", "rb"))
max_diff, max_diff_rho = empty(len(N_c_list)), empty(len(N_c_list))
y_to_plot = empty((n_max - n_min + 1, size))
x_list = linspace(0, 1, size)
for i in N_c_list:
print(i)
N_c, N_s = i, i
x_c = shift_chebyshev(0, 1, chebyshev_n(N_c))
x_s = x_c
A = fredholm_lhs(d, x_c, x_s, x_q, w_q, f)
b = F_analytic(x_c, d)
rho_hat = solve(A, b)
y_to_plot[i - n_min] = get_biggest_difference(x_s, rho_hat, x_list)
max_diff_rho[i - n_min] = max(abs(y_to_plot[i - n_min] - rho(x_list)))
max_diff[i - n_min] = max(abs(rho_hat - rho(x_s)))
fig, ax = init_plot('Question 5')
plot_normal(ax, N_c_list, max_diff_rho, 'b-', r'Err whole intervall')
plot_normal(ax, N_c_list, max_diff, 'r-', r'Err(N$_c$)')
show_plot(fig, ax)
b_tilde = disturb_rhs(b)
for i in range(n_lambda):
rho_lambda = solve((dot(A.transpose(), A) + lambdas[i]*eye(N_c)), dot(A.transpose(), b_tilde))
max_error[i] = max(abs(rho_lambda-rho_analytical))
errors_by_lambda[argmin(max_error)] += 1
fig, ax = init_plot('Oppgave 7 -b')
ax.scatter(lambdas, errors_by_lambda, c='r', s=30)
ax.set_xscale('log')
ax.set_xlim(1e-6, 1.5*1e-3)
ax = set_axis_specs(ax, r'$\lambda$', r'# min |Error|', 23, 23)
plt.show()
file = rel_path + r'/Data_files/Oppgave7d025'
savez(file, lambdas=lambdas, errors_by_lambda=errors_by_lambda)"""
n_lambda = 100000
lambdas = geomspace(1e-14, 1, n_lambda)
max_error = empty(n_lambda)
seed(int(time()))
b_tilde = disturb_rhs(b)
for i in range(n_lambda):
rho_lambda = solve((dot(A.transpose(), A) + lambdas[i] * eye(N_c)),
dot(A.transpose(), b_tilde))
max_error[i] = max(abs(rho_lambda - rho_analytical))
fig, ax = init_plot('Oppgave 7 -b')
plot_loglog(ax, lambdas, max_error, 'r-', "Error($\lambda$)")
ax = set_axis_specs(ax, r'$\lambda$', r'Error', 30, 30)
show_plot(fig, ax)
x_c = shift_chebyshev(0, 1, chebyshev_n(N_c))
x_s = shift_chebyshev(0, 1, chebyshev_n(N_s))
N_q = 900
x_q, w_q = legendre_gauss(0, 1, N_q)
#---------------------------------------
d= 0.025
A = fredholm_lhs(d, x_c, x_s, x_q, w_q, f)
b = F_analytic(x_c, d)
b_tilde = disturb_rhs(b)
rho_hat = solve(A, b)
rho_hat_tilde = solve(A, b_tilde)
fig1, ax1 = init_plot('Question 6-1 - d=0,025')
ax1 = set_axis_specs(ax1, r'$x^s$', r'$b$', 18, 18)
ax1 = plot_normal(ax1, x_c, b, 'r-', r'Unperturbed $b$')
ax1 = plot_small(ax1, x_c, b_tilde, 'b--', r'Perturbed $\~{b}$')
fig2, ax2 = init_plot('Question 6-2 - d=0,025')
ax2 = set_axis_specs(ax2, r'$x^s$', r'$\rho$', 18, 18)
ax2 = plot_normal(ax2, x_s, rho_hat, 'r-', r'Unperturbed $\hat{\rho}$')
ax2 = plot_normal(ax2, x_s, rho_hat_tilde, 'b-', r'Perturbed $\hat{\rho}$')
ax2 = plot_small(ax2, x_s, rho(x_s), 'g--', r'Analytic $\rho$')
file = rel_path + r'/Data_files/Oppgave6_d0025'
savez(file, b=b, b_tilde=b_tilde, rho_hat=rho_hat, rho_hat_tilde=rho_hat_tilde)
#-----------------------------------------------------------------
d = 0.25
from numpy import load
from sys import path
from os.path import dirname
rel_path = dirname(dirname(__file__))
path.insert(0, rel_path + r'/Help_files')
from Plotting import init_plot, plot_normal, show_plot, save_fig, plot_logy_test, save_fig_legend_on_top, set_axis_specs, plot_small
path.__delitem__(0)
file = rel_path + r'/Data_files/Oppgave5.npz'
if __name__ == "__main__":
npz_file = load(file)
fig, ax = init_plot('Question 5 - Error')
ax = set_axis_specs(ax, r'$N_c$', r'Max $|$Error$_j|$', 36, 36)
N_c_list, d_0025, d_025, d_25 = npz_file['N_c_list'], npz_file[
'max_diff_1'], npz_file['max_diff_2'], npz_file['max_diff_3']
plot_logy_test(ax,
N_c_list,
d_0025,
'ro--',
r'Err(N$_{c}$) - d = ' + '{}'.format(0.025),
linewidth=4,
ms=10)
plot_logy_test(ax,
N_c_list,
d_025,
'bo--',
r'Err($N_{c}$) - d = ' + '{}'.format(0.25),
return sin(w * x) * exp(y * x)
if __name__ == "__main__":
d = 0.025
n_c = 40
n_s = 40
x_c = shift_chebyshev(0, 1, chebyshev_n(n_c))
x_s = shift_chebyshev(0, 1, chebyshev_n(n_s))
w_s = get_lagrange_poly_weights(x_s, array([1 for i in range(n_s)]))
rho_hat = array([rho(x_s[i]) for i in range(n_s)])
F_analytic = load(open(rel_path + "/Data_files/F.pkl", "rb"))
f_eval = F_analytic(x_c, d)
fig, ax = init_plot('Oppgave 3')
ax = set_axis_specs(ax, '$N_q$', 'Max Error', 24, 24)
panel_list = arange(20, 301, 1)
y_list_midpoint = empty(len(panel_list))
y_list_simpson = empty(len(panel_list))
y_list_LG = empty(len(panel_list))
for i in range(len(panel_list)):
x_q, w_q = midpoint(0, 1, panel_list[i])
A = fredholm_lhs(d, x_c, x_s, w_s, x_q, w_q, f)
F = dot(A, rho_hat)
y_list_midpoint[i] = norm((F - f_eval), 0)
ax = plot_logy(ax, panel_list, y_list_midpoint, 'r-',
"Err($N_q$) - midpoint")
if __name__ == "__main__":
d = 0.25
N_c, N_s = 30, 30
n_lambda = 14
N_q = 900
seed(1)
F_analytic = load(open(rel_path + "/Data_files/F.pkl", "rb"))
x_c = shift_chebyshev(0, 1, chebyshev_n(N_c))
x_s = shift_chebyshev(0, 1, chebyshev_n(N_s))
x_q, w_q = legendre_gauss(0, 1, N_q)
b = F_analytic(x_c, d)
b_tilde = disturb_rhs(b)
fig, ax = init_plot('Question 6 - b')
rho_analytical = rho(x_c)
A = fredholm_lhs(d, x_c, x_s, x_q, w_q, f)
lambdas = array([10**(-i) for i in flip(linspace(1, 14, n_lambda), 0)])
max_error = empty(n_lambda)
for i in range(n_lambda):
rho_lambda = solve((dot(A.transpose(), A) + lambdas[i] * eye(N_c)),
A.transpose())
max_error[i] = max(abs(rho_lambda - rho_analytical))
ax = plot_loglog(ax, lambdas, max_error, 'r-', 'Err(lambda')
show_plot(fig, ax)
if __name__ == "__main__":
n_min, n_max = 5, 30
N_c_list = array([i for i in range(n_min, n_max + 1)])
d_list = array([0.025, 0.25, 2.5])
c_list = array(['r-', 'b-', 'g-'])
N_q = 900
x_q, w_q = legendre_gauss(0, 1, N_q)
max_diff_1, max_diff_2, max_diff_3 = empty(len(N_c_list)), empty(
len(N_c_list)), empty(len(N_c_list))
F_analytic = load(open(rel_path + "/Data_files/F.pkl", "rb"))
fig, ax = init_plot('Question 5 - Error d=0.025 & 0.25')
d = 0.025
for i in N_c_list:
print(i)
N_c, N_s = i, i
x_c = shift_chebyshev(0, 1, chebyshev_n(N_c))
x_s = x_c
A = fredholm_lhs(d, x_c, x_s, x_q, w_q, f)
b = F_analytic(x_c, d)
rho_hat = solve(A, b)
max_diff_1[i - n_min] = max(abs(rho_hat - rho(x_c)))
plot_logy_test(ax, N_c_list, max_diff_1, 'ro--',
r'Err(N$_{c}$) - d = ' + '{}'.format(d))
d = 0.25
