def calc_z1_fourier(initial_func, d_initial_func, eval_f1, a, nu, k, R0, R, M):
arc_dst = lambda func: fourier.arc_dst(a, func, N=fourier_N)
my_print('R0: {}'.format(R0))
my_print('tol: {}'.format(atol))
my_print('mxstep: {}'.format(mxstep))
# Estimate the accuracy of the DFT
r = R
d1 = arc_dst(lambda th: eval_f1(r, th))[:M]
d2 = fourier.arc_dst(a, lambda th: eval_f1(r, th), N=8192)[:M]
my_print('Fourier discretization error: {}'.format(np.max(np.abs(d1-d2))))
global n_dst
n_dst = 0
def eval_deriv(Y, r):
global n_dst
assert r != 0
n_dst += 1
f_fourier = arc_dst(lambda th: eval_f1(r, th))[:M]
derivs = np.zeros(2*M)
for i in range(0, 2*M, 2):
m = i//2+1
z1 = Y[i]
z2 = Y[i+1]
derivs[i] = z2
derivs[i+1] = -z2/r - (k**2 - (m*nu/r)**2) * z1 + f_fourier[m-1]
return np.array(derivs)
initial_fourier = arc_dst(lambda th: initial_func(R0, th))[:M]
d_initial_fourier = arc_dst(lambda th: d_initial_func(R0, th))[:M]
ic = np.zeros(2*M)
for i in range(0, 2*M, 2):
m = i//2+1
ic[i] = initial_fourier[m-1]
ic[i+1] = d_initial_fourier[m-1]
sol = odeint(eval_deriv, ic, [R0, R], atol=atol, rtol=rtol, mxstep=mxstep)
my_print('Number of dst: {}'.format(n_dst))
# Fourier coefficients at r=R
return sol[1, 0::2]
def get_expected_a_coef(self):
if self.problem.name == 'iz-bessel':
return np.zeros(self.M)
# Arc only
r = self.problem.R
def eval_bc0(th):
return self.problem.eval_phi0(th) - self.problem.eval_v(r, th)
def eval_diff(th):
return self.problem.eval_v(r, th) - self.v_interp(r, th)
interp_error = arc_dst(self.a, eval_diff)[:self.M]
print('b interp error:')
print(interp_error)
print()
b_coef = arc_dst(self.a, eval_bc0)[:self.M]
return abcoef.b_to_a(b_coef, self.k, self.problem.R, self.nu)
def __init__(self, **kwargs):
super().__init__(**kwargs)
if 'to_dst' in kwargs:
self.to_dst = kwargs.pop('to_dst')
else:
self.to_dst = lambda th: 0
self.fft_b_coef = fourier.arc_dst(self.a, self.to_dst)[:self.m_max]
self.fft_a_coef = abcoef.b_to_a(self.fft_b_coef, self.k,
self.R, self.nu)
def get_expected_z1_fourier(self):
"""
Compute the expected Fourier coefficients of z1 from
z1 = v - (v_asympt g + q)
For checking the accuracy of the ODE method or
skipping the ODE method during testing
"""
R = self.arc_R
def z1_expected(th):
return self.problem.eval_v(R, th) - self.eval_gq(R, th)
# This should be close to 0
return arc_dst(self.a, z1_expected)[:self.M]
