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
a = 0
b = 1
# d is the distance from the measurements in the kernel
d = 2.5E-02
# we use rho(y) = exp(gamma*y)*sin(omega*y) as an example
gamma = -2
omega = 3*np.pi
# maximal order of the Taylor series expansion
Nmax = 75
# evaluate the integral expression at x_eval
N_eval = 40
Nq = 40
xq,w = np.polynomial.legendre.leggauss(Nq)
t = 0.5*(xq + 1)*(b - a) + a
xc = chebyshev(a,b,N_eval)
xs = chebyshev(a,b,N_eval)
F = analytical_solution(a,b,omega,gamma,Nmax)
F = pickle.load( open( "F.pkl", "rb" ) )
F_eval = F(xc,d)
A_ganger_rho = np.matmul(fredholm_lhs(xc,xs,t,w/2),rho(omega,gamma,xs,N_eval))
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)
import numpy as np
from Vitber.Prosjekt1.F_analytisk import analytical_solution
from Vitber.Prosjekt1.metoder import chebyshev, fredholm_lhs, rho
F = pickle.load(open("F.pkl", "rb"))
Nc = Ns = 30
a = 0
b = 1
gamma = -2
omega = 3 * np.pi
delta = 10 ** (-3)
d1 = 0.25
d2 = 2.5
xs = chebyshev(a, b, Ns)
xc = chebyshev(a, b, Nc)
F_eval = F(xc, d1)
xq_old, w = np.polynomial.legendre.leggauss(Nc ** 2)
xq = 0.5 * (xq_old + 1) * (b - a) + a
def b_pert(d):
F_eval = F(xc, d)
F_error = np.zeros(Nc)
for i in range(Nc):
F_error[i] = F_eval[i] * (1 + np.random.uniform(-delta, delta, Nc)[i])
return F_error