def setUp(self):
self.sys_basic = system.Cylinder1D(radius=1,
wavenumber=1,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1)
self.sys_low_wvn = system.Cylinder1D(radius=1,
wavenumber=0.8,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1)
self.sys_high_wvn = system.Cylinder1D(radius=1,
wavenumber=1.2,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1)
def setUp(self):
self.sys_basic = system1D.Cylinder1D(radius=1,
wavenumber=1,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1)
self.sys_small_radius = system1D.Cylinder1D(radius=0.5,
wavenumber=1,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1)
self.sys_n6 = system1D.Cylinder1D(radius=1,
wavenumber=1,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=6)
def setUp(self):
self.sys_basic = system.Cylinder1D(
radius=1,
wavenumber=1.001,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=0
) # not exactly wavenumber 1 to know expected stability: surface area should decrease with a !=0
self.sys_low_wvn = system.Cylinder1D(radius=1,
wavenumber=0.8,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=0)
self.sys_high_wvn = system.Cylinder1D(radius=1,
wavenumber=1.2,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=0)
def setUp(self):
self.sys_basic = system1D.Cylinder1D(radius=1,
wavenumber=1,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=3)
# 1D field z-wavenumber = [-n ,..., 0, ..., +n]
self.sys_basic_2d = system2D.Cylinder2D(radius=1,
wavenumber=1,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=(3, 0))
# functionally identical system with 2D field
# theta-wavenumebr = [0] only, z-wavenumber = [-n ,..., 0, ..., +n]
random_values = [(random.uniform(-1, 1) + random.uniform(-1, 1) * 1j)
for i in range(7)] #random complex coeffs
self.field_coeffs = np.array(random_values)
self.field_coeffs_2d = np.array([random_values
]) #same values, as 7x1 2D array
def setUp(self):
"""
with num_field_coeffs=1, the A matrix is 3x3
"""
self.radius=1
self.wavenumber=1
self.sys_basic = cylinder1D.Cylinder1D(radius=self.radius, wavenumber=self.wavenumber, gamma=1, kappa=1,
alpha=-1, C=1, u=1, n=1, num_field_coeffs=1)
#prompt fillling of tmp_A_integrals[diff], tmp_A_matrix[j,j'], with a!=0
#so we can see if it's filled "the wrong way around" when assymetrix
self.sys_basic.evaluate_A_integrals(amplitude=.9)
def setUp(self):
"""
with num_field_coeffs=1, the A matrix is 3x3
"""
self.radius = 1
self.wavenumber = 1
self.expected_A_integral_0 = math.pi * 2 * self.radius / self.wavenumber
self.sys_basic = cylinder1D.Cylinder1D(radius=self.radius,
wavenumber=self.wavenumber,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=1)
#prompt evaluation of integrals, fill of matrix elemnts
self.sys_basic.evaluate_A_integrals(amplitude=0)
def setUp(self):
"""
with num_field_coeffs=0, there will be 1 field mode j=0 and one
matrix element of A j=0, j'=0
"""
self.radius = 1
self.wavenumber = 1
self.expected_A_integral_0 = math.pi * 2 * self.radius / self.wavenumber + 0j
self.sys_basic = cylinder1D.Cylinder1D(radius=self.radius,
wavenumber=self.wavenumber,
gamma=1,
kappa=1,
alpha=-1,
C=1,
u=1,
n=1,
num_field_coeffs=0)
#prompt fillling of tmp_A_integrals[diff], tmp_A_matrix[j,j']
self.sys_basic.evaluate_A_integrals(amplitude=0)
alpha = 1
u = 0
C = 0
n = 0
wavenumber = 1
kappa = 0
a = .9
n_coeffs = 20
title = "-.png"
sys = system.Cylinder1D(alpha=alpha,
n=n,
C=C,
u=u,
wavenumber=wavenumber,
kappa=kappa,
radius=1,
gamma=1,
num_field_coeffs=n_coeffs)
#prompt cylinder to fill A, B, D matrices
sys.evaluate_A_integrals(amplitude=a)
sys.evaluate_B_integrals(amplitude=a)
matrix = alpha * sys.tmp_A_matrix + C * sys.tmp_B_integrals
print(matrix)
plt.imshow(abs(matrix))
plt.xticks(range(0, 2 * n_coeffs + 2, 5), range(-n_coeffs, n_coeffs + 1, 5))
plt.yticks(range(0, 2 * n_coeffs + 2, 5), range(-n_coeffs, n_coeffs + 1, 5))
plt.colorbar()
plt.title("G^-1, a = " + str(a) + " C = " + str(C) + " n = " + str(n))
plt.savefig(title)