def error_lg(Nq_liste,a,b):
#error = np.zeros(Nq)
error = np.zeros(len(Nq))
F = fredholm_rhs(xc,F_eval)
for i in Nq_liste:
xq,w = np.polynomial.legendre.leggauss(i)
t = 0.5*(xq + 1)*(b - a) + a
A_rho = np.matmul(fredholm_lhs(xc,xs,t,w/2),rho(omega,gamma,xs,N_eval))
ny_liste = np.zeros(N_eval)
for j in range(N_eval):
ny_liste[j] = F[j] - A_rho[j]
error[i-1] = np.linalg.norm(ny_liste,np.inf)
return error
def error(Nq_liste, a, b):
# error = np.zeros(Nq)
error = np.zeros(len(Nq_liste))
F = fredholm_rhs(xc, F_eval)
for i in range(len(Nq_liste)):
xq, w = Newton_Cotes(a, b, Nq_liste[i])
A_rho = np.matmul(fredholm_lhs(xc, xs, xq, w),
rho(omega, gamma, xs, N_eval))
ny_liste = np.zeros(N_eval)
for j in range(N_eval):
ny_liste[j] = F[j] - A_rho[j]
error[i] = np.linalg.norm(ny_liste, np.inf)
return error
def rho_error(Ns, Nc, F, d):
error = np.zeros(len(Ns))
for i in range(len(Ns)):
xs = chebyshev(a, b, Ns[i])
xc = chebyshev(a, b, Nc[i])
xq_old, w = np.polynomial.legendre.leggauss(Ns[i]**2)
xq = 0.5 * (xq_old + 1) * (b - a) + a
A = fredholm_lhs(xc, xs, xq, w / 2)
F_eval = F(xc, d)
B = fredholm_rhs(xc, F_eval)
losning = np.linalg.solve(A, B)
ny_liste = np.zeros(Ns[i])
for j in range(Ns[i]):
ny_liste[j] = rho(omega, gamma, xs, Ns[i])[j] - losning[j]
error[i] = np.linalg.norm(ny_liste, np.inf)
return error
for i in range(len(xc)):
F_error[i] = F_eval[i] * (1 +
np.random.uniform(-delta, delta, N_eval)[i])
return F_eval, F_error
F_eval1, F_error1 = finn_b(0.025)
F_eval2, F_error2 = finn_b(0.25)
F_eval3, F_error3 = finn_b(2.5)
analytisk_rho = rho(omega, gamma, xs, N_eval)
xq_old, w = np.polynomial.legendre.leggauss(N_eval**2)
xq = 0.5 * (xq_old + 1) * (b - a) + a
A = fredholm_lhs(xc, xs, xq, w / 2)
B = fredholm_rhs(xc, F_eval1)
losning = np.linalg.solve(A, B)
# analytisk rho uten perturbering
rho1 = np.linalg.solve(A, F_eval1)
rho2 = np.linalg.solve(A, F_eval2)
rho3 = np.linalg.solve(A, F_eval3)
# analytisk rho med perturbering
rho1_error = np.linalg.solve(A, F_error1)
rho2_error = np.linalg.solve(A, F_error2)
rho3_error = np.linalg.solve(A, F_error3)
plt.figure('F og F med feil')
plt.plot(xc, F_eval1, label='F ved d = 0.025')
plt.plot(xc, F_error1, label='F med feil ved d = 0.025')