def fredholm_lhs(d, x_c, x_s, x_q, w_q, f):
N_c, N_s = x_c.shape[0], x_s.shape[0]
w_s = get_lagrange_poly_weights(x_s, array([1 for i in range(N_s)]))
A = empty((N_c, N_s))
for i in range(N_c):
for j in range(N_s):
A[i][j] = num_quadrature(x_q, w_q, get_kernel(f, x_c[i], x_s, w_s, j, d))
return A
def get_biggest_difference(x_s, rho_hat, x_list):
w_s = get_lagrange_poly_weights(x_s, rho_hat)
ylist = zeros(len(x_list))
for i in range(len(x_list)):
for j in range(len(x_s)):
ylist[i] += w_s[j] * evaluate_lagrange(x_s, x_list[i], j)
return ylist
return sum_q
def rho(x):
w, y = 3 * pi, -2
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)